Computation of fluid flow and pore-space properties estimation on micro-CT images of rock samples

This work was jointly sponsored by EPSRC (EP/I010971/1) and NSFC China.Peer reviewedPostprin

An explicit stabilised finite element method for Navier-Stokes-Brinkman equations

We present an explicit stabilised finite element method for solving Navier-Stokes-Brinkman equations. The proposed algorithm has several advantages. First, the lower equal-order finite element space for velocity and pressure is ideal for presenting the pixel images. Stabilised finite element allows the continuity of both tangential and normal velocities at the interface between regions of different micro-permeability or at the interface free/porous domain. Second, the algorithm is fully explicit and versatile for describing complex boundary conditions. Third, the fully explicit matrix–free finite element implementation is ideal for parallelism on high-performance computers. In the last, the implicit treatment of Darcy term allowed larger time stepping and a stable computation, even if the velocity varies for several orders of magnitude in the micro-porous regions (Darcy regime). The stabilisation parameter, that may affect the velocity field, has been discussed and an optimal parameter was chosen based on the numerical examples. Velocity stability at interface between different micro-permeability has been also studied with mesh refinement. We analysed the influence of the micro-permeability field on the regime of the flow (Stokes flow, Darcy flow or a transitional regime). These benchmark tests provide guidelines for choosing the resolution of the grayscale image and its segmentation. We applied the method on real Berea Sandstone micro-CT images, and proceeded the three-phases segmentation. We studied the influence of the micro-porosity field, using the well-known Kozeny-Carman relation to derive the micro-permeability field from the micro-porosity field, on the effective permeability computed. Our analysis shows that a small fraction of micro-porosity in the rock has a significant influence on the effective permeability computed

New stochastic pore-scale simulation and machine learning approach to predicting permeability and tortuosity of heterogeneous porous media

A new 3D stochastic pore-scale simulation approach was introduced in this study to investigate how stochastic pore connectivity impacts the permeability and hydraulic tortuosity of heterogeneous porous media. Multiple three-dimensional pore microstructures with the same porosity, pore size distribution, and number of pores were created to examine the role that pore connectivity plays in permeability and hydraulic tortuosity of rocks. According to the findings of this study, stochastic pore connectivity has a sizeable influence on permeability but a comparatively insignificant influence on hydraulic tortuosity. In addition, there is a negative correlation between the amount of heterogeneity and the predictability of permeability based on hydraulic tortuosity. The study used four carbonate and five siliciclastic rock cores to validate the findings, and the predicted permeability was generally closer to the measured permeability than five popular empirical model equations. In addition, machine learning was utilized to optimize the workflow, which resulted in a reduction in the necessary number of pore-scale simulations by a factor of 157 and the reproduction of pore-scale permeability estimates was with a mean absolute percentage error of 10%. The conventional use of SEM and micro-CT technologies in generating pore microstructures was augmented through the addition of MICP data to capture high-resolution information in rocks at a representative scale. Pore microstructures generated through the approach were validated via a comparable permeability of the pore microstructure with the measured permeability of the rock sample modelled. The findings of this study has a broad range of geoscience applications including, petroleum exploration and production, carbon storage, environmental protection, and groundwater exploration