An implicit two-phase numerical simulator for modeling secondary water recovery by air injection

Abstract

A secondary water recovery operation was proposed in order to recover additional amounts of water stored in the unsaturated zone of depleted aquifers and currently unavailable with conventional techniques. The proposed operation consisted of three stages: an air injection stage, a recovery stage, and a production stage. Hysteresis was counted upon to prevent water, forced into the saturated zone from the unsaturated zone during air injection, from migrating back to the unsaturated zone. A Finite Difference (FD) two-phase flow numerical model, based on techniques of petroleum reservoir engineering, was developed to simulate the process of secondary water recovery. Increased levels of "implicitness" and a Simultaneous Solution formulation were introduced in order to alleviate potential numerical instability problems, due to the extreme non-linearities inherent in the treatment of air compressibility, capillarity, and hysteresis. A new direct matrix solving method, the MEPC D4 was developed in order to drastically reduce the execution time and storage requirements for the solution of the FD equations. The model was able to handle large time-steps, extremely non-linear conditions and unstable flow regimes, giving stable non-oscillatory solutions and maintaining very accurate phase material balance ([less than or equal to] 3.5 x 10 ⁻⁶ [o/o]). The model was verified against analytical and numerical solutions available in the oil industry. The numerical simulation indicated that the secondary water recovery could be technically feasible in aquifers with low intrinsic permeabilities, high permeability ratios, thick unsaturated zones, confining top layers, and high residual air saturations. Injection at the top of the unsaturated zone, venting the well immediately after the end of injection, low injection rates and large volumes of injected air seemed to enhance water recovery.