Mark L. Porter

Measurement and prediction of the relationship between capillary pressure, saturation, and interfacial area in a NAPL-water-glass bead system

(1) In this work, the constitutive relationship between capillary pressure (Pc), saturation (Sw), and fluid-fluid interfacial area per volume (IFA) is characterized using computed microtomography for drainage and imbibition experiments consisting of a nonaqueous phase liquid and water. The experimentally measured relationship was compared to a thermodynamic model that relates the area under the PcSw curve to the total IFA, an, and the capillary-associated IFA, anw. Surfaces were fit to the experimental and modeled PcSwan and PcSwanw data in order to characterize the relationship in three dimensions (3D). For the experimental system, it was shown that the PcSwan relationship does not exhibit hysteresis. The model is found to provide a reasonable approximation of the magnitude of the 3D surfaces for an and anw, with a mean absolute percent error of 26% and 15%, respectively. The relatively high mean absolute percent errors are primarily the result of discrepancies observed at the wetting- and nonwetting-phase residual saturation values. Differences in the shapes of the surfaces are noted, particularly in the curvature (arising from the addition of scanning curves and presence of anSw hysteresis in the predicted results) and endpoints (particularly the inherent nature of thermodynamic models to predict significant anw associated with residual nonwetting-phase saturation). Overall, the thermodynamic model is shown to be a practical, inexpensive tool for predicting the PcSwan and PcSwanw surfaces from PcSw data. Citation: Porter, M. L., D. Wildenschild, G. Grant, and J. I. Gerhard (2010), Measurement and prediction of the relationship between capillary pressure, saturation, and interfacial area in a NAPL-water-glass bead system, Water Resour. Res., 46, W08512,

Understanding hydraulic fracturing: a multi-scale problem

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical and experimental efforts/methods. At the field scale, we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir. At the core scale, we use triaxial fracture experiments and a finite-discrete element model to study dynamic fracture/crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore-scale flow and transport phenomena, including multi-phase flow and fluids mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs. Finally, we discuss the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities, beyond its environmental advantages. This article is part of the themed issue ‘Energy and the subsurface’.

Taxila LBM: a parallel, modular lattice Boltzmann framework for simulating pore-scale flow in porous media

The lattice Boltzmann method is a popular tool for pore-scale simulation of flow. This is likely due to the ease of including complex geometries such as porous media and representing multiphase and multifluid flows. Many advancements, including multiple relaxation times, increased isotropy, and others have improved the accuracy and physical fidelity of the method. Additionally, the lattice Bolzmann method is computationally very efficient, thanks to the explicit nature of the algorithm and relatively large amount of local work. The combination of many algorithmic options and efficiency means that a software framework enabling the usage and comparison of these advancements on computers from laptops to large clusters has much to offer. In this paper, we introduce Taxila LBM, an open-source software framework for lattice Boltzmann simulations. We discuss the design of the framework and lay out the features available, including both methods in the literature and a few new enhancements which generalize methods to complex geometries. We discuss the trade-off of accuracy and performance in various methods, noting how the Taxila LBM makes it easy to perform these comparisons for real problems. And finally, we demonstrate a few common applications in pore-scale simulation, including the characterization of permeability of a Berea sandstone and analysis of multifluid flow in heterogenous micromodels.

Upscaling Diffusion and Nonlinear Reactive Mass Transport in Homogeneous Porous Media

In this work, we revisit the upscaling process of diffusive mass transfer of a solute undergoing a homogeneous reaction in porous media using the method of volume averaging. For linear reaction rate kinetics, the upscaled model exhibits a vis-à-vis correspondence with the mass transfer governing equation at the microscale. When nonlinear reactions are present, other methods must be adopted to upscale the nonlinear term. In this work, we explore a linearization approach for the purpose of solving the associated closure problem. For large rates of nonlinear reaction relative to diffusion, the effective diffusion tensor is shown to be a function of the reaction rate, and this dependence is illustrated by both numerical and analytical means. This approach leads to a macroscale model that also has a similar structure as the microscale counterpart. The necessary conditions for the vis-à-vis correspondence are clearly identified. The validation of the macroscale model is carried out by comparison with pore-scale simulations of the microscale transport process. The predictions of both concentration profiles and effectiveness factors were found to be in acceptable agreement. In an appendix, we also briefly discuss an integral formulation of the nonlinear problem that may be useful in developing more accurate results for the upscaled transport and reaction equations; this approach requires computing the Green function corresponding to the linear transport problem.

Heterogeneity‐enhanced gas phase formation in shallow aquifers during leakage of CO2‐saturated water from geologic sequestration sites

A primary concern for geologic carbon storage is the potential for leakage of stored carbon dioxide (CO2) into the shallow subsurface where it could degrade the quality of groundwater and surface water. In order to predict and mitigate the potentially negative impacts of CO2 leakage, it is important to understand the physical processes that CO2 will undergo as it moves through naturally heterogeneous porous media formations. Previous studies have shown that heterogeneity can enhance the evolution of gas phase CO2 in some cases, but the conditions under which this occurs have not yet been quantitatively defined, nor tested through laboratory experiments. This study quantitatively investigates the effects of geologic heterogeneity on the process of gas phase CO2 evolution in shallow aquifers through an extensive set of experiments conducted in a column that was packed with layers of various test sands. Soil moisture sensors were utilized to observe the formation of gas phase near the porous media interfaces. Results indicate that the conditions under which heterogeneity controls gas phase evolution can be successfully predicted through analysis of simple parameters, including the dissolved CO2 concentration in the flowing water, the distance between the heterogeneity and the leakage location, and some fundamental properties of the porous media. Results also show that interfaces where a less permeable material overlies a more permeable material affect gas phase evolution more significantly than interfaces with the opposite layering.

Intermediate-Scale Experimental Study to Improve Fundamental Understanding of Attenuation Capacity for Leaking CO2 in Heterogeneous Shallow Aquifers

To assess the risks of Geologic Carbon Sequestration (GCS), it is crucial to understand the fundamental physicochemical processes that may occur if and when stored CO2 leaks upward from a deep storage reservoir into the shallow subsurface. Intermediate-scale experiments allow for improved understanding of the multiphase evolution processes that control CO2 migration behavior in the subsurface, because the boundary conditions, initial conditions, and porous media parameters can be better controlled and monitored in the laboratory than in field settings. For this study, a large experimental test bed was designed to mimic a cross section of a shallow aquifer with layered geologic heterogeneity. As water with aqueous CO2 was injected into the system to mimic a CO2-charged water leakage scenario, the spatiotemporal evolution of the multiphase CO2 plume was monitored. Similar experiments were performed with two different sand combinations to assess the relative effects of different types of geologic facies transitions on the CO2 evolution processes. Significant CO2 attenuation was observed in both scenarios, but by fundamentally different mechanisms. When the porous media layers had very different permeabilities, attenuation was caused by local accumulation (structural trapping) and slow redissolution of gas phase CO2. When the permeability difference between the layers was relatively small, on the other hand, gas phase continually evolved over widespread areas near the leading edge of the aqueous plume, which also attenuated CO2 migration. This improved process understanding will aid in the development of models that could be used for effective risk assessment and monitoring programs for GCS projects.

Bacterial Chemotaxis in Porous Media: Theory Derivation and Comparison with Experiments

Chemotaxis is the movement of organisms toward or away from the concentration gradient of a chemical species. Microbial chemotaxis has been shown to significantly increase contaminant degradation in subsurface environments with respect to traditional methods such as pump‐and‐treat. This type of transport phenomena often involves diffusion and convection along several scales. In this work we use the method of volume averaging to upscale the governing equations for in situ bioremediation by bacterial chemotaxis. The results are effective medium mass balance equations for both the bacteria and the chemical attractant. These equations are expressed in terms of average transport coefficients, which can be computed from the solution of the associated closure problems. For the bacteria, we introduce a total motility tensor and a total velocity vector, which are dependent upon the porous medium geometry, the fluid flow and the macroscale concentration and flux of the attractant. An attractive feature of this appr...

Dynamic Effects in Oil/Water and Air/Water Capillary Pressure-Saturation Curves: Experiments and Lattice-Boltzmann Simulations

The capillary pressure-saturation curve is widely used to characterize hydraulic properties of porous media. It is often assumed that curves measured under equilibrium or steady-state flow conditions can be applied to transient flow conditions, and vice versa. Yet, substantial experimental evidence suggests that capillary pressure-saturation curves obtained during transient conditions differ from those obtained under equilibrium or steady-state conditions. It has been shown that the capillary pressure-saturation curve shows signs of dynamic behavior depending on the inflow and outflow rate applied to the porous system. The exact cause of the observed shift is not yet fully understood. It is hypothesized that the mechanisms responsible for dynamic behavior include: (1) the geometry of the pore space, (2) interfacial phenomena at the pore scale, and (3) the interplay of inertial and viscous forces. In this investigation, air/water and oil/water imbibition and drainage experiments were conducted on a column of packed glass beads. Various inflow and outflow rates were applied to each multi-phase system, which resulted in capillary pressure-saturation curves that exhibit varying degrees of dynamic behavior. The dynamic behavior observed in preliminary oil/water experiments was less pronounced than the behavior observed in past air/water experiments. This suggests that the viscous and inertial forces may only be a major factor when the density and viscosity ratios are large, as is the case for the air/water system. The dynamic behavior was examined using conceptual 2D and 3D lattice-Boltzmann (LB) simulations. We used the multi-phase, multi-component model developed by Shan and Chen for these simulations. The conceptual LB simulations can provide insights into pore-scale interfacial phenomena and help explain the dynamic behavior observed in the experiments. Scaling of time and space from LB parameters to physical parameters was performed to make comparisons between simulation and experimental results possible.

Linking Experimental Capillary Pressure-Saturation Data with Lattice Boltzmann Simulations.

Recent advances in observational and computational techniques have facilitated the study of fluid dynamics and interfacial geometry in porous media. Within some experimental limitations, computed tomography X-ray (CMT) and magnetic resonance imaging (MRI) are now able to accurately map the 3D structure of porous geometries. Computational advances largely concern Lattice Boltzmann (LB) method that has been shown to be useful in simulating microscale flow in porous media. With some phenomenological or thermodynamic extensions, the LB method is also able to deal with microscale interfacial phenomena in single or multiphase systems. The goal of this presentation is to provide insight into what is needed to make a link between 3D experimental observations of interfacial geometry and LB simulations. The experimental data consist of CMT observations several Sotrol-water displacements inside a glass bead system with a resolution of 17 microns. Also available are capillary pressure-saturation curves between 0 and 1kPa. The LB model is that of Shan-Chen as modified by Martys and Chen (1996). We present the most parsimonious way to calibrate the surface tension and contact angle in the model, define space, pressure and time scaling. We will also identify potential problems relating to pore-size and digitization effects that are present in the simulations, but not in the original observations. The analyses are partly performed on idealized systems and finally applied to large scale (107 voxel) simulations of the real physical systems. Observations are simulations are compared in terms of pressure-saturation curves, and where possible, in terms of fluid distribution and interfacial curvatures.