True-to-mechanism model of steady-state two-phase flow in porous media, using decomposition into prototype flows

A true-to-mechanism model is proposed, which considers steady-state two-phase flow in porous media (SS2ϕPM) as a composition of two prototype flows, namely ganglion dynamics (GD) and connected-oil pathway flow (CPF). Coupling of the prototype flows is effected with the simple rule that the macroscopic pressure gradient is the same in both. For a given set of values of the flow system parameters, a domain of admissible flow combinations is obtained. The solution is determined by assuming that each point in this domain has equal probability of being `visitedʹ. This leads to unique values for the flow arrangement variables (FAV), the rate of mechanical energy dissipation, and the relative permeabilities. The new model accounts for the non-linearity of the flow as well as for the effects of all the system parameters (notably those affecting interfaces), and its predictions are in very good agreement with existing data.