Two-phase flow in porous media

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] ... 

To determine the saturation for any of the models, the capillary pressure must be known at every position within a diffusion medium. Hence, the two-phase models must determine the gas and liquid pressure profiles. In typical two-phase flow in porous media, the movement of both liquid and gas is determined by Darcy s law for each phase and eq 47 relates the two pressures to each other. Many models utilize the capillary pressure functionality as the driving force for the liquid-water flow... 

The success of waterflooding as a petroleum recovery process and the realization that even it leaves behind a substantial amount of residual oil have been major factors stimulating research on two-phase flow in porous media during the past fifty years. Most of the knowledge pertinent to two-phase flow under normal waterflooding conditions is summarized in existing books (l ). Recently, the... 

The mathematical formulation of this model was made by Dever-eux 36) based on the classical Buckley-Leverett theory for two-phase flow in porous media (49) and equations developed by Scheidegger (44). They solve a set of eight equations ... 

Ganesan V, Brenner H (2000) A diffuse interface model of two-phase flow in porous media. Proc R Soc Lond A 456 731-803... 

The two-phase flow in porous media (a three-phase system) is approached from the pore-level fluid mechanics The pertinent forces and their expected contributions are examined, and when available, empirical results are used. After arriving at a set of volume-averaged governing conservation and constitutive equations, some liquid-vapor phase change problems are examined. 

In the following, we examine the experimental results [127], that support these two asymptotic behaviors, that is. Bo > 1, the high-permeability asymptote, and Bo 1, the low-permeability asymptote. Then, we discuss the low-permeability asymptote using a onedimensional model [109,125,128], The one-dimensional model is also capable of predicting qa, that is, the onset of dryout. We note that the hysteresis observed in isothermal two-phase flow in porous media is also found in evaporation-condensation and that the q versus T0 - Ts curve shows a decreasing q (or T0 - Ts) and an increasing q (or T0 - Ts) branch. 

Larson, R., L. Scriven, and H. Davis, Percolation theory of two phase flow in porous media. Chemical Engineering Science, 1981, 36, 57-73. 

Kolditz O. and De Jonge J. 2(K)3. Non-lsothemial Two-Phase Flow in Porous Media. Submitted to Computational Mechanics. 

Kolditz, O. J. De Jonge. 2003. Non-isothermal two-phase flow in porous media. (Submitted to Computational Mechanics). 

Two-phase flow in porous media is strongly influenced by surface forces these generally lead to incomplete displacement of one phase by another in... 

Many water-management advances have been made (Figure 2). However, fundamental properties associated with two-phase flow in porous media, including capillary pressure, liquid water content and, intrinsic and relative permeabilities, are still lacking and are needed for predictive models. This situation is due to the absence of measurement methods for thin materials. Contact porosimetry [57] does not presently allow measurement of the permeabilities or during wetting (to evaluate the presence of hysteresis). Fluorescence microscopy [58] can provide additional information about liquid water flow through porous media. 

The main impact for modeling two-phase flow in porous media came from petroleum reservoir simulation [4, 5] and from hydrology [6]. Most available models are based on the concept of capillary pressure and on some upscaling of capillary information from the micro to the macro scale. We will restrict ourselves to that case. 

Figure 1.7 Packed-bed microchannels, (a) Two-phase flow in porous media is described using multiscale approaches that seek to combine channel-level descriptions with the analysis of connected networks [108-110]. (b) The description of microfluidic multiphase networks can be modeled with networks-of-resistances models, which require very accurate estimates of...

Pan, C., Hilpert, M., Miller, C.T. Lattice-Boltzmaim simulation of two-phase flow in porous media. Water Resources Research 40(1), W01501 (2004)... 

Saad, B., Saad, M. Study of full implicit petroleum engineering finite volume scheme for compressible two phase flow in porous media. SIAM Journal of Numerical Analysis, 1-34 (2013)... 

Multiphase flow in porous media is a very important topic for low-temperature PEFCs because water produced at the cathode flows through the porous catalyst layers and porous gas diffusion media. Any local blockage of normally open pores restricts reactant flow to the reaction sites, a phenomenon known as flooding. The water balance and flooding in a PEFC is described in detail in Chapter 6. Here, the basic fundamentals that describe two-phase flow in porous media are described to guide and understanding. 

Wettability can also be considered as a measure of the speed with which fluids spread over solid surfaces. The speed of spreading is directly controlled by the interfacial forces at the solid surface. The spreading can be increased by lower surface tension and lower fluid viscosity. For two-phase flow in porous media, the wetting angle influences the capillary pressure and liquid transport considerably hence, an important aspect of PEFC material design is hydrophobic content. 

Relative Permeability In liquid-gas two-phase flow in porous media, the available pore space is shared by the liquid and gas, and thus the effective cross-sectional area available for each fluid is less than the total available pore space. This effect is taken into account by the relative permeability, kr, which is defined as the ratio of the actual permeability for a phase at a given saturation to the total intrinsic permeability of the porous media ... 

---