Capillary Pressure-saturation Relationship Research Articles

Semi-analytical Model to Predict Dynamic Capillary Pressure–Saturation Relationship for Flows in Heterogeneous Porous Media

The capillary pressure defines pressure difference between non-wetting and wetting fluids. The capillary pressure is part of the flow governing equations, and its definition can have a profound impact on the nature of fluids displacement in a multiphase flow environment. Conventionally, capillary pressure–saturation relationships are determined under equilibrium conditions which signify that all the fluid–fluid interfaces that exist at the pore scale maintain a static configuration at a certain instant in time. However, there exist experimental and numerical evidences that state that the dynamic nature of fluid flows indeed plays a prominent role in defining the trends of the capillary pressure–saturation relationships. In this paper, we develop a first of a kind semi-analytical model to predict the capillary pressure–saturation curves during drainage displacement by integrating the dynamics of fluid flow based on fundamental laws of fluid mechanics. The proposed semi-analytical model can potentially be incorporated into existing multiphase flow simulators to rapidly compute the capillary pressure at various saturations of the flow medium under dynamic flow conditions. The presented semi-analytical model has been validated against experimental and numerical data sets available in the literature at various flow conditions and considering different sets of fluid properties. We noticed a satisfactory match of the results predicted by the proposed semi-analytical model against the literature data. After performing a holistic sensitivity analysis, we notice that the properties of the porous medium, and the fluid–solid interactions play a significant role in defining the trends of the capillary pressure–saturation curves.

Comparative analysis of hydrogen, methane and nitrogen relative permeability: Implications for Underground Hydrogen Storage

Underground Hydrogen Storage (UHS) is an emerging technology which aims to store terawatt-scale energy in the subsurface to alleviate daily and seasonal fluctuations in the ever-increasing renewable energy market. Depleted gas reservoirs and aquifers will be the main targets of storage which requires an understanding of the interaction between formation or cushion gas with native brine. A comprehensive comparison of the petrophysical and two-phase flow properties of the hydrogen-water, methane-water and nitrogen-water systems at in-situ conditions is the focus of our work. We conduct steady-state relative permeability experiments at 2.13 MPa and 298 K using identical capillary numbers of Nc=2.92×10−7 for all three systems. The saturation and in-situ contact angles are determined with segmentation of 3D micro-CT images. The contact angle of each system is almost identical at the irreducible water saturation, Swi, 44°, 46°, 45°, respectively, as is the interfacial tension of 72.0, 71.5 and 71mN/m, respectively. The capillary pressure-saturation relationships for each system have a maximum difference of 3.8 % which leads to approximately equivalent relative permeability in the Bentheimer sandstone core. The end-point relative permeabilities are krg0=0.049, krg0=0.045 and krg0=0.062 at irreducible water saturations of Swi=0.24, Swi=0.25 and Swi=0.23, respectively. All three gases demonstrate equivalent flow properties which indicates that both nitrogen and methane are suitable analogue gases for laboratory multiphase flow experiments and cushion gas to improve safety and the economics of commercial UHS projects. The results enable history matched depleted gas reservoir performance to be used as a guide for UHS.

A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media, this problem has been seldom investigated using direct numerical simulation (DNS). Only a few studies have sought to numerically solve Navier–Stokes equations with level-set (LS) or volume-of-fluid (VoF) methods, each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume (CV) domain. The Shan–Chen multiphase multicomponent lattice Boltzmann method (SC-LBM) has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations. Therefore, this study applied it to explore two-phase displacement in a single representative elementary volume (REV) of two-dimensional (2D) porous media. As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media, this work seeks to identify dynamic nonequilibrium effects on capillary pressure–saturation relationship ( P c – S ) for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions. The simulation outcomes show that P c , S and specific interfacial area ( a nw ) had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions. With finer adjustments to the increase in pressure over more steps, dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasi-steady-state inflow/outflow conditions. Furthermore, triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical P c – S . The results showed overshoot and undershoot of P c to S in loops of the nonequilibrium hysteresis. In addition, the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers ( Re and Ca ). The analysis of REV-scale flow regimes showed higher Re (1 < Re < 10) for more significant dynamic nonequilibrium effects. This indicates that inertia is critical for transient two-phase flow in porous media under dynamic nonequilibrium conditions.

Effects of Enzymatically Induced Carbonate Precipitation on Capillary Pressure–Saturation Relations

Leakage mitigation methods are an important part of reservoir engineering and subsurface fluid storage, in particular. In the context of multi-phase systems of subsurface storage, e.g., subsurface CO2 storage, a reduction in the intrinsic permeability is not the only parameter to influence the potential flow or leakage; multi-phase flow parameters, such as relative permeability and capillary pressure, are key parameters that are likely to be influenced by pore-space reduction due to leakage mitigation methods, such as induced precipitation. In this study, we investigate the effects of enzymatically induced carbonate precipitation on capillary pressure–saturation relations as the first step in accounting for the effects of induced precipitation on multi-phase flow parameters. This is, to our knowledge, the first exploration of the effect of enzymatically induced carbonate precipitation on capillary pressure–saturation relations thus far. First, pore-scale resolved microfluidic experiments in 2D glass cells and 3D sintered glass-bead columns were conducted, and the change in the pore geometry was observed by light microscopy and micro X-ray computed tomography, respectively. Second, the effects of the geometric change on the capillary pressure–saturation curves were evaluated by numerical drainage experiments using pore-network modeling on the pore networks extracted from the observed geometries. Finally, parameters of both the Brooks–Corey and Van Genuchten relations were fitted to the capillary pressure–saturation curves determined by pore-network modeling and compared with the reduction in porosity as an average measure of the pore geometry’s change due to induced precipitation. The capillary pressures increased with increasing precipitation and reduced porosity. For the 2D setups, the change in the parameters of the capillary pressure–saturation relation was parameterized. However, for more realistic initial geometries of the 3D samples, while the general patterns of increasing capillary pressure may be observed, such a parameterization was not possible using only porosity or porosity reduction, likely due to the much higher variability in the pore-scale distribution of the precipitates between the experiments. Likely, additional parameters other than porosity will need to be considered to accurately describe the effects of induced carbonate precipitation on the capillary pressure–saturation relation of porous media.

Modeling drainage in porous media considering locally variable contact angle based on pore morphology method

The pore morphology method (PMM) has been widely applied to simulate the quasi–static drainage process of porous media, which requires less computational time and computer memory compared to other two–phase flow simulation methods. However, most of the existing pore morphology simulations were restricted to totally wetting systems (i.e., contact angle is equal to zero). Here, we propose a new pore morphology method (Lvca–PMM) enhanced by considering locally variable contact angles, which now enables a reproduction of the primary drainage process for porous media under different wettability conditions featuring the full range of contact angle for wetting phase for various spatial distribution. A series of simulations are performed by using the Lvca–PMM to a porous medium under different uniform and mixed wettability conditions. The proposed Lvca–PMM presents a better result compared to the method by Schulz et al. (2014) for different wettability conditions. The capillary pressure–saturation relations as well as the pore–scale fluid distributions can be well captured by the proposed Lvca-PMM.

Application of benchtop humidity and temperature chamber in the measurement of water vapor sorption in US shales from Mancos, Marcellus, Eagle Ford and Wolfcamp formations

A benchtop humidity and temperature chamber was used to assess water vapor sorption in four US shale samples at 90 °C. Water sorption isotherms were measured at relative humidity ranging from 10 to 99% and temperature of 90 °C. Shale fractal properties were then evaluated, and capillary pressure (ranging from 1.70 to 386 MPa) was obtained using Kelvin relationship. The results show that Mancos shale, from the US, adsorbed more absorbed water due to its high clay concentration and low TOC. However, Wolfcamp shale, from the US, has the lowest TOC and clay concentration, adsorbing the lowest amount of water. There is little hysteresis between adsorption and desorption isotherms explaining water retention phenomenon in some shales. The obtained fractal dimension values ranged between 2.45 and 2.76 and average of 2.56 indicating irregular pore surface and complex pore structure. All shale sample's capillary curves were fitted to Brooks & Corey and van Genuchten models with nonlinear regression. The fitting coefficient, R2, which represents the proportion of variance for Brooks & Corey fits ranged from 0.90 to 0.97 for imbibition and 0.85 to 0.98 for drainage, while R2 for the van Genuchten model ranged from 0.94 to 0.99 for both imbibition and drainage. Thus, the proposed method can be used to measure capillary pressure–saturation relationships in gas shales.

Lattice Boltzmann Simulation of Water Transport through Gas Diffusion Layers with Homogeneous and Heterogeneous PTFE Distributions

In recent years Polymer Electrolyte Fuel Cells have gained increasing attention in the e-mobility sector being a compelling powertrain solution and alternative to battery-driven electrical vehicles. Short refueling periods, long range capacity and reliability at high loads amongst others render the fuel cell technology advantageous, especially for heavy duty applications such as public transport and commercial vehicles [1]. These use cases however come along with challenging demands for stable operation due to their dynamic load profiles. In fuel cell operation such requirements can only be fulfilled when reactant gases are steadily provided while at the same time product water is efficiently removed. This multiphase counterflow is typically realized using carbon-based gas diffusion layers (GDLs) coated with a hydrophobic additive easing water removal. However, multiphase flow in GDLs is very complex and underlying transport phenomena not yet sufficiently understood. In addition, material design and experimental testing is expensive and long-lasting. A simulation approach offers therefore a large potential to deepen understanding of occurring transport phenomena while promoting material development.In our work we simulate the flow of liquid water through porous gas diffusion media using a 3D color-gradient Lattice Boltzmann model [2]. The simulations are carried out on complex geometries as derived by binarization of µCT images for a real microstructure of a Freudenberg GDL. To investigate the influence of mixed wettability on multiphase flows a hydrophobic additive (PTFE) is furthermore included using an in-house distribution algorithm. With this routine different homogeneous and heterogeneous spatial distributions of PTFE are realized within the GDL. Imposing variable capillary pressures we then derive material dependent effective transport parameters such as capillary pressure-saturation curves for different additive contents and distributions. By simulating the consecutive intrusion and drainage of water we recover a characteristic hysteresis behavior for the liquid saturation depending on the PTFE distribution. These investigations contribute on the one hand to a better comprehension of transport mechanisms within GDLs. On the other hand can these effective transport parameters be used in cell-level simulation suites offering a more realistic description for multiphase flow in porous GDL material as compared to commonly used relations such as the standard Leverett approach [3].The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation program within the project ID Fast: Investigations on degradation mechanisms and Definition of protocols for PEM Fuel cells Accelerated Stress Testing, under grant agreement n°779565. Literature [1] Cullen, D.A., Neyerlin, K.C., Ahluwalia, R.K. et al., "New roads and challenges for fuel cells in heavy-duty transportation", Nat Energy, (2021), doi: 10.1038/s41560-021-00775-z[2] Rothman, D.H., Keller, J.M., "Immiscible cellular-automaton fluids", J. Stat. Phys. 52, 1119–1127 (1988), doi: 10.1007/BF01019743[3] Leverett, M.C., "Capillary Behavior in Porous Solids", Trans. 142, 152–169 (1941), doi: 10.2118/941152-G Figure 1: Workflow as developed for this research. Top left: GDL microstructures are reconstructed by binarization of µCT images. Top right: PTFE is distributed as a hydrophobic agent onto the binarized fiber structure using an in-house algorithm. Bottom: Effective transport parameters such as capillary pressure-saturation relations are derived by simulating liquid water transport through GDL microstructures using the Lattice Boltzmann Method (LBM). Figure 1

Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

On an averaged model for immiscible two‐phase flow with surface tension and dynamic contact angle in a thin strip

AbstractWe consider a model for the flow of two immiscible fluids in a two‐dimensional thin strip of varying width. This represents an idealization of a pore in a porous medium. The interface separating the fluids forms a freely moving interface in contact with the wall and is driven by the fluid flow and surface tension. The contact‐line model incorporates Navier‐slip boundary conditions and a dynamic and possibly hysteretic contact angle law. We assume a scale separation between the typical width and the length of the thin strip. Based on asymptotic expansions, we derive effective models for the two‐phase flow. These models form a system of differential algebraic equations for the interface position and the total flux. The result is Darcy‐type equations for the flow, combined with a capillary pressure–saturation relationship involving dynamic effects. Finally, we provide some numerical examples to show the effect of a varying wall width, of the viscosity ratio, of the slip boundary condition as well as of having a dynamic contact angle law.

Sensitivity and Uncertainty Analysis for Parameterization of Multiphase Flow Models

The long-standing question on the adequate description of multiphase flow in porous media may be ultimately decided based on the ability to estimate model parameters with sufficient accuracy that make the models distinguishable. Since the most-common Darcy scale multiphase flow models all use a somewhat phenomenological relative permeability or resistance factor formulation, the key question is what the associated uncertainty really is when derived from flow experiments by inverse modeling. In this work, a recently developed workflow for systematic assessment of uncertainty was used to analyze the impact of the choice of relative permeability models and associated uncertainty. In an exemplary fashion, the Corey and LET relative permeability parameterizations were compared. The choice of Corey and LET models in the inverse modeling workflows showed differences in the derived relative permeability relations. The Corey parameterization is found to be more restrictive and imposed additional constraints on parameters. For example, varying the connate water saturation and residual oil saturation did not improve the match with experimental data. The pressure drop, saturation profiles and the capillary pressure–saturation relationship constrained the solution and imposing additional constraints on, e.g., residual oil saturation has very little impact on the result. In contrast, the LET function provided more degrees of freedom in order to accommodate the shape of the relative permeability curves. The findings also suggested that both Corey and LET models may not necessarily provide optimum parameterizations of the experimental data. The cross-correlations of fit parameters and non-Gaussian residuals indicated that we were still dealing with a phenomenological parameterization that is not yet the fully adequate description of the data. This may be the starting point for a comparison of different flow models beyond the uncertainty imposed by the choice of model parameterizations. Future work is aimed at assessing whether better choices in interpretation workflows and optimized experimental workflows can minimize these issues.

Lnapl Leakage and Resulting Contaminant Transport in The Unsaturated and Saturated Zones(Dept.C)

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Comparison of pore-scale capillary pressure to macroscale capillary pressure using direct numerical simulations of drainage under dynamic and quasi-static conditions

Conventional macroscale two-phase flow equations for porous media (such as Darcy's law and Richards Equation) require a constitutive relation for capillary pressure (Pc). The capillary pressure relation significantly impacts the behavior and prediction of fluid flow in porous media, and needs to accurately characterize the capillary forces. In a typical laboratory experiment, a functional macroscopic capillary pressure-saturation (Pc-Sw) relationship is measured as the difference between the pressures of the non-wetting-phase reservoir at the inlet (Pnw) and wetting-phase reservoir at the outlet (Pw) of a porous medium. It is well-known that this traditional macroscopic capillary pressure definition is valid only at equilibrium conditions and if the phases are connected. Under non-equilibrium (dynamic) conditions, when the fluids are moving, the macroscopic capillary pressure measured in experiments implicitly includes the pressure head caused by viscous effects.The goal of the present effort is to understand how well the traditional macroscopic capillary pressure definition represents the pore-scale capillary forces under different flow conditions. Using direct numerical simulations (DNS) of two-phase flow in a porous medium, we evaluate the capillary pressure at the pore-scale, and compare it to the macroscopic capillary pressure, Pc(Sw), that is typically measured in experiments using pressure transducers. The pore-scale capillary pressure is the pressure difference across the interface between two fluids as the fluids move through a porous medium; the interface pressure differences at fluid-fluid invasion front are averaged across all the pores of the porous medium to yield a representative pore-scale capillary pressure curve, referred to as the interface capillary pressure. The pore-scale interface capillary pressure represents the “true” capillary forces in the system, since depends only on the pore morphology (shape) and interfacial energy of the two fluids, and does not account for the viscous dissipation. In experiments it is difficult to measure the interface capillary pressure jump without accounting for the viscous pressure head, which is at least an order of magnitude larger. Upscaling the pore-scale capillary pressure is an essential step for complete characterization of capillary-dominant two-phase flow in a porous medium at the laboratory scale.Drainage is simulated under equilibrium (quasi-static) and non-equilibrium (dynamic) conditions for various capillary numbers. The Navier–Stokes (NS) equations are solved in the pore space using the open-source finite-volume computational fluid dynamics (CFD) code, OpenFOAM. The Volume-of-Fluid (VOF) method is employed to track the evolution of the fluid–fluid interfaces, and a contact angle is used to account for the effect of wall adhesion. The simulations are first validated with published experimental data for dynamic and quasi-static drainage in a micromodel. From the microscale simulations, the interface capillary pressure is determined, and compared to the macroscopic capillary pressure under equilibrium and non-equilibrium conditions. Our results show the traditionally-measured macroscopic capillary pressure curves exhibit a strong dependence on the capillary number under dynamic flow conditions. In contrast, the interface capillary pressure-saturation relation, which relies on pore-scale pressure differences at the invasion front, is almost invariant of flow conditions (dynamic and quasi-static).

A Numerical Analysis of the Effects of Supercritical CO2 Injection on CO2 Storage Capacities of Geological Formations

One of the most promising means of reducing carbon content in the atmosphere, which is aimed at tackling the threats of global warming, is injecting carbon dioxide (CO2) into deep saline aquifers (DSAs). Keeping this in mind, this research aims to investigate the effects of various injection schemes/scenarios and aquifer characteristics with a particular view to enhance the current understanding of the key permanent sequestration mechanisms, namely, residual and solubility trapping of CO2. The paper also aims to study the influence of different injection scenarios and flow conditions on the CO2 storage capacity and efficiency of DSAs. Furthermore, a specific term of the permanent capacity and efficiency factor of CO2 immobilization in sedimentary formations is introduced to help facilitate the above analysis. Analyses for the effects of various injection schemes/scenarios and aquifer characteristics on enhancing the key permanent sequestration mechanisms is examined through a series of numerical simulations employed on 3D homogeneous and heterogeneous aquifers based on the geological settings for Sleipner Vest Field, which is located in the Norwegian part of the North Sea. The simulation results highlight the effects of heterogeneity, permeability isotropy, injection orientation and methodology, and domain-grid refinement on the capillary pressure–saturation relationships and the amounts of integrated CO2 throughout the timeline of the simulation via different trapping mechanisms (solubility, residual and structural) and accordingly affect the efficiency of CO2 sequestration. The results have shown that heterogeneity increases the residual trapping of CO2, while homogeneous formations promote more CO2 dissolution because fluid flows faster in homogeneous porous media, inducing more contact with fresh brine, leading to higher dissolution rates of CO2 compared to those in heterogeneous porous medium, which limits fluid seepage. Cyclic injection has been shown to have more influence on heterogenous domains as it increases the capillary pressure, which forces more CO2 into smaller-sized pores to be trapped and exposed to dissolution in the brine at later stages of storage. Storage efficiency increases proportionally with the vertical-to-horizontal permeability ratio of geological formations because higher ratios facilitate the further extent of the gas plume and increases the solubility trapping of the integrated gas. The developed methodology and the presented results are expected to play key roles in providing further insights for assessing the feasibility of various geological formations for CO2 storage.

Modeling of methane migration from gas wellbores into shallow groundwater at basin scale

Methane contamination of drinking water resources is one of the major concerns associated with unconventional gas development. This study assesses the potential contamination of shallow groundwater via methane migration from a leaky natural gas well through overburden rocks, following hydraulic fracturing. A two-dimensional, two-phase, two-component numerical model is employed to simulate methane and brine upward migration toward shallow groundwater in a generic sedimentary basin. A sensitivity analysis is conducted to examine the influence of methane solubility, capillary pressure–saturation relationship parameters and residual water saturation of overburden rocks, gas leakage rate from the well, tilted formations, and low-permeability sediments (i.e., claystones) on the transport of fluids. Results show that the presence of lithological barriers is the most important factor controlling the temporal–spatial distribution of methane in the subsurface and the arrival time to shallow groundwater. A pulse of high leakage rate is required for early manifestation of methane in groundwater wells. Simulations reveal that the presence of tilted features could further explain fast-growing methane contamination and extensive lateral spreading reported in field studies.

Dynamic permeability functions for partially saturated porous media

SUMMARY While the frequency-dependence of permeability under fully saturated conditions has been studied for decades, the corresponding characteristics of partially saturated porous media remain unexplored. Notably, it is not clear whether the use of effective pore fluid approaches under such conditions is valid. To address this issue, we propose a method that allows us to obtain dynamic permeability functions for partially saturated porous media. To this end, we conceptualize the considered pore space as a bundle of capillary tubes of different radii saturated by two immiscible fluid phases. We then solve the Navier–Stokes equations within the pore space and define a capillary pressure–saturation relationship, which permits to obtain saturation- and frequency-dependent effective permeability estimates. The application of this method to a realistic model of an unconsolidated granular sediment demonstrates that dynamic effective permeability functions for wetting and non-wetting fluid phases exhibit distinct characteristics, thus rendering effective pore fluid approaches inadequate. Finally, we explore the capability of the seminal dynamic permeability model developed by Johnson et al.[J. Fluid Mech. 176, 379 (1987)] to account for the effects of partial saturation. We find that the frequency scaling proposed by Johnson et al. prevails in partially saturated scenarios. However, the parameters associated with this model need to be redefined to account for saturation-dependent effects.

Impacts of dynamic capillary pressure effects in supercritical CO2-Water flow: Experiments and numerical simulations

Contrary to report that dynamic capillary pressure effect was insignificant in the supercritical CO2-water (scCO2-water) flow system, this work found the effect to be considerable in the displacement of water or brine by injected scCO2 in the geological carbon sequestration, especially prior to the attainment of equilibrium in the system. Series of controlled laboratory scale experimental measurements and numerical simulations of the dynamic capillary pressure effect and its magnitude (dynamic coefficient, τ) for supercritical CO2-water(scCO2-water) system are reported in unconsolidated silica sand. Novel measurement technique has been developed to achieve this purpose, by applying the concept of two-phase flow system in the context of geological carbon sequestration. This work considers the injection of scCO2 into storage aquifer as a two-phase flow system, where the CO2 displaces the resident fluid (brine or water). Using a high-pressure and high-temperature experimental rig, capillary pressure–saturation relationships (Pc-S) for this flow system and the saturation rate dependencies of the Pc-S relationships (quantified by dynamic coefficient, τ), known as dynamic capillary pressure effect were determined. This τ was previously unreported for scCO2-water system. In scCO2-water flow system, τ ranges from 2 × 105 to 6 × 105 Pa s at high water saturation and 1.3 × 106 to 8 × 106 Pa saround the irreducible saturation. τ increases with rising temperature but decreases with increase in porous medium permeability. Numerically determined τ-S relationships compare well with the corresponding experimental results for wide range of water saturation.The implication was that water saturation of the porous media will be considerably underestimated, if the dynamic capillary pressure effect was ignored in the characterization of the scCO2-water flow system, i.e., if only equilibrium Pcrelationship was used.

Exploring the effect of flow condition on the constitutive relationships for two-phase flow

Empirical relationships that describe two-phase flow in porous media have been largely hysteretic in nature, thereby requiring different relationships depending on whether the system is undergoing drainage or imbibition. Recent studies have suggested using interfacial area to close the well-known capillary pressure-saturation relationship, while others expand upon this by including the Euler characteristic for a geometric description of the system. With the advancement of fast x-ray microtomography at synchrotron facilities, three-dimensional experiments of two-phase quasi- and non-equilibrium flow experiments were conducted to quantify the uniqueness of constitutive relationships under different flow conditions. We find that the state functions that include the Euler characteristic provide the most unique prediction of the state of the system for both quasi- and non-equilibrium flow. Of these functions, those that infer volume fraction from the other state variables are independent of flow condition (quasi- or non-equilibrium). This enhances the applicability of new constitutive relationships allowing for more robust models of two-phase flow.

Testing an Analytical Model for Predicting Subsurface LNAPL Distributions from Current and Historic Fluid Levels in Monitoring Wells: A Preliminary Test Considering Hysteresis

Knowledge of subsurface light nonaqueous phase liquid (LNAPL) saturation is important for developing a conceptual model and a plan for addressing LNAPL contaminated sites. Investigators commonly predict LNAPL mobility and potential recoverability using information such as LNAPL physical properties, subsurface characteristics, and LNAPL saturations. Several models exist that estimate the LNAPL specific volume and transmissivity from fluid levels in monitoring wells. Commonly, investigators use main drainage capillary pressure–saturation relations because they are more frequently measured and available in the literature. However, main drainage capillary pressure–saturation relations may not reflect field conditions due to capillary pressure–saturation hysteresis. In this paper, we conduct a preliminary test of a recent analytical model that predicts subsurface LNAPL saturations, specific volume, and transmissivity against data measured at a LNAPL contaminated site. We call our test preliminary because we compare only measured and predicted vertical LNAPL saturations at a single site. Our results show there is better agreement between measured and predicted LNAPL saturations when imbibition capillary pressure–saturation relations are employed versus main drainage capillary pressure–saturation relations. Although further testing of the model for different conditions and sites is warranted, the preliminary test of the model was positive when consideration was given to capillary pressure–saturation hysteresis, which suggests the model can yield reasonable predictions that can help develop and update conceptual site models for addressing subsurface LNAPL contamination. Parameters describing capillary pressure–saturation relations need to reflect conditions existing at the time when the fluid levels in a well are measured.

Characterization of Capillary Pressure–Saturation Relationships for Double-Porosity Medium Using Light Transmission Visualization Technique

Capillary pressure saturation (Pc–Sw) relationship plays a central role in the description of fluid flow in porous media. In this research, the light transmission visualization (LTV) technique was applied to characterize the Pc–Sw relationship in a double-porosity medium. Four experiments were conducted in two-dimensional (2-D) flow chambers packed with a double-porosity medium composed of a mixture of silica sand and sintered kaolin clay spheres. In each experiment, a different volumetric fraction of macropores and micropores was used. The experiment was also repeated by compacting the flow chamber with silica sand only to represent single-porosity medium. Variable saturations of water across the height of the system were applied by controlling the capillary pressure. Images of the 2-D model were collected using a digital camera and analyzed pixel by pixel to determine water saturation in the double-porosity medium. Results from the LTV technique showed that the Pc–Sw relationships for all experiments in double-porosity soil medium were similar in shape but varied depending on the porous media composition. Comparison with the pressure cell test results showed that the Pc–Sw curves for all experiments consistent comparable to those obtained by the LTV technique. The Pc–Sw curves were also fit to van Genuchten model for comparison and validation. For double-porosity media, the best-fit parameters were consistent with published data for sandy clay. Moreover, little variability was observed in the best-fit α and n values for the different double porosity. Overall, this study proves that the LTV technique is a noninvasive laboratory tool that can provide high-resolution spatial data for water saturation distribution in different types of porous media and is capable of producing highly resolved Pc–Sw relationships.

Evaluation of van Genuchten-Mualem model on the relative permeability for unsaturated flow in aperture-based fractures

The relative permeability versus saturation relation is fundamental for modeling unsaturated flow processes in aperture-based fractures. On the basis of the local cubic law and the connectivity probability of aperture distribution within single fractures, an analytical relationship between the relative permeability and saturation is established. When the van Genuchten function on the description of the capillary pressure-saturation relationship is applied, an explicit mathematical expression between the relative permeability and saturation is gained similar to the form of the van Genuchten-Mualem (VG-M) model of porous media. Through the comparisons between the several series of laboratory-measured data available in the literature and theoretical results, good agreements are both presented and they suggest that the proposed VG-M model can be successfully used for aperture-based fractures as well as porous media. To understand aperture variation dependence of the relative permeability properties, a computational method combining fractal theory and the invasion percolation model to determine the empirical parameters associated with the spatial correlation of aperture distribution is developed. Simulated fractures with spatially correlated and uncorrelated aperture distributions corresponding respectively to small and large fractal dimensions are both studied. According to the simulated results, the residual saturation generally increases with fractal dimension increments. However, the value of m exhibits a weak dependence on fractal dimension. The proposed model can be applied to various engineering such as seepage control for rock slopes, petroleum reservoirs, nuclear waste disposal and geologic storage of carbon dioxide.