Abstract
A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in $l^2$ norm. Numerical example is given to testify theoretical analysis and numerical data show that this method is effective in solving actual applications. Then it can solve the well-known problem.
Highlights
Mathematical Model and Physical BackgroundHigh-pressure pump injects water into oil storage and displaces crude oil out from production wells
A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined
The flow equation is discretized by the method of mixed finite element and the saturation is approximated by a domain decomposition scheme of modified characteristic finite element
Summary
High-pressure pump injects water into oil storage and displaces crude oil out from production wells. The compressibility must be considered in new numerical simulation of modern enhanced oil displacement (Douglas, & Roberts, 1983; Yuan, 1992,2013). Decomposing computational domain into several subdomains, we define a special function to approximate the value at interior boundary explicitly and obtain numerical solution implicitly in parallel in subdomains. It is an important and powerful tool in model analysis, numerical method, principle research and engineering applicable software design of modern oil reservoir exploration and development and it can solve the well-known problem (Douglas, & Roberts, 1983; Ewing, 1983; Shen, Liu, & Tang, 2002).
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