Transport Phenomena Modelled on Pore-Space Images

Fluid flow and dispersion of solute particles are modelled directly on three-dimensional pore-space images of rock samples. To simulate flow, the finite-difference method combined with a standard predictor-corrector procedure to decouple pressure and velocity is applied. We study the permeability and the size of representative elementary volume (REV) of a range of consolidated and unconsolidated porous media. We demonstrate that the flow-based REV is larger than for geometry-based properties such as porosity and specific surface area, since it needs to account for the tortuosity and connectedness of the flow paths. For solute transport we apply a novel streamline-based algorithm that is similar to the Pollock algorithm common in field-scale reservoir simulation, but which employs a semi-analytic formulation near solid boundaries to capture, with sub-grid resolution, the variation in velocity near the grains. A random walk method is used to account for mixing by molecular diffusion. The algorithm is validated by comparison with published results for Taylor-Aris dispersion in a single capillary with a square cross-section. We then accurately predict experimental data available in the literature for longitudinal dispersion coefficient as a function of Peclet number. We study a number of sandpack, sandstone and carbonate samples for which we have good quality three-dimensional images. There is a power-law dependence of dispersion coefficient as a function of Peclet number, with an exponent that is a function of pore-space heterogeneity: the carbonates we study have a distinctly different behaviour than sandstones and sandpacks. This is related to the differences in transit time probabilities of solute particles travelling between two neighbouring voxels. We then study the non-Fickian behaviour of solute transport in porous media by modelling the NMR propagators and the time-dependent dispersion coefficients of different rock types. The behaviour is explained using Continuous Time Random Walk (CTRW) theory: transport is qualitatively different for the complex porous media such as carbonates compared to the sandstone or sandpack, with long tailing and an almost immobile peak concentration. We discuss extensions of the work to reactive transport and the simulation of transport in finely-resolved images with billions of voxels

DeepAngle: Fast calculation of contact angles in tomography images using deep learning

DeepAngle is a machine learning-based method to determine the contact angles of different phases in the tomography images of porous materials. Measurement of angles in 3--D needs to be done within the surface perpendicular to the angle planes, and it could become inaccurate when dealing with the discretized space of the image voxels. A computationally intensive solution is to correlate and vectorize all surfaces using an adaptable grid, and then measure the angles within the desired planes. On the contrary, the present study provides a rapid and low-cost technique powered by deep learning to estimate the interfacial angles directly from images. DeepAngle is tested on both synthetic and realistic images against the direct measurement technique and found to improve the r-squared by 5 to 16% while lowering the computational cost 20 times. This rapid method is especially applicable for processing large tomography data and time-resolved images, which is computationally intensive. The developed code and the dataset are available at an open repository on GitHub (https://www.github.com/ArashRabbani/DeepAngle)

Insights, Trends and Challenges Associated with Measuring Coal Relative Permeability

Due to the poroelasticity of coal, both porosity and permeability change over the life of the field as pore pressure decreases and effective stress increases. The relative permeability also changes as the effective stress regime shifts from one state to another. This paper examines coal relative permeability trends for changes in effective stress. The unsteady-state technique was used to determine experimental relativepermeability curves, which were then corrected for capillary-end effect through history matching. A modified Brooks-Corey correlation was sufficient for generating relative permeability curves and was successfully used to history match the laboratory data. Analysis of the corrected curves indicate that as effective stress increases, gas relative permeability increases, irreducible water saturation increases and the relative permeability cross-point shifts to the right

Effective permeability of an immiscible fluid in porous media determined from its geometric state

Based on the phenomenological extension of Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process/path dependent with an underlying dependency on pore structure. For applications, fuel cells to underground $CO_2$ storage, it is imperative to determine the effective phase permeability relationships where the traditional approach is based on the inverse modelling of time-consuming experiments. The underlying reason is that the fundamental upscaling step from pore to Darcy scale, which links the pore structure of the porous medium to the continuum hydraulic conductivities, is not solved. Herein, we develop an Artificial Neural Network (ANN) that relies on fundamental geometrical relationships to determine the mechanical energy dissipation during creeping immiscible two-fluid flow. The developed ANN is based on a prescribed set of state variables based on physical insights that predicts the effective permeability of 4,500 unseen pore-scale geometrical states with $R^2 = 0.98$.Comment: 6 Pages, 2 Figures, and Supporting Materia

Digital Rock Segmentation for Petrophysical Analysis With Reduced User Bias Using Convolutional Neural Networks

Pore‐scale digital images are usually obtained from microcomputed tomography data that has been segmented into void and grain space. Image segmentation is a crucial step in the process of digital rock analysis that can influence pore‐scale characterization studies and/or the numerical simulation of petrophysical properties. This is concerning since all segmentation methods have user‐selected parameters that result in biases. Convolutional neural networks (CNNs) provide a way forward since once trained, CNN can provide consistent and reliable image segmentation with no user‐defined inputs. In this paper, a CNN is used to segment digital sandstone data, and various ground truth data sets are tested. The ground truth images are created based on high‐resolution microcomputed tomography data and corresponding scanning electron microscope data. The results are evaluated in terms of porosity, permeability, and pore size distribution computed from the segmented data. We find that watershed‐based segmentation provides a wide range of possible petrophysical values depending on user‐selected thresholds, whereas CNN provides a smaller variance when trained on scanning electron microscope data. It can be concluded that CNN offers a reliable and consistent way to segment digital sandstone data for petrophysical analyse

The impact of wettability on the co-moving velocity of two-fluid flow in porous media

The impact of wettability on the co-moving velocity of two-fluid flow in porous media is analyzed herein. The co-moving velocity, developed by Roy et al. (2022), is a novel representation of the flow behavior of two fluids through porous media. Our study aims to better understand the behavior of the co-moving velocity by analyzing simulation data under various wetting conditions. The simulations were conducted using the Lattice-Boltzmann color-fluid model and evaluated the relative permeability for different wetting conditions on the same rock. The analysis of the simulation data followed the methodology proposed by Roy et al. (2022) to reconstruct a constitutive equation for the co-moving velocity. Surprisingly, it was found that the coefficients of the constitutive equation were nearly the same for all wetting conditions. Based on these results, a simple approach was proposed to reconstruct the oil phase relative permeability using only the co-moving velocity relationship and water phase relative permeability. This proposed method provides new insights into the dependency of relative permeability curves, which has implications for the history matching of production data and solving the associated inverse problem. The research findings contribute to a better understanding of the impact of wettability on fluid flow in porous media and provide a practical approach for estimating relative permeability based on the co-moving velocity relationship, which has never been shown before.Comment: 14 pages, 6 figure