Pierre Horgue

Computational Permeability Determination from Pore-Scale Imaging: Sample Size, Mesh and Method Sensitivities

In this work, a complete work flow from pore-scale imaging to absolute permeability determination is described and discussed. Two specific points are tackled, concerning (1) the mesh refinement for a fixed image resolution and (2) the impact of the determination method used. A key point for this kind of approach is to work on enough large samples to check the representativity of the obtained evaluations, which requires efficient parallel capabilities. Image acquisition and processing are realized using a commercial micro-tomograph. The pore-scale flows are then evaluated using the finite volume method implemented in the open-source platform OpenFOAM®. For this numerical method, the influence of the different aspects mentioned above are studied. Moreover, the parallel efficiency is also tested and discussed. We observe that the level of mesh refinement has a non-negligible impact on permeability tensor. Moreover, increasing the refinement level tends to reduce the gap between the methods of computational measurements. The increase in computation time with the mesh is balanced with the good parallel efficiency of the platform.

An open-source toolbox for multiphase flow in porous media

Multiphase flow in porous media provides a wide range of applications: from the environmental understanding (aquifer, site-pollution) to industrial process improvements (oil production, waste management). Modeling of such flows involve specific volume-averaged equations and therefore specific computational fluid dynamics (CFD) tools. In this work, we develop a toolbox for modeling multiphase flow in porous media with OpenFOAM®, an open-source platform for CFD. The underlying idea of this approach is to provide an easily adaptable tool that can be used in further studies to test new mathematical models or numerical methods. The package provides the most common effective properties models of the literature (relative permeability, capillary pressure) and specific boundary conditions related to porous media flows. To validate this package, a solvers based on the IMplicit Pressure Explicit Saturation (IMPES) methodare developed in the toolbox. The numerical validation is performed by comparison with analytical solutions on academic cases. Then, a satisfactory parallel efficiency of the solver is shown on a more complex configuration.

A Comparison of Various Methods for the Numerical Evaluation of Porous Media Permeability Tensors from Pore-Scale Geometry

In this work, several boundary value problems used to numerically evaluate the absolute permeability tensors of porous media using core-scale images are compared and discussed. The various configurations differ by the type of boundary conditions used to compute the flow at the micro-scale. The issue is the ability of the method to capture anisotropy correctly and to avoid possible percolation artifacts. This study is carried on two-dimensional synthetic, isotropic or anisotropic, porous media that are chosen to illustrate the various difficulties mentioned above. A new method is proposed which consists in embedding the porous medium in question in a homogenized one. Using an iterative optimization procedure on the surrounding permeability, the method determines the absolute permeability tensor of the original medium. The equivalent permeability tensor that minimizes the effect on the surrounding porous medium is, unlike that of classical methods, de facto symmetrical due to the use of periodic boundary conditions and exhibits significantly lower permeabilities. The way in which non-diagonal terms of the permeability tensor are obtained with the various methods is thoroughly discussed.

Assessment of percolation through a solid leach bed in dry batch anaerobic digestion processes.

This work aimed at assessing water percolation through a solid cow manure leach bed in dry batch AD processes. A laboratory-scale percolation column and an experimental methodology were set up. Water behaviour was modelled by a double porosity medium approach. An experimental procedure was proposed to determine the main hydrodynamic parameters of the multiphase flow model: the porosity, the permeability and the term for water exchange from macro- to micro-porosity. Micro- and macro-porosity values ranged from 0.42 to 0.70 m(3) m(-3) and 0.18 to 0.50 m(3) m(-3). Intrinsic permeability values for solid cow manure ranged from 5.55·10(-11) to 4.75·10(-9) m(2). The term for water exchange was computed using a 2nd order model. The CFD tool developed was used to simulate successive percolation and drainage operations. These results will be used to design leachate recirculation strategies and predict biogas production in full-scale dry AD batch processes.

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

This 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.