ALBERT

Description:    In this, the third part of our paper, we continue consideration of the major elements of the poroelastic theory which we started in Parts I and II (in Lopatnikov and Gillespie, Transp Porous Media, 84:471–492, 2010 ; Transp Porous Media, 89:475–486, 2011 ). This third part is devoted to considering the general interfacial conditions, consistent with the governing differential equations of the theory. Specifically, we will consider associated mass and momentum conservation laws. Because we developed the theory by construction, general boundary conditions obtained can be applied to the arbitrary interfaces: boundaries between different materials or, for example, moving interfaces of the shock fronts. We do not consider here the last group of conservation laws: the energy conservation laws, which we are going to introduce and investigate in the special part, devoted to the shock wave propagation. In the meantime, special attention is devoted to discussing the problem of “partial permeability” of the interfaces reflected in the literature. Particularly we show, that in the stationary case, the general theory allows only two conditions: either the interface is completely penetrable, or the interface is completely impenetrable. Thus, “partial permeability” solution always appears as only an approximation of an exact dynamic problem, which includes either thin low-permeable interfacial layer (with permeable boundaries), or a non-homogeneous boundary containing permeable and non-permeable patterns. Content Type Journal Article Pages 1-11 DOI 10.1007/s11242-012-9971-6 Authors Sergey Lopatnikov, Center for composite Materials, University of Delaware, Newark, DE 19716, USA John W. Gillespie, Center for composite Materials, University of Delaware, Newark, DE 19716, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this study, the main recovery mechanisms behind oil/water/gas interactions during the water-alternating-gas (WAG) injection process, in a network of matrix/fracture, were fundamentally investigated. A visual micromodel was utilized to provide insights into the potential applications of WAG process in fractured oil-wet media as well as the possibility of observing microscopic displacement behavior of fluids in the model. The model was made of an oil-wet facture/matrix network system, comprised of four matrix blocks surrounded with fractures. Different WAG injection scenarios, such as slug arrangements and the effects of fluid injection rates on oil recovery were studied. A new equation representing the capillary number, considering the fracture viscous force and matrix capillary force, was developed to make the experimental results more similar to a real field. In general, WAG tests performed in the fractured model showed a higher oil recovery factor compared with the results of gas and water injection tests at their optimum rates. The results showed that the presence of an oil film, in all cases, was the main reason for co-current drainage and double displacement of oil under applied driving forces. Furthermore, the formation of oil liquid bridges improved the recovery efficiency, which was greatly influenced by the size of fracture connecting the two matrix blocks; these connecting paths were more stable when there was initial water remaining in the media. Analyzing different recovery curves and microscopic view of the three phases in the transparent model showed that starting an injection mode with gas (followed by repeated small slugs of water and gas), could considerably improve oil recovery by pushing water into the matrix zone and increasing the total sweep efficiency. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-9970-7 Authors A. A. Dehghan, Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran S. Ghorbanizadeh, Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Sh. Ayatollahi, EOR Research Center, School of Chemical and Petroleum Engineering, Shiraz University, P.O. Box 71345-1719, Shiraz, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves. Content Type Journal Article Pages 1-8 DOI 10.1007/s11242-012-9963-6 Authors Huajun Fan, Department of Geotechnology, Delft University of Technology, Delft, The Netherlands D. M. J. Smeulders, Department of Geotechnology, Delft University of Technology, Delft, The Netherlands Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Porous filters are often used in laboratory and in situ diffusion and retention experiments. The proper interpretation of these experiments requires knowing the effective diffusion, D e , of the filter which is commonly determined from laboratory diffusion experiments or estimated from the filter porosity. The D e of the filter in the in situ experiment may differ from the D e of the filter measured in the laboratory due to pore clogging. Here, we present an inverse method to estimate the D e of the filter of in situ diffusion experiments. The method has been tested for several sampling schemes, numbers of synthetic data, N , and standard deviations of the noise, σ . It has been applied to the following tracers used in the in situ diffusion and retention (DR) experiment performed in the Opalinus clay at Mont Terri underground research laboratory: HTO/HDO, Br − ,I − , 22 Na + , 133 Ba 2+ , 85 Sr 2+ , Cs + / 137 Cs + , and 60 Co 2+ . The estimation error increases with the standard deviation of the noise of the data and decreases with the number of data. It is smallest for sorbing tracers. The D e of the filter can be properly estimated from 12 data collected within the first 3 days for conservative tracers as long as σ  ≤ 0.02 and for sorbing tracers as long as σ  ≤ 0.05. The estimate of D e for conservative tracers is poor when data are collected from a 10-day experiment with daily sampling. The convergence of the estimation algorithm for conservative tracers improves by starting with a value of the D e smaller than the true value. The choice of the initial value of D e does not affect the convergence of the estimation algorithm for sorbing tracers. Filter clogging and vertical flow though the filter can influence the tracer transport through the filter. The use of the D e of the filter obtained from a laboratory test for the in situ experiment may result in large errors for strongly sorbing tracers. Such errors can be overcome by estimating the equivalent D e of the filter with the proposed inverse method which will be useful for the design of in situ diffusion experiments. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9960-9 Authors Shuping Yi, ETS Ingenieros de Caminos, Canales y Puertos, Universidad de A Coruña, Campus de Elviña, 15192 A Coruña, Spain Javier Samper, ETS Ingenieros de Caminos, Canales y Puertos, Universidad de A Coruña, Campus de Elviña, 15192 A Coruña, Spain Acacia Naves, ETS Ingenieros de Caminos, Canales y Puertos, Universidad de A Coruña, Campus de Elviña, 15192 A Coruña, Spain Josep M. Soler, Institute of Environmental Assessment and Water Research (IDAEA-CSIC), Jordi Girona 18-26, 08034 Barcelona, Spain Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The length and spatial distribution of the touching-vugs channels affect the degree of permeability variations and is the main contributor to heterogeneity in vuggy carbonates. Hence, this article focuses on vug connectivity characterization and its impact on fluid flow. A whole core sample was scanned by X-ray computed tomography (CT). Image segmentation was used to obtain a binarized three-dimensional (3D) model of the vuggy pore space. Analysis of the binarized 3D model is used to calculate the correlation function and correlation length for the vuggy pore space. Connectivity analysis of the binarized 3D model shows that 79% of the vugs connected network spanning along the sample. The remaining 21% vug porosity exists in a large number of isolated vugs. The correlation length for the connected vug network is found to be larger than for vugs in general. NMR T 2 measurements at increasing capillary pressure is tested on the vuggy material and used to investigate the amount of connected- and isolated vugs. The results verify the large fraction of connected vugs. Application of NMR T 2 measurements in combination with capillary pressure experiments can also reveal matrix properties that play an important role in recovery processes. The transition between non-Fickian and Fickian regimes for tracer/solute transport is studied by laboratory experiments performed at various sample lengths, from cm to m scale. For the largest sample measured in our experiments show that effluent concentration curve conform to the CDE solution, suggesting that the Fickian regime has been established. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9969-0 Authors B. Vik, Centre of Integrated Petroleum Research, University of Bergen, Postboks 7800, 5020 Bergen, Norway K. E. Sylta, Centre of Integrated Petroleum Research, University of Bergen, Postboks 7800, 5020 Bergen, Norway A. Skauge, Centre of Integrated Petroleum Research, University of Bergen, Postboks 7800, 5020 Bergen, Norway Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this study, Knudsen diffusion of low-pressure gases of infinite mean free path through various tubes is studied using the integral equation theory (IET), standard diffusion theory, and Monte Carlo (MC) simulations. We investigated the transmission probabilities (TPs) of linearly diverging–converging, sinusoidally bulging, and periodic tubes as compared with TPs of conventional straight cylinders. An exact analytic solution for the TP through the straight cylindrical tube was developed using the standard diffusion theory with a linear concentration approximation. IET for the TPs through the diverging–converging and bulging tubes were developed. MC simulation techniques were applied to calculate TPs through all the tube types azimuthal symmetry of which was held with tube radius changing only along the axial coordinate ( z ). The linearly diverging–converging and sinusoidally bulging tubes provide noticeably higher TPs than those of the equivalent straight tubes. Periodic tubes show that if the tube length scaled by the equivalent diameter is of an order of or greater than the periodicity coefficient (equal to the number of peaks on the tube wall), then the TP of the periodic tube is larger than that of the equivalent straight tube. Content Type Journal Article Pages 1-25 DOI 10.1007/s11242-012-9966-3 Authors Yong Shi, Civil and Environmental Engineering, University of Hawaii at Manoa, 2540 Dole Street, Honolulu, HI 96822, USA Yong Taek Lee, Chemical Engineering, College of Engineering, Kyung Hee University, Gyeonggi-do, 449-701 South Korea Albert S. Kim, Civil and Environmental Engineering, University of Hawaii at Manoa, 2540 Dole Street, Honolulu, HI 96822, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy–Brinkman–Forchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed. Content Type Journal Article Pages 1-13 DOI 10.1007/s11242-012-9959-2 Authors M. J. Maghrebi, Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran M. Nazari, Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box: 3619995161, Shahrood, Iran T. Armaghani, Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box: 3619995161, Shahrood, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Diffusion is a slow transport mechanism and advective transport tends to dominate in large-size systems. An alternative transport mechanism is explored herein, whereby zero time-average cyclic fluid flow is compounded with pore-scale mixing to render effective transport. Two one-dimensional cyclic flow cases are analyzed: a rigid porous network with two open boundaries subjected to cyclic flow through, and a compressible porous network with only one open boundary subjected to cyclic compression. The corresponding analytical models predict diffusion-like macroscale response and provide explicit expressions for the effective diffusion coefficients in terms of the microstructure of the porous medium and flow conditions. A parallel experimental study is conducted to corroborate analytical predictions. Results confirm the relevance of pore-scale mixing in cyclic flow as a transport mechanism in porous networks. Content Type Journal Article Pages 1-11 DOI 10.1007/s11242-012-9943-x Authors J. J. Claria, Georgia Institute of Technology, Atlanta, GA, USA G. H. Goldsztein, Georgia Institute of Technology, Atlanta, GA, USA J. C. Santamarina, Georgia Institute of Technology, Atlanta, GA, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Heterogeneous catalysis is of paramount importance in many areas of gas conversion and processing in chemical engineering industries. In porous pellets, the catalytic reactions may be affected by diffusional limitations such that the global rate can be different from the intrinsic reaction rate. In the literature, a number of multicomponent diffusion flux closures have been applied to characterize the diffusion process within different units in chemical process plants. The main purpose of this paper is to outline the derivation of the different diffusion flux models: the rigorous Maxwell–Stefan and dusty gas models, and the simpler Wilke and Wilke–Bosanquet models. Usually the diffusion fluxes are derived and presented with respect to the molar average velocity definition. In this study, also the diffusion flux closures with respect to the mass average velocity definition is outlined. Thus, if the temperature equation and the momentum equation are used in the pellet model, a consistently closed set of pellet equations is obtained on mass basis holding only the mass average velocity. On the other hand, for the closed set of pellet equations on molar basis, the component balances hold the molar averaged velocity whereas the temperature and momentum equations hold the mass average velocity due to the physical laws applied deriving these fundamental balances. Nevertheless, the Maxwell–Stefan and dusty gas models are manipulated and put on the convenient Fickian form. The second purpose of this article is the evaluation of the diffusion flux closures derived. For this purpose, a transient model is developed to describe the evolution of the species composition, pressure, velocity, temperature, total concentration, and fluxes within a spherical pellet. The catalyst problem has been simulated for the methanol dehydration process producing dimethyl ether (DME), with computed efficiency factor values in the range 0.06–0.6 for pellet pore diameters of 0.1–100 nm. Identical results are expected for the mole and mass based pellet equations. However, deviations are obtained in the component fractions comparing the mass and mole based pellet model formulations where the mass fluxes were described according to the Wilke and Wilke–Bosanquet models. On the other hand, the rigorous Maxwell–Stefan and dusty gas models gave identical results. Content Type Journal Article Pages 1-28 DOI 10.1007/s11242-012-9946-7 Authors Jannike Solsvik, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway Hugo A. Jakobsen, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description: Reply to the “Comments on the Paper ‘Quantification of Density-Driven Natural Convection for Dissolution Mechanism in CO 2 Sequestration’ by R. Nazari Moghaddam et al. (2011)” Content Type Journal Article Pages 1-4 DOI 10.1007/s11242-012-9950-y Authors Rasoul Nazari Moghaddam, Institute of Petroleum Engineering, School of Chemical Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran Behzad Rostami, Institute of Petroleum Engineering, School of Chemical Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The anomalous reactive transport considered here is the migration of contaminants through strongly sorbing permeable media without significant retardation. It has been observed in the case of heavy metals, organic compounds, and radionuclides, and it has critical implications on the spreading of contaminant plumes and on the design of remediation strategies. Even in the absence of the well-known fast migration pathways, associated with fractures and colloids, anomalous reactive transport arises in numerical simulations of reactive flow. It is due to the presence of highly pH-dependent adsorption and the broadening of the concentration front by hydrodynamic dispersion. This leads to the emergence of an isolated pulse or wave of a contaminant traveling at the average flow velocity ahead of the retarded main contamination front. This wave is considered anomalous because it is not predicted by the classical theory of chromatography, unlike the retardation of the main contamination front. In this study, we use the theory of chromatography to study a simple pH-dependent surface complexation model to derive the mathematical framework for the anomalous transport. We analyze the particular case of strontium (Sr 2+ ) transport and define the conditions under which the anomalous transport arises. We model incompressible one-dimensional (1D) flow through a reactive porous medium for a fluid containing four aqueous species: H + , Sr 2+ , Na + , and Cl − . The mathematical problem reduces to a strictly hyperbolic 2 × 2 system of conservation laws for effective anions and Sr 2+ , coupled through a competitive Langmuir isotherm. One characteristic field is linearly degenerate while the other is not genuinely nonlinear due to an inflection point in the pH-dependent isotherm. We present the complete set of analytical solutions to the Riemann problem, consisting of only three combinations of a slow wave comprising either a rarefaction, a shock, or a shock–rarefaction with fast wave comprising only a contact discontinuity. Highly resolved numerical solutions at large Péclet numbers show excellent agreement with the analytic solutions in the hyperbolic limit. In the Riemann problem, the anomalous wave forms only if: hydrodynamic dispersion is present, the slow wave crosses the inflection locus, and the effective anion concentration increases along the fast path. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-9947-6 Authors Valentina Prigiobbe, Department of Petroleum and Geosystems Engineering, University of Texas at Austin, 1 University Station, Austin, TX 78712, USA Marc A. Hesse, Department of Geological Sciences, University of Texas at Austin, 1 University Station, Austin, TX 78712, USA Steven L. Bryant, Department of Petroleum and Geosystems Engineering, University of Texas at Austin, 1 University Station, Austin, TX 78712, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The paper presents an investigation of the influence of thermal radiation and viscous dissipation on the mixed convective flow due to a vertical plate immersed in a non-Darcy porous medium saturated with a Newtonian fluid. The physical properties of the fluid are assumed to be constant. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically using a shooting method. The results are analyzed for the effects of various physical parameters such as viscous dissipation, thermal radiation, mixed convection parameters, and the modified Reynolds number on dynamics. The heat transfer coefficient is also tabulated for different values of the physical parameters. Content Type Journal Article Pages 1-10 DOI 10.1007/s11242-012-0096-8 Authors Mahesha Narayana, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209 South Africa Ahmed A. Khidir, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209 South Africa Precious Sibanda, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209 South Africa P. V. S. N. Murthy, Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The removal of salt from porous building materials under the influence of an applied voltage gradient normally results in high pH gradients due to the formation of protons and hydroxyl ions at the electrodes. The formed acidic and alkaline regions not only lead to disintegration of the porous material, but also affect the salt transport. In this work we use ion exchange membranes between the electrodes and the porous material to prevent the protons and hydroxyl ions from intruding into the material. The porous material used in this study is fired clay brick, which has been saturated with a 4 mol/l sodium chloride solution prior to the desalination treatment. In order to experimentally determine the salt removal, we monitored the sodium ion concentration profiles across the material with nuclear magnetic resonance (NMR). In addition, we present theoretical predictions for the salt removal according to a model based on the Poisson–Nernst–Planck theory for ion transport. From the work reported here, we can conclude that the use of ion exchange membranes to desalinate porous building materials is not useful since it reduces the salt removal rate to such an extent that desalination with poultices, which is driven by diffusion only, is more efficient. The reason behind this is twofold. First, the ion exchange membranes provide a penalty for the ions to leave the material. Second, in the absence of acidic and alkaline regions, the salt concentration at the edges of the porous material will reduce to almost zero, which leads to a locally increased electrical resistance, and thus a reduction of the electrical field in the bulk of the material. Due to this reduction the effect of the applied voltage gradient across the material vanishes, and the salt removal is limited by diffusion. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-0083-0 Authors K. Kamran, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands M. van Soestbergen, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands L. Pel, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The 3D description of the soil structure at the pore scale level can help to elucidate the biological functioning of soil. The water–air distribution in the 3D-pore space is of particular interest because it determines the diffusion pathways of nutrients and the localisation of active soil microorganisms. We used the Shan–Chen interparticle-potential approach to simulate spontaneous phase separation in complex academic and real 3D-porous media using the advanced TRT lattice Boltzmann scheme. The equation of state and phase diagram were calculated and the model was verified using hydrostatic laws. The 3D pattern of water/air interface in two complex academic pore geometries was accurately computed. Finally, 3D maps of static liquid–gas distribution were simulated in a real 3D X-ray computed tomography image obtained from an undisturbed soil column sampled in a silty clay loam soil. The simulated soil sample of 1.7 cm 3 was described at a voxel-resolution of 60 μm. The range of the simulated saturations (from 0.5 to 0.9) was in a good agreement with the expected saturations calculated from the phase diagram. Content Type Journal Article Pages 1-24 DOI 10.1007/s11242-012-0087-9 Authors Alain Genty, Commissariat à l’Énergie Atomique et aux Énergies Alternatives, CEA-Saclay, DEN DANS DM2S STMF, 91191 Gif sur Yvette Cedex, France Valérie Pot, INRA, AgroParis Tech, UMR 1091 EGC, 78850 Thiverval-Grignon, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In recent years, the effective stress approach has received much attention in the constitutive modeling of unsaturated soils. In this approach, the effective stress parameter is very important. This parameter needs a correct definition and has to be determined properly. In this paper, a thermodynamic approach is used to develop a physically-based formula for the effective stress tensor in unsaturated soils. This approach accounts for the hydro-mechanical coupling, which is quite important when dealing with hydraulic hysteresis in unsaturated soils. The resulting formula takes into account the role of interfacial energy and the contribution of air–water specific interfacial area to the effective stress tensor. Moreover, a bi-quadratic surface is proposed to represent the contribution of the so-called suction stress in the effective stress tensor. It is shown that the proposed relationship for suction stress is in agreement with available experimental data in the full hydraulic cycle (drying, scanning, and wetting). Content Type Journal Article Pages 1-28 DOI 10.1007/s11242-012-0093-y Authors Ehsan Nikooee, Department of Civil and Environmental Engineering, Shiraz University, P.O. Box 7134851156, Shiraz, Iran Ghassem Habibagahi, Department of Civil and Environmental Engineering, Shiraz University, P.O. Box 7134851156, Shiraz, Iran S. Majid Hassanizadeh, Earth Sciences Department, Utrecht University, P.O. Box 80021, 3508 TA Utrecht, The Netherlands Arsalan Ghahramani, Department of Civil and Environmental Engineering, Shiraz University, P.O. Box 7134851156, Shiraz, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This article looks at the starting solutions for magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid in cylindrical domains. The fluid is electrically conducting under the influence of a uniform external magnetic field and occupies the porous space between two infinite circular cylinders. Exact solutions for oscillating motions are obtained using Hankel transform and presented as Fourier–Bessel series in terms of some suitable eigenfunctions. In the absence of inner cylinder, all solutions that have been obtained reduce to those corresponding to the flow through a circular cylinder. The corresponding solutions for the hydrodynamic flow as well those in the absence of porous space appear as limiting cases of our solutions. The effects of the pertinent parameters of flow are discussed in detail and shown graphically. Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-0094-x Authors M. Khan, Department of Mathematics, Quaid-i-Azam University, 44000 Islamabad, Pakistan Madiha Ajmal, Department of Mathematics, Quaid-i-Azam University, 44000 Islamabad, Pakistan C. Fetecau, Department of Mathematics, Technical University of Iasi, 700050 Iasi, Romania Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Dynamic spontaneous imbibition (DSI) plays an important role in oil reservoir characterization. Conventional equations used to characterize DSI consider neither interfacial coupling effects (ICE) nor variable inlet saturation ( S *) for DSI. Yazzan et al. (Transp Porous Media 87(1):309–333, 2011a ; 86(3):705–717, 2011b ) developed a set of equations, and a numerical solution scheme, to take into account ICE and variable S * for DSI. Based on these, a graphical user interface (GUI) simulator was built. A sensitivity analysis has been conducted to study the effect of the fluid and rock properties on DSI. The results reveal that including a variable S * has no significant impact; however, neglecting ICE results in an overestimation of the imbibition flow rate. Moreover, it is shown that the capillary and relative permeability curves determine the type of frontal advance, and that the imbibition recovery is proportional to the square root of time. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-0095-9 Authors Saddam K. Yazzan, Department of Civil and Environmental Engineering, School of Mining and Petroleum Engineering, University of Alberta, 3-112 Markin CNRL-NREF, Edmonton, AB T6G 2W2, Canada Ramon G. Bentsen, Department of Civil and Environmental Engineering, School of Mining and Petroleum Engineering, University of Alberta, 3-112 Markin CNRL-NREF, Edmonton, AB T6G 2W2, Canada Japan Trivedi, Department of Civil and Environmental Engineering, School of Mining and Petroleum Engineering, University of Alberta, 3-112 Markin CNRL-NREF, Edmonton, AB T6G 2W2, Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This work address a number of fundamental issues and concepts related to local thermal non-equilibrium and the heat flux bifurcation phenomenon in porous media. Different types of heat flux bifurcation phenomenon are discussed in relation to previous works by the authors. Content Type Journal Article Pages 1-4 DOI 10.1007/s11242-012-0080-3 Authors Kambiz Vafai, Department of Mechanical Engineering, University of California, Riverside, CA 92691, USA Kun Yang, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, 430074 People’s Republic of China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In carbonate reservoirs, acid is injected into the formation under breakdown pressure to react with the rock to remove the contaminations caused by drilling and production, which is called carbonate acidizing in reservoir development. In carbonate acidizing, acid flows selectively through large pores to create wormholes. Wormhole propagation under experimental condition has been studied by many experts. In this paper, a model which couples a two-scale continuum model simulating wormholing in the invaded zone and a reservoir flow model for the compressed zone was used to study the wormhole propagation behavior under reservoir condition. In this model, the porosity values which are uniformly distributed used in former literature follow the normal law. Based on the model, we first compared the results of the two porosity generation methods, and then studied the wormhole propagation behavior under reservoir condition, and finally simulated a two-layer formation to study the effects of distance and permeability ratio between the two layers. The results show that the normally distributed porosities simulate wormholing better. The effect of compressed zone on wormhole propagation increases with the decrease of compressibility factor and wormhole has a maximal value in length. The effect of distance between the two layers on wormhole lengths and acid distributions can be divided into three zones based on the wormhole length in the lower layer. A critical value of permeability ratio between the two layers exists, below and above which the wormhole length in the low permeability layer decreases sharply and almost keeps constant, respectively. Content Type Journal Article Pages 1-18 DOI 10.1007/s11242-012-0084-z Authors Ming Liu, MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249 China Shicheng Zhang, MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249 China Jianye Mou, MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249 China Fujian Zhou, Research Institute of Petroleum Exploration & Development, PetroChina, Beijing, 100083 China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The reduction in permeability of sediments due to blockages caused by the trapping of suspended particles is a common concern for the extraction processes of oil or natural gas. In this study, the effect of trapped fine particles in sand sediments is studied numerically using a three-dimensional lattice Boltzmann method. The geometrical properties of larger, immobile, sand grains are digitally extracted by the spherical harmonics series expansions of CT scans of real sand grains. The migrating fine particles are assumed to be spherical in shape with their volumes following a log-normal distribution. These fine particles, together with larger frame sands, are positioned, without overlapping, within a microscopic, cubic, domain with periodic boundaries. The remaining empty volume is filled with water and imposing a pressure gradient simulates the flow of fluid through the sediment. As a result of fine particles becoming trapped by the frame sand, the initial porosity of which is 0.589, the absolute permeability of the system is reduced by approximately 60–90 %, corresponding to fine particle saturations of 0.15–0.29, respectively. The permeability change due to the trapping of fine particles is also modelled theoretically using not only volume saturations but also specific surface areas of both the frame sands and the fine particles with a coefficient of proportionality. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-0079-9 Authors Toru Sato, Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Keisuke Mitsuhori, Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Shinichiro Hirabayashi, Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Paul E. Brumby, Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Jiro Nagao, Methane Hydrate Research Centre, National Institute of Advanced Industrial Science and Technology, 17-2-1 Higashi-Nijo, Toyohira, Sapporo 062-8517, Japan Norio Temma, Methane Hydrate Research Centre, National Institute of Advanced Industrial Science and Technology, 16-1 Onogawa, Tsukuba, 305-8569 Japan Hideo Narita, Methane Hydrate Research Centre, National Institute of Advanced Industrial Science and Technology, 17-2-1 Higashi-Nijo, Toyohira, Sapporo 062-8517, Japan Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Air sparging is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air through air sparging well below the zone of contamination. To investigate the rate-dependent flow properties during multistep air sparging, a rule-based dynamic two-phase flow model was developed and applied to a 3D pore network which is employed to characterize the void structure of porous media. The simulated dynamic two-phase flow at the pore scale or microscale was translated into functional relationships at the continuum-scale of capillary pressure–saturation ( P c – S ) and relative permeability—saturation ( K r – S ) relationships. A significant contribution from the air injection pressure step and duration time of each air injection pressure on both of the above relationships was observed during the multistep air sparging tests. It is observed from the simulation that at a given matric potential, larger amount of water is retained during transient flow than that during steady flow. Shorter the duration of each air injection pressure step, there is higher fraction of retained water. The relative air/water permeability values are also greatly affected by the pressure step. With large air injection pressure step, the air/water relative permeability is much higher than that with a smaller air injection pressure step at the same water saturation level. However, the impact of pressure step on relative permeability is not consistent for flows with different capillary numbers ( N ca ). When compared with relative air permeability, relative water permeability has a higher scatter. It was further observed that the dynamic effects on the relative permeability curve are more apparent for networks with larger pore sizes than that with smaller pore sizes. In addition, the effect of pore size on relative water permeability is higher than that on relative air permeability. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0081-2 Authors Shengyan Gao, Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ, USA Jay N. Meegoda, Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ, USA Liming Hu, Department of Hydraulic Engineering, State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing, 100084 People’s Republic of China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The “effective interfacial tension” effect on the instability of the plane interface between two uniform, superposed, and streaming Rivlin–Ericksen viscoelastic fluids through a porous medium is considered. The case of two uniform streaming Rivlin–Ericksen viscoelastic fluids separated by a horizontal boundary is studied. In the absence of ‘effective interfacial tension’, stability/instability of the system as well as perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if the perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions, there exists instability for a certain wave number range. ‘Effective interfacial tension’ is able to suppress this Kelvin–Helmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities. Content Type Journal Article Pages 1-10 DOI 10.1007/s11242-012-0082-1 Authors Pardeep Kumar, Department of Mathematics, ICDEOL, Himachal Pradesh University, Shimla, 171005 India Hari Mohan, Department of Mathematics, ICDEOL, Himachal Pradesh University, Shimla, 171005 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    A problem derived previously (Rohni et al., Transp Porous Media 92:1–14, 2012 ) for unsteady mixed convection flow in a porous medium involving a ‘temperature slip’ boundary condition and fluid transfer through the boundary is considered. It is shown that the solution to this problem can be directly related to the solution of the corresponding problem for a prescribed surface temperature, involving a mixed convection parameter λ, an unsteadiness parameter A and transpiration parameter s . This latter problem is discussed in detail, particular attention being given to the steady analogue, A  = 0, allowing for fluid transfer through the surface, and to the unsteady problem, A  〉 0, for an impermeable surface, s  = 0. Asymptotic results are obtained for large fluid transfer rates, s 〉〉 1 and s 〈 0 , | s | 〉〉 1 and for large A . Particular attention is given to deriving asymptotic results for the critical points which determine the range of existence of solutions. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9993-0 Authors John H. Merkin, Department of Applied Mathematics, University of Leeds, LS2 9JT Leeds, UK Azizah Mohd Rohni, UUM College of Arts & Sciences, Physical Science Division, Building of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia Syakila Ahmad, School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia Ioan Pop, Faculty of Mathematics, University of Cluj, CP 253, 400082 Cluj, Romania Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The development of heat and moisture transport in concrete is critical to the development of pore pressures, which are thought to be a primary driver of damage and thermal spalling in concrete exposed to elevated temperatures. In the light of uncertainty and variation in the value of certain material properties and constitutive or parametric descriptions found in the literature, various sets of numerical experiments were conducted to investigate the significance of the intrinsic permeability, the evolution of permeability related to temperature and the relative permeability of the fluid phases as functions of saturation in predicting and analysing the behaviour of concrete drying under normal, low temperature, isothermal conditions and under exposure to very high temperature conditions as might be encountered during a fire. A fully coupled hygro-thermo-mechanical finite element model for concrete was employed with the permeability values and parametric functions altered in the model as required. Results of mass loss and the development of gas pressures with time were considered in relation to the potential for the occurrence of damage and thermal spalling, which is thought to be variously related to these processes. The analyses showed that permeability, and its variation with temperature, are very important in controlling the predicted behaviour at both low and high temperatures. Most significant of all were the relationships chosen to define the relative permeabilities. These were shown to strongly control the results of analyses of both low and high temperature problems and to potentially imply apparently different permeability values for the same concrete. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0066-1 Authors C. T. Davie, School of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne, NE1 7RU UK C. J. Pearce, School of Engineering, University of Glasgow, Glasgow, UK N. Bićanić, School of Engineering, University of Glasgow, Glasgow, UK Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Immobilization and trapping of carbon dioxide (CO 2 ) enhances the security of geological storage. Trapping mechanisms have been characterized in four groups: structural, residual, dissolution, and mineralization. While structural trapping acts immediately when injection starts and is well investigated, the contribution of residual and dissolution trapping increases over storage time and these contributions need to be better understood for better predictions. This paper focuses on an experimental pore-scale investigation of residual and capillary trapping. CO 2 –water imbibition experiments were conducted in micromodels whose homogenous pore space is geometrically and topologically similar to Berea sandstone. Microvisual data, photographs and video footage, describes the trapping mechanism and, especially, the disconnection and shrinkage of the CO 2 phase. Results show that depending on the flow rate of the imbibing water different trapping mechanisms are observed. Lower flow rates, comparable to the trailing edge of a CO 2 plume, lead to more snap-off events and greater trapped residual saturation, whereas rates comparable to the near wellbore area during enhanced sequestration showed displacement of gas bubbles and greater dissolution that ultimately leads to very low or zero gas saturations. Furthermore, complete dissolution events showed that homogenous as well as heterogeneous dissolution occurs. Whereas the latter is subdivided into microbubble formation and dissolution on crevices or pore roughness, the former occurs without the influence of pore walls. Based on the observations we suggest that the type of rock and its roughness as well as the fines present at the CO 2 brine interface are important factors determining the dissolution mechanism. Content Type Journal Article Pages 1-22 DOI 10.1007/s11242-012-0067-0 Authors Markus Buchgraber, Department of Energy Resources Engineering, Stanford University, 367 Panama St., Stanford, CA 94305, USA Anthony R. Kovscek, Department of Energy Resources Engineering, Stanford University, 367 Panama St., Stanford, CA 94305, USA Louis M. Castanier, Department of Energy Resources Engineering, Stanford University, 367 Panama St., Stanford, CA 94305, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Numerical simulations to characterize fluid flow through porous media have been carried out using tomography-derived real geometry data that has been manipulated using digital image processing techniques to obtain a wide range of porosities. Two kinds of porous media have been analyzed: (a) a reticulated porous ceramic (RPC) foam and (b) a packed bed of CaCO 3 particles. The porosity of the media is varied via morphological operations between 0.727 and 0.913 in case of the RPC and between 0.329 and 0.824 in case of the packed bed. A mesh generator based on the pore space indicator function is then used to generate unstructured tetrahedral grids from the processed tomography data. Fluid flow simulations are carried out for Reynolds numbers ranging from 0.1 to 200 and the results are used to determine the permeability and the Dupuit–Forchheimer coefficient in each case. The results are then compared with existing analytical models and the applicability of the models is examined. In the RPC case, the Happel–Brenner (parallel-flow) model predicts the permeability with a normalized root mean square error (NRMSE) of 11.8 % across the porosity range and Modified Ergun (Macdonald et. al) model predicts the Dupuit–Forchheimer coefficient within a NRMSE of 13.5 %. In the packed-bed case, the Brinkman drag model predicts the permeability within a NRMSE of 8.26 % across the porosity range and the Modified Ergun model predicts the Dupuit–Forchheimer coefficient within an NRMSE of 5.94 %. For each material, an adjusted Kozeny constant is determined. For the RPC, the Kozeny constant is evaluated at 7.73 and for the CaCO 3 packed bed, it is found to be 6.10, leading to predictions of the permeability with an NRMSE of 4.16 and 3.37 %, respectively. Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-0060-7 Authors A. Akolkar, Mechanical and Aerospace Engineering, University of Florida, 330, MAE-B, University of Florida, Gainesville, FL 32611, USA J. Petrasch, Vorarlberg University of Applied Sciences, Hochschulstr. 1, 6850 Dornbirn, Austria Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Near wellbore flow in high rate gas wells shows the deviation from Darcy’s law that is typical for high Reynolds number flows, and prediction requires an accurate estimate of the non-Darcy coefficient ( β factor). This numerical investigation addresses the issues of predicting non-Darcy coefficients for a realistic porous media. A CT-image of real porous medium (Castlegate Sandstone) was obtained at a resolution of 7.57 μm. The segmented image provides a voxel map of pore-grain space that is used as the computational domain for the lattice Boltzmann method (LBM) based flow simulations. Results are obtained for pressure-driven flow in the above-mentioned porous media in all directions at increasing Reynolds number to capture the transition from the Darcy regime as well as quantitatively predict the macroscopic parameters such as absolute permeability and β factor (Forchheimer coefficient). Comparison of numerical results against experimental data and other existing correlations is also presented. It is inferred that for a well-resolved realistic porous media images, LBM can be a useful computational tool for predicting macroscopic porous media properties such as permeability and β factor. Content Type Journal Article Pages 1-18 DOI 10.1007/s11242-012-0062-5 Authors C. P. Chukwudozie, The Craft and Hawkins Department of Petroleum Engineering, Louisiana State University and A&M College, Baton Rouge, LA 70803, USA M. Tyagi, The Craft and Hawkins Department of Petroleum Engineering, Louisiana State University and A&M College, Baton Rouge, LA 70803, USA S. O. Sears, The Craft and Hawkins Department of Petroleum Engineering, Louisiana State University and A&M College, Baton Rouge, LA 70803, USA C. D. White, The Craft and Hawkins Department of Petroleum Engineering, Louisiana State University and A&M College, Baton Rouge, LA 70803, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Fast water infiltration during heavy rainfall events is an important issue for hillslope hydrology and slope stability. Most hillslopes are strongly heterogeneous and contain macropores and soil pipes, so that infiltrating water can bypass the soil matrix and reach rapidly deeper regions. Water infiltration into macroporous soils is usually simulated with dual-permeability models based on Richards equation (RDPM) which only describes water flow. In this article, we present a two-phase dual-permeability model (TPDPM) for simulating water and air flow in macroporous soils. Water and air flow are simulated in both domains and mass transfer for water and air between the domains is included with first-order transfer terms. The main objectives of this article are to discuss the differences between TPDPM and RDPM and to test the application of the TPDPM on the slope scale. First, the differences between RDPM and TPDPM were studied using a one-dimensional layered soil. For the chosen high infiltration rate, we observed significant differences in the macropore domain and small differences in the matrix depending on the transfer parameter. Second, we applied the model to simulate fast water infiltration and flow through an alpine hillslope, where the water flow mainly occurs in the macropore domain and the matrix domain is bypassed because it is low permeability. A good agreement of simulated and measured travel times of Wienhöfer et al. (Hydrol Earth Syst Sci 13(7):1145–1161, 2009 ) was obtained. Finally, we recommend using TPDPM for high infiltration in layered macroporous soils. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-0064-3 Authors L. Stadler, Chair of Water Resources Management and Modeling of Hydrosystems, Department of Civil Engineering, Technische Universität Berlin, Sec. TIB1-B14, Gustav-Meyer-Allee 25, 13355 Berlin, Germany R. Hinkelmann, Chair of Water Resources Management and Modeling of Hydrosystems, Department of Civil Engineering, Technische Universität Berlin, Sec. TIB1-B14, Gustav-Meyer-Allee 25, 13355 Berlin, Germany R. Helmig, Department of Hydromechanics and Modeling of Hydrosystems, Institute for Modeling Hydraulic and Environmental Systems, Universität Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart, Germany Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Homogenisation of consolidation and compressible fluid flow in dual-porosity media has highlighted the existence of three characteristic macroscopic behaviours. These three behaviours are, namely, a dual-porosity description which includes memory effects, a single-porosity description with which the microporosity is simply ignored and an intermediate behaviour which we refer as behaviour with reservoir effect. With this latter, the whole dual-porosity medium is represented by an equivalent single-porosity medium. In contrast with a single-porosity behaviour, the porosity of the entire dual-porosity medium is accounted for. During solute transport in dual-porosity media, while memory effects are most often experimentally observed, the homogenised model obtained for the most general values of the involved parameters leads to a model with reservoir effect. Therefore, the observed memory effects are not reproduced by this model and a clear interpretation of the origins of these effects remains an unresolved issue. The study is presented in two complementary articles. The objective of this article is, first, to determine a physical interpretation of the existence of the three characteristic behaviours of dual-porosity media. This is performed by exploring the homogenised models and their domains of validity for the analogy of heat conduction in a dual-conductivity composite. This leads to the original result that consists to relate each type of behaviour to a specific relationship between two characteristic times. This is then used for interpreting the results obtained for compressible flow in dual-porosity media. Finally, it allows to elucidate the conditions under which memory effects may occur during solute transport in dual-porosity media. Content Type Journal Article Pages 1-24 DOI 10.1007/s11242-012-0065-2 Authors P. Royer, Laboratoire de Mécanique et Génie Civil (LMGC), UMR 5508 CNRS, Université Montpellier II, Place Eugène Bataillon 34095, Montpellier Cedex 5, France C. Boutin, DGCB-CNRS 3237, Université de Lyon – Ecole Nationale des Travaux Publics de l’Etat, Rue Maurice Audin, 69518 Vaulx-en-Velin, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Recent work on what has been called the phenomenon of heat flux bifurcation, that occurs at a boundary of a porous medium, or at an interface with a fluid clear of solid material, when a two-temperature model for the porous medium is employed, is discussed. An alternative interpretation of the situation, one in which the physics of the problem is emphasized, is presented. Content Type Journal Article Pages 1-4 DOI 10.1007/s11242-012-0063-4 Authors D. A. Nield, Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, 1142 New Zealand Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This note presents results of a laboratory test program that examines the influence of pore volumes on soil water coefficient of permeability in different saturation conditions. Comparing the results, it is observed that the dependency of water coefficient of permeability to void spaces in unsaturated soils follow a different trend than associated in saturated state. The shift of the soil–water characteristic curve within the change of pore spaces is utilized to qualify the opposite detected response of unsaturated water permeability to the change of pore spaces. Content Type Journal Article Pages 1-9 DOI 10.1007/s11242-012-0058-1 Authors Ali Mirzaii, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, P.O. Box: 14115-111, Tehran, Iran Seyed Shahaboddin Yasrobi, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, P.O. Box: 14115-111, Tehran, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior. Content Type Journal Article Pages 1-30 DOI 10.1007/s11242-012-0041-x Authors Denis Biryukov, Schlumberger, 1 rue Henri Becquerel, 92142 Clamart Cedex, France Fikri J. Kuchuk, Schlumberger, 1 rue Henri Becquerel, 92142 Clamart Cedex, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this paper, oscillatory convection in a horizontal layer of nanofluid in porous medium is studied. For porous medium, Darcy model is applied. A linear stability theory and normal mode analysis method is used to find the solution confined between two free boundaries. The onset criterion for oscillatory convection is derived analytically and graphically. Regimes of oscillatory and non-oscillatory convection for various parameters are derived. The effects of Lewis number, concentration Rayleigh number, Prandtl–Darcy number (Vadasz Number) and modified diffusivity ratio on the oscillatory convection are investigated graphically. We examine the validity of ‘PES’ and concluded that ‘PES’ is not valid for the problem. Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-0042-9 Authors Ramesh Chand, Department of Mathematics, Government P. G. College, Dhaliara, 177103 Himachal Pradesh, India G. C. Rana, Department of Mathematics, NSCBM Government P. G. College, Hamirpur, 177005 Himachal Pradesh, India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description: Pore-Scale Modeling of Multiphase Flow and Transport: Achievements and Perspectives Content Type Journal Article Pages 1-4 DOI 10.1007/s11242-012-0047-4 Authors V. Joekar-Niasar, Innovation and Research & Development, Shell Global Solutions International, Kessler Park 1, 2288 GS Rijswijk, The Netherlands M. I. J. van Dijke, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK S. M. Hassanizadeh, Department of Earth Sciences, Utrecht University, 3584 CD Utrecht, The Netherlands Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Most of the developed models for fractured reservoirs assume ideal matrix block size distribution. This assumption may not be valid in reality for naturally fractured reservoirs and possibly lead to errors in prediction of production from the naturally fractured reservoirs especially during a transient period or early time production from the matrix blocks. In this study, we investigate the effect of variable block size distribution on one- dimensional flow of compressible fluids in fractured reservoirs. The effect of different matrix block size distributions on the single phase matrix-fracture transfer is studied using a recently developed semi-analytical approach. The proposed model is able to simulate fluid exchange between matrix and fracture for continuous or discrete block size distributions using probability density functions or structural information of a fractured formation. The presented semi-analytical model demonstrates a good accuracy compared to the numerical results. There have been recent attempts to consider the effect of variable block size distribution in naturally fractured reservoir modeling for slightly compressible fluids with a constant viscosity and compressibility. The main objective of this study is to consider the effect of variable block size distribution on a one-dimensional matrix-fracture transfer function for single-phase flow of a compressible fluid in fractured porous media. In the proposed semi-analytical model, the pressure variability of viscosity and isothermal compressibility is considered by solving the nonlinear partial differential equation of compressible fluid flow in the fractured media. The closed form solution provided can be applied to flow of compressible fluids with variable matrix block size distribution in naturally fractured gas reservoirs. Content Type Journal Article Pages 1-28 DOI 10.1007/s11242-012-0039-4 Authors Ehsan Ranjbar, Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada Hassan Hassanzadeh, Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada Zhangxin Chen, Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food, as well as petroleum and groundwater engineering, and in many other industrial applications. Under the majority of operating conditions typically explored, the dependence of pressure drops on flow rate is non-linear and the development of models capable of describing accurately this dependence, in conjunction with non-trivial rheological behaviors, is of paramount importance. In this work, pore-scale single-phase flow simulations conducted on synthetic two-dimensional porous media are performed via computational fluid dynamics for both Newtonian and non-Newtonian fluids and the results are used for the extension and validation of the Darcy–Forchheimer law, herein proposed for shear-thinning fluid models of Cross, Ellis and Carreau. The inertial parameter β is demonstrated to be independent of the viscous properties of the fluids. The results of flow simulations show the superposition of two contributions to pressure drops: one, strictly related to the non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic one, arising at higher Reynolds numbers, is dependent on the porous medium properties. The use of pore-scale flow simulations on limited portions of the porous medium is here proposed for the determination of the macroscale-averaged parameters (permeability K, inertial coefficient β and shift factor α ), which are required for the estimation of pressure drops via the extended Darcy–Forchheimer law. The method can be applied for those fluids which would lead to critical conditions (high pressures for low permeability media and/or high flow rates) in laboratory tests. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0070-5 Authors Tiziana Tosco, Dipartimento di Ingegneria dell’Ambiente, del Territorio e delle Infrastrutture (DIATI), Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy Daniele L. Marchisio, Dipartimento Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy Federica Lince, Dipartimento Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy Rajandrea Sethi, Dipartimento di Ingegneria dell’Ambiente, del Territorio e delle Infrastrutture (DIATI), Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this article we study the combined effect of internal heating and time-periodic gravity modulation on thermal instability in a closely packed anisotropic porous medium, heated from below and cooled from above. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the porous medium. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg–Landau equation derived for the stationary mode of convection. The effects of various parameters such as; internal Rayleigh number, amplitude and frequency of gravity modulation, thermo-mechanical anisotropies, and Vadász number on heat transport has been analyzed. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further it is found that the heat transport can also be controlled by suitably adjusting the external parameters of the system. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-0071-4 Authors B. S. Bhadauria, Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, 226 025 India I. Hashim, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia P. G. Siddheshwar, Department of Mathematics, Bangalore University, Central College Campus, Bangalore, 560 001 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    We consider colloidal dynamics and single-phase fluid flow within a saturated porous medium in two space dimensions. A new approach in modeling pore clogging and porosity changes on the macroscopic scale is presented. Starting from the pore scale, transport of colloids is modeled by the Nernst–Planck equations. Here, interaction with the porous matrix due to (non-)DLVO forces is included as an additional transport mechanism. Fluid flow is described by incompressible Stokes equations with interaction energy as forcing term. Attachment and detachment processes are modeled by a surface reaction rate. The evolution of the underlying microstructure is captured by a level set function. The crucial point in completing this model is to set up appropriate boundary conditions on the evolving solid–liquid interface. Their derivation is based on mass conservation. As a result of an averaging procedure by periodic homogenization in a level set framework, on the macroscale we obtain Darcy’s law and a modified averaged convection–diffusion equation with effective coefficients due to the evolving microstructure. These equations are supplemented by microscopic cell problems. Time- and space-dependent averaged coefficient functions explicitly contain information of the underlying geometry and also information of the interaction potential. The theoretical results are complemented by numerical computations of the averaged coefficients and simulations of a heterogeneous multiscale scenario. Here, we consider a radially symmetric setting, i.e., in particular we assume a locally periodic geometry consisting of circular grains. We focus on the interplay between attachment and detachment reaction, colloidal interaction forces, and the evolving microstructure. Our model contributes to the understanding of the effects and processes leading to porosity changes and pore clogging from a theoretical point of view. Content Type Journal Article Pages 1-28 DOI 10.1007/s11242-012-0068-z Authors Nadja Ray, Department of Mathematics, Friedrich-Alexander University of Erlangen-Nuremberg, Cauerstraße 11, 91058 Erlangen, Germany Tycho van Noorden, Department of Mathematics, Friedrich-Alexander University of Erlangen-Nuremberg, Cauerstraße 11, 91058 Erlangen, Germany Florian Frank, Department of Mathematics, Friedrich-Alexander University of Erlangen-Nuremberg, Cauerstraße 11, 91058 Erlangen, Germany Peter Knabner, Department of Mathematics, Friedrich-Alexander University of Erlangen-Nuremberg, Cauerstraße 11, 91058 Erlangen, Germany Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The aim of this Letter is to show that, the Nusselt number sign might be changed without changing of heat transfer direction at the wall of channels, even for flows without viscous dissipation. Content Type Journal Article Pages 1-7 DOI 10.1007/s11242-012-0075-0 Authors Eren Ucar, Department of Mechanical Engineering, Izmir Institute of Technology, Urla, 35430 Izmir, Turkey Moghtada Mobedi, Department of Mechanical Engineering, Izmir Institute of Technology, Urla, 35430 Izmir, Turkey Baris Ozerdem, Department of Energy Systems Engineering, Bahcesehir University, 34353 Besiktas, Istanbul, Turkey Ioan Pop, Department of Mathematics, Babeş-Bolyai University, 40084 Cluj-Napoca, Romania Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Single-walled carbon nanotube-silica nanohybrid particles are a very promising material that could be used for enhanced oil recovery because of their interfacial activity. To demonstrate the basic principle, aqueous nanohybrid particle dispersions were evaluated by looking at the effect of pH, surfactant, and polymer. The results showed that pH did not have significant effect on the dispersion stability of nanohybrid particles. Although surfactant could improve the dispersion stability, it reduced the interfacial activity of the nanohybrid particles, causing them to stay in the aqueous phase. The best nanohybrid particle dispersion stability was found upon polymer addition, where the dispersions were stable for more than a week even at low polymer concentration (50 ppm). One-dimensional sand-pack studies were performed to evaluate the flow of the nanohybrid particles through porous media. The results showed that most of the nanohybrid particles (〉99%) could pass through a column packed with glass beads while a measurable fraction of the particles was retained in the column packed with crushed Berea. When the columns contained a residual saturation of decane, additional nanohybrid particles were retained at the oil/water interface in both glass beads and crushed Berea sand media. The sand pack studies showed that not only can the nanohybrid particles flow through porous media but also about half of the particles injected will go the O/W interface when the porous medium contains a residual saturation of hydrocarbon, where they could be used to support a catalytic conversion of components of the oil in reservoirs. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-0073-2 Authors Luis C. Villamizar, Petroleum and Geological Engineering, University of Oklahoma, 1210 Sarkey’s Energy Center, 100 E. Boyd St., Norman, OK 73019-1003, USA Prapas Lohateeraparp, Chemical, Biological, and Materials Engineering, University of Oklahoma, Sarkey’s Energy Center, Rm T-335, 100 E. Boyd St., Norman, OK 73019-1003, USA Jeffrey H. Harwell, Chemical, Biological, and Materials Engineering, University of Oklahoma, Sarkey’s Energy Center, Rm T-335, 100 E. Boyd St., Norman, OK 73019-1003, USA Daniel E. Resasco, Chemical, Biological, and Materials Engineering, University of Oklahoma, Sarkey’s Energy Center, Rm T-335, 100 E. Boyd St., Norman, OK 73019-1003, USA Bor Jier Shiau, Petroleum and Geological Engineering, University of Oklahoma, 1210 Sarkey’s Energy Center, 100 E. Boyd St., Norman, OK 73019-1003, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The effect of periodic Ohm’s heating on hyperbolic heat conduction in porous media is studied analytically with the objective of identifying the thermal resonance conditions. Local thermal equilibrium conditions are assumed to apply. The paper focuses initially on the temperature solution and looks at the conditions required for resonating the temperature signal. The heat flux solution is then evaluated. While a discrete infinite set of modes can be resonated, it is shown that in practice the resonance in the temperature signal is felt starting from moderately small values of Fourier numbers and becomes too small to be noticed if the Fourier number is extremely small. The temperature solution is shown to represent a standing wave the amplitude of which is strongly affected by the Fourier number. While the heat flux solution is shown to differ from the one obtained for the temperature, it also shows similar features such as the standing wave behavior the amplitude of which is strongly affected by the Fourier number. Content Type Journal Article Pages 1-28 DOI 10.1007/s11242-012-0059-0 Authors Peter Vadasz, Department of Mechanical Engineering, Northern Arizona University, P. O. Box 15600, Flagstaff, AZ 86011-5600, USA Milan Carsky, Faculty of Engineering, University of KZ Natal, Durban, 4041 South Africa Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Vapor extraction (VAPEX) is a process to recover heavy oil by injecting vaporized solvent into a reservoir. Reliable prediction of VAPEX performance is crucial to ensure successful commercial application of VAPEX process. The current practice for VAPEX performance prediction is using analytical scale-up methods which translate the laboratory result to field application. However, the drawbacks associated with the analytical scale-up methods are they only consider about the single phase flow and gravity drainage, and cannot take reservoir heterogeneity into account, which limit the application for the real field cases. In this study, an effort was made to investigate the capability of predicting up-scaled VAPEX performance through numerical simulation method. 2D test was conducted under the same conditions as those for the 3D test, and a numerical model was established to simulate the 2D test. History match of the 2D test was conducted by tuning the uncertainties such as relative permeability and capillary pressure. Then the tuned parameters were applied to predict the 3D test performance. Through comparison of the predicted and experimental results in the 3D test, the capability of predicting up-scaled VAPEX processes through numerical simulation was examined. The results show that numerical simulation, compared to analytical method, has more potential to be used as scale-up method because of the improved prediction results. The initial waterflooding performance can be successfully predicted, whereas the uncertainty in upscaling the VAPEX process is large. The difference between the predicted and measured oil recovery factors was in the range of 0.75–25.14%, depending on the different combinations of uncertain parameters. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-0069-y Authors S. Xu, Petroleum Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada F. Zeng, Petroleum Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada Y. Gu, Petroleum Systems Engineering, University of Regina, Regina, SK S4S 0A2, Canada K. D. Knorr, Saskatchewan Research Council, Regina, SK S4S 7J7, Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this paper, we follow the pore-level simulation approach to investigate fluid flow over an open-porous interface using the lattice Boltzmann method. As this approach does not require any specific treatment for the interface, the predicted pore-level velocity field is averaged and used to evaluate the available macroscopic boundary conditions for the interface. Two most common interface boundary conditions are evaluated, and the unknown fitting parameters in them are calculated as a function of porosity of the porous region. Analytical solutions of the velocity profile in the close vicinity of the interface are used to validate the numerical methodology. It is shown that the predicted numerical results for penetration depth in the porous region, flow rate in open channel, and velocity profile in the open and porous regions are in excellent agreement with the predictions of the two available models, if the proposed values of their fitting parameters are used. Content Type Journal Article Pages 1-13 DOI 10.1007/s11242-012-0074-1 Authors Aydin Nabovati, Department of Mechanical & Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, Canada Cristina H. Amon, Department of Mechanical & Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    We introduce a finite-difference method to simulate pore scale steady-state creeping fluid flow in porous media. First, a geometrical approximation is invoked to describe the interstitial space of grid-based images of porous media. Subsequently, a generalized Laplace equation is derived and solved to calculate fluid pressure and velocity distributions in the interstitial space domain. We use a previously validated lattice-Boltzmann method (LBM) as ground truth for modeling comparison purposes. Our method requires on average 17 % of the CPU time used by LBM to calculate permeability in the same pore-scale distributions. After grid refinement, calculations of permeability performed from velocity distributions converge with both methods, and our modeling results differ within 6 % from those yielded by LBM. However, without grid refinement, permeability calculations differ within 20 % from those yielded by LBM for the case of high-porosity rocks and by as much as 100 % in low-porosity and highly tortuous porous media. We confirm that grid refinement is essential to secure reliable results when modeling fluid flow in porous media. Without grid refinement, permeability results obtained with our modeling method are closer to converged results than those yielded by LBM in low-porosity and highly tortuous media. However, the accuracy of the presented model decreases in pores with elongated cross sections. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-0024-y Authors Vahid Shabro, Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station C0300, Austin, TX 78712-0228, USA Carlos Torres-Verdín, Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station C0300, Austin, TX 78712-0228, USA Farzam Javadpour, Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X, Austin, TX 78713-8924, USA Kamy Sepehrnoori, Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station C0300, Austin, TX 78712-0228, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this work, we investigate the accuracy of some physical models that are frequently used to describe and interpret dispersive mixing and mass transfer in compositional reservoir simulation. We have designed a quaternary analog fluid system (alcohol–water–hydrocarbon) that mimics the phase behavior of CO 2 -hydrocarbon mixtures at high pressure and temperature. A porous medium was designed using PolyTetraFlouroEthylene (PTFE) materials to ensure that the analog oil acts as the wetting phase, and the properties of the porous medium were characterized in terms of porosity, permeability and dispersivity. Relative permeability and interfacial tension (IFT) measurements were also performed to delineate interactions between the fluid system and the porous medium. The effluent concentrations from two-component first-contact miscible (FCM) displacement experiments exhibit a tailing behavior that is attributed to imperfect sweep of the porous medium: A feature that is not captured by normal dispersion models. To represent this behavior in displacement calculations, we use dual-porosity (DP) models including mass transfer between flowing and stagnant porosities. Two 4-component two-phase displacement experiments were performed at near-miscible and multicontact miscible (MCM) conditions and the effluent concentrations were interpreted by numerical calculations. We demonstrate that the accuracy of our displacement calculations relative to the experimental observations is sensitive to the selected models for dispersive mixing, mass transfer between flowing and stagnant porosities, and IFT scaling of relative permeability functions. We also demonstrate that numerical calculations substantially agree with the experimental observations for some physical models with limited need for model parameter adjustment. The combined experimental and modeling effort presented in this work identifies and explores the impact of a set of physical mechanisms (dispersion and mass transfer) that must be upscaled adequately for field-scale displacement calculations in DP systems. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-0027-8 Authors Hasan Shojaei, Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, CA, USA Reza Rastegar, Chevron Energy Technology Company, Bakersfield, CA, USA Kristian Jessen, Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, CA, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    During CO 2 injection into brine aquifers-containing residual and/or dissolved CH 4 , three distinct regions develop: (1) a single-phase, dry-out region around the well-bore filled with pure supercritical CO 2 ; (2) a two-phase, two-component system containing CO 2 and brine; and (3) a two-phase, two-component system containing CH 4 , and brine. This article extends an existing analytical solution, for pressure buildup during CO 2 injection into brine aquifers, by incorporating dissolved and/or residual CH 4 . In this way, the solution additionally accounts for partial miscibility of the CO 2 –CH 4 –brine system and the relative permeability hysteresis associated with historic imbibition of brine and current drainage due to CO 2 injection and CH 4 bank development. Comparison of the analytical solution results with commercial simulator, CMG-GEM, shows excellent agreement among a range of different scenarios. The presence of residual CH 4 in a brine aquifer summons two competing phenomena, (1) reduction in relative permeability (phase interference), which increases pressure buildup by reducing total mobility, and (2) increase in bulk compressibility which decreases pressure buildup of the system. If initial CH 4 is dissolved (no free CH 4 ), these effects are not as important as they are in the residual gas scenario. Relative permeability hysteresis increased the CH 4 bank length (compared to non-hysteretic relative permeability), which led to further reduction in pressure buildup. The nature of relative permeability functions controls whether residual CH 4 is beneficial or disadvantageous to CO 2 storage capacity and injectivity in a candid brine aquifer. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-0025-x Authors Seyyed Abolfazl Hosseini, Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX, USA Simon A. Mathias, Department of Earth Sciences, Durham University, Durham, UK Farzam Javadpour, Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions, and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability–porosity relationships represented by the Kozeny–Carman equations and Archie’s law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The aim of this article is the evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability–porosity relationships are derived analytically. Several examples of the tube bundles are constructed, and the relevance of the derived permeability–porosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literature. Content Type Journal Article Pages 1-11 DOI 10.1007/s11242-012-0022-0 Authors I. Zinovik, Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, 8092 Switzerland D. Poulikakos, Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, 8092 Switzerland Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Since 1942 Archie’s law is used every day to estimate, from electrical measurements, the quantity of oil present in oil fields. In this article, we perform the first experimental analysis of electric conductivity in well controlled models of porous media. We used microfluidic networks (called micromodels in the oil industry jargon), incorporating thousands of pores, with controlled wettability. Different electrode and pore geometries are considered. In all cases the evolution of the conductivity with the conductive fluid fraction (“saturation”) clearly reveals the presence of percolation thresholds, signaling that as the fraction of the conductive fluid decreases below some critical value, there are no more pathways involving only channels entirely filled with the conductive fluid that connect the electrodes. This behavior is observed in all cases, for all the network/electrode geometries and wetting properties we investigated, and is consequently likely to reflect a genuine behavior for microfluidic “2D” networks. The existing models—based on percolation theory or on mean field approach—reproduce correctly the structure of this behavior, but generally at a semi-quantitative level. The most successful case is obtained with the effective medium theory (EMT) model, with drainage and perpendicular electrodes. This outcome suggests that, despite the complexity of these systems, very simple models can describe correctly the physics of the system. Nonetheless, more precise modeling requires case-by-case studies. Our results are consistent with the current body of knowledge accumulated for decades on three-dimensional samples. The key point is that in 3D systems, owing to topological reasons, the threshold is extremely low in terms of water saturations. Archie’s law completely neglects the threshold effect. Nonetheless the percolation threshold should not be overlooked, and modeling should take this aspect systematically into account, as it is already done by several investigators. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0029-6 Authors B. Kozlov, Laboratory of Microfluidics, UMR Gulliver, ESPCI, 10 rue Vauquelin, 75005 Paris, France M. H. Schneider, Laboratory of Microfluidics, UMR Gulliver, ESPCI, 10 rue Vauquelin, 75005 Paris, France B. Montaron, Schlumberger, 14 Jiuxianqiao Road, Chaoyang District, Beijing, 100015 China M. Laguës, Espace Pierre-Gilles de Gennes, ESPCI, 10 rue Vauquelin, 75005 Paris, France P. Tabeling, Laboratory of Microfluidics, UMR Gulliver, ESPCI, 10 rue Vauquelin, 75005 Paris, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    We examine the pore space structure evolution of ordered uniform sphere packs: simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC), undergoing simple diagenetic processes that reduce their pore spaces. Focus is on the occurrence of pore space microstructure changes or transitions, which are followed through their characteristic or critical pore lengths ( l c ). For almost all the cubic packings undergoing either compaction or cementation there are no singularities in l c . This is a consequence of having a single pore shape controlling flow at all stages of the process. However, this is not so for the BCC packing under cementation, for which l c is non-monotonic exhibiting a kink at f » 0.1452 , the porosity at which the pore shape controlling flow switches to a different form and position. These results for uniform compaction/cementation complement our previous works on pore networks under random shrinkage. Kinks in l c as porosity decreases signal pore space microstructure transitions that anticipate sudden changes in the permeability–porosity relation as porosity decreases. The consequences are great; clearly l c is not a constant unless the diagenetic process is mild. A l c function of compaction/cementation advancement should be used above a transition and a different l c function below. For the sphere packs here, once the diagenetic process has reduced the pore space substantially, a l c function of compaction/cementation advancement is mandatory if we are to capture all significant flow features. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-0033-x Authors Ariel Narváez, Chemical Engineering Department and Surface Analysis Laboratory (ASIF), University of Concepción, Casilla 53-C, Correo 3, Concepción, Chile Pedro G. Toledo, Chemical Engineering Department and Surface Analysis Laboratory (ASIF), University of Concepción, Casilla 53-C, Correo 3, Concepción, Chile Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The effect of vertical throughflow on the onset of penetrative convection simulated via internal heating in a two-layer system in which a layer of fluid overlies and saturates a layer of porous medium is studied. Flow in the porous medium is governed by Forchheimer-extended Darcy equation, and Beavers–Joseph slip condition is applied at the interface between the fluid and the porous layers. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The eigenvalue problem is solved using a regular perturbation technique with wave number as a perturbation parameter. The ratio of fluid layer thickness to porous layer thickness, ζ , the direction of throughflow, and the presence of volumetric internal heat source in fluid and/or porous layer play a decisive role on the stability characteristics of the system. In addition, the influence of Prandtl number arising due to throughflow is also emphasized on the stability of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and vertical throughflow so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0034-9 Authors S. P. Suma, Department of Mathematics, New Horizon College of Engineering, Bangalore, 560 103 India Y. H. Gangadharaiah, Department of Mathematics, New Horizon College of Engineering, Bangalore, 560 103 India R. Indira, Department of Mathematics, Nitte Meenakshi Institute of Technology, Bangalore, India I. S. Shivakumara, UGC Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore, 560 001 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this work, we develop a macroscopic model for diffusion–migration of ionic species in saturated porous media, based on periodic homogenization. The prior application is chloride transport in cementitious materials. The dimensional analysis of Nernst–Planck equation lets appear dimensionless numbers characterizing the ionic transfer in porous media. Using experimental data, these dimensionless numbers are linked to the perturbation parameter e . For a weak-imposed electrical field, or in natural diffusion, the asymptotic expansion of Nernst–Planck equation leads to a macroscopic model coupling diffusion and migration at the same order. The expression of the homogenized diffusion coefficient only involves the geometrical properties of the material microstructure. Then, parametric simulations are performed to compute the chloride diffusion coefficient through different complexity of the elementary cell to go on as close as possible to experimental diffusion coefficient of the two cement pastes tested. Content Type Journal Article Pages 1-23 DOI 10.1007/s11242-012-0013-1 Authors K. Bourbatache, La Rochelle University, LaSIE, Avenue Michel Crépeau, 17000 La Rochelle, France O. Millet, La Rochelle University, LaSIE, Avenue Michel Crépeau, 17000 La Rochelle, France A. Aït-Mokhtar, La Rochelle University, LaSIE, Avenue Michel Crépeau, 17000 La Rochelle, France O. Amiri, La Rochelle University, LaSIE, Avenue Michel Crépeau, 17000 La Rochelle, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This paper analyses the classical problem of transient surface–groundwater interaction in a stream–aquifer system under rather realistic conditions. The downward sloping unconfined aquifer is in contact with a constant water level at one end, and a fully penetrating stream at the other end whose water level is rising at a uniform speed. Furthermore, the aquifer is replenished by a vertical time-varying recharge. Closed form analytical expressions for hydraulic head and flow rate in the aquifer are obtained by solving the linearized Boussinesq equation using Laplace transform method. Effects of aquifer parameters on transient water table and flow rate are illustrated with a numerical example. To assess the efficiency of the linearization method, analytical solutions are compared with numerical solutions of the corresponding non-linear equation. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0026-9 Authors Rajeev K. Bansal, Department of Mathematics, National Defence Academy, Khadakwasla, Pune, 411023 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The objective of the present work is to investigate theoretically the Hiemenz flow and heat transfer of an incompressible viscous nanofluid past a porous wedge sheet in the presence of thermal stratification due to solar energy (incident radiation). The wall of the wedge is embedded in a uniform Darcian porous medium to allow for possible fluid wall suction or injection and has a power–law variation of the wall temperature. The partial differential equations governing the problem under consideration are transformed by a special form of Lie symmetry group transformations viz., one-parameter group of transformation into a system of ordinary differential equations which are solved numerically by Runge–Kutta–Gill-based shooting method. The conclusion is drawn that the flow field and temperature are significantly influenced by convective radiation, thermal stratification, buoyancy force, and porosity of the sheet. Content Type Journal Article Pages 1-18 DOI 10.1007/s11242-012-0011-3 Authors R. Kandasamy, Research Centre for Computational Mathematics, FSTPI, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia I. Muhaimin, Research Centre for Computational Mathematics, FSTPI, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia N. Siva Ram, RMK Engineering College, Anna University, Chennai, India K. K. Sivagnana Prabhu, RMK Engineering College, Anna University, Chennai, India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    An ensemble-based technique has been developed and successfully applied to simultaneously estimate the relative permeability and capillary pressure by history matching the observed production profile. Relative permeability and capillary pressure curves are represented using a power-law model. Then, forward simulation is performed with the initial coefficients of the power-law model, all of which are to be tuned automatically and finally determined once the observed data is assimilated completely and history matched. The newly developed technique has been validated by a synthetic coreflooding experiment with two scenarios. The endpoints are fixed for the first scenario, whereas they are completely free in the second scenario. Simultaneous estimation of relative permeability and capillary pressure has been found to improve gradually as more observation data is assimilated. There exists an excellent agreement between both the updated relative permeability and the capillary pressure and their corresponding reference values, once the discrepancy between the simulated and the observed production history has been minimized. Compared with coefficients of capillary pressure curve, coefficients of relative permeability curves, irreducible water saturation, and residual oil saturation are found to be more sensitive to the observed data. In addition, water relative permeability is more sensitive to the observation data than either oil relative permeability or capillary pressure. It is shown from its application to a laboratory coreflooding experiment that relative permeability and capillary pressure curves can be simultaneously evaluated once all the experimental measurements are assimilated and history matched. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-0007-z Authors Yin Zhang, Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, S4S 0A2 Canada Heng Li, Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, S4S 0A2 Canada Daoyong Yang, Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, S4S 0A2 Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The two-phase mixture model has been widely used to describe the performances of fluid flow and heat transfer within porous media with liquid phase change. However, this model was based on two important assumptions: the temperature is constant ( T f = const) in two phase region, while fluid temperature is locally equal to the solid matrix temperature ( T s =  T f ). These assumptions result in an inveracious numerical phenomenon, i.e.,: a thermal insulating layer within the porous matrix in numerical simulations. This numerical phenomenon is not real, because the solid matrix is made of thermal conductive material. To modify the mathematical model of the transpiration cooling problem with boiling, this paper presents an improved model, which is based on that the Gibbs free energy of liquid phase and vapor phase are equal in two-phase region. Temperature variation in two-phase region is considered, and fluid temperature is locally different from the solid matrix temperature ( T s  ≠ T f ), therefore the local heat transfer through the convection between solid and fluid is considered as well. Numerical calculations of the transpiration cooling problem with boiling are carried out with the improved model. The numerical results such as the variations of temperatures of fluid and solid, the saturation and pressure of fluid within porous media, are reasonable, and the inveracious issue of the thermal insulating layer is successfully resolved. Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-0006-0 Authors Kuan Wei, Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96, Hefei, 230027 Anhui, People’s Republic of China Jianhua Wang, Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96, Hefei, 230027 Anhui, People’s Republic of China Mao Mao, Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96, Hefei, 230027 Anhui, People’s Republic of China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Fractures serve as primary conduits having a great impact on the migration of injected fluid into fractured permeable media. Appropriate transport properties such as relative permeability and capillary pressure are essential for successful simulation and prediction of multi-phase flow in such systems. However, the lack of a thorough understanding of the dynamics governing immiscible displacement in fractured media, limits our ability to properly represent their macroscopic transport properties. Previous experimental observations of imbibition front evolution in fractured rocks are examined in the present study using an automated history-matching approach to obtain representative relative permeability and capillary pressure curves. Predicted imbibition front evolution under different flow conditions resulted in an excellent agreement with experimental observations. Sensitivity analyses, in combination with direct experimental observation, allowed exploring the competing effects of relative permeability and capillary pressure on the development of saturation distribution and imbibing front evolution in fractured porous media. Results show that residual saturations are most sensitive to matrix relative permeability to oil, while the ratio of oil and water relative permeability, rock heterogeneity, boundary condition, and matrix–fracture capillary pressure contrast, affect displacement shape, speed, and geometry of the imbibing front. Content Type Journal Article Pages 1-25 DOI 10.1007/s11242-012-0009-x Authors C.-H. Lee, John and Willie Leone Family Department of Energy and Mineral Engineering, EMS Energy Institute, The Pennsylvania State University, 110 Hosler Building, University Park, PA 16802-5000, USA Z. T. Karpyn, John and Willie Leone Family Department of Energy and Mineral Engineering, EMS Energy Institute, The Pennsylvania State University, 110 Hosler Building, University Park, PA 16802-5000, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Similarity solutions are proposed for the analysis of free convection flow over a non-isothermal body of arbitrary shape embedded in porous media in the presence of internal heat generation. The porous medium is saturated with non-Newtonian power law fluid. The effect of temperature dependent viscosity on heat transfer rates is investigated. The linearized version of the Arrhenius law for temperature dependent viscosity is considered and it is shown that the heat transferred is more for a less viscous fluid. Content Type Journal Article Pages 1-12 DOI 10.1007/s11242-012-0004-2 Authors Shobha Bagai, Department of Mathematics, University of Delhi, New Delhi, India Chandrashekhar Nishad, Department of Mathematics, University of Delhi, New Delhi, India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Heap leaching of precious metals from low-grade ores is modeled using the slow and fast zone concept of liquid movement in porous media (Kartha and Srivastava Transport in Porous Media 75, 227–247, 2008 ). The heap is conceptualized as a porous medium with the pores filled by liquid and/or air. The liquid phase is further divided into three zones—immobile, slow moving, and fast moving, with only the immobile and slow-moving liquids interacting with the solid particles. The conceptual model is applied to simulate two- dimensional leaching of a shallow gold ore heap. Temporal evolution of gold concentration in the solid and the liquid phases are analyzed to ascertain the effect of several parameters on the leaching process. Sensitivity analyses are performed with respect to the irrigation rate, the equilibrium sorption coefficient, and the fractional volume of the slow-moving liquid. For a constant volume of the leaching solution and for the same duration of leaching, the metal extraction is higher when a larger number of irrigation cycles are used. The metal extraction is found to be smaller for higher values of the sorption coefficient. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-0020-2 Authors Suresh A. Kartha, Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039 India Rajesh Srivastava, Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Quantitative in situ monitoring of oil recovery from sedimentary rock is demonstrated for the first time using advanced two-dimensional (2D) nuclear magnetic resonance (NMR) correlation measurements on a low field spectrometer. The laboratory-scale NMR system was chosen to provide a common physics of measurement with NMR well-logging tools. The NMR protocols are used to monitor recovery of a heavy Middle East crude oil from high permeability sandstone plugs using a brine (water) flood followed by chemical enhanced oil recovery agents: polymer and alkaline–surfactant–polymer solutions. 2D correlations between relaxation time ( T 1 , T 2 ) and apparent self-diffusion coefficient D app are used to obtain simultaneously a volumetric determination of the oil and aqueous fluid-phase saturations present in the porous material. The T 1 − T 2 and D app − T 2 correlations are bulk measurements of the entire rock core-plug; excellent agreement is shown between the measures of remaining oil (from NMR) and recovered oil (from gravimetric assay of the effluent). Furthermore, we introduce the capability to measure spatially resolved T 2 distributions on a low field spectrometer using a rapid frequency-encoded y − T 2 map. A non-uniform distribution of remaining oil is observed due to viscous instabilities in the flowing liquids; the final oil saturation ranges from S o ( final ) » 0 to 20 % along the direction of flow. These results highlight the quantitative nature of the NMR data obtainable in low field NMR core analysis and also the importance of spatially resolved measurements when studying short core-plugs. Content Type Journal Article Pages 1-24 DOI 10.1007/s11242-012-0019-8 Authors Jonathan Mitchell, Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge, CB2 3RA UK John Staniland, Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge, CB3 0EL UK Romain Chassagne, Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge, CB3 0EL UK Edmund J. Fordham, Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge, CB3 0EL UK Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Leakage of CO 2 through fractures in saline formations will increase the CO 2 —brine interface and promote CO 2 dissolution. We use a 2D, finite difference MATLAB model to simulate dissolution rates from a vertical fracture, with CO 2 flowing through it, in a secondary storage formation. The instigation of convection currents increases dissolution rates leading to higher dissolution in higher Rayleigh number systems. Comparison of our results with fracture flow rates shows that for typical fracture apertures dissolution from a fracture is small relative to the amount of CO 2 flowing through the fracture. Temporal and spatial variations in fracture permeability may reduce fracture flow rates and increase the relative amount of CO 2 dissolved from the fracture compared to the CO 2 flowing through the fracture. Further work on CO 2 dissolution in relation to fracture heterogeneity, flow of CO 2 within fractures and the interaction of multiple fractures will improve our ability to predict CO 2 dissolution rates for site characterisation. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-0021-1 Authors Francesca E. Watson, Geospatial Research Ltd., Department of Earth Sciences, Durham University, Durham, UK Simon A. Mathias, Department of Earth Sciences, Durham University, Durham, UK Jeroen van Hunen, Department of Earth Sciences, Durham University, Durham, UK Susie E. Daniels, Geospatial Research Ltd., Department of Earth Sciences, Durham University, Durham, UK Richard R. Jones, Geospatial Research Ltd., Department of Earth Sciences, Durham University, Durham, UK Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This study is focused on the transport of Pseudomonas (P.) putida bacterial cells in a 3-D model aquifer. The pilot-scale aquifer consisted of a rectangular glass tank with internal dimensions: 120 cm length, 48 cm width, and 50 cm height, carefully packed with well-characterized quartz sand. The P. putida decay was adequately represented by a first-order model. Transport experiments with a conservative tracer and P. putida were conducted to characterize the aquifer and to investigate the bacterial behavior during transport in water saturated porous media. A 3-D, finite-difference numerical model for bacterial transport in saturated, homogeneous porous media was developed and was used to successfully fit the experimental data. Furthermore, theoretical interaction energy calculations suggested that the extended-DLVO theory seems to predict bacteria attachment onto the aquifer sand better than the classical DLVO theory. Content Type Journal Article Pages 1-26 DOI 10.1007/s11242-012-0015-z Authors Constantinos V. Chrysikopoulos, Environmental Engineering Laboratory, Department of Civil Engineering, University of Patras, 26500 Patras, Greece Vasiliki I. Syngouna, Environmental Engineering Laboratory, Department of Civil Engineering, University of Patras, 26500 Patras, Greece Ioanna A. Vasiliadou, Environmental Engineering Laboratory, Department of Civil Engineering, University of Patras, 26500 Patras, Greece Vasileios E. Katzourakis, Environmental Engineering Laboratory, Department of Civil Engineering, University of Patras, 26500 Patras, Greece Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In fractured oil reservoirs, the gravity drainage mechanism has great potentials to higher oil recovery in comparison with other mechanisms. Recently, the forced gravity drainage assisted by gas injection has also been considered; however, there are few comprehensive studies in the literature. Dual porosity model, the most common approach for simulation of fractured reservoirs, uses transfer function concept to represent the fluid exchange between matrix and its neighborhood fractures. This study compares the results of different available transfer functions with those of fine grid simulations when forced gravity drainage contributes to oil production from a single matrix block. These comparisons can lead to a more sophisticated formulation including the interplay of capillary, gravity and viscous forces. As a result, a new matrix-fracture transfer function can be developed and its results can be tested against the results of fine-grid simulations. Moreover, the reliability of this model for simulation of forced gravity drainage has been demonstrated by performing some sensitivity analysis. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-9999-7 Authors S. Ehsan Samimi, Department of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran Mohsen Masihi, Department of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran Shahab Gerami, IOR/EOR Research institute, NIOC R&D Directorate, No. 22, Negar Alley, Valiasr Ave., Vanak Sq., Tehran, Iran Mostafa Ganjeh Ghazvini, IOR/EOR Research institute, NIOC R&D Directorate, No. 22, Negar Alley, Valiasr Ave., Vanak Sq., Tehran, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The upscaled models of reservoirs result in coarse representation of flow for simulation gridblocks. This representation discards subgrid heterogeneities and flow complexities which can lead to an inaccurate performance prediction for reservoir processes. To tackle the problem, reconstruction techniques such as multiscale or upscaling–downscaling methods have been developed to recapture the subgrid flow details which have been approximated at the upscaling stage. In this study, we propose a modified downscaling procedure applied on local–global upscaling method. The modification accounts for using approximate fine-scale velocities obtained from the upscaling stage to partition the coarse-scale fluxes to local boundary conditions in the reconstruction of fine-scale solutions. This modification enhances quality of saturation profiles obtained by resultant reconstructed velocities. In this stage, we also investigate the application of basis functions for velocity reconstruction. These functions are computed numerically by solving at initial time a set of decomposed Neumann boundary condition problems for each coarse block. The values of boundary fine fluxes are derived from apportioning a unit-value coarse flux over that boundary. These functions are stored and reused for the rest of the simulation. This leads to computational gain compared to conventional downscaling where velocity is refined at any time and any where. We simulate incompressible tracer and multiphase flow in two and three dimensions on a range of test cases by fine-scale reference model and upscaling–downscaling model. For comparison purposes a pressure solver upscaling is used as a base method. The results show a better reconstruction quality for saturation profiles obtained by modified scheme and the practicality of application of basis functions with minimal deterioration of results. Content Type Journal Article Pages 1-23 DOI 10.1007/s11242-012-9981-4 Authors Masoud Babaei, Department of Earth Science & Engineering, Imperial College London, Prince Consort Road, London, SW7 2AZ UK Peter R. King, Department of Earth Science & Engineering, Imperial College London, Prince Consort Road, London, SW7 2AZ UK Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In swelling porous media, the potential for flow is much more than pressure, and derivations for flow equations have yielded a variety of equations. In this article, we show that the macroscopic flow potentials are the electro-chemical potentials of the components of the fluid and that other forms of flow equations, such as those derived through mixture theory or homogenization, are a result of particular forms of the chemical potentials of the species. It is also shown that depending upon whether one is considering the pressure of a liquid in a reservoir in electro-chemical equilibrium with the swelling porous media, or the pressure of the vicinal liquid within the swelling porous media, a critical pressure gradient threshold exists or does not. Content Type Journal Article Pages 1-22 DOI 10.1007/s11242-012-9987-y Authors Lynn Schreyer-Bennethum, Department of Mathematical and Statistical Sciences, University of Colorado Denver, Campus Box 170, 1250 14th Street Suite 600, Denver, CO 80217, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The flow properties of complex fluids through porous media give rise to multiphase flow displacement mechanisms that operate at different scales, from pore-level to Darcy scale. Experiments have shown that injection of oil-in-water emulsions can be used as an effective enhanced-oil recovery (EOR) method, leading to substantial increase in the volume of oil recovered. Pore-scale flow visualization as well as core flooding results available in the literature have demonstrated that the enhanced recovery factor is regulated by the capillary number of the flow. However, the mechanisms by which additional oil is displaced during emulsion injection are still not clear. In this work, we carried out two different experiments to evaluate the effect of emulsion flooding both at pore and macro scales. Visualization of the flow through sand packed between transparent plexiglass parallel plates shows that emulsion flooding improves the pore-level displacement efficiency, leading to lower residual oil saturation. Oil recovery results during emulsion flooding in tertiary mode (after waterflooding) in parallel sandstone cores with very different absolute permeability values prove that emulsion flooding also leads to enhancement of conformance or volumetric sweep efficiency. Combined, the results presented here show that injection of emulsion offers multiscale mechanisms resulting from capillary-driven mobility control. Content Type Journal Article Pages 1-10 DOI 10.1007/s11242-012-9997-9 Authors V. R. Guillen, Department of Mechanical Engineering, PUC-Rio, Rua Marques de São Vicente, 225 Gávea, Rio de Janeiro, RJ 22453-900, Brazil M. S. Carvalho, Department of Mechanical Engineering, PUC-Rio, Rua Marques de São Vicente, 225 Gávea, Rio de Janeiro, RJ 22453-900, Brazil V. Alvarado, Department of Chemical and Petroleum Engineering, University of Wyoming, Dept. 3295, 1000 E University Avenue, Laramie, WY 82071, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The mathematical model for transient fluid flow in porous media is based in general on mass conservation principle. Because of the small compressibility of formation fluid, the quadratic term of pressure gradient is always ignored to linearize the non-linear diffusion equation. This may result in significant errors in model prediction, especially at large time scale. In order to solve this problem, it may be necessary to keep the quadratic term in the non-linear equations. In our study, the quadratic term is reserved to fully describe the transient fluid flow. Based on this rigorous treatment, the mathematical models are established to analyze the transient flow behavior in a double porosity, fractal reservoir with spherical and cylindrical matrix. In addition, Laplace transformation method is employed to solve these mathematical models and the type curves are provided to analyze the pressure transient characteristics. This study indicates that the relative errors in calculated pressure caused by ignoring the quadratic term may amount to 10 % in a fractal reservoir with double porosity, which can’t be neglected in general for fractal reservoirs with double porosity at large time scale. Content Type Journal Article Pages 1-13 DOI 10.1007/s11242-012-9995-y Authors Yuedong Yao, MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249 China Yu-Shu Wu, Department of Petroleum Engineering, Colorado School of Mines, Golden, CO, USA Ronglei Zhang, Department of Petroleum Engineering, Colorado School of Mines, Golden, CO, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The fiber has great advantages in hydraulic fracturing when considering fluid leak off and flow friction, proppant transportation and fracture damage, proppant or sand production, and fracture geometry. However, some drawbacks, such as poor chemical stability, mechanical properties, heat denaturation, and dispersivity, always emerge in oilfield cases. Accordingly, a new type of nanocomposite fiber is used to overcome these shortcomings in our research. Generally, fiber’s conventional performance, dispersivity and proppant suspension capability can be evaluated easily, but reliable evaluation and optimization of fiber applications could not be obtained by normal indoor experimental instruments. So we developed the “fracture filling model”, a specially designed instrument to evaluate the performances of fracture conductivity, proppant backflow, and sand control. All the performances of the nanocomposite fiber were evaluated, and the length and concentration of the fiber were optimized. The results have great influences on both theoretical study and field treatments of the new nanocomposite fiber. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-0002-4 Authors T. K. Guo, CMOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China S. C. Zhang, CMOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China B. Xiao, CMOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China G. Q. Liu, CMOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China F. Wang, CMOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China J. C. Zhang, Herio-Watt University, Edinburgh, UK X. B. Bian, CMOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description: Waves in Porous Media Content Type Journal Article Pages 1-2 DOI 10.1007/s11242-012-9998-8 Authors Holger Steeb, Institute of Mechanics, Ruhr-University Bochum, Bochum, Germany David Smeulders, TU Eindhoven, Eindhoven, The Netherlands Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Upscaling procedures and determination of effective properties are of major importance for the description of flow in heterogeneous porous media. In this context, we study the statistical properties of effective hydraulic conductivity ( K eff ) distributions and their dependence on the coarsening scale. First, we focus on lognormal stationary isotropic media. Our results suggest that K eff is lognormally distributed independently on the coarsening scale. The scale dependence of the mean and variance of K eff are in agreement with recent analytical derivations obtained using coarse graining filtering techniques. In the second part, we focus on binary media, analysing the dependence of K eff distributions on the coarsening scale and also on the high- K facies volume fraction p . When p is near the percolation threshold p c , the decrease of the normalized variance with the coarsening scale is remarkably (10 2 times) slower compared to the situation in which p far from p c , but also compared to the cases of lognormal media studied before. This result permits to assess the degree of difficulty that systems with p near p c pose for upscaling procedures. Also we point out in terms of K eff statistics the relative influence of the coarsening scale and of the high- K facies connectivity. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-9991-2 Authors A. Boschan, IFP Energies Nouvelles, Rueil Malmaison, France B. Nœtinger, IFP Energies Nouvelles, Rueil Malmaison, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This paper investigates how the regime (quasi-static, transient, out of equilibrium) of the phenomena occurring at pores scale determine the nature of the (non)-local effect—in time and/or space—involved in the macroscopic behavior of a porous medium. The study focuses on sound propagation examining—through the homogenization method of periodic media—situations of single porosity, Rayleigh scattering and double porosity. Non-locality effects reveals the loss of a perfect quasi-static equilibrium free of volume loading at the local scale. The non-locality in time is due to phenomena in transient regime at the ERV scale, while non-locality in space is due to the non-homogeneity in space of the macrofields. The generality of the arguments lead to infer that the conclusions about non-locality versus pores scale regime, could be extended to other physical phenomena in heterogeneous media. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-9984-1 Authors Claude Boutin, Université de Lyon, DGCB CNRS 3237, Ecole Nationale des Travaux Publics de l’Etat, 69518 Vaulx-en-Velin Cedex, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Rarefied gas flow in channels and computer-aided reconstructions of porous media is simulated using the direct simulation Monte Carlo (DSMC) method and a modified lattice-Boltzmann (LB) method that can account for rarefaction effects. An increase of two orders of magnitude was noted for the gas permeability as the Knudsen number increased from 0.1 to 10. It was found that incorporation of a Bosanquet expression for the viscosity in the dusty gas flux equations leads to the recovery of the well known Klinkenberg expression for the gas permeability, revealing an explicit relation of the, thus far empirical, permeability correction factor to the fluid and structure properties. The expression for the effective gas viscosity in the transition flow regime is also incorporated in the LB method, which is then validated against the DSMC method by comparing predictions for the velocity profiles in straight channels over the entire transition flow regime. The new LB method offers the additional advantages of simplicity in the code implementation and great savings in computational time and memory compared to the DSMC method. It is shown that the rough adjustment of a single parameter suffices to make the LB method suitable for the reliable prediction of the gas permeability in porous media over the entire transition flow regime. Content Type Journal Article Pages 1-14 DOI 10.1007/s11242-012-0010-4 Authors A. N. Kalarakis, Institute of Chemical Engineering and High Temperature Chemical Processes, Foundation for Research and Technology, Hellas, Patras, Greece V. K. Michalis, Institute of Chemical Engineering and High Temperature Chemical Processes, Foundation for Research and Technology, Hellas, Patras, Greece E. D. Skouras, Institute of Chemical Engineering and High Temperature Chemical Processes, Foundation for Research and Technology, Hellas, Patras, Greece V. N. Burganos, Institute of Chemical Engineering and High Temperature Chemical Processes, Foundation for Research and Technology, Hellas, Patras, Greece Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Based on the poroelasticity theory, this article investigates the reflection and transmission characteristics of an incident plane transverse wave at a plane interface between an isotropic elastic half-space and an unsaturated poroelastic solid half-space. For this purpose, the effect of the saturation degree and frequency on the properties of the four bulk waves in unsaturated porous medium, i.e., three longitudinal waves and one transverse wave, are discussed at first. Two general cases of mode conversion are considered: (i) The initial transverse wave is incident from an unsaturated poroelastic half-space to the interface, and (ii) the initial transverse wave is incident from an elastic solid half-space to the interface. The expressions for the partition of energy at the interface during transmission and reflection process of waves are presented in explicit forms. At last, numerical computations are performed for these two cases and the results obtained are depicted, respectively. The variation of the amplitude ratios and energy ratios with the saturation degree and incident angle is illustrated in detail. It is also verified that, at the interface, the sum of energy ratios is approximately equal to unity as expected. Content Type Journal Article Pages 1-20 DOI 10.1007/s11242-012-0012-2 Authors Wei-yun Chen, MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou, 310027 People’s Republic of China Tang-dai Xia, MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou, 310027 People’s Republic of China Miao-miao Sun, Zhejiang Institute of Hydraulics & Estuary, Hangzhou, 310027 People’s Republic of China Chao-jiao Zhai, MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou, 310027 People’s Republic of China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Due to inherent heterogeneities in structure, mineral placement and fluid velocity in rock, bulk reaction rates realized during reactive flow through porous media may differ significantly from that predicted by laboratory-measured rate laws. In particular, rate laws determined in batch reactor experiments do not capture any of the flow dependence that will be experienced in the porous medium. Based on network flow model simulations of anorthite and kaolinite reactions in two sandstone pore networks under acidic conditions commensurate with CO2 sequestration, we compute up-scaled reaction rates at the core scale and investigate the dependence of the observed reaction rates on flow rate. For the anorthite reaction which, under these acidic conditions is far from equilibrium and dominated by pH, we find a power law dependence of reaction rate on flow rate. For the kaolinite reaction, which is near equilibrium, a more complex dependence emerges, with the up-scaled rate tending to rapidly increasing net precipitation at low-flow rates, then reversing and tending toward net dissolution at high-flow rates. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-0014-0 Authors D. Kim, Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA W. B. Lindquist, Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The onset of Darcy–Brinkman double-diffusive convection in a binary viscoelastic fluid-saturated porous layer is studied using both linear and weakly nonlinear stability analyses. The Oldroyd-B model is employed to describe the rheological behavior of the fluid. An extended form of Darcy–Oldroyd law incorporating the Brinkman’s correction and time derivative is used to describe the fluid flow and the Oberbeck–Boussinesq approximation is invoked. The onset criterion for stationary and oscillatory convection is derived analytically. The effects of rheological parameters, Darcy number, normalized porosity, Lewis number, solute Rayleigh number, and Darcy–Prandtl number on the stability of the system is investigated. The results indicated that there is a competition among the processes of thermal, solute diffusions and viscoelasticity that causes the convection to set in through the oscillatory modes rather than the stationary. The Darcy–Prandtl number has a dual effect on the threshold of oscillatory convection. The nonlinear theory based on the method of truncated representation of Fourier series is used to find the transient heat and mass transfer. Some existing results are reproduced as the particular cases of present study. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-0008-y Authors Mahantesh S. Swamy, Department of Mathematics, Government College, Gulbarga, 585105 India N. B. Naduvinamani, Department of Mathematics, Gulbarga University, Jnana Ganga, Gulbarga, 585106 India W. Sidram, Department of Mathematics, Gulbarga University, Jnana Ganga, Gulbarga, 585106 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The influence of isopropyl alcohol and non-ionic surfactant solutions on aqueous droplet wetting behaviour on porous coated paper was determined. Paper coatings provide a micro- and nano-porous surface structure, which strictly speaking cannot be described in simple roughness terms as sub-surface lateral absorption directly impacts on the apparent contact angle. It is this very deviation from an idealised system that leads to novel wetting phenomena. Isopropyl alcohol and surfactant-based systems, both of which are commonly used in the printing industry, show differences in wetting behaviour, on both short and long timescales, with changes in the relative composition of the mixtures. Small variations of 0.1 wt% in surfactant concentration have a dramatic influence on the dynamic surface tension, and thus the wetting. It was observed that the wetting kinetics for isopropyl alcohol and surfactant solutions were different in terms of both wetting area and the penetration rate, even in cases where the dynamic surface tension of the solutions was kept the same. Different stages in the wetting and following drying processes could be observed with near infrared spectral imaging. In addition, the surfactant chemistries such as their degrees of hydrophilicity and molecular weights generated comparative differences in the wetting kinetics. The dominating factor affecting the wetting was, as expected, the solid–liquid interfacial energy defined on the practical porous substrate, which differed from the direct comparison with dynamic surface tension, thus exemplifying the deviation from idealised surface roughness behaviour when considering porous materials. An apparent “equivalent” surface roughness value for the porous material was determined, and it was seen that an increase in this equivalent parameter enhanced the rate of wetting behaviour with decreasing solution surface tension, and so also affected the wetting evolution. The wetting was enhanced by cavities in the coating layer, which were enlarged by the penetrating liquids. Content Type Journal Article Pages 1-18 DOI 10.1007/s11242-012-0001-5 Authors C.-M. Tåg, Laboratory of Physical Chemistry, Center for Functional Materials, Åbo Akademi University, 20500 Åbo, Finland M. Toiviainen, VTT Technical Research Centre of Finland, P.O. Box 1199, 70211 Kuopio, Finland M. Juuti, VTT Technical Research Centre of Finland, P.O. Box 1199, 70211 Kuopio, Finland J. B. Rosenholm, Laboratory of Physical Chemistry, Center for Functional Materials, Åbo Akademi University, 20500 Åbo, Finland K. Backfolk, Laboratory of Fiber and Paper Technology, Department of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland P. A. C. Gane, Department of Forest Products Technology, School of Chemical Technology, Aalto University, 00076 Aalto, Helsinki, Finland Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    We predict capillary-pressure (drainage) curves in tight-gas sandstones which have little matrix or microporosity using a quantitative grain-scale model. The model accounts for the geometric results of some depositional and diagenetic processes important for porosity and permeability reduction in tight-gas sandstones, such as deformation of ductile grains during burial and quartz cementation. The model represents the original sediment as a dense, disordered packing of spheres. We simulated the evolution of this model sediment into a low-porosity sandstone by applying different amounts of ductile grains and quartz precipitation. A substantial fraction of original pore throats in the sediment is closed by the simulated diagenetic alteration. Because the percolation threshold corresponds to closure of half of the pore throats, the pore space in this type of tight-gas sandstone is poorly connected and is often close to being completely disconnected. The drainage curve for different model rocks was computed using invasion percolation in a network taken directly from the grain-scale geometry and topology of the model. Some general trends follow classical expectations and were confirmed by experimental measurements: increasing the amount of cement shifts the drainage curve to larger pressures. This is related to reduction of the connectivity of pore space resulting from closure of throats. Existence of ductile grains in the ductile grain model also reduces the connectivity of pore space but it treats the throats distribution differently causing the drainage curves to be shifted to larger irreducible water saturation when cement is added to the model. The range of porosities in which these connectivity effects are important corresponds to the range of porosities common for tight gas sandstones. Consequently these rocks can exhibit small effective permeability to gas even at large gas saturations. This problem occurs at larger porosities in rocks with significant content of ductile grains because ductile deformation blocks a significant fraction of pore throats even before cementation begins. Predicted drainage curves agree with measurements on two samples with little microporosity, one dominated by rigid grains, the other containing a significant fraction of ductile grains. We conclude that connectivity of the matrix pore space is an important factor for an understanding of flow properties of tight-gas sandstones. Content Type Journal Article Pages 1-18 DOI 10.1007/s11242-012-0017-x Authors Maryam A. Mousavi, Bureau of Economic Geology, The University of Texas at Austin, 10100 Burnet Rd., Austin, TX 78758, USA Steven L. Bryant, Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station C0300, Austin, TX 78712-0228, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Peristaltic motion induced by sinusoidal traveling wave of incompressible, electrically conducting Maxwell fluid in the porous walls of a two-dimensional channel through a porous medium has been investigated in the presence of a constant magnetic field. The Hall effect has been taken into account. Modified Darcy’s law has been used in the flow modeling. The fluid entering the flow region through one plate is considered at the same rate as it is leaving through the other plate. The problem is formulated using a perturbation expansion in terms of small amplitude ratio. We have discussed the problem only for free pumping case. This work can be considered as mathematical modeling to the case of gall bladder with stones. Finally, the effects of various parameters of interest are discussed and shown graphically. Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-0016-y Authors Soliman R. El Koumy, Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt El Sayed I. Barakat, Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt Sara I. Abdelsalam, Basic Science Department, Faculty of Engineering, The British University in Egypt, Al-Shorouk City, Misr-Suez Desert Road, P.O. Box 43, Cairo, 11837 Egypt Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The conditions for the onset of convection in a horizontal rectangular channel filled with a fluid saturated porous medium are studied. The vertical sidewalls are assumed to be impermeable and adiabatic. The horizontal upper and lower boundary walls are considered as impermeable and subject to external heat transfer, modelled through a third-kind boundary condition on the temperature field. The external fluid environments above and below the channel, kept at different temperatures, provide the heating-from-below mechanism which may lead to the onset of the thermal instability in the porous medium. The linear response of the fluid saturated porous channel, in a basic motionless state, is tested with respect to three-dimensional normal mode disturbances of the temperature field and of the pressure field. The linearised disturbance equations are solved analytically leading to an implicit-form expression of the neutral stability condition, formulated as a functional relationship between the Darcy–Rayleigh number and the continuous longitudinal wave number of the normal modes, for any assigned aspect ratio of the cross-section and for any given Biot number. The analysis of the neutral stability is carried out. The analysis is extended to the case of a channel with a finite length in the longitudinal direction, and with adiabatic and impermeable capped ends. Content Type Journal Article Pages 1-23 DOI 10.1007/s11242-012-0018-9 Authors A. Barletta, DIENCA, Alma Mater Studiorum-Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy L. Storesletten, Department of Mathematics, University of Agder, Postboks 422, 4604 Kristiansand, Norway Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This article presents a numerical method for determining tortuosity in porous beds consisting of randomly packed spherical particles. The calculation of tortuosity is carried out in two steps. In the first step, the spacial arrangement of particles in the porous bed is determined by using the discrete element method (DEM). Specifically, a commercially available discrete element package (PFC 3 D ) was used to simulate the spacial structure of the porous bed. In the second step, a numerical algorithm was developed to construct the microscopic (pore scale) flow paths within the simulated spacial structure of the porous bed to calculate the lowest geometric tortuosity (LGT), which was defined as the ratio of the shortest flow path to the total bed depth. The numerical algorithm treats a porous bed as a series of four-particle tetrahedron units. When air enters a tetrahedron unit through one face (the base triangle), it is assumed to leave from another face triangle whose centroid is the highest of the four face triangles associated with the tetrahedron, and this face triangle will then be used as the base triangle for the next tetrahedron. This process is repeated to establish a series of tetrahedrons from the bottom to the top surface of the porous bed. The shortest flow path is then constructed geometrically by connecting the centroids of base triangles of consecutive tetrahedrons. The tortuosity values calculated by the proposed numerical method compared favourably with the values obtained from a CT image published in the literature for a bed of grain (peas). The proposed model predicted a tortuosity of 1.15, while the tortuosity estimated from the CT image was 1.14. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-9961-8 Authors Wojciech Sobieski, Faculty of Technical Sciences, University of Warmia and Mazury in Olsztyn, M. Oczapowskiego 11, 10-957 Olsztyn, Poland Qiang Zhang, Department of Biosystems Engineering, University of Manitoba, Winnipeg, MB, Canada Chuanyun Liu, Department of Biosystems Engineering, University of Manitoba, Winnipeg, MB, Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Many applications involve the flow of non-Newtonian fluids in porous, subsurface media including polymer flooding in enhanced oil recovery, proppant suspension in hydraulic fracturing, and the recovery of heavy oils. Network modeling of these flows has become the popular pore-scale approach for understanding first-principles flow behavior, but strong nonlinearities have prevented larger-scale modeling and more time-dependent simulations. We investigate numerical approaches to solving these nonlinear problems and show that the method of fixed-point iteration may diverge for shear-thinning fluids unless sufficient relaxation is used. It is also found that the optimal relaxation factor is exactly equal to the shear-thinning index for power-law fluids. When the optimal relaxation factor is employed it slightly outperforms Newton’s method for power-law fluids. Newton-Raphson is a more efficient choice (than the commonly used fixed-point iteration) for solving the systems of equations associated with a yield stress. It is shown that iterative improvement of the guess values can improve convergence and speed of the solution. We also develop a new Newton algorithm (Variable Jacobian Method) for yield-stress flow which is orders of magnitude faster than either fixed-point iteration or the traditional Newton’s method. Recent publications have suggested that minimum-path search algorithms for determining the threshold pressure gradient (e.g., invasion percolation with memory) greatly underestimate the true threshold gradient when compared to numerical solution of the flow equations. We compare the two approaches and reach the conclusion that this is incorrect; the threshold gradient obtained numerically is exactly the same as that found through a search of the minimum path of throat mobilization pressure drops. This fact can be proven mathematically; mass conservation is only preserved if the true threshold gradient is equal to that found by search algorithms. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-9956-5 Authors Matthew Balhoff, Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, 1 University Station, C0300, Austin, TX 78712-0300, USA Daniel Sanchez-Rivera, Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, 1 University Station, C0300, Austin, TX 78712-0300, USA Alan Kwok, Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, 1 University Station, C0300, Austin, TX 78712-0300, USA Yashar Mehmani, Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, 1 University Station, C0300, Austin, TX 78712-0300, USA Maša Prodanović, Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, 1 University Station, C0300, Austin, TX 78712-0300, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The capillary pressure–saturation ( P c – S w ) relationship is one of the central constitutive relationships used in two-phase flow simulations. There are two major concerns regarding this relation. These concerns are partially studied in a hypothetical porous medium using a dynamic pore-network model called DYPOSIT, which has been employed and extended for this study: (a) P c – S w relationship is measured empirically under equilibrium conditions. It is then used in Darcy-based simulations for all dynamic conditions. This is only valid if there is a guarantee that this relationship is unique for a given flow process (drainage or imbibition) independent of dynamic conditions; (b) It is also known that P c – S w relationship is flow process dependent. Depending on drainage and imbibition, different curves can be achieved, which are referred to as “hysteresis”. A thermodynamically derived theory (Hassanizadeh and Gray, Water Resour Res 29: 3389–3904, 1993a ) suggests that, by introducing a new state variable, called the specific interfacial area ( a nw , defined as the ratio of fluid–fluid interfacial area to the total volume of the domain), it is possible to define a unique relation between capillary pressure, saturation, and interfacial area. This study investigates these two aspects of capillary pressure–saturation relationship using a dynamic pore-network model. The simulation results imply that P c – S w relation not only depends on flow process (drainage and imbibition) but also on dynamic conditions for a given flow process. Moreover, this study attempts to obtain the first preliminary insights into the global functionality of capillary pressure–saturation–interfacial area relationship under equilibrium and non-equilibrium conditions and the uniqueness of P c – S w – a nw relationship. Content Type Journal Article Pages 1-22 DOI 10.1007/s11242-012-9958-3 Authors Vahid Joekar-Niasar, Earth Sciences Department, Utrecht University, Utrecht, The Netherlands S. Majid Hassanizadeh, Earth Sciences Department, Utrecht University, Utrecht, The Netherlands Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this article, free convection heat transfer over a vertical cylinder with variable surface temperature distributions in a porous medium is analyzed. It is assumed that the fluid and solid phases are not in local thermal equilibrium and, therefore, a two-temperature model of heat transfer is applied. The coupled momentum and energy equations are presented and then they are transformed into ordinary differential equations. The similarity equations are solved numerically. The resulting velocity, streamlines, temperature distributions for fluid and solid phases are shown for different values of parameters entering into the problem. The calculated values of the local Nusselt numbers for both solid and fluid phases are also shown. Content Type Journal Article Pages 1-8 DOI 10.1007/s11242-012-9962-7 Authors E. Shakeri, Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran M. Nazari, Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran M. H. Kayhani, Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The study of moisture transfer inside building materials is an important issue in building physics. The hygric characterization of such materials has become a common practice for the estimation of the hygrothermal performance of buildings. However, their aging caused by mechanical loading and environmental factors inevitably affects their permeability to moisture ingress, and the knowledge of how this permeability is affected by damage and cracks is still incomplete. The effects of diffuse damage caused by mechanical loading on the water vapour permeability of fibre-reinforced mortar were studied. A full experimental setup is presented including observation of the porous structure, mechanical, and hygric characterization. Uniaxial tensile loading was applied on prismatic samples while their damage level was measured. Then, the moisture content of damaged and undamaged samples was monitored during variations of ambient relative humidity. Two numerical methods are presented and used for the comparison of the water vapour permeability of multiple samples presenting various levels of damage. By this methodology, diffuse damage caused by mechanical loading is shown to have an impact on the water vapour transfer inside the material. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-9967-2 Authors Simon Rouchier, Université Claude-Bernard Lyon 1, CETHIL UMR 5008, Bât. S. Carnot, 9 rue de la Physique, 69621 Villeurbanne, France Geneviève Foray, Université de Lyon, CNRS, Villeurbanne, France Monika Woloszyn, Université de Lyon, CNRS, Villeurbanne, France Jean-Jacques Roux, Université de Lyon, CNRS, Villeurbanne, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    A numerical method system to estimate the permeability of sand sediments, at a microscopic scale, was developed. Initially, 3D geometrical representations of the sand grains are reconstructed from a series of 2D X-ray CT scans of real sand grains. 2D cross-sectional slices of the grain outlines are combined together to produce 3D objects via spherical harmonics series expansions. Then, the reconstructed sand grains are packed randomly inside a cubic, microscopic, domain by a combination of a growth method and a simulated annealing method to achieve a predefined porosity. Finally, a single-phase water flow within the domain was simulated numerically, using the lattice Boltzmann method. The calculated permeability of these systems compares well with the values provided by conventional theoretical models. One of the contributions of this study is to show that it is possible to predict the permeability of sand sediments of variable porosities, using sand grains from CT images with changing size distributions and orientations. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-9975-2 Authors Toshio Sugita, Department of Environment Systems, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Toru Sato, Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Shinichiro Hirabayashi, Department of Ocean Technology, Policy, and Environment, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8563 Japan Jiro Nagao, Methane Hydrate Research Center, National Institute of Advanced Industrial Science and Technology, 17-2-1 Higashi-Nijo, Toyohira, Sapporo, 062-8517 Japan Yusuke Jin, Methane Hydrate Research Center, National Institute of Advanced Industrial Science and Technology, 17-2-1 Higashi-Nijo, Toyohira, Sapporo, 062-8517 Japan Fumio Kiyono, Environmental Fluid Engineering Research Group, National Institute of Advanced Industrial Science and Technology, 16-1 Onogawa, Tsukuba, 305-8569 Japan Takao Ebinuma, Methane Hydrate Research Center, National Institute of Advanced Industrial Science and Technology, 17-2-1 Higashi-Nijo, Toyohira, Sapporo, 062-8517 Japan Hideo Narita, Methane Hydrate Research Center, National Institute of Advanced Industrial Science and Technology, 17-2-1 Higashi-Nijo, Toyohira, Sapporo, 062-8517 Japan Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This article presents the PTA on the multi-stage fractured horizontal well in shale gas reservoirs incorporating desorption and diffusive flow in the matrix. Currently, most PTA models are simply based on Darcy flow both in natural fractures and matrix without considering the mechanisms of desorption and diffusion in shale matrix. Source function and Laplace transform with the numerical discrete method are employed to solve the mathematical model. The solution is presented in the Laplace domain so that the wellbore storage effect and skin factor can be easily incorporated by convolution. Type curves are plotted with Stehfest algorithm and different flow regimes are identified. The presented model could be used to interpret pressure signals more accurately for shale gas reservoirs. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-9973-4 Authors Jingjing Guo, State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 8 Xindu Avenue, Xindu District, Chengdu, 610500 People’s Republic of China Liehui Zhang, State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 8 Xindu Avenue, Xindu District, Chengdu, 610500 People’s Republic of China Haitao Wang, State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 8 Xindu Avenue, Xindu District, Chengdu, 610500 People’s Republic of China Guoqing Feng, State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 8 Xindu Avenue, Xindu District, Chengdu, 610500 People’s Republic of China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    For two-phase flows of immiscible displacement processes in porous media, we proposed a simplified model to capture the interfacial fronts, which is given by explicit expressions and satisfies the continuity conditions of pressure and normal velocity across the interface. A new similarity solution for the interfacial evolution in the rectangular coordinate system was derived by postulating a first-order approximation of the velocity distribution in the region that the two-phase fluids co-exist. The interfacial evolution equation can be explicitly expressed as a linear function, where the slope of the interfacial equation is simply related to the mobility ratio of two-phase fluids in porous media. The application of the proposed solutions to predictions of interfacial evolutions in carbon dioxide injected into saline aquifers was illustrated under different mobility ratios and operational parameters. For the purpose of comparison, the numerical solutions obtained by level set method and the similarity solutions based on the Dupuit assumptions were presented. The results show that the proposed solution can give a better approximation of interfacial evolution than the currently available similarity solutions, especially in the situation that the mobility ratio is large. The proposed approximate solutions can provide physical insight into the interfacial phenomenon and be readily used for rapidly screening carbon dioxide storage capacity in subsurface formations and monitoring the migration of carbon dioxide plume. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9979-y Authors Le Wang, Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an, 710049 Shaanxi, China Yongzhong Liu, Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an, 710049 Shaanxi, China Khim Chu, Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an, 710049 Shaanxi, China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this paper, we consider the problem of control of hydrodynamic instability arising in the displacement processes during enhanced oil recovery by SP-flooding (Surfactant–Polymer). In particular, we consider a flooding process involving displacement of a viscous fluid in porous media by a less viscous fluid containing polymer and surfactant over a finite length which in turn is displaced by a even less viscous fluid such as water. The maximum stabilization capacities of several monotonic and non-monotonic viscous profiles created by non-uniform polymer concentration are studied in the presence of interfacial tensions created by surfactants. The study has been carried out numerically to determine and characterize the most optimal viscous profiles of each family. Similarities in optimal monotonic viscous profiles of this constant-time injection policy and other injection policies by previous workers are noted. The presence of interfacial instability (due to viscosity jump) and layer instability (due to viscosity gradient) in appropriate proportions has been numerically demonstrated to be a necessary condition for monotonic as well as optimal non-monotonic profiles except in the limiting case of infinite time injection in which case maximum stabilization appears to result from pure layer instability. It has also been demonstrated numerically that the optimal non-monotonic viscous profiles can have better stabilization potential than the optimal monotonic profiles. Many other new features of this injection policy which have not been recognized before have been discussed. Content Type Journal Article Pages 1-29 DOI 10.1007/s11242-012-9977-0 Authors Prabir Daripa, Department of Mathematics, Texas A&M University, College Station, TX 77843, USA Xueru Ding, Department of Petroleum Engineering, Texas A&M University at Qatar, Doha, Qatar Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The wettability of the reservoir rock has an important effect on the displacement of fluids on a microscopic scale in all EOR processes, especially in the microbial improved oil recovery (MIOR) process. This study describes the effect of wettability on microscopic two-phase flow displacement mechanisms of bacterial flooding. It enables us to get better understanding and prediction capability of macroscale flow behavior of the MIOR process. To achieve the goal, a number of visualization experiments have been carried out in glass micromodels with water wet and oil wet wettability status. Synthetic brine and model oil and an alkane oxidizing bacterium are used to explain the different behavior of microscopic displacement mechanisms in the water wet and oil wet micromodels. The results obtained in the two media are presented and compared. The observational results show the effect of wettability of porous media on remaining oil saturation and oil phase transportation. In water wet model, the oil is remained mostly as isolated drops while in oil wet model, the remaining oil is the continuous phase. The bacteria have the ability to displace the residual oil trapped in the micromodel. It is shown that the bacteria have various performances in the oil wet and water wet systems. The acting mechanisms supporting the displacement process are the interfacial tension reduction, wettability changes, and pore blocking. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9978-z Authors Mehdi Shabani Afrapoli, Norwegian University of Science and Technology, NTNU, Trondheim, Norway Samaneh Alipour, Norwegian University of Science and Technology, NTNU, Trondheim, Norway Ole Torsaeter, Norwegian University of Science and Technology, NTNU, Trondheim, Norway Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The analytical solution for temperature distribution in an aquifer was derived from Lauwerier’s plane-symmetric model (J. Appl. Sc. Res., A5(2–3):145–150, 1955 ). A deficiency of this solution is that it does not consider the effect of heat conduction in the aquifer. Six years later, an analytical solution that considered the effect of heat conduction under adiabatic conditions was presented by Ogata and Banks (US Geol. Survey, 1961 ). Closed form solutions for the plane-symmetric model of heat transport during steady-state flow that considered both heat conduction and heat convection were provided by Barends (SPE Annual Technical Conference and Exhibition, Florence, 2010 ). The distinctions between these solutions are discussed in this paper. Barends’ solution is more complete than those offered in previous studies. But it could be readily used for engineering applications as long as users can evaluate numerically or analytically the integrals involved in this solution. This paper introduces a plane-symmetric model under Cauchy’s boundary condition that considers heat conduction and convection. The Laplace transform technique is applied to obtain the solution for this model, and two important parameters (the Peclet number and the convective heat transfer coefficient) are discussed in detail. The result of this simplified solution agrees well with that of the numerical solutions (Ansys and Comsol). Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-9980-5 Authors Haochen Tan, Department of Civil Engineering, Tsinghua University, Room 401, Heshanheng Building, Beijing, China Xiaohui Cheng, Department of Civil Engineering, Tsinghua University, Room 401, Heshanheng Building, Beijing, China Hongxian Guo, Department of Civil Engineering, Tsinghua University, Room 401, Heshanheng Building, Beijing, China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Fluid flow through random two-dimensional fracture networks is investigated, with the aim of establishing a methodology for estimating the macroscopic effective hydraulic conductivity based on the parameters of the fracture network. A wide range of isotropic networks is examined: the lengths are either uniform, or follow a power law or lognormal distribution; the apertures are either uniform, or proportional to the fracture lengths. A methodology is developed that utilises the fracture density and the aperture distribution, but does not require explicit solution of the flow equations. This method provides an accurate estimate of the macroscopic hydraulic conductivity, for all cases considered, spanning ten orders of magnitude. Content Type Journal Article Pages 1-21 DOI 10.1007/s11242-012-9982-3 Authors Colin T. O. Leung, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ UK Robert W. Zimmerman, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ UK Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The desorption rate of 60 Co, 85 Sr, 137 Cs, 152 Eu, and 241 Am from soil collected from Inshas disposal site in Egypt was investigated to understand the desorption and mobility of these radionuclides in the environment. Effect of a synthetic groundwater (GW) and the GW amended to 2 × 10 −5 M of ethylenediaminetetraacetic acid (EDTA) or ethylenediaminediacetic acid (EDDA), GW+ETDA and GW+EDDA, respectively, was studied in flow-through experiments. These experiments were designed to compare the influence of EDTA relative to one of its degradation products that can exist in natural water, EDDA. First-order desorption and two-site first-order desorption equations were used to describe the time-dependent desorption data. The desorption rate for 85 Sr and 137 Cs was high in the first 50 h followed by a slow release suggesting that two different mechanisms involved. The trace metal removal was not completely reversible for all radionuclides tracers except for 85 Sr. The quantity of 85 Sr, 137 Cs, 152 Eu, and 241 Am desorbed from soil follows the order GW+EDTA 〉  GW+EDDA 〉  GW, while 60 Co gives unexpected trends where the effect of EDDA is twice as high as that of EDTA. This behavior was discussed based on the aqueous species distribution of 60 Co in both aqueous solutions. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9983-2 Authors A. F. Seliman, Department of Analytical Chemistry and Environmental Control, Hot Laboratory Center, Atomic Energy Authority, Cairo, Egypt E. H. Borai, Department of Analytical Chemistry and Environmental Control, Hot Laboratory Center, Atomic Energy Authority, Cairo, Egypt Y. F. Lasheen, Department of Analytical Chemistry and Environmental Control, Hot Laboratory Center, Atomic Energy Authority, Cairo, Egypt T. A. DeVol, Department of Environmental Engineering and Earth Sciences, Clemson University, Clemson, SC, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this work, the authors introduce the shock-tube model for a hydrothermal eruption in a geothermal reservoir. The governing equations, based on the multiphase Euler equations and a Darcy-type law, are solved using a three-phase weighted sub-system numerical solver. Results are then presented which show the importance of the geometry of the geothermal reservoir in predicting the initiation of a hydrothermal eruption. In particular, the porosity, permeability, and cohesion of the reservoir are shown to significantly affect the pressure difference required to initiate an eruption. Finally, the authors show the importance of the initial liquid water/water vapour volume fractions in determining the size of an eruption, and further show boiling to be of major importance. Content Type Journal Article Pages 1-28 DOI 10.1007/s11242-012-9986-z Authors L. A. Fullard, Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand T. A. Lynch, Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Experimental coal cores were collected from a coalbed of Sihe colliery and Zhaozhuang colliery, Qinshui Basin, China. Their gas effective permeability was studied under effects of water content and effective stress. The experiments were mainly carried out on a self-made “Triaxial Stress Thermal–hydrological–mechanical Coal Gas Permeameter.” The results showed that when the temperatures of gas and coal were constant, a negative effect of either water content or effective stress was reported on the gas transportation, i.e., the gas effective permeability decreased with the increasing of water content under constant effective stress and it also decreased as the effective stress increased when the water content was constant. Under experimental conditions as in this study, the effects of water content and effective stress on the gas effective permeability was described by a linear–exponential equation, which presented that the gas effective permeability had a linear relationship with the water content and an exponential relationship with the effective stress. The permeation pores were defined as the primary places of transporting the coalbed gas. They were affected by water content and effective stress in different ways. The water content occupied the space of permeation pores, while the effective stress changed the shape of permeation pores. Consequently, the gas effective permeability was also affected by the two aspects. Content Type Journal Article Pages 1-13 DOI 10.1007/s11242-012-9990-3 Authors Guangzhi Yin, State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400030 China Changbao Jiang, State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400030 China Jiang Xu, State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400030 China Lisha Guo, modelEAU, Département de génie civil et degénie des eaux, Université Laval, 1065 Av. de la Médecine, Quebec, QC G1V 0A6, Canada Shoujian Peng, State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400030 China Wenpu Li, College of Resource and Environmental Sciences, Chongqing University, Chongqing, 400030 China Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    This work investigates the existence and importance of the micro bubbles in heavy oil subjected to solution–gas drive. The term ‘micro bubble’ will be used to refer to the free-gas phase that flows with the oil, no faster and no slower. Two types of experiments are reported here; slow and fast experiments. These experiments were previously reported by Sheikha and Pooladi-Darvish (SPE Res Eval Eng 12(3):390–398, 2009 ) and were used to investigate the effects of pressure gradient and depletion rate of oil recovery. In this work, we investigate the nature of two-phase flow, and find that in the slow runs, the flow was characterized by single-phase flow of oil until a gas saturation of 2±1% was reached. Above this gas saturation, bulk flow of gas was observed at mobilities much higher than that of micro bubbles. Recovery factor of the slow tests was below 4%. In the fast runs, flow of bubbles is observed shortly after they are formed in porous media. The gas mobility and fractional flow remain low until a gas saturation of 7±1% is reached. Flow of gas between approximately 2 and 7% gas saturation is consistent with that of micro bubbles. Gas fractional flow increases sharply at gas saturations above approximately 7%. The results indicate that the attainment of high recovery values (12–14%) observed in the fast experiments is partially as a result of low mobility of micro-gas bubbles. The pressure decline rate of each flow experiment was varied independent of its respective withdrawal rate. This did not alter the difference in recovery and mobility behaviour of the fast and slow experiments; the fast experiments exhibited a significant period of low mobility gas flow consistent with flow of micro bubbles. Regardless of the pressure decline rate, the slow experiments did not exhibit this period of low mobility gas flow. Content Type Journal Article Pages 1-22 DOI 10.1007/s11242-012-9965-4 Authors H. Sheikha, Suncor Energy, Calgary, AB T2P 3E3, Canada M. Pooladi-Darvish, Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    In this note, the mixed unsteady stagnation-point boundary layer over a vertical plate with mass transfer in a fluid-saturated porous medium is revisited. Closed-form analytical solutions are found and presented for a special value of the flow unsteadiness parameter. Multiple solution branches are obtained for certain controlling parameters. These solutions might offer more insights into the mixed convection flow characteristics compared with the numerical solutions. Content Type Journal Article Pages 1-8 DOI 10.1007/s11242-012-9996-x Authors Tiegang Fang, Mechanical and Aerospace Engineering Department, North Carolina State University, 3246 Engineering Building III—Campus Box 7910, 911 Oval Drive, Raleigh, NC 27695, USA Hua Tao, 421 Egret Lane, Secaucus, NJ 07094, USA Yongfang Zhong, School of Engineering, Penn State Erie, The Behrend College, 5101 Jordan Road, Erie, PA 16563, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Many problems in regional groundwater flow require the characterization and forecasting of variables, such as hydraulic heads, hydraulic gradients, and pore velocities. These variables describe hydraulic transients propagating in an aquifer, such as a river flood wave induced through an adjacent aquifer. The characterization of aquifer variables is usually accomplished via the solution of a transient differential equation subject to time-dependent boundary conditions. Modeling nonlinear wave propagation in porous media is traditionally approached via numerical solutions of governing differential equations. Temporal or spatial numerical discretization schemes permit a simplification of the equations. However, they may generate instability, and require a numerical linearization of true nonlinear problems. Traditional analytical solutions are continuous in space and time, and render a more stable solution, but they are usually applicable to linear problems and require regular domain shapes. The method of decomposition of Adomian is an approximate analytical series to solve linear or nonlinear differential equations. It has the advantages of both analytical and numerical procedures. An important limitation is that a decomposition expansion in a given coordinate explicitly uses the boundary conditions in such axis only, but not necessarily those on the others. In this article we present improvements of the method consisting of a combination of a partial decomposition expansion in each coordinate in conjunction with successive approximation that permits the consideration of boundary conditions imposed on all of the axes of a transient multidimensional problem; transient modeling of irregularly-shaped aquifer domains; and nonlinear transient analysis of groundwater flow equations. The method yields simple solutions of dependent variables that are continuous in space and time, which easily permit the derivation of heads, gradients, seepage velocities and fluxes, thus minimizing instability. It could be valuable in preliminary analysis prior to more elaborate numerical analysis. Verification was done by comparing decomposition solutions with exact analytical solutions when available, and with controlled experiments, with reasonable agreement. The effect of linearization of mildly nonlinear saturated groundwater equations is to underestimate the magnitude of the hydraulic heads in some portions of the aquifer. In some problems, such as unsaturated infiltration, linearization yields incorrect results. Content Type Journal Article Pages 1-16 DOI 10.1007/s11242-012-9989-9 Authors Sergio E. Serrano, HydroScience Inc., 1217 Charter Lane, Ambler, PA, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The equations governing plane steady-state flow in heterogeneous porous media containing curved-line intersecting cracks (Pouya and Ghabezloo in Transp Porous Media 84:511–532, 2010 ) and the potential solution obtained for these equations are considered here. The theoretical results are first completed for the mass balance at crack intersections points. Then, a numerical procedure based on a singular integral equations method is described concretely to derive this solution for cracked materials. Closed-form expressions of elementary integrals for special choice of collocation points lead to a very quick and easy numerical method. It is shown that this method can be applied efficiently to the study of the steady-state flow in cracked materials with anisotropic matrix permeability and a dense distribution of curved-line intersecting cracks. Some applications of this method to the permeability of cracked materials are given. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-012-9968-1 Authors Ahmad Pouya, Université Paris-Est, Laboratoire Navier (UMR CNRS-IFSTTAR-ENPC), IFSTTAR, 58 bd Lefebvre, 75732 Paris, France Minh-Ngoc Vu, Université Paris-Est, Laboratoire Navier (UMR CNRS-IFSTTAR-ENPC), IFSTTAR, 58 bd Lefebvre, 75732 Paris, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Computer simulations of non-sorbing tracers diffusing in fluid-saturated porous sediment/rock were performed using pore-scale X-ray microtomographic images to reveal the following. (i) The histogram of the magnitude of the local diffusive flux vector obeys a unimodal log-normal distribution having a long positive tail. Simulations using model images were also performed to show that the flux broadening in large pores and the flux mixing at the pore network junctions are responsible for the log-normal shape. (ii) The simulation enabled us to directly visualize pore voxels with large and small fluxes, confirming the existence of transport pores and stagnant pores. Because of the unimodal nature, however, it was difficult to distinguish transport pores from stagnant pores using an objective threshold in the histogram. (iii) Another histogram of the flux vector component along the direction of the macroscopic concentration gradient was analyzed. A negative tail was found in the histogram, indicating that local counter diffusion exists in the porous geo-materials. However, the population and intensity of the counter diffusion fluxes are too small and weak to contribute to the overall diffusive transport across the porous media system. A long positive tail representing a large-flux diffusive pathway was also observed in the histogram. However, again, the population of the large-flux transport pores is small. As a result, the main conveyer of the tracer is the stagnant pores (not the transport pores), which have small positive flux values but a large population. Content Type Journal Article Pages 1-17 DOI 10.1007/s11242-012-9976-1 Authors Yoshito Nakashima, National Institute of Advanced Industrial Science and Technology (AIST), Central 7, Higashi 1-1-1, Tsukuba, Ibaraki 305-8567, Japan Tsukasa Nakano, National Institute of Advanced Industrial Science and Technology (AIST), Central 7, Higashi 1-1-1, Tsukuba, Ibaraki 305-8567, Japan Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface. Content Type Journal Article Pages 1-15 DOI 10.1007/s11242-012-9985-0 Authors Franck J. Vernerey, Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Gas transfer experiments on claystone and numerical simulations have been conducted to enhance the knowledge of gas transport in nuclear waste repositories in the Callovo-Oxfordian clay formation in Bure, France. Laboratory Gas transfer experiments were performed with a specific device dedicated to very low permeability measurement (10 −23 to 10 −20 m 2 ). Experiments were performed on both dry and close to saturation claystone. The Dusty Gas Model, based on multi-component gas transfer equations with Knudsen diffusion, was used to describe the experimental results. The parameters obtained are the effective permeability, the Knudsen diffusion (Klinkenberg effect) and molecular diffusion coefficients and the porosity accessible to gas. Numerical simulations were carried with various boundary conditions and for different gases (helium vs hydrogen) and were compared with experiments to test the reliability of the model parameters and to better understand the mechanisms involved in clays close to saturation. The numerical simulation fitted the experimental data well whereas simpler models cannot describe the complexity of the Knudsen/Klinkenberg effects. Permeabilities lie between 10 −22 and 10 −20 m 2 . Claystones close to saturation have an accessible porosity to gas transfer that is lower than 0.1–1% of the porosity. Analysis of the Klinkenberg effect suggests that this accessible pore network should be made of 50–200 nm diameter pores. It represents pore networks accessible at capillary pressure lower than 4 MPa. Content Type Journal Article Pages 1-26 DOI 10.1007/s11242-012-9972-5 Authors P. F. Boulin, ANDRA, Chatenay Malabry, France R. Angulo-Jaramillo, Université de Grenoble, LTHE/CNRS, Grenoble, France J. Talandier, ANDRA, Chatenay Malabry, France P. Berne, Liten/DTNM/L2T, CEA, Grenoble, France J. F. Daian, Université de Grenoble, LTHE/CNRS, Grenoble, France Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913