The characteristics-mixed finite element method for enhanced oil recovery simulation and optimal order \(L^ 2\) error estimate
In order to drive more crude oil from a waterflooded oil field, a practical approach by means of adding chemicals (such as polymers, surfactants and alcohol, etc.) into the flooding fluid has been developed by Chinese field engineers in the past ten years. For theoretical analysis of such an important mathematical model employed for enhanced oil recovery in an oil deposit, the two-dimensional material balance equations for multi-component and multi-phase Darcy flow are established. For solving the material balance equations, a characteristics-mixed element scheme, considering the cross interference, is suggested by the author. The existence and uniqueness of the mixed finite element solution can be easily demonstrated by known theory [\textit{M. F. Wheeler}, SIAM J. Numer. Analysis 10, 723-759 (1973; Zbl 0258.35041); \textit{F. Brezzi}, Revue Franc. Automat. Inform. Rech. operat. 8, R-2, 129-151 (1974; Zbl 0338.90047)] for approximating solution. The convergence analysis of the solution is also intensively studied and proved. It is gained the optimal error estimate in \(L^ 2\) norm.
scientific article; zbMATH DE number 541470