Acta mathematica scientia, Series B >

2018 , Vol. 38 >Issue 2: 519 - 545

DOI: https://doi.org/10.1016/S0252-9602(18)30764-1

Articles

CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM

  • Yirang YUAN ,
  • Aijie CHENG ,
  • Dangping YANG ,
  • Changfeng LI ,
  • Qing YANG
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  • 1. Institute of Mathematics, Shandong University, Jinan 250100, China;
    2. School of Economics, Shandong University, Jinan 250100, China

Received date: 2016-08-22

  Revised date: 2017-05-25

  Online published: 2018-04-25

Supported by

Supported by the National Natural Science Foundation of China (11101124 and 11271231), Natural Science Foundation of Shandong Province (ZR2016AM08), and National Tackling Key Problems Program (2011ZX05052, 2011ZX05011-004)

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Abstract

The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in l2 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.

Key words： Chemical oil recovery; mixed volume element-characteristic mixed volume element; characteristic fractional step differences; local conservation of mass; second-order error estimate in l2-norm

Cite this article

Yirang YUAN , Aijie CHENG , Dangping YANG , Changfeng LI , Qing YANG . CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM[J]. Acta mathematica scientia, Series B, 2018 , 38(2) : 519 -545 . DOI: 10.1016/S0252-9602(18)30764-1

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