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Abstract: Efficient multiphysics (or hybrid) models that can adapt to the varying complexity of physical processes in space and time are desirable for modeling fluid migration in the subsurface. Vertical equilibrium (VE) models are simplified mathematical models that are computationally efficient but rely on the assumption of instant gravity segregation of the two phases, which may not be valid at all times or at all locations in the domain. Here we present a multiphysics model that couples a VE model to a full multidimensional model that has no reduction in dimensionality. We develop a criterion that determines subdomains where the VE assumption is valid during simulation. The VE model is then adaptively applied in those subdomains, reducing the number of computational cells due to the reduction in dimensionality, while the rest of the domain is solved by the full multidimensional model. We analyze how the threshold parameter of the criterion influences accuracy and computational cost of the new multiphysics model and give recommendations for the choice of optimal threshold parameters. Finally, we use a test case of gas injection to show that the adaptive multiphysics model is much more computationally efficient than using the full multidimensional model in the entire domain, while maintaining much of the accuracy. [ABSTRACT FROM AUTHOR]

We study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and G, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R²/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ ≪ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ ≪ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ ≪ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ ≫ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)]. The various axisymmetric flows are summarized in a G-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime. The implications of the regime diagram are discussed using practical engineering projects of geological CO2 sequestration, enhanced oil recovery, and underground waste disposal. [ABSTRACT FROM AUTHOR]

Subsurface two-phase flow in porous media often takes place in reservoirs with a high ratio between the associated lateral and vertical extent and the lateral and vertical flow time scales. This allows for a two-scale approach with effective quantities for two-dimensional horizontal flow equations obtained from reconstructed hydrostatic vertical pressure and saturation distributions. Here, we derive explicit expressions for the two dimensional constitutive relationships for a play-type hysteretic Brooks-Corey capillary pressure function with a pore-size distribution index of 2 and quadratic relative permeabilities. We obtain an explicit hysteretic parametrization for the upscaled capillary pressure function and the upscaled relative permeabilities. The size of the hysteresis loop depends on the ratio between buoyancy and the entry pressure, i.e. it scales with the reservoir height and the ratio between drainage and imbibition capillary pressure. We find that the scaling for the relative permeability is non-monotonic and hysteresis vanishes for both small and large reservoirs. [ABSTRACT FROM AUTHOR]

• Air-water flow through thin porous layers is studied using a state-of-the-art dynamic pore-network model. • Our pore-scale results provide insight into the continuum-scale modeling of thin porous layers. • We demonstrate the role of phase change in water removal from the cathode gas diffusion layer of a polymer electrolyte fuel cell. Thin porous layers, that have large aspect ratios, are seen in many applications such as hydrogen fuel cells and hygiene products, in which air-water immiscible flow is of great interest. Direct numerical simulations based on Navier-Stokes equation are computationally expensive, and even prohibitive for low capillary number flow such as water flooding in low-temperature polymer electrolyte fuel cells. Alternatively, the pore-network modeling needs much less computational resources, while still retaining essentials of the pore-structure information. In this work, a dynamic pore-network model of air-water flow with phase change has been developed. We focus on drainage processes through thin porous layers, in which liquid water is the nonwetting phase. Three test cases are conducted, namely, air-water flow through a thin porous layer, air-water flow through a bilayer of fine and coarse thin porous layers, and water flooding in the gas diffusion layer of a polymer electrolyte fuel cell with phase change between water and its vapor. Using these test cases, we aim to demonstrate the application of dynamic pore-network modeling in thin porous media studies. In particular, we discuss the challenge of modeling thin porous media at the average scale, and highlight the role of phase change in removing liquid water from the cathode gas diffusion layer. [ABSTRACT FROM AUTHOR]

This work examines the applicability of averaged concentrations, a mathematical analog of field-measured solute concentrations averaged over a large number of pores, in determining mineral reaction rates in heterogeneous porous media. Pore-scale network models were used to represent sandstones with anorthite and kaolinite as reactive minerals that are heterogeneously distributed in space. Reaction rates calculated from averaged concentrations were compared to true reaction rates that take into account variabilities in individual pore properties. Simulations were run under the highly acidic conditions relevant to geological CO2 sequestration in deep brine formations under various mineralogical and flow conditions. Results show that, under conditions where incomplete mixing arises, the averaged concentrations and analogously the field-measured concentrations, do not accurately reflect reaction progress. Over the length scale of several millimeters, the anorthite dissolution rates can be overestimated by a factor of three. For kaolinite, due to its highly nonlinear reaction rate law, even the reaction direction may be incorrectly determined, with precipitation predicted as dissolution. The extent of errors introduced depends on the extent of incomplete mixing. Conditions that homogenize the concentration fields, such as small reactive mineral clusters, abundant reactive minerals, and very fast or very slow flow rates, minimize errors introduced from averaging. These results indicate that the averaging scheme may partly contribute to the often-cited laboratory-field rate discrepancy and have important implications for the interpretation of concentration data obtained from field investigation. [ABSTRACT FROM AUTHOR]

In theories of multiphase flow through porous media, capillary pressure–saturation and relative permeability–saturation curves are assumed to be intrinsic properties of the medium. Moreover, relative permeability is assumed to be a scalar property. However, numerous theoretical and experimental works have shown that these basic assumptions may not be valid. For example, relative permeability is known to be affected by the flow velocity (or pressure gradient) at which the measurements are carried out. In this article, it is suggested that the nonuniqueness of capillary pressure–relative permeability–saturation relationships is due to the presence of microheterogeneities within a laboratory sample. In order to investigate this hypothesis, a large number of “numerical experiments” are carried out. A numerical multiphase flow model is used to simulate the procedures that are commonly used in the laboratory for the measurement of capillary pressure and relative permeability curves. The dimensions of the simulation domain are similar to those of a typical laboratory sample (a few centimeters in each direction). Various combinations of boundary conditions and soil heterogeneity are simulated and average capillary pressure, saturation, and relative permeability for the “soil sample” are obtained. It is found that the irreducible water saturation is a function of the capillary number; the smaller the capillary number, the larger the irreducible water saturation. Both drainage and imbibition capillary pressure curves are found to be strongly affected by heterogeneities and boundary conditions. Relative permeability is also found to be affected by the boundary conditions; this is especially true about the nonaqueous phase permeability. Our results reveal that there is much need for laboratory experiments aimed at investigating the interplay of boundary conditions and microheterogeneities and their effect on capillary pressure and relative permeability. [Copyright &y& Elsevier]

Various modeling approaches, including fully three-dimensional (3D) models and vertical-equilibrium (VE) models, have been used to study the large-scale storage of carbon dioxide (CO2) in deep saline aquifers. 3D models solve the governing flow equations in three spatial dimensions to simulate migration of CO2 and brine in the geological formation. VE models assume rapid and complete buoyant segregation of the two fluid phases, resulting in vertical pressure equilibrium and allowing closed-form integration of the governing equations in the vertical dimension. This reduction in dimensionality makes VE models computationally much more efficient, but the associated assumptions restrict the applicability of VE models to geological formations with moderate to high permeability. In the present work, we extend the VE models to simulate CO2 storage in fractured deep saline aquifers in the context of dual-continuum modeling, where fractures and rock matrix are treated as porous media continua with different permeability and porosity. The high permeability of fractures makes the VE model appropriate for the fracture domain, thereby leading to a VE dual-continuum model for the dual continua. The transfer of fluid mass between fractures and rock matrix is represented by a mass transfer function connecting the two continua, with a modified transfer function for the VE model based on vertical integration. Comparison of the new model with a 3D dual-continuum model shows that the new model provides comparable numerical results while being much more computationally efficient. [ABSTRACT FROM AUTHOR]

We develop a probabilistic collocation Eulerian–Lagrangian localized adjoint method on sparse grids for assessing CO 2 leakage through wells in randomly heterogeneous porous media, by utilizing the intrinsic mathematical, numerical, and physical properties of the mathematical model. We model the process in which CO 2 is injected into a deep aquifer, spreads within the aquifer and, upon reaching a leaky well, rises up to a shallower aquifer, to quantify the leakage rate, which depends on the pressure build-up in the aquifer due to injection and the buoyancy of CO 2 . The underlying Eulerian–Lagrangian framework has high potential to improve the efficiency and accuracy for the numerical simulation of complex flow and transport processes in CO 2 sequestration. The sparse grid probabilistic collocation framework adds computationally efficient uncertainty quantification functionality onto pre-existing Eulerian–Lagrangian methods in a nonintrusive manner. It also provides a scalable framework to consider uncertainty in a straightforward parallel manner. Preliminary numerical experiments show the feasibility and potential of the method. [ABSTRACT FROM AUTHOR]