ALBERT

Description: Erratum to: The Role of Tortuosity in Upscaling Content Type Journal Article Pages 1-3 DOI 10.1007/s11242-011-9787-9 Authors Francisco J. Valdés-Parada, Area de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana-Iztapalapa, Mexico, D.F. 09340, Mexico Mark L. Porter, EES-14, MS D462, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Brian D. Wood, School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis, OR 97331, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Pore networks can be extracted from 3D rock images to accurately predict multi-phase flow properties of rocks by network flow simulation. However, the predicted flow properties may be sensitive to the extracted pore network if it is small, even though its underlying characteristics are representative. Therefore, it is a challenge to investigate the effects on flow properties of microscopic rock features individually and collectively based on small samples. In this article, a new approach is introduced to generate from an initial network a stochastic network of arbitrary size that has the same flow properties as the parent network. Firstly, we characterise the realistic parent network in terms of distributions of the geometrical pore properties and correlations between these properties, as well as the connectivity function describing the detailed network topology. Secondly, to create a stochastic network of arbitrary size, we generate the required number of nodes and bonds with the correlated properties of the original network. The nodes are randomly located in the given network domain and connected by bonds according to the strongest correlation between node and bond properties, while honouring the connectivity function. Thirdly, using a state-of-the-art two-phase flow network model, we demonstrate for two samples that the rock flow properties (capillary pressure, absolute and relative permeability) are preserved in the stochastic networks, in particular, if the latter are larger than the original, or the method reveals that the size of the original sample is not representative. We also show the information that is necessary to reproduce the realistic networks correctly, in particular the connectivity function. This approach forms the basis for the stochastic generation of networks from multiple rock images at different resolutions by combining the relevant statistics from the corresponding networks, which will be presented in a future publication. Content Type Journal Article Pages 1-23 DOI 10.1007/s11242-011-9792-z Authors Z. Jiang, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK M. I. J. van Dijke, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK K. Wu, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK G. D. Couples, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK K. S. Sorbie, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK J. Ma, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS UK Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    We consider the effects of rotation in a mushy layer being cast from a vertical surface where the effects of Coriolis acceleration, gravity and centrifugal effects are included. It is demonstrated that the Coriolis acceleration and gravity play a passive role in convection and are excluded from the stability criteria. The stability criteria is presented as the critical centrifugal Rayleigh numbers referenced for locations far away (start of solidification) and close to (nearing end of solidification) the axis or rotation. Content Type Journal Article Pages 1-10 DOI 10.1007/s11242-011-9790-1 Authors S. Govender, Corporate Specialist Gas Turbines, Generation Business Engineering, ESKOM Holdings Ltd., Maxwell Drive Sunninghill, Johannesburg, 2000 South Africa Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The onset of thermal convection in a two-dimensional porous box is investigated analytically. One of the two lateral boundaries is in contact with a hydrostatic reservoir, where the saturating fluid can flow freely in and out. This open boundary is thermally insulating, but with the buoyancy of the fluid taken into account. For the second lateral wall, we study five different options for the boundary conditions. This leads to five different eigenvalue problems for the onset of convection. These five solutions are compared with the known solutions where the buoyancy along open sidewalls is neglected (Tyvand 2002 ). Content Type Journal Article Pages 1-18 DOI 10.1007/s11242-011-9791-0 Authors Heidi S. Nygård, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, 1432 Norway Peder A. Tyvand, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, 1432 Norway Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Image-based network modeling has become a powerful tool for modeling transport in real materials that have been imaged using X-ray computed micro-tomography (XCT) or other three-dimensional imaging techniques. Network generation is an essential part of image-based network modeling, but little quantitative work has been done to understand the influence of different network structures on modeling. We use XCT images of three different porous materials (disordered packings of spheres, sand, and cylinders) to create a series of four networks for each material. Despite originating from the same data, the networks can be made to vary over two orders of magnitude in pore density, which in turn affects network properties such as pore-size distribution and pore connectivity. Despite the orders-of-magnitude difference in pore density, single-phase permeability predictions remain remarkably consistent for a given material, even for the simplest throat conductance formulas. Detailed explanations for this beneficial attribute are given in the article; in general, it is a consequence of using physically representative network models. The capillary pressure curve generated from quasi-static drainage is more sensitive to network structure than permeability. However, using the capillary pressure curve to extract pore-size distributions gives reasonably consistent results even though the networks vary significantly. These results provide encouraging evidence that robust network modeling algorithms are not overly sensitive to the specific structure of the underlying physically representative network, which is important given the variety image-based network-generation strategies that have been developed in recent years. Content Type Journal Article Pages 1-29 DOI 10.1007/s11242-011-9789-7 Authors Pradeep Bhattad, Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA 70803, USA Clinton S. Willson, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA Karsten E. Thompson, Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA 70803, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Low salinity water injections for oil recovery have shown seemingly promising results in the case of clay-bearing sandstones saturated with asphaltic crude oil. Reported data showed that low salinity water injection could provide up to 20% pore volume (PV) of additional oil recovery for core samples and up to 25% PV for reservoirs in near wellbore regions, compared with brine injection at the same Darcy velocity. The question remains as to whether this additional recovery is also attainable in reservoirs. The answer requires a thorough understanding of oil recovery mechanism of low salinity water injections. Numerous hypotheses have been proposed to explain the increased oil recovery using low salinity water, including migration of detached mixed-wet clay particles with absorbed residual oil drops, wettability alteration toward increased water-wetness, and emulsion formation. However, many later reports showed that a higher oil recovery associated with low salinity water injection at the common laboratory flow velocity was neither necessarily accompanied by migration of clay particles, nor necessarily accompanied by emulsion. Moreover, increased water-wetness has been shown to cause the reduction of oil recovery. The present study is based on both experimental and theoretical analyses. Our study reveals that the increased oil recovery is only related to the reduction of water permeability due to physical plugging of the porous network by swelling clay aggregates or migrating clay particles and crystals. At a fixed apparent flow velocity, the value of negative pressure gradient along the flow path increases as the water permeability decreases. Some oil drops and blobs can be mobilized under the increased negative pressure gradient and contribute to the additional oil recovery. Based on the revealed mechanism, we conclude that low salinity water injection cannot be superior to brine injection in any clay-bearing sandstone reservoir at the maximum permitted injection pressure. Through our study of low salinity water injection, the theory of tertiary oil recovery has been notably improved. Content Type Journal Article Pages 1-30 DOI 10.1007/s11242-011-9788-8 Authors Y. Li, Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, WY 82071, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The impracticality of MHD convection in a porous medium is further clarified. Content Type Journal Article Pages 1-2 DOI 10.1007/s11242-011-9770-5 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:    The effect of rotation on the onset of double diffusive convection in a sparsely packed anisotropic porous layer, which is heated and salted from below, is investigated analytically using the linear and nonlinear theories. The Brinkman model that includes the Coriolis term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and a dispersion relation are obtained analytically using linear theory. The effect of anisotropy parameters, Taylor number, Darcy number, solute Rayleigh number, Lewis number, Darcy–Prandtl number, and normalized porosity on the stationary, oscillatory and finite amplitude convection is shown graphically. It is found that contrary to its usual influence on the onset of convection in the absence of rotation, the mechanical anisotropy parameter show contrasting effect on the onset criterion at moderate and high rotation rates. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfers. The effect of various parameters on heat and mass transfer is shown graphically. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study. Content Type Journal Article Pages 1-31 DOI 10.1007/s11242-011-9741-x Authors M. S. Malashetty, Department of Mathematics, Gulbarga University, Jnana Ganga Campus, Gulbarga, 585106 India Irfana Begum, Department of Mathematics, Gulbarga University, Jnana Ganga Campus, Gulbarga, 585106 India Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K r ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure. Content Type Journal Article Pages 1-12 DOI 10.1007/s11242-011-9743-8 Authors H. Saleh, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, UKM, Bangi, 43600 Selangor Malaysia N. H. Saeid, Department of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham Malaysia Campus, 43500 Semenyih, Selangor Malaysia I. Hashim, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, UKM, Bangi, 43600 Selangor Malaysia Z. Mustafa, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, UKM, Bangi, 43600 Selangor Malaysia Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913

Description:    The injection of supercritical CO 2 through wells into deep brine reservoirs is a topic of interest for geologic carbon sequestration. The injected CO 2 is predominantly immiscible with the brine and its low density relative to brine leads to strong buoyancy effects. The displacement of brine by CO 2 in general is a multidimensional, complex nonlinear problem that requires numerical methods to solve. The approximations of vertical equilibrium and complete gravity segregation (sharp interface) have been introduced to reduce the complexity and dimensionality of the problem. Furthermore, for the radial displacement process considered here, the problem can be formulated in terms of a similarity variable that reduces spatial and temporal dependencies to a single variable. However, the resulting ordinary differential equation is still nonlinear and exact solutions are not available. The existing analytical solutions are approximations limited to certain parameter ranges that become inaccurate over a large portion of the parameter space. Here, I use a matched boundary extrapolation method to provide much greater accuracy for analytical/semi-analytical approximations over the full parameter range. Content Type Journal Article Pages 1-19 DOI 10.1007/s11242-011-9874-y Authors J. E. Houseworth, Division of Earth Sciences, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA Journal Transport in Porous Media Online ISSN 1573-1634 Print ISSN 0169-3913