Porous media, multiphase flow

For the case of multiphase flow in a porous medium, the flow rate of a phase j can be calculated from... 

A comprehensive review of the important factors that affect the flow of emulsions in porous media is presented with particular emphasis on petroleum emulsions. The nature, characteristics, and properties of porous media are discussed. Darcy s law for the flow of a single fluid through a homogeneous porous medium is introduced and then extended for multiphase flow. The concepts of relative permeability and wettability and their influence on fluid flow are discussed. The flow of oil-in-water (OfW) and water-in-oil (W/O) emulsions in porous media and the mechanisms involved are presented. The effects of emulsion characteristics, porous medium characteristics, and the flow velocity are examined. Finally, the mathematical models of emulsion flow in porous media are also reviewed. 

The additional sink is added to the usual conservation equations corrected for the volume fraction of the porous media. The governing equations look similar to those for Eulerian multiphase flow processes (Section 4.2.2) except that the volume fraction of the porous medium is not a variable. In the enthalpy equation, it is possible to include influence of porous media by considering an effective thermal conductivity, fceff, of the form ... 

A porous medium shapes foam to its own liking as confined, porefilling bubbles and lamellae. Foam in porous media is not a continuous fluid. The three mechanisms of foam generation (snap-off, division, and leave-behind) are all pore geometry specific. Snap-off is a mechanical process that occurs in multiphase flow without surfactant. For successful gas-bubble snap-off, the pore-body to pore-throat constriction ratio must be sufficiently large (roughly 2) and gently sloped. Otherwise stable wet-... 

Porous medium is a material consisting of a solid matrix with interconnected pores. The interconnected pores are responsible for allowing a fluid to traverse through the material. For the simplest situation, the medium is saturated with a single fluid ( single fluid flow ). In multiphase fluid flow, several fluids (liquids and/or gas) share the open pores. Porous media are classified as unconsolidated and consolidated. 

In Biot formalism, there exist several assumptions that restrict its generality and make true liquid-solid coupling impossible. Biot assumed that for a REV in a multiphasic porous medium, a single energy functional could be stipulated to define the energy state. It has been shown that for N continuous contiguous phases, N functionals are needed to fully describe behavior. (For example, simultaneous countercurrent flow of two immiscible liquids is evidence that at least two separate energy functionals are needed.)... 

When setting up such a model, two building blocks are available which come from different modeling fields, namely, the Stefan Maxwell equations describing the flow of a gas mixture through a porous medium and the equations of multiphase flow in a porous medium. We will shortly describe both of them. After that, we make an attempt to join both of them into a combined model. The discussion of open problems and future directions concludes the section. 

The single layer glass bead model is a closer representation of a porous medium. This was used by Sharma to study toe foam drive process and Egbogah and Dawe to study toe size distribution of oil droplets. Mattax and Kyte used a network of etched capillaries to study fluid distributions under various wettability conditions. Davis and Jones studied the flow of foam in porous media using etched glass micromodels. A study of toe multiphase flow of oil and water di ersed in toe porous medium was carried out by Bonnet using an etched plastic micromodel. 

In the model developed by Iliuta et al. [120], a cocurrent two-phase trickle flow through a porous medium of uniform initial porosity and single-sized catalytic particles is considered (Figure 5.7a and b). Two-phase flow is assumed unidirectional, and both the flowing phases are assumed as viscous Newtonian. The gas/liquid + fine/porous medium + fine multiphase system is viewed as a system of three interpenetrated continua (i) a flowing gas, (ii) a dilute pseudohomogeneous suspension consisting of liquid and fine particles, and (iii) a stationary... 

Davis, A. James, D. Slow Flow Through a Model Fibrous Porous Medium, Int J. Multiphase Flow 22, 969-989 1996,. 

---