Single-phase flow, in porous

Shear Factor, F. The shear factor F is a generalized hydrodynamic resistivity of porous media. It appears in the momentum equation 63 and is needed to solve the problem of single-phase flow in porous media. The shear factor F can be related to the pressure drop of a unidirectional flow without bounding wall effects, that is, in a one-dimensional medium through equation 21. In this section, we give a detailed account for the derivation of the expressions for fv and F. 

Hence, we have formed the closure for the single-phase flow in porous media using a model of the shear factor for both consolidated and granular media. For the term closure, we mean that the shear factor F of equation 63, which was introduced through averaging procedures, is now defined. 

Relative permeability is defined as the ratio between the permeability for a phase at a given saturation level to the total (or single-phase) permeability of the studied material. This parameter is important when the two-phase flow inside a diffusion layer is investigated. Darcy s law (Equation 4.4) can be extended to two-phase flow in porous media [213] ... 

Liu, S. Masliyah, J.H. Principles of Single-Phase Flow Through Porous Media in Suspensions, Fundamentals and Applications in the Petroleum Industry, Schramm, L.L. (Ed.), American Chemical Society Washington, 1996, pp. 227-286. 

Fio. 9. Streamlines showing steady-state velocity profile during single-phase flow in a reconstructed porous medium. 

The effects of the pressure drawdown on the oil-production rate are shown in Figure 2. Both the experimental data and theoretical calculations based on the Darcy s law are shown. Initially the oil-production rate increased linearly with the increasing pressure drawdown across the porous medium, in agreement with Darcy s law for single-phase flow through porous media. At low drawdown pressures, the dissolved gas remained largely in solution, and therefore, the oil was flowing as a... 

We then discussed the modeling for single-fluid phase flow in porous media. In particular, the shear factor and permeability model of Liu et al. (32) is discussed in detail. The bounding wall effects are presented. This section completed the modeling requirements for single-phase incompressible flow in porous media. We showed how to solve the governing equations for flow in porous media and an approximate solution of the pressure drop for an incompressible flow through a cylindrically bounded porous bed was constructed. 

Slattery JC (1969) Single-phase flow through porous media. AIChE J 15(6) 866-872 Slattery JC (1972) Momentum, energy, and mass transfer in continua, 2nd edn. McGraw-HiU Kogakusha LTD, Tokyo... 

The pore geometry described in the above section plays a dominant role in the fluid transport through the media. For example, Katz and Thompson [64] reported a strong correlation between permeability and the size of the pore throat determined from Hg intrusion experiments. This is often understood in terms of a capillary model for porous media in which the main contribution to the single phase flow is the smallest restriction in the pore network, i.e., the pore throat. On the other hand, understanding multiphase flow in porous media requires a more complete picture of the pore network, including pore body and pore throat. For example, in a capillary model, complete displacement of both phases can be achieved. However, in real porous media, one finds that displacement of one or both phases can be hindered, giving rise to the concept of residue saturation. In the production of crude oil, this often dictates the fraction of oil that will not flow. 

Homogeneous Models. The basic assumption in these models is that the emulsion is a continuum, single-phase liquid that is, its microscopic features are unimportant in describing the physical properties or bulk flow characteristics. It ignores interactions between the droplets in the emulsions and the rock surface. The emulsion is considered to be a single-phase homogeneous fluid, and its flow in a porous medium is modeled by using well-documented concepts of Newtonian and non-Newtonian fluid flow in porous media (26, 38). 

The focus of this review has been on mass transfer in laminar, single-phase flows. Significant work is necessary for the rigorous analysis of current distribution in turbulent flows. Progress is also required for the analysis of current distribution in multiphase flows, especially in porous media relevant to fuel cell or battery applications. 

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

Single-Component Systems. As an example of solid-liquid phase change in porous media, we consider melting of the solid matrix by flow of a superheated liquid through it. The analysis, based on local thermal nonequilibrium between solid and liquid phases, has been performed by Plumb [140] and is reviewed here. 

Suction involves either vapor removal through a porous heated surface in nucleate or film boiling, or fluid withdrawal through a porous heated surface in single-phase flow. 

Flow in porous media can be classified as a single- or multiphase flow. In a limiting sense, single-phase flow need not be considered alone be-... 

Single-phase fluid flow in porous media is a well-studied case in the literature. It is important not only for its application, but the characterization of the porous medium itself is also dependent on the study of a single-phase flow. The parameters normally needed are porosity, areal porosity, tortuosity, and permeability. For flow of a constant viscosity Newtonian fluid in a rigid isotropic porous medium, the volume averaged equations can be reduced to the following the continuity equation,... 

Subchannel analysis codes, ASFRE for single-phase flow and SABENA for two-phase flow, have been developed for the purpose of predicting fuel element temperature and thermalhydraulic characteristics in the FBR fuel assemblies. ASFRE has the detailed wire-spacer model called distributed flow resistance model, which calculates the effect of wire-spacer on thermalhydraulics. Also planer and porous blockage models are implemented for fuel assembly accident analysis. In this reporting period, three dimensional thermal conduction model was used for the evaluation of local blockage in a fuel assembly. In addition, the comparison of pressure losses in the assembly with the water experimental data has been performed. Regarding SABENA, based on the two-fluid model, no activity is reported. 

The rheological description of foam flow in porous media has been treated in different ways. one approach has been to use the single-phase fluid viscosities to calculate relative permeabilities to each fluid on the basis of experimental measurements of flow rates and pressure drop in foam flow through a porous medium. 

Mathematical models of polymer solution flow in porous media must substitute the effective polymer porosity in certain places, in place of the total porosity as a multiplier of the time derivative of fluid concentration. Thus, the polymer balance equation for single-phase flow can be written... 

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