Matthew T. Balhoff

Multiblock Pore-Scale Modeling and Upscaling of Reactive Transport: Application to Carbon Sequestration

In order to safely store CO2 in depleted reservoirs and deep saline aquifers, a better understanding of the storage mechanisms of CO2 is needed. Reaction of CO2 with minerals to form precipitate in the subsurface helps to securely store CO2 over geologic time periods, but a concern is the formation of localized channels through which CO2 could travel at large, localized rates. Pore-scale network modeling is an attractive option for modeling and understanding this inherently pore-level process, but the relatively small domains of pore-scale network models may prevent accurate upscaling. Here, we develop a transient, single-phase, reactive pore-network model that includes reduction of throat conductivity as a result of precipitation. The novelty of this study is the implementation of a new mortar/transport method for coupling pore networks together at model interfaces that ensure continuity of pressures, species concentrations, and fluxes. The coupling allows for modeling at larger scales which may lead to more accurate upscaling approaches. Here, we couple pore-scale models with large variation in permeability and porosity which result in initial preferential pathways for flow. Our simulation results suggest that the preferential pathways close due to precipitation, but are not redirected at late times.

Numerical Algorithms for Network Modeling of Yield Stress and other Non-Newtonian Fluids in Porous Media

Many applications involve the flow of non-Newtonian fluids in porous, subsurface media including polymer flooding in enhanced oil recovery, proppant suspension in hydraulic fracturing, and the recovery of heavy oils. Network modeling of these flows has become the popular pore-scale approach for understanding first-principles flow behavior, but strong nonlinearities have prevented larger-scale modeling and more time-dependent simulations. We investigate numerical approaches to solving these nonlinear problems and show that the method of fixed-point iteration may diverge for shear-thinning fluids unless sufficient relaxation is used. It is also found that the optimal relaxation factor is exactly equal to the shear-thinning index for power-law fluids. When the optimal relaxation factor is employed it slightly outperforms Newton’s method for power-law fluids. Newton-Raphson is a more efficient choice (than the commonly used fixed-point iteration) for solving the systems of equations associated with a yield stress. It is shown that iterative improvement of the guess values can improve convergence and speed of the solution. We also develop a new Newton algorithm (Variable Jacobian Method) for yield-stress flow which is orders of magnitude faster than either fixed-point iteration or the traditional Newton’s method. Recent publications have suggested that minimum-path search algorithms for determining the threshold pressure gradient (e.g., invasion percolation with memory) greatly underestimate the true threshold gradient when compared to numerical solution of the flow equations. We compare the two approaches and reach the conclusion that this is incorrect; the threshold gradient obtained numerically is exactly the same as that found through a search of the minimum path of throat mobilization pressure drops. This fact can be proven mathematically; mass conservation is only preserved if the true threshold gradient is equal to that found by search algorithms.

Pore-scale and continuum simulations of solute transport micromodel benchmark experiments

Four sets of nonreactive solute transport experiments were conducted with micromodels. Each set consisted of three experiments with one variable, i.e., flow velocity, grain diameter, pore-aspect ratio, and flow-focusing heterogeneity. The data sets were offered to pore-scale modeling groups to test their numerical simulators. Each set consisted of two learning experiments, for which all results were made available, and one challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the transverse dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing, and considerably enhanced mixing due to flow focusing. Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice Boltzmann (LB) approach, and one used a computational fluid dynamics (CFD) technique. The learning experiments were used by the PN models to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used the learning experiments to appropriately discretize the spatial grid representations. For the continuum modeling, the required dispersivity input values were estimated based on published nonlinear relations between transverse dispersion coefficients and Peclet number. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values, resulting in reduced dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models, which account for the micromodel geometry and underlying flow and transport physics, needed up to several days on supercomputers to resolve the more complex problems.

Quantification of bulk solution limits for liquid and interfacial transport in nanoconfinements.

Liquid imbibition, the capillary-pressure-driven flow of a liquid into a gas, provides a mechanism for studying the effects of solid-liquid and solid-liquid-gas interfaces on nanoscale transport. Deviations from the classic Washburn equation for imbibition are generally observed for nanoscale imbibition, but the identification of the origin of these irregularities in terms of transport variables varies greatly among investigators. We present an experimental method and corresponding image and data analysis scheme that enable the determination of independent effective values of nanoscale capillary pressure, liquid viscosity, and interfacial gas partitioning coefficients, all critical transport variables, from imbibition within nanochannels. Experiments documented herein are performed within two-dimensional siliceous nanochannels of varying size and as small as 30 nm × 60 nm in cross section. The wetting fluid used is the organic solvent isopropanol and the nonwetting fluid is air, but investigations are not limited to these fluids. Optical data of dynamic flow are rare in geometries that are nanoscale in two dimensions due to the limited resolution of optical microscopy. We are able to capture tracer-free liquid imbibition with reflected differential interference contrast microscopy. Results with isopropanol show a significant departure from bulk transport values in the nanochannels: reduced capillary pressures, increased liquid viscosity, and nonconstant interfacial mass-transfer coefficients. The findings equate to the nucleation of structured, quasi-crystalline boundary layers consistently ∼10-25 nm in extent. This length is far thicker than the boundary layer range prescribed by long-range intermolecular force interactions. Slower but linear imbibition in some experimental cases suggests that structured boundary layers may inhibit viscous drag at confinement walls for critical nanochannel dimensions. Probing the effects of nanoconfinement on the definitions of capillary pressure, viscosity, and interfacial mass transfer is critical in determining and improving the functionality and fluid transport efficacy of geological, biological, and synthetic nanoporous media and materials.

Pore to continuum upscaling of permeability in heterogeneous porous media using mortars

Pore-scale modelling has become an accepted method for estimating macroscopic properties (such as permeability) that describe flow and transport in porous media. In many cases extracted macroscopic properties compare favourably to experimental measurements. However, computational and imaging restrictions generally limit the network size to the order of 1.0 mm3 and these models often ignore effects of surrounding flow behaviour. In this work permeability is upscaled in large (~106 pores), heterogeneous pore-scale network models using an efficient domain decomposition method. The large pore network is decomposed into 100 smaller networks (sub-domains) and then coupled with the surrounding models to determine accurate boundary conditions. Finite element mortars are used as a mathematical tool to ensure interfacial pressures and fluxes are matched at the network boundaries. The results compare favourably to the more computationally intensive (and impractical) approach of upscaling the medium as a single model. Additionally, the results are more accurate than straightforward hierarchical upscaling methods.

A streamline splitting pore‐network approach for computationally inexpensive and accurate simulation of transport in porous media

Several approaches have been developed in the literature for solving flow and transport at the pore scale. Some authors use a direct modeling approach where the fundamental flow and transport equations are solved on the actual pore-space geometry. Such direct modeling, while very accurate, comes at a great computational cost. Network models are computationally more efficient because the pore-space morphology is approximated. Typically, a mixed cell method (MCM) is employed for solving the flow and transport system which assumes pore-level perfect mixing. This assumption is invalid at moderate to high Peclet regimes. In this work, a novel Eulerian perspective on modeling flow and transport at the pore scale is developed. The new streamline splitting method (SSM) allows for circumventing the pore-level perfect-mixing assumption, while maintaining the computational efficiency of pore-network models. SSM was verified with direct simulations and validated against micromodel experiments; excellent matches were obtained across a wide range of pore-structure and fluid-flow parameters. The increase in the computational cost from MCM to SSM is shown to be minimal, while the accuracy of SSM is much higher than that of MCM and comparable to direct modeling approaches. Therefore, SSM can be regarded as an appropriate balance between incorporating detailed physics and controlling computational cost. The truly predictive capability of the model allows for the study of pore-level interactions of fluid flow and transport in different porous materials. In this paper, we apply SSM and MCM to study the effects of pore-level mixing on transverse dispersion in 3-D disordered granular media.

Discrete element modeling of indentation tests to investigate mechanisms of CO2-related chemomechanical rock alteration

During CO2 injection into geological formations, petrophysical and geomechanical properties of host formations can be altered due to mineral dissolution and precipitation. Field and laboratory results have shown that sandstone and siltstone can be altered by CO2-water mixtures, but few quantitative studies have been performed to fully investigate underlying mechanisms. Based on the hypothesis that CO2-water mixtures alter the integrity of rock structure by attacking cements rather than grains, we attempt to explain the degradation of cementation due to long-term contact with CO2 and water and mechanisms for changes in rock mechanical properties. Many sandstones, including calcite-cemented quartzitic sandstone, chlorite-cemented quartzitic sandstone, and hematite-cemented quartzitic sandstone contain interparticle cements that are more readily affected by CO2-water mixtures than grains. A model that couples the Discrete Element Method (DEM) and the Bonded-Particle Model (BPM) is used to perform simulations of indentation tests on synthetic rocks with crystal and random packings. The model is verified against the analytical Cavity Expansion Model (CEM) and validated against laboratory indentation tests on Entrada sandstone with and without CO2-alteration. Sensitivity analysis is performed for cementation microscopic parameters including stiffness, size, axial and shear strength. The simulation results indicate that the CO2-related degradation of mechanical properties in bleached Entrada sandstone can be attributed to the reduction of cement size rather than cement strength. Our study indicates that it is possible to describe the CO2-related rock alteration through particle-scale mechanisms.

Bridging from Pore to Continuum: A Hybrid Mortar Domain Decomposition Framework for Subsurface Flow and Transport

Flow and transport in the subsurface occurs over a wide range of spatial scales (nanometer to kilometer). Modeling at the pore scale becomes imperative where scales are not separable. Since pore-scale models are computationally limited to small domain sizes, accurate field-scale modeling requires simulating parts of the reservoir at the pore scale and other parts at the continuum. The need for modeling large pore-scale domains for ascertaining macroscopic parameters is prevalent in the literature. We develop a hybrid mortar domain decomposition framework for parallel modeling (linear and nonlinear) flow and transport across scales and in large pore-scale domains. Novel and efficient mortar methods for coupling flow and transport are adapted and developed and comparisons are presented. Mortars are developed for pore-to-pore and pore-to-continuum interfaces and shown to be more suitable than the commonly used Lagrangian mortars for these interfaces. The methods are shown to produce accurate results and demo...

Eulerian network modeling of longitudinal dispersion: EULERIAN NETWORK MODELING OF DISPERSION

Work was performed at UT-Austin Normalized longitudinal dispersion coefficient vs. Ped for STMpar, STMplug, and MCM against experimental data [Jha et al., 2011 Scientific Achievement Developed novel Eulerian network model (Superposing Transport Method; STM) that accounts for shear dispersion Significance and Impact Pore‐level model is able to accurately predict mixing and dispersion in CO2 sequestration

Influence of dynamic factors on nonwetting fluid snap-off in pores: DYNAMIC FACTORS ON SNAP-OFF

Snap-off is an important dynamic multiphase flow phenomenon which occurs in porous media. It plays a dominant role in the residual trapping and mobilization/immobilization of nonwetting fluids such as hydrocarbons or CO2. Current studies, applications, and threshold criteria of snap-off are mostly based on static or equilibrium conditions. Thus, the dynamics of snap-off which is relevant for many real world applications has rarely been systematically studied. While a static criterion indicates the snap-off potential for nonwetting fluids, the competition between the time required for snap-off and the local pore throat capillary number determines whether snap-off actually occurs. Using a theoretical model to couple the wetting film thickness to the local capillary number at the pore throat, we analyzed the dynamics of the wetting/nonwetting interface instability in sinusoidally constricted capillary tubes. The influence of dynamic factors as encapsulated by the effect of local capillary number on nonwetting fluid snap-off time were investigated for varying pore throat to pore body aspect ratio and pore body distances. The analysis showed that snap-off can be inhibited by a sufficiently large local capillary number even in cases where the static snap-off criterion has been met.