Review of Steady-State Two-Phase Flow in Porous Media: Independent Variables, Universal Energy Efficiency Map, Critical Flow Conditions, Effective Characterization of Flow and Pore Network

Abstract

In many applications of two-phase flow in porous media, a wetting phase is used to displace through a network of pore conduits as much as possible of a non-wetting phase, residing in situ. The energy efficiency of this physical process may be assessed by the ratio of the flow rate of the non-wetting phase over the total mechanical power externally provided and irreversibly dissipated within the process. Fractional flow analysis, extensive simulations implementing the DeProF mechanistic model, as well as a recent retrospective examination of laboratory studies have revealed universal systematic trends of the energy efficiency in terms of the actual independent variables of the process, namely the capillary number, Ca, and the flow rate ratio, r. These trends can be cast into an energy efficiency map over the (Ca, r) domain of independent variables. The map is universal for all types of non-wetting/wetting phase porous medium systems. It demarcates the efficiency of steady-state two-phase flow processes in terms of pertinent system parameters. The map can be used as a tool for designing more efficient processes, as well as for the normative characterization of two-phase flows, as to the predominance of capillary or viscous effects. This concept is based on the existence of a unique locus of critical flow conditions, for which the energy efficiency takes locally maximum values. The locus shape depends on the physicochemical characteristics of the non-wetting phase/wetting phase/porous medium system, and it shows a significant mutation as the externally imposed flow conditions change the type of flow, from capillary- to viscosity-dominated. The locus can be approached by an S-type functional form in terms of the capillary number and the system properties (viscosity ratio, wettability, pore network geometry, etc.), suggesting that formative criteria can be derived for flow characterization in any system. A new, extended definition of the capillary number is also proposed that effectively takes into account the critical properties of all the system constituents. When loci of critical flow conditions pertaining to processes with different viscosity ratio in the same pore network, are expressed in terms of this true-to-mechanism capillary number, they collapse into a unique locus. In this context, a new methodology for the effective characterization of pore networks is proposed.