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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508
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A LOCAL EXPANSION METHOD FOR SOLVING THE MACROSCOPIC MOMENTUM EQUATION OF THE SINGLE PHASE FLOW IN HIGHLY PERMEABLE POROUS MEDIA
ABSTRAKT
The macroscopic momentum equation is derived from the pore-scale Navier–Stokes equations using the volume averaging method. The macroscopic pressure gradient can be expressed as a power series of the averaged velocity with a group of tensorial coefficients. Each tensorial coefficient is intrinsic and can be calculated by solving its corresponding closure problem. Thus the specific form of the cubic filtration law for isotropic porous structure in weak inertia regime can be determined from the power series equation. In order to avoid the complex calculations of the tensorial coefficients for the high order terms, a local expansion method is proposed where only a series of auxiliary Stokes problems are successively solved. In the procedure of the derivation of the filtration law for fluid flows in porous media considering the inertial effects, the proposed method can avoid the complex calculations of solving the full Navier–Stokes equations and therefore reduce computation cost tremendously. Several numerical tests are performed and the numerical results are consistent with the calculations published in previous literature.