Calculating the internodal transmissibilities using finite analytic method and its application for multi‐phase flow in heterogeneous porous media

Abstract

In the traditional numerical reservoir simulations, the internodal transmissibility is usually defined as the harmonic mean of the permeabilities of the adjacent grids. This definition underestimates the phase flux and the speed of the saturation front, especially for the strong heterogeneous case. In this article, the internodal transmissibility is recalculated according to the nodal analytic solution. The redefined internodal transmissibility can be used directly to calculate the multiphase flow in the numerical reservoir simulations. Numerical examples show that, compared to the traditional numerical methods, the proposed scheme makes the convergences much faster as the refinement parameter increases, and the accuracy is independent of the heterogeneity. calculated from the relation (21) rather than the traditional harmonic mean algorithm. NUMERICAL EXAMPLES Example Ia test from SPE comparative solution projectA test from SPE Comparative Solution Project [11] is performed here. The model is a two-phase (oil and gas) flow, where fluids are assumed to be incompressible and immiscible. The oil is displaced by the gas from the injection well to the producing well. The simulation area is 762 m long, 7.62 m wide and 15.24 m thick. The grid system is of 100 × 1 × 20 uniform cubic cells. Thus, Δx = 7.62m, Δy = 7.62m and Δz = 0.762m. It is in fact a 2D case. Other conditions, such as the permeability distribution, porosity, viscosities, densities and the relative permeability curve, can be found in the corresponding website (http://www.spe.org/web/csp/datasets/set01.htm). The gas is injected from a well located at the cell (1,1,10) and the dead oil is produced from a well located at the cell 84 X.-L. ZHENG ET AL.

Numerical and experimental investigation on the performance of hybrid porous gas journal bearings

“…Assuming the porous graphite has the same permeability in different directions, the gas in the porous graphite is expressed based on Darcy's law as follow 18 : where ρ is the gas density, μ is the gas viscosity, p is the gas pressure and k is the permeability of porous graphite.…”

“…Assuming the porous graphite has the same permeability in different directions, the gas in the porous graphite is expressed based on Darcy's law as follow 18 :…”

Finite analytical method on corner‐point grid for fluid flow in heterogeneous porous media

“…To improve the accuracy of calculating the internodal transmissibility, the FAM for the flow in heterogeneous porous media was constructed by Liu and Wang. [12][13][14][15][16][17][18][19] The local analytical solution of the quasi-Laplacian equation containing the singular point was found, and based on this, the internodal transmissibility of the two adjacent cells can be calculated accurately. The effect of applying the interface transmissibility calculated from FAM is amazing, and its biggest advantage is that its accuracy is independent of the strength of heterogeneity.…”

“…It is known that the harmonic mean algorithm underestimates the interface flux, especially for strong heterogeneities, and the error is unbounded. To improve the accuracy of calculating the internodal transmissibility, the FAM for the flow in heterogeneous porous media was constructed by Liu and Wang 12–19 . The local analytical solution of the quasi‐Laplacian equation containing the singular point was found, and based on this, the internodal transmissibility of the two adjacent cells can be calculated accurately.…”