Abstract
A kind of second-order implicit upwind fractional steps finite difference method is presented in this paper to numerically simulate the coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and optimal order error estimates in l2 norm are derived.
Highlights
A mass of residual crude oil stays in the reservoir after water-flooding exploiting because of the constraint of capillary force preventing the motion and the slight influence of injected water and the undesirable fluidity ratio between displacement phase and driven phase weakening the displacement force
A kind of second-order implicit upwind fractional steps finite difference method is presented in this paper to numerically simulate the coupled system of enhanced oil production in porous media
This paper discusses a second-order upwind fractional steps difference method for numerical simulation of enhanced oil production in porous media, and gives the theoretical analysis
Summary
A mass of residual crude oil stays in the reservoir after water-flooding exploiting because of the constraint of capillary force preventing the motion and the slight influence of injected water and the undesirable fluidity ratio between displacement phase and driven phase weakening the displacement force. Axelsson, Ewing, and Lazarov present upwind finite differences (Axelsson & Gustafasson, 1979; Ewing, Lazarov & Vassilevski, 1994; Lazarov, Mishev & Vassilevski, 1996) It can overcome numerical oscillation and cancel extra interpolation computation of grids nearby the boundary along characteristics. Considering actual application, numerical stability and accuracy, the authors present one second-order upwind fractional steps finite difference method for three-dimensional compressible two-phase displacement coupled problem of enhanced oil production. This algorithm can overcome numerical oscillation and dispersion, and decrease the computational scale by decomposition three-dimensional problem into three successive one-dimensional subproblems. M and ε denote a general positive constant and a general positive small constant, respectively, and they may have different meanings at different places
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