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  • Articles  (11,675)
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  • 1
    Electronic Resource
    Electronic Resource
    A computerized technique for measuringin-situ concentrations during miscible displacements in porous media (1992)
    Springer
    Transport in porous media 7 (1992), S. 127-145 
    Details
    ISSN: 1573-1634
    Keywords: Miscible displacement ; dispersion ; in-situ concentration measurement ; computerized data acquisition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A technique for measurement of thein-situ concentration in an unconsolidated porous medium has been developed. The method involves measurement of electrical conductivityin-situ, under dynamic conditions, for flow involving brine of differing concentrations, at selected locations along the porous medium and relating it to the brine strength. Data acquisition and analysis is carried out using a Hewlett — Packard micro-computer and its interface. A user-friendly software was designed and developed for the system. The measurement technique was evaluated by studying the effect of brine concentration, brine flow rate, and by conducting miscible displacements experiment. The experimentally measured dispersion coefficients for the porous medium agreed closely with the value predicted by the correlation available in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00647393
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  • 2
    Electronic Resource
    Electronic Resource
    Analytic Solution to a Problem of Seepage in a Chequer-Board Porous Massif (1997)
    Springer
    Transport in porous media 28 (1997), S. 109-124 
    Details
    ISSN: 1573-1634
    Keywords: seepage ; conductivity ; double-periodic structure ; advection ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A study is made of steady two-dimensional seepage in a porous massif composed by a double-periodic system of ‘white’ and ‘black’ chequers of arbitrary conductivity. Rigorous matching of Darcy's flows in zones of different conductivity is accomplished. Using the methods of complex analysis, explicit formulae for specific discharge are derived. Stream lines, travel times, and effective conductivity are evaluated. Deflection of marked particles from the ‘natural’ direction of imposed gradient and stretching of prescribed composition of these particles enables the elucidation of the phenomena of transversal and longitudinal dispersion. A model of pure advection is related with the classical one-dimensional vective dispersion equation by selection of dispersivity which minimizes the difference between the breakthrough curves calculated from the two models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006505908858
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  • 3
    Electronic Resource
    Electronic Resource
    Waves in partially saturated porous media (1992)
    Springer
    Transport in porous media 9 (1992), S. 25-37 
    Details
    ISSN: 1573-1634
    Keywords: Waves ; dispersion ; shock tube ; gas bubbles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The propagation of compressional waves in a porous medium is investigated in case the pore liquid contains a small volume fraction of gas. The effect of oscillating gas bubbles is taken into account by introducing a frequency-dependent fluid bulk modulus, which is incorporated in the Biot theory. Using a shock tube technique, new experimental data are obtained for a porous column subjected to a pressure step wave. An oscillatory behaviour is observed, consisting of two distinct frequency bands, which is predicted by the theoretical analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01039623
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  • 4
    Electronic Resource
    Electronic Resource
    On the transient non-Fickian dispersion theory (1996)
    Springer
    Transport in porous media 23 (1996), S. 107-124 
    Details
    ISSN: 1573-1634
    Keywords: solute transport ; Fick's law ; dispersion ; dispersivity ; equation of motion ; non-Fickian dispersion equation ; scale effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The Fickian dispersion equation is the basic relationship used to describe the nonconvective mass flux of a solute in a porous medium. This equation prescribes a linear relationship between the dispersive mass flux and the concentration gradient. An important characteristic of the Fickian relationship is that it is independent of the history of dispersion (e.g. the time rate of change of the dispersion flux). Also, the dispersivities are supposed to be medium constants and invariant with temporal and spatial scales of observation. It is believed that in general these restrictions do not hold. A number of authors have proposed various alternative relationships. For example, differential equations have been employed that prescribe a relationship between the dispersion flux and its time and space derivatives. Also, stochastic theories result in integro-differential equations in which dispersion tensor grow asymptotically with time or distance. In this work, three different approaches, which lead to three different non-Fickian equations with a transient character, are discussed and their primary features and differences are highlighted. It is shown that an effective dispersion tensor defined in the framework of the transient non-Fickian theory, grows asymptotically with time and distance; a result which also follows from stochastic theories. Next, principles of continuum mechanics are employed to provide a solid theoretical basis for the non-Fickian transient dispersion theory. The equation of motion of a solute in a porous medium is used to provide a rigorous derivation of various dispersion relationships valid under different conditions. Under various simplifying assumptions, the generalized theory is found to agree with the conventional Fickian theory as well as several other non-Fickian relationships found in the literature. Moreover, it is shown that for nonconservative solutes, the traditional dispersion tensor is affected by the rate of mass exchange of the solute.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00145268
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  • 5
    Electronic Resource
    Electronic Resource
    Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution (1988)
    Springer
    Transport in porous media 3 (1988), S. 473-489 
    Details
    ISSN: 1573-1634
    Keywords: Advection ; dispersion ; particles ; characteristics ; finite-element ; continuous fluid velocity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A Eulerian-Lagrangian scheme is used to solve the two-dimensional advection-dispersion equation. Concentration and its partial differential operator are decomposed into advection and dispersion terms. Thus, advection is formally decoupled from dispersion and solved by continuous forward particle tracking. Dispersion is handled by implicit finite elements on a fixed Eulerian grid. Translation of steep gradients of concentration in advection-dominated flow regimes, is done without numerical distortion. Continuous spatial distribution of velocities are evaluated by using Galerkin's approach in conjunction with Darcy's law based on hydraulic input data from each element. The method was implemented on coarse FE grid with linear shape functions, demonstrating no over/under shooting and practically no numerical dispersion. Simulations, covering a wide range of Peclet numbers, yield high agreement with analytic and practical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00138612
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  • 6
    Electronic Resource
    Electronic Resource
    The effect of dispersion model on the linear stability of miscible displacement in porous media (1989)
    Springer
    Transport in porous media 4 (1989), S. 85-96 
    Details
    ISSN: 1573-1634
    Keywords: Stability ; linear stability analysis ; miscible displacement ; aspect ratio ; mobility control ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Chang and Slattery (1986, 1988b) introduced a simplified model of dispersion that contains only two empirical parameters. The traditional model of dispersion (Nikolaevskii, 1959; Bear, 1961; Scheidegger, 1961; de Josselin de Jong and Bossen, 1961; Peaceman, 1966; Bear, 1972) has three empirical parameters, two of which can be measured in one-dimensional experiments while the third, the transverse dispersivity, must be measured in experiments in which a two-dimensional concentration profile develops. It is found that nearly the same linear stability behavior results from using either model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00134743
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  • 7
    Electronic Resource
    Electronic Resource
    The influence of free convection on soil salinization in arid regions (1996)
    Springer
    Transport in porous media 23 (1996), S. 275-301 
    Details
    ISSN: 1573-1634
    Keywords: free convection ; through flow ; vadoze zone ; salinization ; dispersion ; multigrid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Evaporation of groundwater in a region with a shallow water table and small natural replenishment causes accumulation of salts near the ground surface. Water in the upper soil layer becomes denser than in the depth. This is a potentially unstable situation which may result in convective currents. When free convection takes place, estimates of the salinity profile, salt precipitation rate, etc., obtained within the framework of a 1-D (vertical) model fail. Very simplified model of the process is proposed, in which the unsaturated zone is represented by a horizontal soil layer at a constant water saturation, and temperature changes are neglected. The purpose of the model is to obtain a rough estimate of the role of natural convection in the salinization process. A linear stability analysis of a uniform vertical flow is given, and the stability limit is determined numerically as a function of evaporation rate, salt concentration in groundwater, and porous medium dispersivity. The loss of stability corresponds to quite realistic Rayleigh numbers. The stability limit depends in nonmonotonic way on the evaporation rate. The developed convective regime was simulated numerically for a 2-D vertical domain, using finite volume element discretization and FAS multigrid solver. The dependence of the average salt concentration in the upper layer on the Rayleigh number was obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00167100
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  • 8
    Electronic Resource
    Electronic Resource
    Influence of capillary pressure, adsorption and dispersion on chemical flood transport phenomena (1996)
    Springer
    Transport in porous media 24 (1996), S. 275-296 
    Details
    ISSN: 1573-1634
    Keywords: chemical flooding ; ternary ; immiscible ; surfactant ; numerical simulation ; interfacial tension ; phase behavior ; miscibility ; capillarity ; numerical grid ; adsorption ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This is the second of two joint papers which study the influence of several physical properties on the transport phenomena in chemical flooding. To that aim, we use a previously reported ternary two-phase model into which representative physical properties have been incorporated as concentration-dependent functions. Physical properties such as phase behavior, interfacial tensions, residual saturations, relative permeabilities, phase viscosities and wettability have been analyzed in the first paper. In this paper, we discuss the influence of capillary pressure, adsorption of the chemical component onto the rock and dispersion. Although arising from different phenomenological sources, these transport mechanisms show some similar effects on concentration profiles and on oil recovery. They are studied for systems with different phase behavior. A numerical analysis is also presented in order to determine the relevance of the number of grid blocks taken in the discretization of the differential equations. This numerical analysis provides useful guidelines for the selection of the appropriate numerical grid in each type of displacement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00154094
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  • 9
    Electronic Resource
    Electronic Resource
    Saltwater transport in a heterogeneous formation: A case study (1988)
    Springer
    Transport in porous media 3 (1988), S. 217-256 
    Details
    ISSN: 1573-1634
    Keywords: Salinity ; advection ; dispersion ; aquifers ; flow model ; transport model ; simulation ; sea water ; connate water ; leakage
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Historical information of the hydraulic and salinity aspect, detailed geological information, and information on the physical characteristics of the different layers comprising the formation, are needed for simulating the saltwater transport process in aquifers. In most simulation studies of field situations, there is an inadequacy of data and the modeller has to make justifiable assumptions to analyze a particular situation in order to provide an insight into the problem. A quasi-three-dimensional solute transport model is used to analyze the saltwater encroachment phenomena in aquifers underlying the City of Bangkok; first by calibrating the model's performance with available historical data and then by assessing the extent of future saltwater encroachment with the implementation of the regulatory pumpage to be followed in order to restrict the alarming rate of land subsidence. Model simulation indicates a substantial reduction in the rate of encroachment of the saltwater front with a reduction of pumpage after 1987.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00235330
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  • 10
    Electronic Resource
    Electronic Resource
    An adaptive domain decomposition method for simulation of transport in porous media (1988)
    Springer
    Transport in porous media 3 (1988), S. 549-562 
    Details
    ISSN: 1573-1634
    Keywords: Adaptive mesh ; finite element method ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A Galerkin finite element method is used along with a self-adaptive strategy of domain discretisation to model dispersion in an axisymmetric cylindrical porous medium. A solution strategy is proposed based on the use of a Gear scheme for the time stepping and partial vectorisation of the code. The domain is highly discretised in the area of the sharp transient front, while the remainder is coarsely discretised. The area covered by the fine mesh is determined by the value of the local concentration gradients. Numerical results are presented for the one and two dimensional cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00959102
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  • 11
    Electronic Resource
    Electronic Resource
    On the Influence of Pore-Scale Dispersion in Nonergodic Transport in Heterogeneous Formations (1998)
    Springer
    Transport in porous media 30 (1998), S. 57-73 
    Details
    ISSN: 1573-1634
    Keywords: groundwater ; nonergodic transport ; dispersion ; heterogeneous formations ; hydrogeology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Flow of an inert solute in an heterogeneous aquifer is usually considered as dominated by large-scale advection. As a consequence, the pore-scale dispersion, i.e. the pore scale mechanism acting at scales lower than that characteristic of the heterogeneous field, is usually neglected in the computation of global quantities like the solute plume spatial moments. Here the effect of pore-scale dispersion is taken into account in order to find its influence on the longitudinal asymptotic dispersivity D11we examine both the two-dimensional and the three-dimensional flow cases. In the calculations, we consider the finite size of the solute initial plume, i.e. we analyze both the ergodic and the nonergodic cases. With Pe the Péclat number, defined as Pe=Uλ/D, where U, λ, D are the mean fluid velocity, the heterogeneity characteristic length and the pore-scale dispersion coefficient respectively, we show that the infinite Péclat approximation is in most cases quite adequate, at least in the range of Péclat number usually encountered in practice (Pe 〉 102). A noteworthy exception is when the formation log-conductivity field is highly anisotropic. In this case, pore-scale may have a significant impact on D11, especially when the solute plume initial dimensions are not much larger than the heterogeneities' lengthscale. In all cases, D11 appears to be more sensitive to the pore-scale dispersive mechanisms under nonergodic conditions, i.e. for plume initial size less than about 10 log-conductivity integral scales.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006548529015
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  • 12
    Electronic Resource
    Electronic Resource
    A Solute Transport in Stratified Media (1998)
    Springer
    Transport in porous media 31 (1998), S. 133-143 
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    ISSN: 1573-1634
    Keywords: transport ; solute ; flux-averaged concentration ; stratification ; conductivity ; distribution ; arrival time ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Two-dimensional and steady solute transport in a stratified porous formation is analysed under assumption that the effect of pore-scale dispersion is negligible. The longitudinal dispersion produced as a result of the vertical variation of hydraulic conductivity is analysed by averaging the variability of a solute flux concentration and conductivity. The evolution of the solute flux concentration is expressed with respect to the correlated variable, that is the travel (arrival) time τ at a fixed location and the averaging procedure is constructed to satisfy the boundary condition where the inlet concentration is a known function of time. In such a statement, a velocity-averaged solute flux concentration is described by a conventional dispersion model (CDM) with a dispersion coefficient which is a function of the arrival time. It is demonstrated that such CDM satisfies the assumption that hydraulic conductivity of the layers is gamma distributed with the parameter of distribution which is chosen to represent a reasonable value of the field scale solute dispersion. The overall behaviour of the model is illustrated by several examples of two-dimensional mass transport.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006557032656
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  • 13
    Electronic Resource
    Electronic Resource
    Comment on ‘fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media’, by Muhammad Sahimi (1995)
    Springer
    Transport in porous media 21 (1995), S. 175-188 
    Details
    ISSN: 1573-1634
    Keywords: diffusion ; dispersion ; percolation ; fractals ; scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Two fundamental questions regarding the application of percolation theory to transport in porous media are addressed. First, when ‘critical path’ arguments (based on a sufficiently wide spread of microscopic transition rates) are invoked (in analogy to the case of transport in disordered semiconductors) to justify the application of percolation theory to the determination of relevant transport properties, then for long time scales (compared to the inverse of the ‘critical’ percolation rate), the fractal structure of the ‘critical’ path is relevant to transport, but not at short time scales. These results have been demonstrated concretely in the case of disordered semiconductors, and are in direct contradiction to the claims of the review. Second, the relevance of deterministic or stochastic methods to transport has been treated heretofore by most authors as a question of practicality. But, at least under some conditions, concrete criteria distinguish between the two types of transport. Percolative (deterministic) transport is temporally reproducible and spatially inhomogeneous while diffusive (stochastic) transport is temporally irreproducible, but homogeneous, and a cross-over from stochastic to percolative transport occurs when the spread of microscopic transition rates exceeds 4–5 orders of magnitude. It is likely that such conditions are frequently encountered in soil transport. Moreover, clear evidence for deterministic transport (although not necessarily percolative) exists in such phenomena as preferential flow. On the other hand, the physical limitation of transport to (fractally connected) pore spaces within soils (analogously to transport in metal-insulator composites) can make transport diffusive on a fractal structure, rather than percolative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00613755
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  • 14
    Electronic Resource
    Electronic Resource
    A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media (1996)
    Springer
    Transport in porous media 24 (1996), S. 1-33 
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    ISSN: 1573-1634
    Keywords: unsaturated flow ; large-scale averaging ; dispersion ; high-resolution numerical simulations ; NAPL spills
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Infiltration of water and non-aqueous phase liquids (NAPLs) in the vadose zone gives rise to complex two- and three-phase immiscible displacement processes. Physical and numerical experiments have shown that ever-present small-scale heterogeneities will cause a lateral broadening of the descending liquid plumes. This behavior of liquid plumes infiltrating in the vadose zone may be similar to the familiar transversal dispersion of solute plumes in single-phase flow. Noting this analogy we introduce a mathematical model for ‘phase dispersion’ in multiphase flow as a Fickian diffusion process. It is shown that the driving force for phase dispersion is the gradient of relative permeability, and that addition of a phase-dispersive term to the governing equations for multiphase flow is equivalent to an effective capillary pressure which is proportional to the logarithm of the relative permeability of the infiltrating liquid phase. The relationship between heterogeneity-induced phase dispersion and capillary and numerical dispersion effects is established. High-resolution numerical simulation experiments in heterogeneous media show that plume spreading tends to be diffusive, supporting the proposed convection-dispersion model. Finite difference discretization of the phase-dispersive flux is discussed, and an illustrative application to NAPL infiltration from a localized source is presented. It is found that a small amount of phase dispersion can completely alter the behavior of an infiltrating NAPL plume, and that neglect of phase-dispersive processes may lead to unrealistic predictions of NAPL behavior in the vadose zone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00175602
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  • 15
    Electronic Resource
    Electronic Resource
    A linear stability analysis for miscible displacements (1986)
    Springer
    Transport in porous media 1 (1986), S. 179-199 
    Details
    ISSN: 1573-1634
    Keywords: Stability ; linear stability analysis ; miscible displacement ; dispersion ; mobility control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A linear stability analysis has been performed for a miscible displacement in a semi-infinite system of finite thickness and unbounded width. A more general description of dispersion has been adopted than those used by previous workers. It is shown that, when there is a step change in concentration and the mobility ratio is unfavorable, the displacement can be unstable at the injection boundary. But, if the concentration is changed sufficiently slowly with time at the entrance to the system, the displacement is stable to infinitesimal perturbations, no matter how unfavorable the mobility ratio. When the mobility ratio is favorable, the displacement is unconditionally stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714691
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  • 16
    Electronic Resource
    Electronic Resource
    Issues in flow and transport in heterogeneous porous media (1986)
    Springer
    Transport in porous media 1 (1986), S. 319-338 
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    ISSN: 1573-1634
    Keywords: heterogeneity ; dispersion ; saturated flow ; unsaturated flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This invited lecture enumerates various categories of flow and transport in heterogeneous media with particular reference to this Symposium. Specific attention is given to five topics within these categories. (1) We explore the compounding of spatially variable local permeability K to produce an apparent permeability K * on a scale large compared with that of variation of K. An inverse method generates and analyzes flow systems with K spatially periodic in two and three dimensions. (2) Physical arguments indicate that apparent hydraulic properties of an unsaturated composite medium may not represent any conceivable mean of the properties of the component media. (3) Conventionally, buried holes are thought to stay empty during generally unsaturated soil-water flow. The hole, however, acts as an obstacle to flow so that water may seep through it. The larger the hole the more likely this will happen. (4) Dispersion in heterogeneous porous systems with no maximum scale of variation is explored using a Lagrangian mode of analysis. (5) Comments are offered on ‘geostatistics’ and its application to heterogeneous soils and aquifers.
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    URL: http://dx.doi.org/10.1007/BF00208041
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  • 17
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    Advective and dispersive mixing in stratified formations (1995)
    Springer
    Transport in porous media 18 (1995), S. 231-243 
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    ISSN: 1573-1634
    Keywords: Stratified formations ; kinematic mixing ; dispersion ; random fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The mixing process in fluid flow is presented as the bending and stretching of material lines or filaments. A mixing exponent, which quantifies their specific rate of stretching, is defined and analyzed for the case of groundwater flow though stratified formations characterized by a Gaussian autocovariance function. The analysis is performed for purely advective mixing as well as for advective-dispersive mixing. The mixing exponent was found to be proportional to the variance of hydraulic conductivity and inversely proportional to the correlation scale of hydraulic conductivity and to the pore-level dispersion coefficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00616933
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  • 18
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    Scaling mixing during miscible displacement in heterogeneous porous media (1991)
    Springer
    Transport in porous media 6 (1991), S. 607-626 
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    ISSN: 1573-1634
    Keywords: dispersion ; dispersivity ; heterogenity ; miscible ; porous media ; scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This paper discusses scaling of mixing during miscible flow in heterogeneous porous media. In large field systems dispersivity appears to depend on system length due to heterogeneities. Three types of scaling are discussed to investigate the heterogeneous effects. Dimensional analysis of mixing during flow through geometerically scaled heterogeneous models is illustrated using measured dispersion. Fractal analysis of mixing in statistically scaled heterogeneous porous media is discussed. Analog scaling of pressure transients in heterogeneous porous media is suggested as an in-situ method of estimating dispersion.
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    URL: http://dx.doi.org/10.1007/BF00137852
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  • 19
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    Modelling fluid flow in cross-bedded sections (1993)
    Springer
    Transport in porous media 12 (1993), S. 143-159 
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    ISSN: 1573-1634
    Keywords: Heterogeneity ; layers ; displacement ; numerical simulation ; flow in porous media ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Beadpack experiments and numerical simulations have been carried out to study flow displacements, effluent profiles and streamline patterns for layered systems with flow not parallel to the layers. The effects of layer thickness, permeability contrast, angle of layer to flow direction, mobility ratio and flood rate have been examined. Each of these parameters influence the displacement profiles, and disperse the flood front. Such real effects must be considered when subsuming reservoir heterogeneities in average reservoir parameters in simulation studies, or interpreting core tests.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00616977
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  • 20
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    Fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media (1993)
    Springer
    Transport in porous media 13 (1993), S. 3-40 
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    ISSN: 1573-1634
    Keywords: Diffusion ; dispersion ; percolation ; fractals ; scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We review and discuss diffusion and hydrodynamic dispersion in a heterogeneous porous medium. Two types of heterogeneities are considered. One is percolation disorder in which a fraction of the pores do not allow transport to take place at all. In the other type, the permeabilities of various regions of the pore space are fractally distributed with long-range correlations. Both systems give rise to unusual transport in which the mean square displacement 〈r 2(t)〉 of a particle grows nonlinearly with time. Depending on the heterogeneities and the mechanism of diffusion and disperison, we may havefractal transport in which 〈r 2〉 growsslower than linearly with time, orsuperdiffusive transport in which 〈r 2〉 growsfaster than linearly with time. We show that percolation models can give rise to both types of transport with scale-dependent transport coefficients such as diffusivity and dispersion coefficients, which are consistent with many experimental observations.
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    URL: http://dx.doi.org/10.1007/BF00613269
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  • 21
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    A theory of macrodispersion for the scale-up problem (1993)
    Springer
    Transport in porous media 13 (1993), S. 97-122 
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    ISSN: 1573-1634
    Keywords: Scale up ; dispersion ; porous media ; random field
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Dispersion is the result, observable on large length scales, of events which are random on small length scales. When the length scale on which the randomness operates is not small, relative to the observations, then classical dispersion theory fails. The scale up problem refers to situations in which randomness occurs on all length scales, and for which classical dispersion theory necessarily fails. The purpose of this article is to present non-Fickian, theories of dispersion, which do not assume a scale separation between the randomness and the observed consequences, and which do not assume a single length scale. Porous media flow properties are heterogeneous on all length scales. The geological variation on length scales below the observational length scale can be regarded as unknown and unknowable, and thus as a random variable. We develop a systematic theory relating scaling behavior of the geological heterogeneity to the scaling behavior of the fluid dispersivity. Three qualitatively distinct regimes (Fickian, non-Fickian and nonrenormalizable) are found. The theory gives consistent answers within several distinct analytic approximations, and with numerical simulation of the equations of porous media flow. Comparison to field data is made. The use of Kriging to generate constrained ensembles for conditional simulation is discussed.
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    URL: http://dx.doi.org/10.1007/BF00613272
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    An experimental investigation of dispersion in layered porous media (1994)
    Springer
    Transport in porous media 15 (1994), S. 15-30 
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    ISSN: 1573-1634
    Keywords: Experiment ; dispersion ; layered heterogeneity ; permeability ; averaging ; permutation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Experiments were run in three linear, homogeneous, nonuniform porous media constructed in lucite columns using spherical glass beads. The columns were also joined end to end to create an in series layered heterogeneous porous media. Each column, all combinations of columns and several permutations were studied with a factorial experimental design to determine the effects of porosity, permeability, velocity, length, and column order upon dispersion. Attempts to predict the heterogeneous results from the homogeneous results were made, and a statistical regression based on the factorial design was calculated. Results showed that no simple averaging procedure accurately predicted the heterogeneous results. The statistical regression showed permeability, velocity, viscosity, length and column order to be significant.
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    URL: http://dx.doi.org/10.1007/BF01046156
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    A LGA model for dispersion in heterogeneous porous media (1994)
    Springer
    Transport in porous media 17 (1994), S. 19-32 
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    ISSN: 1573-1634
    Keywords: LGA model ; heterogeneous porous media ; miscible displacement ; dispersion ; tracer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The lattice gas automaton (LGA) model proposed in the previous paper is applied to the problem of simulating dispersion and mixing in heterogeneous porous media. We demonstrate here that tracer breakthrough profiles and longitudinal dispersion coefficients can be computed for heterogeneous porous media.
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    URL: http://dx.doi.org/10.1007/BF00624048
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    A stream tube model for miscible flow (1995)
    Springer
    Transport in porous media 18 (1995), S. 245-261 
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    ISSN: 1573-1634
    Keywords: Porous media ; miscible flow ; tracer ; dispersion ; convective flow ; stochastic ; stream tube ; continuous time random walk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.
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    A stream tube model for miscible flow (1995)
    Springer
    Transport in porous media 18 (1995), S. 263-282 
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    ISSN: 1573-1634
    Keywords: Porous media ; dispersion ; miscible flow ; heterogeneities ; stochastic ; stream tube ; layered ; fractal
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Large-scale dispersion in heterogeneous porous media is studied by using a simple model based on stochastic calculation of convective flow in a bundle of stream tubes. The advantage of this approach is that there is a local relationship between velocity and permeability in the 1-dimensional space of the stream tubes. Dispersion is due to the variation in stream tube cross-section, related to the permeability field. First, the arrival times of the tracer in the stream tubes are related to the stochastic properties of the permeability field (variance and covariance). Then, transport equations are derived from the moments of the arrival times. The results agree with more complicated studies. For a permeability field with long-range correlation, the transport equation is not unique. It depends on the assumptions involving moments higher than two. Assuming a Gaussian shape for the tracer flux leads to equations similar to the ones obtained in previous studies of time-dependent dispersivity. Without this approximation, the equation is non-local (integrodifferential) and leads to a memory effect. In the last part of this paper, the general results are illustrated with several correlation functions for the permeability field: purely random, exponential and power law covariance, and perfectly layered media.
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    Experimental investigation of solute transport in large, homogeneous and heterogeneous, saturated soil columns (1995)
    Springer
    Transport in porous media 18 (1995), S. 283-302 
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    ISSN: 1573-1634
    Keywords: Solute transport experiments ; heterogeneous media ; dispersion ; scale-dependency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Laboratory tracer experiments were conducted to investigate solute transport in 12.5-m long, horizontally placed soil columns during steady saturated water flow. Two columns having cross-sectional areas of 10×10cm2 were used: a uniformly packed homogeneous sandy column and a heterogeneous column containing layered, mixed, and lenticular formations of various shapes and sizes. The heterogeneous soil column gradually changed, on average, from coarse-textured at one end to fine-textured at the other end. NaCl breakthrough curves (BTC's) in the columns were measured with electrical conductivity probes inserted at 50- or 100-cm intervals. Observed BTC's in the homogeneous sandy column were relatively smooth and sigmoidal (S-shaped), while those in the heterogeneous column were very irregular, nonsigmoidal, and exhibited extensive tailing. Effective average pore-water velocities (v eff) and dispersion coefficients (D eff) were estimated simultaneously by fitting an analytical solution of the convection-dispersion equation to the observed BTC's. Velocity variations in the heterogeneous medium were found to be much larger than those in the homogeneous sand. Values of the dispersivity,α=D eff/v eff, for the homogeneous sandy column ranged from 0.1 to 5.0 cm, while those for the heterogeneous column were as high as 200cm. The dispersivity for transport in both columns increased with travel distance or travel time, thus exhibiting scale-dependency. The heterogeneous soil column also showed the effects of preferential flow, i.e., some locations in the column showed earlier solute breakthrough than several locations closer to the inlet boundary. Spatial fluctuations in the dispersivity could be explained qualitatively by the particular makeup of the heterogeneities in the column.
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    Dispersion in consolidated sandstone with radial flow (1995)
    Springer
    Transport in porous media 19 (1995), S. 37-66 
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    ISSN: 1573-1634
    Keywords: dispersion ; sandstone ; radial flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This paper presents some experimental and theoretical results for dispersion processes occurring in consolidated Berea sandstone with radial flow geometry. A comprehensive review of the derivation and application of several analytical solutions is also presented. The Galerkin finite element method is applied to solve the advection-dispersion equation for unidimensional radial flow. Individual and combined effects of mechanical dispersion and molecular diffusion are examined using velocity-dependent dispersion models. Comparison of simulated results with experimental data is made. The effect of flow rates is examined. The results suggest that a linear dispersion model,D=αu, whereD is the dispersion coefficient,u the velocity andα a constant, is not a good approximation despite its wide acceptance in the literature. The most suitable mathematical formulation is given by an empirical form of $$D = D_0 + \mathop \alpha \limits^` u^m$$ , whereD ois the molecular diffusion coefficient. For the range of Péclet number (Pe=vd/D m,wherev is the characteristic velocity,d the characteristic length andD mthe molecular diffusion coefficient in porous media) examined (Pe=0.5 to 285), a power constant ofm=1.2 is obtained which agrees with the value reported by some other workers for the same regime. From the results of experiments and numerical modelling, the effect of mobility ratios (defined as the ration of viscosities of displaced and displacing fluids) on dispersion is found to be negligible, provided that the ratio is favourable.
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    Dispersion and Attenuation of Surface Waves in a Fluid-Saturated Porous Medium (1997)
    Springer
    Transport in porous media 29 (1997), S. 207-223 
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    ISSN: 1573-1634
    Keywords: dispersion ; attenuation ; surface waves ; Rayleigh wave ; Love wave
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract An investigation is conducted of propagation of surface waves in a porous medium consisting of a microscopically incompressible solid skeleton in which a microscopically incompressible liquid flows within the interconnected pores, and particularly the case where the solid skeleton deforms linear elastically. The frequency equations of Rayleigh- and Love-type waves are derived relating the dependence of wave numbers, being complex quantities, on frequency, as a result those waves are dispersive as well as inhomogeneous. Nevertheless, the amplitudes of both surface waves attenuate along the surface of the porous medium, whereas they decay exponentially receding from the surface of the medium.
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    URL: http://dx.doi.org/10.1023/A:1006590119031
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    Experiments on Solute Transport in Aggregated Porous Media: Are Diffusions Within Aggregates and Hydrodynamic Dispersion Independent? (1997)
    Springer
    Transport in porous media 29 (1997), S. 281-307 
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    ISSN: 1573-1634
    Keywords: solute transport ; nonequilibrium ; heterogeneous porous media ; dispersion ; diffusion ; experiments ; modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Two region models for solute transport in porous media assume that hydrodynamic dispersion in mobile water and solute diffusion within immobile water regions are independent. Experimental and theoretical results for transport through a macropore indicate that hydrodynamic dispersion and solute exchange are interdependent. Experiments were carried out to investigate this problem for a column packed with spherical porous aggregates. The effective diffusion coefficient of a tracer within the agreggates was determined from specific experiments. The dispersivity of the bed was determined from experiments carried out with a column filled with nonporous beads. We took advantage of the dependence of hydrodynamic dispersion on density ratios between the invading and displaced solutions to obtain a set of breakthrough curves corresponding to situations where the diffusion coefficient remains constant, whereas the dispersivity varies. Simulations reproduce correctly the experiments. Small discrepancies are noted that can be corrected either by increasing the dispersion coefficient or by fitting the external mass transfer coefficient. Increased dispersion coefficients probably reveal a modification of Taylor dispersion due to solute exchange. The fitted external mass transfer coefficients are close to the values obtained with classical correlations of the chemical engineering literature.
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    Stability of vertical miscible displacements with developing density and viscosity gradients (1988)
    Springer
    Transport in porous media 3 (1988), S. 277-297 
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    ISSN: 1573-1634
    Keywords: Stability ; linear stability analysis ; miscible displacement ; aspect ratio ; mobility control ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Viscous fingering and gravity tonguing are the consequences of an unstable miscible displacement. Chang and Slattery (1986) performed a linear stability analysis for a miscible displacement considering only the effect of viscosity. Here the effect of gravity is included as well for either a step change or a graduated change in concentration at the injection face during a downward, vertical displacement. If both the mobility ratio and the density ratio are favorable (the viscosity of the displacing fluid is greater than the viscosity of the displaced fluid and, for a downward vertical displacement, the density of the displacing fluid is less than the density of the displaced fluid), the displacement will be stable. If either the mobility ratio or the density ratio is unfavorable, instabilities can form at the injection boundary as the result of infinitesimal perturbations. But if the concentration is changed sufficiently slowly with time at the entrance to the system, the displacement can be stabilized, even if both the mobility ratio and the density ratio are unfavorable. A displacement is more likely to be stable as the aspect ratio (ratio of thickness to width, which is assumed to be less than one) is increased. Commonly the laboratory tests supporting a field trial use nearly the same fluids, porous media, and displacement rates as the field trial they are intended to support. For the laboratory test, the aspect ratio may be the order of one; for the field trial, it may be two orders of magnitude smaller. This means that a laboratory test could indicate that a displacement was stable, while an unstable displacement may be observed in the field.
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    An analysis of the viability of polymer flooding as an enhanced oil recovery technology (1988)
    Springer
    Transport in porous media 3 (1988), S. 591-618 
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    ISSN: 1573-1634
    Keywords: Polymer flooding ; viscous fingering ; multiphase flow ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The concept of improving oil recovery through polymer flooding is analysed. It is shown that while the injection of a polymer solution improves reservoir conformance, this beneficial effect ceases as soon as one attempts to push the polymer solution with water. Once water injection begins, the water quickly passes through the polymer creating a path along which all future injected water flows. Thus, the volume of the polymer slug is important to the process and an efficient recovery would require that the vast majority of the reservoir be flooded by polymer. It is also shown that the concept of grading a polymer slug to match the mobilities of the fluids at the leading and trailing edges of a polymer slug does not work in a petroleum reservoir. While this process can supply some additional stability to the slug, it is shown that for the purposes of enhanced oil recovery this additional stability is not great enough to be of any practical use. It is found that in this case the instability has simply been hidden in the interior of the slug and causes the same sort of instability to occur as was the case for the uniform slug.
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    Tracer Dispersion in Rough Open Cracks (1998)
    Springer
    Transport in porous media 32 (1998), S. 97-116 
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    ISSN: 1573-1634
    Keywords: dispersion ; anomalous diffusion ; Taylor dispersion ; roughness ; self-affine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface. This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained.
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    Automaton Simulations of Dispersion in Porous Media (1998)
    Springer
    Transport in porous media 32 (1998), S. 187-198 
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    ISSN: 1573-1634
    Keywords: diffusion ; dispersion ; miscible ; automaton
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A thermodynamic lattice gas (automaton) model is used to simulate dispersion in porous media. Simulations are constructed at two distinctly different scales, the pore scale at which capillary models are constructed and large scale or Darcy scale at which probabilistic collision rules are introduced. Both models allow for macroscopic (pore scale) phase separation. The pore scale models clearly show the effect of pore structure on dispersion. The large scale (mega scale) simulations indicate that when the pressure difference between the displacing phase and displaced phase is properly chosen (representing the average pressure gradient between the phases). The simulation results are consistent with both theoretical predictions and experimental observations.
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    Stochastic-Perturbation Analysis of a One-Dimensional Dispersion-Reaction Equation: Effects of Spatially-Varying Reaction Rates (1998)
    Springer
    Transport in porous media 32 (1998), S. 139-161 
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    ISSN: 1573-1634
    Keywords: dispersion ; reaction ; perturbation theory ; stochastic modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We carry out a stochastic-perturbation analysis of a one-dimensional convection–dispersion-reaction equation for reversible first-order reactions. The Damköhler number, Da, is distributed randomly from a distribution that has an exponentially decaying correlation function, controlled by a correlation length, ξ. Zeroth- and first-order approximations of the dispersion coefficient, D are computed from moments of the residence-time distribution obtained by solving a one-dimensional network model, in which each unit of the network represents a Darcy-level transport unit, and the solution of the transfer function in zeroth- and first-order approximations of the transport equation. In the zeroth-order approximation, the dispersion coefficient is calculated using the convection–dispersion-reaction equation with constant parameters, that is, perturbation corrections to the local equation are ignored. This zeroth-order dispersion coefficient is a linear function of the variance of the Damköhler number, 〈(ΔDa)2〉. A similar result was reported in a two-dimensional network simulation. The zeroth-order approximation does not give accurate predictions of mixing or spreading of a plume when Damköhler numbers, Da ≪ 1 and its variance, 〈(ΔDa)2〉 〉 0.25 〈Da2〉. On the other hand, the first-order theory leads to a dispersion coefficient that is independent of the reaction parameters and to equations that do accurately predict mixing and spreading for Damköhler numbers and variances in the range √〈(ΔDa)2〉/〈Da〉≤0.3
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    On the Modelling of Generalized Taylor–Aris Dispersion in Chromatographs via Multiple Scales Expansions (1999)
    Springer
    Transport in porous media 36 (1999), S. 307-339 
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    ISSN: 1573-1634
    Keywords: dispersion ; chromatography ; porous media ; adsorption ; homogenization ; multiple scales expansions.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract This paper is devoted to the computation of effective equations for the transport of a solute in a chromatograph. We focus our attention on models that retain dispersion effects. A chromatograph is a biporous periodic heterogeneous medium, made up of macropores, and of small porous adsorbing crystals that have a retention effect on the solute. We use the method of multiple scales expansions. Various macroscopic behaviours appear, according to the respective orders of magnitude of the dimensionless characteristic parameters: Peclet number in the macropores, ratio of the characteristic time of diffusion in the macropores to the characteristic time of diffusion in the crystals, adsorption coefficient. Dispersion occurs for a Peclet number of order ε−1. We then discuss the effective behaviour of the solute, with respect to the orders of magnitude of the other characteristic parameters. To our knowledge, most of the models are new. Our modelling is not restricted to chromatographs. It applies to various situations of physic and chemical engineering: fixed bed reactors, catalytic cracking, ground water for instance.
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    Experimental Investigation of Mixing in Aperiodic Heterogeneous Porous Media: Comparison with Stochastic Transport Theory (1999)
    Springer
    Transport in porous media 37 (1999), S. 169-182 
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    ISSN: 1573-1634
    Keywords: experiment ; aperiodic heterogeneity ; dispersion ; stochastic modeling.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract An electrochemical technique was used to measure concentration distributions in an aperiodic heterogeneous model for comparison with a stochastic transport theory. Four identical columns, each filled with a homogeneous distribution of glass beads, were threaded together to create a single model with aperiodic heterogeneity. The layers in the model were arranged in different ways providing 24 realizations of the permeability distribution. Comparisons between experimental moment data and moments of simulated mean concentration distributions showed that the model was not able to accurately predict experimentally observed mixing behavior.
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    Influence of the viscoelastic properties of the respiratory system on the energetically optimum breathing frequency (1993)
    Springer
    Annals of biomedical engineering 21 (1993), S. 489-499 
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    ISSN: 1573-9686
    Keywords: Work of breathing ; Inspiratory pressure-time integral ; Respiratory modeling ; Dogs ; Humans
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract We hypothesized that the viscoelastic properties of the respiratory system should have significant implications for the energetically optimal frequency of breathing, in view of the fact that these properties cause marked dependencies of overall system resistance and elastance on frequency. To test our hypothesis we simulated two models of canine and human respiratory system mechanics during sinusoidal breathing and calculated the inspiratory work ( $$\dot W$$ ) and pressure-time integral (PTI) per minute under both resting and exercise conditions. The two models were a two-compartment viscoelastic model and a single-compartment model. Requiring minute alveolar ventilation to be fixed, we found that both models predicted almost identical optimum breathing frequencies. The calculated PTI was very insensitive to increases in breathing frequency above the optimal frequencies, while $$\dot W$$ was found to increase slowly with frequency above its optimum. In contrast, both $$\dot W$$ and PTI increased sharply as frequency decreased below their respective optima. A sensitivity analysis showed that the model predictions were very insensitive to the elastance and resistance values chosen to characterize tissue viscoelasticity. We conclude that the $$\dot W$$ criterion for choosing the frequency of breathing is compatible with observations in nature, whereas the optimal frequency predictions of the PTI are rather too high. Both criteria allow for a fairly wide margin of choice in frequency above the optimum values without incurring excessive additional energy expenditure. Furthermore, contrary to our expectations, the viscoelastic properties of the respiratory system tissues do not pose a noticeable problem to the respiratory controller in terms of energy expenditure.
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    The multiple-scale averaging and dynamics of dispersion-managed optical solitons (1999)
    Springer
    Journal of engineering mathematics 36 (1999), S. 163-184 
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    ISSN: 1573-2703
    Keywords: fiber optics ; nonlinear Schrödinger equation ; multiple scales ; dispersion ; solitons.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Multiple-scale averaging is applied to the nonlinear Schrödinger equation with rapidly varying coefficients, and use the results to analyze pulse propagation in an optical fiber when a periodic dispersion map is employed. The effects of fiber loss and repeated amplification are taken into account by use of a coordinate transformation to relate the pulse dynamics in lossy fibers to that in equivalent lossless fibers. Second-order averaging leads to a general evolution equation that is applicable to both return-to-zero (soliton) and non-return-to-zero encoding schemes. The resulting equation is then applied to the specific case of solitons, and an asymptotic theory for the pulse dynamics is developed. Based upon the theory, a simple and effective design of two-step dispersion maps that are advantageous for wavelength-division-multiplexed soliton transmission is proposed. Theuse of these specifically designed dispersion maps allows simultaneous minimization of dispersive radiation in several different channels.
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    Competition among flow, dissolution, and precipitation in porous media (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1177-1185 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A theoretical and experimental study has been carried out on flow, dissolution, and precipitation in porous media. Flow experiments were performed on linear carbonate cores using acidic ferric chloride solutions. Dissolution of the carbonate by the acid causes an increase in the solution pH, thereby precipitating ferric hydroxide. This precipitate plugs up the pore throats in the medium and increases the resistance to fluid flow. Fluctuations in the permeability ratio were observed during core flood experiments, confirming the competition between channel formation due to dissolution and pore plugging due to precipitation. The evolution of the pore structure was characterized by Wood's metal castings.A network model has also been developed to describe flow and reaction in porous media. The model was used to simulate the ferric chloride system, and pressure oscillations predicted by the model show identical trends to those observed experimentally. Additionally, the evolution of pores in the network were graphically represented.
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    Role of porosity loss in limiting SO2 capture by calcium based sorbents (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 988-994 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The extent of high temperature (900-1,300°C), short time (〈1 s) SO2 capture was found to be limited by temperature-dependent losses in the porosity of calcium based sorbents. At 970°C these porosity losses were caused by CO2-activated sintering. Sulfation of the sorbents either prevented or reduced the extent of porosity losses. Differences in SO2 capture between hydroxides from different commercial sources, and significantly lower levels of capture by calcium carbonates compared to hydroxides were attributed to differences in particle size and the degree of porosity loss.
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    Dynamics and control of quasirational systems (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1017-1028 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Systems having transfer functions of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ G_P (s) = \frac{{P_1 (s) - P_2 (s)e^{ - t_d s} }}{{Q(s)}}, $$\end{document} where P1(s), P2(s) and Q(s) are polynomials, are called quasirational distributed systems (QRDS). They are encountered in processes modeled by hyperbolic partial differential equations. QRDS can have an infinity of right half-plane zeros which causes large phase lags and can result in poor performance of the closed-loop system with PID controllers. Theory on the asymptotic location of zeros of quasipolynomials is used to predict the nonminimum phase characteristics of QRDS and formulas are presented for factoring QRDS models into minimum and non-minimum phase elements.A generalized Smith predictor controller design procedure for QRDS, based on this factorization, is derived. It uses pole placement to obtain a controller parameterization that introduces free poles which are selected to satisfy robustness specifications. The use of pole placement allows for the design of robust control systems in a transparent manner. Controller selection is generally better, simpler and more direct with this procedure than searching for optimal PID controller settings.
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    Heat and mass transfer during the dissociation of hydrates in porous media (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1049-1052 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    From CA to CAS online. By Hedda Schulz, Translated by Elizabeth Mole, VCH Publishers, 1988, 227 pp (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1053-1053 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690350623
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    Adjustable solute distribution between polymers and supercritical fluids (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1097-1106 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The sorption of toluene, dilute in CO2, and likewise the distribution coefficient of toluene between silicone rubber and CO2 have been explored from gaseous to supercritical fluid conditions. Sorption and desorption isotherms were determined by frontal analysis using a new inverse supercritical fluid chromatography technique at 35 and 70°C up to 250 bar. Complementary swelling data are presented for pure CO2 in silicone rubber up to 315 bar. A new result is that the sorption of toluene goes through a maximum and is highly adjustable over a continuum in the highly compressible region of carbon dioxide. This behavior is explained physically and predicted quantitatively with the Flory equation and the Peng-Robinson equation of state using only information from binary systems. These results are useful for a wide variety of applications including impregnation of polymers with pharmaceuticals, fragrances and other additives, and polymer purification.
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    Pellet-model effects on simulation models for fixed-bed desulfurization reactors (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1137-1147 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Detailed mathematical models, pore or grain based, describing diffusion, reaction, and pore structure evolution in pellets of porous solids are used to simulate, along with a macroscopic reactor design model, the transient phenomena that take place during desulfurization of coal gas in fixed-bed reactors of pellets of metal oxide sorbents. Our computer simulation results show that the form of the pore- or grain-size distribution strongly influences the predictions of the overall reactor design model.
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    High-temperature adsorption of alkali vapors on solid sorbents (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1186-1194 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Vapors of alkali metal compounds can be removed from coal combustion and gasification flue gases using high-temperature aluminosilicate sorbents. The fundamentals of alkali adsorption on kaolinite, bauxite, and emathlite are compared and analyzed both experimentally and through theoretical modeling. The results show that the process is not a simple physical condensation, but a complex combination of diffusion and reaction. The kinetics of adsorption on these sorbents have similarities: the process is diffusion-influenced, the rate decreases with time, and there is a final saturation limit. There are, however, differences in reaction mechanisms leading to potentially different applications for each sorbent. In adsorbing alkali chloride vapors, kaolinite and emathlite release all the chlorine back to the gas phase while bauxite retains some of the chlorine. Moreover, the products of reaction with emathlite have a melting point significantly lower than those for kaolinite and bauxite. Therefore, emathlite is more suitable for lower-temperature sorption systems downstream of the combustors/gasifiers, while kaolinite and bauxite are suitable as in-situ additives.
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    Unusual behavior of a pollution abatement system: SO2 capture by red ochre (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1203-1206 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    Errata (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1210-1210 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690350719
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    Axial dispersion of submicron particles in capillary hydrodynamic fractionation (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1351-1364 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In the present investigation, Taylor's analysis of the axial dispersion of a solute in a Newtonian fluid undergoing laminar flow through a circular tube was applied to dispersions of colloidal particles, in which effects of size exclusion, inertial and colloidal forces, and wall retardation must be considered. The results indicate that the product of the particle Reynolds and Peclet numbers determines the importance of the inertial forces on both the effective axial diffusion coefficient and the height of a theoretical plate.The height of a theoretical plate as a function of the eluant ionic strength and average velocity, particle diameter, and tube diameter was determined experimentally. Close agreement with the numerical calculations from the diffusion equation was obtained. The height of a theoretical plate was found to attain a maximum value when the product of Reynolds and Peclet numbers was approximately 10.5.
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    Model for precipitation and dissolution processes with precipitate migration (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1385-1390 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    Effective writing for engineers, managers, scientists. By H. J. Tichy with Sylvia Fourdrinier, 2nd Ed., John Wiley & Sons, 1988 (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1402-1403 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Thin liquid films: Fundamentals and applications. I. B. Ivanov, Ed., Marcel Dekker, Inc., New York, 1988, 1160 pp., $195.00 (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1403-1404 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690350825
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    Partial internal wetting of catalyst particles with a distribution of pore size (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1337-1345 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The recent model of partial internal wetting of catalyst particles (Bhatia, 1988) is extended to allow for pore-size distribution, multicomponent diffusion, and nonlinear kinetics for spherical particles exposed to condensible vapor undergoing an exothermic reaction. Profiles of liqid filling of the pores are computed, and the influence on mass transfer and effectiveness factor is determined. Under certain circumstances, the effectiveness factor has a maximum with respect to the mole fraction of condensible component suggesting an optimum vapor-phase composition. As the bulk vapor approaches saturation the effectiveness factor and particle temperature can drop sharply because of precipitious increase in liquid filling. However, a significant fraction of the pore space is still dry in contradiction to prior models assuming complete internal wetting of catalyst particles. The new model is more realistic than earlier attempts and lays the framework for proper representation of the physical phenomena involved.
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    Wave height estimation in stratified gas-liquid flows (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1346-1350 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Andritsos and Hanratty (1978b) have shown that the increase in interfacial drag caused by waves in stratified gas-liquid flows is related to the wave steepness. Recent analyses of finite amplitude Kelvin-Helmholtz waves are used to develop a correlation for the ratio of the wave height to wavelength.
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    Solid flow in the annular region of a spouted bed (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1328-1336 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The solid circulation in the annular region of a 0.146 and a 0.292 m ID semicylindrical and cylindrical air spouted beds was investigated for different spouting conditions. Stroboscopic photography, stopwatch and fiber optic methods were used to measure the vertical particle velocities in the annular region. The optical fiber probe enabled the measurement of particle velocities inside the dense annular phase and was validated at the walls. Velocity profiles in half beds were very different from those found in full beds. The work was then limited to full beds. Experimental results show that the solids flow is characterized by a point sink at the nozzle entrance with the solids moving almost in plug flow higher in the bed. There is negligible entrainment of solids along the spout wall and slow, thin wall layers are observed near the walls and spout. The velocity profiles are independent of the total height of the bed. A kinematic model successfully describes the observed velocity field.
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    Deadtime compensation for nonlinear processes (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1535-1542 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Many industrially important processes feature both nonlinear system dynamics and a process deadtime. Powerful deadtime compensation methods, such as the Smith predictor structure in state space for linear systems is presented first and then directly extended to nonlinear systems. When combined with input/output linearizing state feedback, this Smith-like predictor makes a nonlinear system with deadtime behave like a linear system with deadtime. The control structure is completed by adding an external linear controller, which provides integral action and compensates for the deadtime in the input/output linear system, and an open-loop state observer. Conditions for robust stability with respect to errors in the deadtime and more general linear unstructured multiplicative uncertainties are given. Computer simulations for an example system demonstrate the high controller performance that can be obtained using the proposed method.
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    Diffusion with instantaneous reaction in a drop with continuous-phase resistance (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1543-1546 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    Thermodynamic modeling of electrolyte precipitation from aqueous solutions (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1569-1571 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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    Masthead (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989) 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690351001
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    Ultrapyrolysis of propane in a spouted-bed reactor with a draft tube (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1617-1624 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Ultrapyrolysis or ultrarapid pyrolysis is a hydrocarbon thermal cracking process which offers the promise of greater product selectivity, higher yield and feedstock flexibility. In this paper, ultrapyrolysis of propane in a spouted bed with a draft tube was used as a test system to demonstrate these advantages. Experiments, carried out on a 20-cm-diameter pilot-scale reactor, illustrate the spouted bed to be capable of achieving the extremely high reactant heating rates of up to 105 K/s and the short gas residence times of less than 500 ms necessary for this process. Moreover, reactant conversion and product yields can be enhanced by controlling the operating temperature of the bed. In addition, application of the propane pryolysis reaction scheme of Sundaram and Froment into a recently developed computer model indicates the ability to correctly simulate the spouted bed as an ultrapyrolysis reactor.
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    Tracer experiments and RTD's in heterogeneous reactor analysis and design (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1651-1658 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This paper focuses on the problem of scale-up of two-phase (e.g., solid-fluid) reactors. It outlines a class of such reactors which, for first-order reactions, scale in the familiar single-phase manner via an analog of the usual residence time distribution formula. The differences lie in the fact that the appropriate tracer experiment entering the formalism for this reactor class refers to a nonadsorbing tracer, and the analog of the plug flow solution is the solution for a fixed bed with fluid-phase plug flow. Surprisingly, unlike single-phase systems, there exist two-phase reactors, outside of the class defined, that do not scale in this manner, even when, say, the true catalyst surface chemistry is purely first-order. The paper discusses a few examples and implications for the design of two-phase reactors, including fluidized beds.
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    Suspension-to-Surface heat transfer in a circulating-fluidized-bed combustor (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1685-1691 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Heat transfer coefficients were measured for ciculating beds of sand particles of mean size 222 to 299 μm at temperatures of 340-880° C. Transfer coefficients were obtained for both a 1.22-m-long, 12.7-mm-OD vertical tube and a 1.59-m-long, 148-mm-wide membrane wall near the top of a 152-mm-square by 7.32-m-tall combustion column. For both surfaces and all temperatures, average heat transfer coefficients increased almost linearly with local suspension density which ranged from 0 to 70 kg/m3. Radiation played a significant role, especially at high temperatures and low suspension densities. Heat transfer coefficients also varied significantly with the lateral position of the tube. The vertical length of heat transfer surface is shown to be an important parameter allowing seemingly discrepant published results to be reconciled.
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    Profile equations for film flows at moderate Reynolds numbers (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1719-1727 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An approximate equation for the evolution of finite-amplitude, long disturbances to Newtonian liquid films is found to be accurate over a wide range of Reynolds numbers. A long-wave expansion leads to a film profile equation asymptotically correct when wave number and Reynolds number are small. Solutions of the film profile equation are compared to exact and other approximate solutions of the Navier-Stokes system. An alternative form of the film profile equation results in remarkably accurate solutions, when Reynolds numbers are moderate, in the cases of standing or monotonically decaying waves in horizonatal films, rising film flow, final acceleration of a moving film, and film flow emerging from a slot coater.
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    Effects of heater and heating methods on pool boiling (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1742-1744 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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    Lubricant retention on a spinning disk (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1753-1756 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 6 Ill.
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    Masthead (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989) 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690351101
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    Aggregation kinetics in salt-induced protein precipitation (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1779-1790 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The kinetics of protein aggregation in salt-induced precipitation processes were studied as a function of salt type, salt concentration, temperature and protein concentration. α-chymotrypsin (αCT) was used as a model protein. Stopped-flow turbidimetry was used to monitor the progress of precipitations. Analysis of the linear portions of the turbidity trajectories indicates that temperature and salt concentration effects are related to protein solubility; the protein concentration dependence is well described by the Smoluchowski collision equation. The aggregation kinetics of partially-inhibited αCT exhibit poisoning behavior, underscoring the importance of dimerization and monomer addition in the precipitation of αCT. Solute particle radius distributions determined via dynamic laser light scattering for low salt and supernatant αCT solutions indicated that significant aggregation does not occur in the absence of supersaturation. A detailed population balance model was proposed that accounted for specific and nonspecific interactions and monomer addition. The model is expected to find general application to protein aggregation phenomena, in particular for proteins that have specific quaternary interactions.
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    The critical properties of n-alkanes using a low-residence time flow apparatus (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1829-1834 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A low residence time flow method for the measurement of the critical temperatures and pressures of thermally-unstable fluids was developed in this work. The low residence time at elevated temperatures minimizes decomposition and other reactions, making it possible to measure the critical properties of many unstable fluids. An extrapolation procedure was developed to obtain the critical properties of rapidly reacting substances, based on the linear behavior of the apparent critical property with residence time. The measured critical properties of 14 n-alkanes (pentane through octadecane) using this method are reported in this paper. The results extend the available data on the critical properties of the higher alkanes and reveal a possible error in the literature value for the critical pressure of tetradecane.
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    An extended horizon feedback/feedforward self-tuning controller (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1835-1844 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A feedforward/feedback version of a single input/single output self-tuning controller has been developed and tested both via simulation studies and experiments on a section of an absorption/desorption pilot plant. The algorithm is based on the recursive least squares estimation of parameters for the linear models relating the output to the controlled input and to the disturbances; adaptation is achieved using a variable forgetting factor. The control input at each time interval is calculated using one of several single-step extended-horizon control strategies.The results show that the performance of the algorithm is insensitive to the choice of initial parameters, all of which have a readily identifiable intuitive basis. The algorithm is especially robust against deterministic disturbances (measurable and unmeasurable) and unknown and varying time delays. Computational load beyond that of a feedback-only version is minimal.
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    Adsorption of gaseous ethylamine on H-form strong-acid ion exchangers (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1869-1875 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Equilibrium isotherms and kinetic data for sorption of ethylamine on two different H-form ion exchangers (a homogeneous gel type and a biporous MR type) have been determined experimentally by the gravimetric method. The gaseous amine is adsorbed on the dry resins according to an acid-base neutralization reaction, and the saturation capacity coincides with the exchange capacity of the resin. For the gel-type resin, the equilibrium is less favorable and the isotherm is almost linear over the experimental range.The kinetic data also reflect the structural difference between the two adsorbents. In the MR-type resin, the sorption rate is controlled by macropore diffusion with rapid equilibration of the adsorbed phase within the microparticles. Since the equilibrium isotherm is highly favorable, approaching the irreversible limit, the uptake curves are well represented by the ‘shrinking core’ model. Diffusion in the gel-type resin is much slower and the pore diffusivities are smaller by several orders of magnitude, presumably reflecting the smaller effective pore diameter.These results suggest that the MR-type resin is a potentially useful adsorbent for removal of traces of light amines from industrial gases.
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    An optimal design technique for multivariable SISO controllers (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1903-1906 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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    Constitutive equations for polymer melts and solutions, by R. G. Larson, Butterworths, Boston, 1988, 364 pp., $39.95 (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1915-1916 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690351122
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    Lumping nonlinear kinetics in a CSTR (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1927-1932 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The model of uniform nonlinear kinetics recently developed for the continuous description of a multicomponent mixture reacting in a batch or plug flow reactor (Astarita, 1989) is applied to the analysis of a continuous stirred tank reactor (CSTR). It is shown that most of the equations can be solved in general, independently of the specific kinetic mechanism. Some specific mechanisms are discussed. The difference between the behavior in a plug flow reactor (PFR) and a CSTR turns out to be quite dissimilar from what one would expect by considering the single-component case.
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    Cocurrently-cooled fixed-bed reactors: A simple approach to optimal cooling design (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1899-1902 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 6 Ill.
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    Masthead (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989) 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    Control mechanisms of fluidized solids circulation between adjacent vessels (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 1933-1941 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Many industrial proceses require the circulation of particles between reacting fluidized compartments at a stable, but flexible rate, so that the processes can be operated at different solids rates. In order to understand the phenomena involved in the circulation and its control, circulation of sand particles has been studied through a new experimental approach, using an open-loop two compartment circulating system.Experimental results show that the control of the circulation rate depends on three phenomena: the vertical resisting force in the fluidized compartments, the contraction of flow in the communication zone, and the bypass of gas between the compartments. For industrial purposes, the first appears to be predominant in the control of the solids rate. The second ensures neither the strict control of this rate nor the required flexibility. The link between the gas bypass and the circulation phenomena is explained and recommendations for the design and operation of circulating systems are given.
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    A simple method for on-line identification and controller tuning (1989)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 35 (1989), S. 2037-2039 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
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    Masthead (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990) 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    Capillary experiments of flow induced crystallization of HDPE (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 13-18 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Flow-induced crystallization experiments are made in a capillary apparatus modified with a downstream reservoir under pressure. Capillary length, diameter, and entrance angle are changed, as well as flow rate. The results show that the crystallization temperature is influenced both by the elongational flow at the capillary entrance and by the shear flow along the capillary. The independent effect of the pressure equals that obtained under static conditions. The effect of shear is correlated in terms of shearing work.
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    Calculation of the compression zone height in continuous thickeners (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 3-12 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method to calculate the compression zone height in continuous thickeners is presented. With this method, it is necessary to know the variations of the pulp-supernatant interface and the sediment height vs. time in a batch test. This method is discussed considering the following aspects: relationship between the settling rate of solids and their concentration in the settling zone; and the compression of solids due to the squeeze transmitted by the upper layers - unbuoyed weight of particles minus force of friction due to the Darcian flow. When the variation of the sediment height vs. time becomes linear, it is possible to calculate the maximum solids concentration which can be reached by sedimentation. The change of the solids matrix permeability and its influence on the method proposed are also analyzed.
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    Fluidized bed drying of solids (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 29-38 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A kinetic model is developed for the drying of solids in fluidized beds, assuming a falling rate period following a constant rate period. Experimental data obtained using batch and continuous single and spiral fluidized beds are satisfactorily matched with the assumed drying kinetics and the residence time distribution of solids appropriate for the type of dryer.
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    The backfill cycle of the pressure swing adsorption process (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 53-65 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The backfill cycle in the pressure swing adsorption (PSA) separation of air to produce an enriched oxygen product using a zeolite 5A molecular sieve was studied theoretically and experimentally. The effects of the backfill cycle, cycle configuration, backfill rate, pressurisation rate, and product rate were studied. The theory agreed well with the experimental results in predicting the product oxygen concentration over a wide range of backfill pressures, thus giving a basic understanding of the bed dynamics of the backfill cycle. The theory showed that the backfill rate and adsorption capacity of the adsorbent were the most important parameters governing the efficiency of the PSA process. We showed that, given an adequate backfill pressure, a separate pressurization step could be omitted by incorporating it with the product release step with no detrimental effect on the product oxygen concentrations while increasing adsorbent productivity.
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    Bubble-size distribution in Fischer-Tropsch-derived waxes in a bubble column (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 93-105 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Bubble sizes were measured for molten wax-nitrogen systems using photography and dynamic gas disengagement. The effects of operating conditions, system geometry and wax type were studied in 0.05- and 0.23-m-diameter by 3-m-tall bubble columns. Both techniques were used with FT-300 wax, while only the dynamic gas disengagement technique could be used with reactor waxes due to their dark color. For FT-300 wax, Sauter mean diameters obtained from photographs taken near the column wall were significantly lower than those obtained from photographs taken near the center. The ds values obtained from dynamic gas disengagement and photographic (near the column center) methods, for this noncoalescing medium, were in the range 0.5-1.6 mm in the large-diameter column. For reactor waxes, ds values were significantly higher (1-2 mm for Sasol and 1-5.5 mm for Mobil's reactor wax) and are in agreement with results reported in earlier studies with similar waxes (ds = 2-4 mm), where different experimental techniques (light transmission or hot wire anemometry) were employed.
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    An approach to organizing the EOS model in process simulators (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 132-136 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 7 Ill.
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    Ullman's encyclopedia of industrial chemistry. vols. B2, B3: Unit operations I, II edited by Barbara Elvers, Michael Ravenscroft, James Rounsaville, Gail Schulz; Wolfgang Gerhartz, Executive Editor, VCH Publishers, New York, 1988, approx. 850 pp. / vol., $190.00 vol (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 157-158 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690360121
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    Melt blowing: General equation development and experimental verification (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 175-186 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A model has been developed for steady polymer melt blowing. This model includes the dominant effect that the forwarding air has upon the process. Inertial, gravitational and heat transfer effects are also included. The model equations are solved numerically with both Newtonian and viscoelastic (Phan-Thien and Tanner) constitutive equations. The predicted results compare favorably with actual experimental data.
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    Unifying indicator and instantaneous reaction methods of measuring micromixing (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 227-232 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Instantaneous chemical reactions, either themselves or together with chemical indicators, have previously been used as probes of turbulent micromixing. Both methods obtain statistics of the micromixing from measurement of time mean quantities. The mean reactant concentration, which is the quantity measured in the instantaneous reaction method, is shown here to be the integral with respect to feed concentration ratio of the mean color density, which is the quantity measured in the chemical indicator method. Differentiation of the mean color density gives the scalar probability density while integration gives the mean reactant concentration. Measurements of the color density of bromothymol blue at the centerline of a turbulent jet of base mixing with acid are used as an example.
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    Interpretation of the magnetic resonance imaging signal from a foam (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 287-290 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 4 Ill.
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    Gas-liquid two-phase flow in symmetrically dividing horizontal tubes (1991)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 111-122 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The time-averaged void fraction, pressure drop and flow regime transition behavior of horizontal air-water two-phase flows is studied experimentally and numerically for 2-cm-inner-diameter tubes with various flow dividing junctions at its end. The time-average void and pressure drop behavior along the channel is simulated using a two fluid separated flow model. The results show that two-phase behavior (flow regime, void fraction, and pressure drop) is affected strongly by the presence of a flow division in the system. These effects extend far upstream of the junction for low-momentum flows and far downstream for high-momentum flows. Both numerical and experimental results show that there occurs a large increase in void just downstream of the junction owing to the halving of the fluid volume flow rates and the liquid deceleration.
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    Fault diagnosis in complex chemical plants using artificial neural networks (1991)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 137-141 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Ill.
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    Masthead (1991)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991) 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690370201
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    Influence of chemical and electrostatic gradients on diffusion in microemulsions (1991)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 169-181 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Nonequilibrium diffusion behavior in nonionic and ionic surfactant microemulsion systems has been studied experimentally using the open-ended capillary method. Experimental results for these systems have been compared with a drop theory of diffusion for microemulsions under conditions where large concentration and electrostatic gradients exist. The results show good agreement in concentration profiles between theory and experiment for the microemulsion components - water, benzene, and phenol. Furthermore, under certain conditions the theory predicts that over a limited time interval phenol will diffuse from low-concentration regions to regions of higher concentration. This phenomenon has been observed.
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    Use of a second endothermic reaction to desensitize a tubular reactor (1991)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 37 (1991), S. 225-232 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Three parametric sensitivity criteria were examined for application to a pseudohomogeneous tubular reactor system, in which both methanol dehydration (exothermic) and methanol dissociation (endothermic) were catalyzed. The addition of the endothermic reaction was shown to lead to a desensitized reactor. It was illustrated, however, that the relative activities of the two catalysts should be somewhat similar to maintain the overall conversion of the resulting reactor for a given residence time.The three criteria investigated tended to disagree with one another more, as the system was made less sensitive by the addition of more endothermic catalyst. A potential application of the resulting nonsensitive reactor design would be in methanol-fueled vehicles.
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    Flue gas desulfurization by in-duct dry scrubbing using calcium hydroxide (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 473-477 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: No Absract.
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    A bubbling fluidization model using kinetic theory of granular flow (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 523-538 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Detailed knowledge of solids circulation, bubble motion, and frequencies of porosity oscillations is needed for a better understanding of tube erosion in fluidized bed combustors. A predictive two-phase flow model was derived starting with the Boltzman equation for velocity distribution of particles. The model is a generalization of the Navier-Stokes equations of the type proposed by R. Jackson, except that the solids viscosities and stresses are computed by simultaneously solving a fluctuating energy equation for the particulate phase. The model predictions agree with time-averaged and instantaneous porosities measured in two-dimensional fluidized beds. Observed flow patterns and bubbles were also predicted.
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    Study of restricted diffusion in porous catalysts by NMR (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 559-564 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The diffusion of 1,3,5 tri-tert-butylbenzene (TTB) into cylindrical γ-alumina extrudates of varying micropore diameter and macropore volume has been studied by NMR spectroscopy. The proton NMR signal of the methyl proton of TTB in the micropores of the alumina extrudate was found to be well resolved and shifted upfield relative to that in the bulk liquid by 0.55 ppm. The area under the shifted peak is proportional to the liquid concentration of TTB in the micropores. The change in the intensity of this peak as a function of time and measurements of the amount of TTB absorbed on the surface alumina at equilibrium were used to calculate the effective diffusivity of TTB in each extrudate. Measured values of the effective diffusivity are in reasonable agreement with predictions using correlations in the literature. These observations suggest a new method for measuring the liquid-phase effective diffusivity in porous materials.
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    Analytical solutions of emulsion polymerization models (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 623-626 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    Initial condition for population balance in an MSMPR crystallizer (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 630-632 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1002/aic.690360415
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    Genetic engineering fundamentals: An introduction to principles and applications. by Carl Kammermeyer and Virginia L. Clark, Marcel Dekker, New York, 1989, 261 pp., $45.00 (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 639-640 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690360417
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    Growth and dissolution of succinic acid crystals in a batch stirred crystallizer (1990)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 36 (1990), S. 665-676 
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    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Growth and dissolution of succinic acid crystals have been studied in an isothermal stirred tank crystallizer. Seeded desupersaturation and deundersaturation experiments have been performed. Parameters of a desired growth rate equation are estimated by fitting the supersaturation balance equation directly to the supersaturation measurements. The procedure is based on nonlinear optimization techniques. Thus, uncertainties in the traditional approximation of the concentration vs. time curve are circumvented. The growth process for succinic acid crystals in an aqueous solution is found to be controlled by a significant resistance in both the volume diffusion step and in the surface integration step. An implicit equation is given to accurately represent the crystal growth rate as a function of the supersaturation. When extrapolating outside the range of experiments, this equation is shown to predict growth rates that are significantly different from those predicted by a corresponding power law expression. The dissolution rate exhibits a nonlinear dependence on undersaturation which is interpreted as changes in the crystal shape. Initial dissolution rate coefficients are in good agreement with volume diffusion coefficients obtained from growth experiments.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690360504
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