Multi-phase multi-component flow processes are fundamental to engineering applications in hydrocarbon and geothermal reservoirs but also to many classical geological processes. This review will highlight recent developments in the mathematical modelling and numerical simulations of the underlying physical processes from the pore- to the reservoir scale. Many modern approaches now rely on integrating numerical and analytical methods and incorporate results across the different length scales. This provides new insights into the fundamental properties of multi-phase multi-component flow and helps to mitigate some of the inherent difficulties in quantifying them in subsurface reservoirs.

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We present a finite element - finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. The advantage of the proposed methodology with respect to other pore-scale modelling approaches is that no simplifications regarding the geometry of the porous space are required and no approximations to the flow equations are introduced. We apply this method in a proof-of-concept study of a digitised Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale transport and diffusion of the adsorbing solute. We also demonstrate how analysis of the pore geometry can be used to identify the locations of oil during the two-phase flow and couple this with the reactive transport modeling to show how this procedure can be used to estimate the potential of the enhanced oil recovery techniques.

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Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element-finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection-diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion D_m of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated.

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We present a finite element-finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. We solve the stationary Stokes equation on the computational domain with the FE method using the same set of nodes and the same order of basis functions for both velocity and pressure. The resulting linear system is solved by employing the algebraic multigrid library SAMG. To simulate large 3D samples we partition them into subdomains and treat each separately on a different computing node. This approach allows us to use meshes with millions of elements as input geometries without facing limitations in computer resources. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale solute transport and diffusion. This allows us to demonstrate the correct emerging behaviour of sample s hydrodynamic dispersivity. Finally, we model the transport of an adsorbing solute and the surface coverage dynamics is demonstrated. This information can be used to estimate the local change of a sample wettability state and the ensuing changes of the two-phase flow characteristics.@en

We have developed a new finite element - finite volume based simulation approach to study flow and transport processes at sub-grid scales, i.e. at scales below the typical size of a reservoir simulation grid block, using real 3D geometries in carbonate reservoirs. We complement the simulations by high-resolution X-Ray CT experiments which provide us with the 3D structures, allow us to visualise flow processes at the core-scale in real time, and help us to compare the observed processes to numerical simulations to validate and verify the latter. We use this combined numerical-experimental approach to analyse the fundamental processes controlling fluid flow in carbonates at sub-grid scales. Results can be incorporated in existing reservoir simulation workflows to increase the confidence in reservoir performance forecasting. We show applications related to fractured carbonate reservoirs and enhanced oil recovery processes due to injection of low-salinity fluids and hot water.@en