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In this paper, we investigate phase-field interface capturing equations for two-fluid systems to probe their accuracy and computational cost. Two different schemes are considered: In the first scheme, one of the two order parameters is numerically solved based on a phase-field equation, while the other order parameter is determined through the summation relation; the summation of order parameters equals unity. In the second scheme, the two order parameters are both obtained numerically by solving their respective phase-field equations. A phase-field model based on the color-gradient (CG) method is chosen, and available lattice Boltzmann models are employed for solving the interface-capturing equations together with the hydrodynamic equation. It is shown that for the first scheme, which includes the summation relation, numerical results become asymmetrical. Also, in some cases, it results in nonphysical interfaces. In terms of computational resources, this first scheme is about 11% faster with 25% less computational memory usage than the second scheme. It is shown that only for a zero velocity domain do the two schemes lead to equal results. Also, a theoretical analysis is conducted to highlight the differences between the two approaches. [ABSTRACT FROM AUTHOR]

The capillary pressure‐saturation relation is one of the key constitutive equations used for modeling multiphase (or partially saturated) flow in porous materials. It is known that this empirical relation depends strongly on dynamic conditions, but the impact of a heterogeneity interface on this relationship has been studied less. The present study employed optical imaging to visualize two‐phase drainage under different injection rates and two flow directions, in a heterogeneous micromodel. By analyzing the curvatures of the fluid‐fluid interfaces, the averaged capillary pressures for the coarse and fine sections of the micromodel, and the entire micromodel were estimated. Results show that the capillary pressure‐saturation relation in the vicinity of a heterogeneity interface does not follow the conventional models proposed in the literature. The averaged capillary pressure over the entire micromodel for the fine‐to‐coarse (FtC) direction shows decreasing capillary pressure with decreasing wetting phase saturation. However, in the coarse‐to‐fine direction, a non‐monotonic trend was observed. These initial findings highlight the gaps in the knowledge of upscaling capillary pressure in heterogeneous porous materials. Moreover, discontinuity in saturation was clearly more pronounced for the FtC direction, as a result of lower entry capillary resistance against the flow in the coarse section. Key Points: Averaged capillary pressure‐saturation relation was estimated using image processing of microfluidic experimentsThe capillary pressure‐saturation relation varies significantly with the direction of flow with respect to the heterogeneityNonmonotonic capillary pressure‐saturation relations were observed in presence of a heterogeneity interface [ABSTRACT FROM AUTHOR]

The dissolution of carbon‐dioxide (CO2) in deep saline aquifers is an important trapping mechanism in carbon storage. This process is triggered by unstable high‐density CO2 front, which later promotes density‐driven mixing, hydrodynamic dispersion of CO2, and favors the long‐term sequestration. In many former studies, effects of hydrodynamic dispersion and multispecies geochemical reactions have been ignored. This work elaborates the impacts of these simplifications on the dynamics of convective mixing by numerical simulations. Geochemical effects were studied by the implementation of rock‐fluid and fluid‐fluid interactions for a typical carbonate aquifer. Results show that accounting for the hydrodynamic dispersion decreases the convection onset time and increases the CO2 dissolution flux, which is more significant in larger dispersivities and Rayleigh numbers. Results indicate that carbonate geochemical reactions intense the long‐term overall efficiency of the process, while decrease the total amount of sequestered carbon in the diffusion‐dominated period. Results also reinforce the importance of realistic geochemical representation and importance of spatial and temporal dependence of the reactions pathway, subsequent to the finger development for more detailed simulation of the CO2 storage process. Plain Language Summary: Geological carbon storage is one of the technologies envisaged to play a critical role in decarbonization and achieving the net‐zero carbon emission. It is estimated that 17% of the whole decarbonization by 2050 will be achieved by carbon storage. Based on a modeling study, we demonstrate the role of natural geochemistry of the subsurface is important in the dissolution of carbon in brine and its long‐term performance. Key Points: Effect of hydrodynamic dispersion is studied on the dynamics of CO2 convectionChemical reactions have nonmonotonic effects on carbon storage before and after convection onsetThe importance of realistic geochemical modeling and different reaction pathways subsequent to plume propagation is shown [ABSTRACT FROM AUTHOR]

Immiscible two‐phase flow through porous materials exhibits different invasion patterns controlled by dynamic conditions, competition between the viscous and capillary forces, and the contrast between the fluids viscosities. Two distinct invasion patterns are viscous and capillary fingering. While the first one happens under unfavorable viscosity ratios at high injection rates, the second one happens when the viscous forces are very small compared to the capillary forces. Depending on whether the invasion is under the capillary fingering or viscous fingering regime, the remaining oil saturation and the effective permeability of the fluids can significantly change. The contribution of the present work has two key aspects: (a) It addresses how the remaining saturation changes at different flow rates (i.e., capillary numbers) for different unfavorable viscosity ratios in a three‐dimensional system; (b) it presents a new dynamic pore network model using the fully implicit scheme which has been enhanced by the graphic processing unit (GPU) parallel computing. Additionally, the model has been carefully validated against micromodel experiments in both time and space, which to our best knowledge has not been reported in such detail in the literature. The results of the validated 3‐D dynamic pore network model demonstrate the remaining saturation at the breakthrough time as a nonmonotonic trend with the imposed capillary number. Key Points: A fully implicit algorithm with optimized local rules for two‐phase flow in pore networks using the two‐pressure algorithm was proposedThe flow patterns from the dynamic pore network modeling were validated against micromodel experiments in time and spaceThe remaining saturation at the breakthrough point has a nonmonotonic trend with an increased capillary number [ABSTRACT FROM AUTHOR]

Continuum‐scale models for two‐phase flow and transport in porous media are based on the empirical constitutive relations that highly depend on the porous medium heterogeneity at multiple scales including the microscale pore‐size correlation length. The pore‐size correlation length determines the representative elementary volume and controls the immiscible two‐phase invasion pattern and fluids occupancy. The fluids occupancy controls not only the shape of relative permeability curves but also the transport zonation under two‐phase flow conditions, which results in the non‐Fickian transport. This study aims to quantify the signature of the pore‐size correlation length on two‐phase flow and solute transport properties such as the capillary pressure‐ and relative permeability‐saturation, dispersivity, stagnant saturation, and mass transfer rate. Given the capability of pore‐scale models in capturing the pore morphology and detailed physics of flow and transport, a novel graphics processing unit (GPU)‐based pore‐network model has been developed. This GPU‐based model allows us to simulate flow and transport in networks with multimillions pores, equivalent to the centimeter length scale. The impact of the pore‐size correlation length on all aforementioned properties was studied and quantified. Moreover, by classification of the pore space to flowing and stagnant regions, a simple semianalytical relation for the mass transfer between the flowing and stagnant regions was derived, which showed a very good agreement with pore‐network simulation results. Results indicate that the characterization of the topology of the stagnant regions as a function of pore‐size correlation length is essential for a better estimation of the two‐phase flow and solute transport properties. Key Points: A novel fully GPU‐based pore‐network model simulates two‐phase flow and transport at the centimeter‐scaleA semianalytical equation for mass transfer across flowing and stagnant regions is validated against simulation resultsPore‐size correlation length controls the constitutive relations for two‐phase flow and transport through porous media [ABSTRACT FROM AUTHOR]

Density-driven mixing resulting from CO2 injection into aquifers leads to the CO2 entrapment mechanism of solubility trapping. Crucially, the coupled flow-geochemistry and effects of geochemistry on density-driven mixing process for "sandstone rocks" have not been adequately addressed. Often, there are conflicting remarks in the literature as to whether geochemistry promotes or undermines dissolution-driven convection in sandstone aquifers. Against this backdrop, we simulate density-driven mixing in sandstone aquifers by developing a 2-D modified stream function formulation for multicomponent reactive convective-diffusive CO2 mixing. Two different cases corresponding to laboratory and field scales are studied to investigate the effect of rock-fluid interaction on density-driven mixing and the role of mineralization in carbon storage over the project life time. A complex sandstone mineralogical assemblage is considered, and solid-phase reactions are assumed to be kinetic to study the length- and time-scale dependency of the geochemistry effects. The study revealed nonuniform impact of rock-fluid and fluid-fluid interaction in early- and late-time stages of the process. The results show that for moderate Rayleigh (Ra) numbers, rock-fluid interactions adversely affect solubility trapping while improving the total carbon captured through mineral trapping. Simulation results in the range of 1,500 < Ra < 55,000 in the field-scale model showed more pronounced impact of geochemistry for higher Ra numbers, as geochemistry stimulates the convective instabilities and improves the total sequestered carbon. This study gives new insights into the effect of rock-fluid interactions on density-driven mixing and solubility trapping in sandstone aquifers to improve estimation of the carbon storage capacity in deep saline aquifers. [ABSTRACT FROM AUTHOR]

In this paper, the underlying problem with the color-gradient (CG) method in handling density-contrast fluids is explored. It is shown that the CG method is not fluid invariant. Based on nondimensionalizing the CG method, a phase-field interface-capturing model is proposed which tackles the difficulty of handling density-contrast fluids. The proposed formulation is developed for incompressible, immiscible two-fluid flows without phase-change phenomena, and a solver based on the lattice Boltzmann method is proposed. Coupled with an available robust hydrodynamic solver, a binary fluid flow package that handles fluid flows with high density and viscosity contrasts is presented. The macroscopic and lattice Boltzmann equivalents of the formulation, which make the physical interpretation of it easier, are presented. In contrast to existing color-gradient models where the interface-capturing equations are coupled with the hydrodynamic ones and include the surface tension forces, the proposed formulation is in the same spirit as the other phase-field models such as the Cahn-Hilliard and the Allen-Cahn equations and is solely employed to capture the interface advected due to a flow velocity. As such, similarly to other phase-field models, a so-called mobility parameter comes into play. In contrast, the mobility is not related to the density field but a constant coefficient. This leads to a formulation that avoids individual speed of sound for the different fluids. On the lattice Boltzmann solver side, two separate distribution functions are adopted to solve the formulation, and another one is employed to solve the Navier-Stokes equations, yielding a total of three equations. Two series of numerical tests are conducted to validate the accuracy and stability of the model, where we compare simulated results with available analytical and numerical solutions, and good agreement is observed. In the first set the interfacial evolution equations are assessed, while in the second set the hydrodynamic effects are taken into account.

Experimental and field studies reported a significant discrepancy between the cleanup and contamination time scales, while its cause is not yet addressed. Using high-resolution fast synchrotron x-ray computed tomography, we characterized the solute transport in a fully saturated sand packing for both contamination and cleanup processes at similar hydrodynamic conditions. The discrepancy in the time scales has been demonstrated by the nonuniqueness of hydrodynamic dispersion coefficient versus injection rate (Péclet number). Observations show that in the mixed advection-diffusion regime, the hydrodynamic dispersion coefficient of cleanup is significantly larger than that of the contamination process. This nonuniqueness has been attributed to the concentration-dependent diffusion coefficient during the cocurrent and countercurrent advection and diffusion, present in contamination and cleanup processes. The new findings enhance our fundamental understanding of transport processes and improve our capability to estimate the transport time scales of chemicals or pollution in geological and engineering systems.