Efficiency of a two-step upscaling method for permeability evaluation at Darcy and pore scales

Abstract

International audienceThis work presents a new subdivision method to upscale absolute permeability fields. This process, called two-step method, consists in (i) solving micro-scale equations on subdomains obtained from the full domain regular decomposition and (ii) solve a second upscaling with Darcy’s law on the permeability fields obtained in the first step. The micro-scale equations used depend on the case studied. The two-step upscaling process is validated on randomly generated Darcy-scale permeability fields by measuring the numerical error induced by upscaling. The method is then applied to real domains obtained from sandstone micro-tomographic images. The method specificities due to pore-space structure are discussed. The main advantage of the two-step upscaling method resides in the drastic reduction of computational costs (CPU time and memory usage) while maintaining a numerical error similar to that of other upscaling procedures. This new upscaling method may improve permeability predictions by the use of finer meshes or larger sample volumes

Image-based effective medium approximation for fast permeability evaluation of porous media core samples

“…Running the same 128 3 voxels image with the CFD OpenFOAM tools [23,25], the observed memory cost also scales linearly, i.e., αn. However since the α factor is close to 50, it leads to a memory cost of 128Mb for a 128 3 voxels image.…”

“…Notably, the very same CFD software was also used in the reference study [41] in order to characterize real rocks. Furthermore, OpenFOAM is also used in several recent studies dealing with real porous media [23,25], and also for other physical configurations such as two-phase flows [42], particle transport [ l l], inertial flows [36], or compressible flows [24].…”

“…CFD computations display finite-size sensitivity, whose origin is discussed in Section 3.1.l . As stressed in [23,25) even if CFD provides a sensible approximation of the permeability, it is difficult to assess its precise accuracy even when the discretization condition of a minimum of five voxels per constriction is fulfilled. It might turn that, These data are provided in [ 41].…”

Multiscale Digital Rock Imaging and Modeling for Measuring the Heterogeneous Carbonate and Conglomerate Permeability at the Laboratory Plug Scale

“…The averaging method failed to provide reliable upscaling permeability when facing the significant permeability contrasts within the highly heterogeneous rock . The two-step upscaling technique and its variation were developed to integrate different scale properties. ,, As shown in Figure , the existing two-step upscaling workflow can be implemented as the following general steps: The core plug is decomposed into a matrix of subdomains and generates a coarse grid with each subdomain corresponding to a grid block. For each micrometer-scale subdomain, the permeability is calculated based on its high-resolution pore structure. The permeability of each subdomain is mapped to the coarse grid block to compose a permeability field. Eventually, an upscaling permeability can be computed by solving the Darcy equation. …”

“…In addition, most previous upscaling studies employed the Darcy equation to lump the subdomain permeabilities into the upscaling permeability in step 3. ,, Nonetheless, the Darcy equation may be invalid for the matrix–fracture system in the carbonate rocks . This susception comes from the fact that the Darcy flow dominates the microporous matrix, while the Stokes flow is developed in the large fractures, the flux of which may be orders of magnitude higher than that in the matrix .…”