Mathematical Analysis of Two-Phase Flow in Low-Permeability Porous Media zy A one-dimensional isothermal transient two-phase flow model of gas and liquid in a low-permeability medium has been developed from the general mass and momentum balances. The characteristic roots of the governing differential equations are real and distinct. Therefore, solution of the flow equations may be attempted by a stable initial-value finite-difference scheme. A numerical solution was obtained using the method of lines. Calculated two-phase flow parameters are consistent with expected flow behavior and reflect the sensitivity of fluid flow to porosity, gas and liquid permeability, and capillary pressure in a tight sands porous medium. Calculated gas flow rates compared well with experimental data obtained at the Institute of Gas Technology (IGT) for low-perme- ability sandstone. zyxwvutsrq Hamid Arastoopour Department of Chemical Engineering Illinois Institute of Technology Chicago, IL 60616 James Semrau Institute of Gas Technology Chicago, IL 60616 Introduction zyxwvutsrqp During the past decade, there has been increasing attention on economical gas recovery from unconventional reservoirs, par- ticularly low-permeability (tight sand) formation. Sharer and OShea (1986) estimated over 14 x loL2 pmJ of natural gas may be recoverable from low permeability sandstone located in the United States. To obtain feasible production capability, signifi- cant research and development, both experimental and theoreti- cal, is needed to develop reliable experimental data and mathe- matical description of two-phase flow as well as to advance massive hydraulic fracturing technology (MHF). Gas bearing, tight (low permeability) reservoirs could be present in sand- stone, siltstone, silty shale, and chalk. They usually have an zyxwvu in- situ permeability to gas of 0.1 md (987 x pm2) or less. Tight gas reserves exhibit several characteristics that are unique when compared to conventional reservoirs. Among the most sig- nificant is the relationship between porosity and permeability which is reasonably consistent for conventional reservoirs, but completely inconsistent for tight gas reservoirs. The uniqueness of naturally-occurring low-permeability ma- terials reduces the reliability of simulation techniques applied to conventional porous media. zyxwvutsr In higher-permeability media, ap- plication of Darcy’s Law, which is not appropriate in some cases, is standard practice under single-phase flow conditions. When more than one flowing phase is present, Darcy’s Law is usually applied to each phase with modification of the permeability terms. Relative permeability is incorporated into the relations to account for the deviation from single-phase flow behavior. Typi- cally relative permeability is expressed as a nonlinear function which is directly proportional to phase saturation. The effective permeability of a fluid approaches its single-phase permeability, as its saturation in the medium increases. In most of gas and liquid flow in high-permeability porous medium, both phases are in intimate contact throughout the medium. On a pore level, both phases are moving in the same space via some mechanism such as annular flow, slug flow, and stratified flow, and the Darcy’s law has been modified in terms of relative velocity between the phases. We believe, in the low- permeability media, surface tension effects can cause the segre- gation of fluids inside the media. Thus, both gas and liquid do not coexist in the individual pores. The literature contains several fundamental studies on the experimental flow behavior in low permeability media, such as Jones and Owens (1980), Walls et al. (1982), Randolph (1983), Freeman and Bush (1983), Chowdiah (1986), and Soeder (1 986). Most of these studies provide us with a better under- standing of tight-sand-media gas permeability in the presence of water and confining stress. There have been, however, few attempts in theoretical analysis of only single-phase flow through dry or partially-saturated low-permeability media. Arastoopour and Adewumi (1983) obtained analytical solution to the linearized gas Row equation in porous media. Newberg and Arastoopour (1 986) developed continuity and momentum balances for flow of gas through low-permeability media and successfully compared their calculated values with IGT’s exper- 1710 October 1989 Vol. 35, No. 10 AICbE Journal