2011/07/27 by Petr N. Vabishchevich, Vabishchevich, P., Maria V. Vasileva +3
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #65F10 #65N22 #76S05 #Advanced Computational Techniques in Science and Engineering #Advanced Numerical Methods in Computational Mathematics #Aquatic and Environmental Studies #Differential Equations and Numerical Methods #FOS: Mathematics #Geotechnical and Geomechanical Engineering #Numerical Analysis (math.NA) #Reservoir Engineering and Simulation Methods
paper · pdf · doi:10.48550/arxiv.1107.5479
openalex publication_date 2011/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Applied problems of oil and gas recovery are studied numerically using the\nmathematical models of multiphase fluid flows in porous media. The basic model\nincludes the continuity equations and the Darcy laws for each phase, as well as\nthe algebraic expression for the sum of saturations. Primary computational\nalgorithms are implemented for such problems using the pressure equation. In\nthis paper, we highlight the basic properties of the pressure problem and\ndiscuss the necessity of their fulfillment at the discrete level. The resulting\nelliptic problem for the pressure equation is characterized by a\nnon-selfadjoint operator. Possibilities of approximate solving the elliptic\nproblem are considered using the iterative methods. Special attention is given\nto the numerical algorithms for calculating the pressure on parallel computers.\n