Solução do problema de Riemann para escoamento de água-óleo na presença de solvente em meio poroso.

Abstract

Solvent waterflooding was one of the first enhanced oil recovery methods in Petroleum Engineering. However, this method became economically less attractive as the solvent value increased. In the late 1970s, interest in recovery methods using solvents re-emerged due to rising oil prices and greater confidence in the recovery predictions. This prompted further studies on this topic. For example, Walsh and Lake 1989 modeled the displacement of oil by a miscible solvent in the presence of an immiscible aqueous phase. They presented a geometric solution of the corresponding Riemann problem based on the fractional flow theory without specifying the system of differential equations. The present work aims to study the system of conservation laws describing the same model as Walsh and Lake 1989. The Riemann problem was solved by classifying possible solutions according to the water saturation at the injection point. Three possibilities were found: (1) shock wave, (2) rarefaction wave, (3) composite waves. The shock wave was shown to be entropic. For this, it was proved the existence of the traveling-wave solution of the associated viscous problem connecting equilibria, corresponding to Riemann problem states, in the form of α- and ω-limits. All theoretical results were validated through numerical simulations.