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Theory and application of numerical simulation method of capillary force enhanced oil production

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Abstract

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced (chemical) oil production with capillary force in the porous media. Some techniques, e.g., the calculus of variations, the energy analysis method, the commutativity of the products of difference operators, the decomposition of high-order difference operators, and the theory of a priori estimate, are introduced. An optimal order error estimate in the l 2 norm is derived. The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields. The simulation results are satisfactory and interesting.

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Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan, 250100, China

    Yirang Yuan, Aijie Cheng, Danping Yang, Changfeng Li & Yunxin Liu

Authors
  1. Yirang Yuan
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  2. Aijie Cheng
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  3. Danping Yang
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  4. Changfeng Li
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  5. Yunxin Liu
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Corresponding author

Correspondence to Yirang Yuan.

Additional information

Project supported by the Major State Basic Research Development Program of China (No. G19990328), the National Natural Science Foundation of China (Nos. 10771124, 10372052, and 11101244), the National Tackling Key Problems Program of China (Nos. 2011ZX05011-004, 2011ZX05052, and 2005020069), the Doctorate Foundation of the Ministry of Education of China (No. 20030422047), and the Natural Science Foundation of Shandong Province of China (No. ZR2011AM015)

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Yuan, Y., Cheng, A., Yang, D. et al. Theory and application of numerical simulation method of capillary force enhanced oil production. Appl. Math. Mech.-Engl. Ed. 36, 379–400 (2015). https://doi.org/10.1007/s10483-015-1917-6

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  • DOI: https://doi.org/10.1007/s10483-015-1917-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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