Theory of Viscous Fingering in Two Phase, Three Component Flow

Abstract

ABSTRACT When a mobile fluid, such as gas, displaces less mobile fluids, such as oil and water, a viscous instability develops and the injected fluid fingers through the system leading to early breakthrough and poor recovery. In a WAG process (Water Alternate Gas) water and a miscible solvent (gas) are injected into a reservoir containing water and oil. Compared with a miscible flood, when only solvent is injected, fingering can be suppressed by the simultaneous injection of water, if it reduces the apparent mobility contrast between the injected and displaced fluids. In order to understand and control this instability, it is necessary to be able to predict the expected extent of fingering. The behavior of a miscible flood, with only hydrocarbon flowing, can be modeled successfully using a Todd & Longstaff fractional flow. We modify the Todd and Longstaff model self-consistently to account for fingering in multi-component systems. The method is verified for WAG floods. The empirical flow equations are solved analytically in one dimension and the results are in excellent agreement with the averaged saturation and concentration profiles computed using two dimensional high resolution simulation, for a variety of injected water saturations, in both secondary and tertiary displacements.