Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

Abstract

We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speedup in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.

Numerical simulation of the impact of polymer rheology on polymer injectivity using a multilevel local grid refinement method

“…However, it was pointed out that it generated high truncations (Rasaei and Sahimi 2009). Gerritsen and Lambers (2008) proposed in their anisotropic grid adaptivity method to use bilinear interpolation to obtain pressures of the auxiliary points (such as P i1 ð Þ and P i2 ð Þ in Fig.…”

“…Forsyth and Sammon (1986) developed an LGR algorithm with a rigorous analysis of discretization of flow equations upon the composite grid geometry. However, the accuracy of their numerical scheme is reported to be low because a direct subtraction of pressures of two adjacent blocks is used to calculate the Darcy velocity across the block interface (Rasaei and Sahimi 2009). Nacul et al (1990) proposed an LGR technique using a domain decomposition method, in which overlapping boundaries are used for the subdomains.…”

Effect of connectivity misrepresentation on accuracy of upscaled models in oil recovery by CO2 injection

“…The non‐uniform coarsening creates smaller grid blocks inside the regions whose pressures or saturations rapidly change. These models may be obtained based on minimizing heterogeneity over fine grids, vorticity of velocity field, or a wavelet transform of a permeability map . The renormalization method estimates the effective permeability by analogy with the concept of equivalent resistor .…”

Wavelet analysis of characteristic length scales and orientation of two-dimensional heterogeneous porous media

“…In two dimensions, analyses have also been conducted to identify anisotropic spatial variations of rainfall [19,20], rock composition [14,15], soil thickness, surface slope, and direct solar radiation [24], and permeability [29,42]. Wavelets have also been applied to upscaling of porous medium properties [7][8][9]28,[32][33][34]36]. More wavelet applications in geophysics can be found in [11].…”