Multiphase Flow In Porous Media Research Articles

Adaptive Space-Time Domain Decomposition for Multiphase Flow in Porous Media with Bound Constraints

Adaptive Space-Time Domain Decomposition for Multiphase Flow in Porous Media with Bound Constraints

A deep learning-based workflow for fast prediction of 3D state variables in geological carbon storage: A dimension reduction approach

Deep learning (DL) models are extensively used as surrogate models for high-fidelity simulations of multiphase fluid flow in porous media at large scales, enabling fast forecasts of the spatial–temporal evolution of three-dimensional (3D) state variables in geological carbon storage (GCS). However, training these models in high-dimensional space remains computationally demanding and prone to overfitting because of limited training data. This paper presents a novel workflow to address these challenges by integrating dimension reduction (DR) methods. The proposed workflow employed pre-trained DR models to extract the latent variables of geological models and state variables and utilized the multi-layer perceptron (MLP) for constructing mapping functions between the input and output variables in latent spaces. Subsequently, the pre-trained reconstruction models converted the MLP-predicted latent state variables to their original high-dimensional form. Furthermore, we proposed a novel strategy for the DR and reconstruction of 3D saturation fields to account for the unique data characteristics of sparsity, nonuniformity, and discontinuity. The proposed strategy applied PCA and inverse PCA for 2D average saturation fields and developed a DL-based 3D reconstruction model, leveraging three 2D average saturation fields as input to produce a 3D saturation field as output. The pre-training of DR and reconstruction models and training of MLP models were conducted on 84 Gulf of Mexico (GoM) simulations and evaluated on 12 testing simulations. Each simulation contained 720 monthly time steps, with the first 360 months as the injection period and the rest as the post-injection period. The proposed workflow, incorporating DR and DL models, accurately predicts the normalized 3D pressure fields, achieving mean square error (MSE) of 2.92 × 10−7 compared to the ground truth obtained from a full-physics simulator. Furthermore, the proposed strategy outperformed PCA and convolutional autoencoder (CAE) models on 3D saturation fields, resulting in minor workflow prediction errors with an MSE of 2.93 × 10−5. The results suggest the proposed workflow provides sufficient predictive fidelity across temporal and spatial scales, and enables a speedup of 160 times compared to the full-physics simulator, facilitating improved decision-making and risk assessment for large-scale GCS management in real-time scenarios.

Overview of the Application of Physically Informed Neural Networks to the Problems of Nonlinear Fluid Flow in Porous Media

To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differential equations. To solve this direct problem, it is necessary to linearize the equation system. Algorithm construction for inverse problem solution is problematic since the numerical solution is unstable. The application of implicit methods is reduced to matrix equations with a high rank of the coefficient matrix, which requires significant computational resources. The authors of this paper investigated the possibility of parameterized function (physics-informed neural networks) application to solve direct and inverse problems of non-Newtonian fluid flows in porous media. The results of laboratory experiments to process core samples and field data from a real oil field were selected as examples of application of this method. Due to the lack of analytical solutions, the results obtained via the finite difference method and via real experiments were proposed for validation.

Highly efficient, robust and unconditionally energy stable second order schemes for approximating the Cahn-Hilliard-Brinkman system

In this paper, we present an efficient, robust, and unconditionally energy stable second-order scheme for solving the Cahn-Hilliard-Brinkman (CHB) model, which mathematically describes multiphase flow in porous media. Solving the CHB model is significantly challenging due to its high coupling and nonlinearity. Here, we utilize the scalar auxiliary variable (SAV) method to handle the nonlinear term in the Cahn-Hilliard system, followed by decoupling the model through the implicit-explicit (IMEX) Crank-Nicolson approach. Our constructed scheme employs an adaptive time step, enhancing the robustness of the scheme compared to a fixed time step. The unconditional energy stability of our scheme that integrates artificial stabilized term, is assured easily owing to the SAV method and is theoretically proven in the paper. Finally, numerical experiments employing the Fourier pseudo-spectral method to discrete the spatial variables were conducted in two-dimensional space to validate the numerical accuracy and efficiency of the proposed approach.

Bridging the gap: Connecting pore-scale and continuum-scale simulations for immiscible multiphase flow in porous media

Bridging the gap: Connecting pore-scale and continuum-scale simulations for immiscible multiphase flow in porous media

Interpreting pore-scale fluctuations: Predicting transport coefficients in multiphase flow through porous media using the Green–Kubo formulation—An experimental investigation

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.

Multiscale modeling and simulation of turbulent flows in porous media

Numerical simulation is an important tool for understanding the physics of flows in porous media and for making predictions. The state of the art of multiscale modeling and simulation of turbulent flows in porous media is reviewed in this paper. Numerical simulations of flows in porous media can be classified as microscopic simulations, in which both macroscopic and pore-scale flows are directly resolved, and macroscopic simulations, in which the pore-scale motions are modeled while the volume-averaged equations are solved. Studies in the past few years have shown that microscopic simulations improve the understanding of turbulent flows in porous media considerably; this motivates the development of more efficient and more accurate turbulence models for macroscopic simulations. On the basis of this review, we believe that simulation of flows with higher Reynolds numbers, understanding the transport of macroscopic turbulence, modeling of turbulent flows in inhomogeneous and anisotropic porous media, simulation of compressible and multiphase turbulent flows in porous media, and fluid–structure interaction in deformable porous matrices are important topics to be studied in the future.

Novel fabrication of mixed wettability micromodels for pore-scale studies of fluid-rock interactions.

Wettability plays a crucial role in multiphase fluid flow in porous media, impacting various geological applications such as hydrocarbon extraction, aquifer remediation, and carbon dioxide sequestration. Microfluidic methods have attracted interest for their capacity to explore and visualize essential multiphase flow dynamics at the pore level, mimicking actual rock pore structures. However, creating micromodels with representative mixed wettability is currently a challenge. Existing technology is limited to producing micromodels with a singular wettability, either water-wet or oil-wet, leaving a gap in representing mixed-wet scenarios. In this study, we introduce a novel method to fabricate microfluidic devices with controlled spatial distribution of wettability at the micro-scale, mimicking actual configurations of mixed-wet rocks arising from varied mineralogy and pore structures. The proposed method combines the soft lithography process with thin film deposition techniques. The micromodels were designed to mimic the pore network of actual reservoir rocks, and a silicon substrate served as the foundation for the photolithography process optimization and wettability alteration methodology. Perfluorodecyltrichlorosilane coating was applied using molecular vapor deposition technology for surface wettability modification. The coated parts of the microdevice substrate altered the localized wetting state of the silicon towards hydrophobic, while the wettability remained unchanged in the non-coated areas. We utilized surface measurements, including contact angle, X-ray photoelectron spectroscopy, transmission electron microscopy, scanning electron microscopy, and atomic force microscopy, to assess the wettability, composition, thickness, shape, roughness, and overall quality of the coating. Our fabrication process successfully produced a microfluidics device with tailored mixed-wet attributes at the micro-scale, which is, to our best knowledge, the first achievement in the field. This method enables the replication of mixed-wet characteristics commonly seen in various applications, such as carbonates and shales within underground rocks, providing a more accurate examination of fundamental multiphase fluid dynamics and rock interactions at the pore level.

Multiscale drainage dynamics with Haines jumps monitored by stroboscopic 4D X-ray microscopy.

Slow multiphase flow in porous media is intriguing because its underlying dynamics is almost deterministic, yet depends on a hierarchy of spatiotemporal processes. There has been great progress in the experimental study of such multiphase flows, but three-dimensional (3D) microscopy methods probing the pore-scale fluid dynamics with millisecond resolution have been lacking. Yet, it is precisely at these length and time scales that the crucial pore-filling events known as Haines jumps take place. Here, we report four-dimensional (4D) (3D + time) observations of multiphase flow in a consolidated porous medium as captured in situ by stroboscopic X-ray micro-tomography. With a total duration of 6.5 s and 2 kHz frame rate, our experiments provide unprecedented access to the multiscale liquid dynamics. Our tomography strategy relies on the fact that Haines jumps, although irregularly spaced in time, are almost deterministic, and therefore repeatable during imbibition-drainage cycling. We studied the time-dependent flow pattern in a porous medium consisting of sintered glass shards. Exploiting the repeatability, we could combine the radiographic projections recorded under different angles during successive cycles into a 3D movie, allowing us to reconstruct pore-scale events, such as Haines jumps, with a spatiotemporal resolution that is two orders of magnitude higher than was hitherto possible. This high resolution allows us to explore the detailed interfacial dynamics during drainage, including fluid-front displacements and velocities. Our experimental approach opens the way to the study of fast, yet deterministic mesoscopic processes also other than flow in porous media.

Spatial Characterization of Wetting in Porous Media Using Local Lattice-Boltzmann Simulations

Wettability is one of the critical parameters affecting multiphase flow in porous media. The wettability is determined by the affinity of fluids to the rock surface, which varies due to factors such as mineral heterogeneity, roughness, ageing, and pore-space geometry. It is well known that wettability varies spatially in natural rocks, and it is still generally considered a constant parameter in pore-scale simulation studies. The accuracy of pore-scale simulation of multiphase flow in porous media is undermined by such inadequate wettability models. The advent of in situ visualization techniques, e.g. X-ray imaging and microtomography, enables us to characterize the spatial distribution of wetting more accurately. There are several approaches for such characterization. Most include the construction of a meshed surface of the interface surfaces in a segmented X-ray image and are known to have significant errors arising from insufficient resolution and surface-smoothing algorithms. This work presents a novel approach for spatial determination of wetting properties using local lattice-Boltzmann simulations. The scheme is computationally efficient as the segmented X-ray image is divided into subdomains before conducting the lattice-Boltzmann simulations, enabling fast simulations. To test the proposed method, it was applied to two synthetic cases with known wettability and three datasets of imaged fluid distributions. The wettability map was obtained for all samples using local lattice-Boltzmann calculations on trapped ganglia and optimization on surface affinity parameters. The results were quantitatively compared with a previously developed geometrical contact angle determination method. The two synthetic cases were used to validate the results of the developed workflow, as well as to compare the wettability results with the geometrical analysis method. It is shown that the developed workflow accurately characterizes the wetting state in the synthetic porous media with an acceptable uncertainty and is better to capture extreme wetting conditions. For the three datasets of imaged fluid distributions, our results show that the obtained contact angle distributions are consistent with the geometrical method. However, the obtained contact angle distributions tend to have a narrower span and are considered more realistic compared to the geometrical method. Finally, our results show the potential of the proposed scheme to efficiently obtain wettability maps of porous media using X-ray images of multiphase fluid distributions. The developed workflow can help for more accurate characterization of the wettability map in the porous media using limited experimental data, and hence more accurate digital rock analysis of multiphase flow in porous media.

Electrode Imbibition and Surfactant Interactions with Vanadium Flow Battery Electrolytes

Redox flow batteries (RFB) are a critical technology for stationary grid-scale energy storage, with potential usage with intermittent power sources, such as wind and solar. RFBs are attractive for long-duration energy storage because the anolyte and catholyte are stored separately external to the electrochemical reactor. Separating the electrolytes and the electrochemical cell decouples energy and power densities, unlike batteries that store charge in the solid-state, such as Li-ion, Pb-acid, or Ni-Cd. A standard RFB chemistry is the all-vanadium redox flow battery (VRFB), which utilizes the four oxidation states of vanadium, with V2+, V3+, V4+, and V5+. Recently our group found that adding small amounts of sodium dodecyl sulfate (SDS) to a VFRB increased the kinetics of the V2+ to V3+oxidation.Furthermore, surfactants play essential roles in battery manufacturing and operation. Surfactants can change metal oxide crystal structure, inhibit dendrite growth, limit corrosion, and prevent nanoparticle agglomeration. Surfactants are never wholly removed during manufacturing and can be present during battery operation. Therefore, it is crucial to understand how surfactants impact battery performance and their effect on the materials.This talk describes SDS's equilibrium surface properties and adsorption characteristics at the liquid−air and liquid-solid interfaces, thus providing insights into the interactions of SDS with a VFRB electrolyte. Experiments focusing on the effects of sulfuric acid and vanadium ions on SDS's equilibrium surface tension and critical micelle concentration (CMC) were completed. The Szyszkowski equation is used to calculate SDS's adsorption parameters, such as interfacial surface excess, Γsz [mol/m2], the surface excess at the saturated interface, Γ∞ [mol/m2], the minimum molecular area in the adsorption layer at the saturated interface, Amin [nm2], and the Gibbs free energy of adsorption, ΔGads [kJ/mol]. Furthermore, an examination of the spontaneous imbibition of the VFRB electrolyte with SDS into a porous carbon electrode is presented. The microstructure of porous systems, interfacial tension, and fluid−solid interactions controls the capillary-driven flow and is vital in multiphase flow in porous media. Therefore, understanding SDS's effects on the VFRB electrolyte in an electrode is critical to understanding the electrochemical reactions and molecular interactions occurring.This work was supported as part of the Breakthrough Electrolytes for Energy Storage and Systems (BEES2), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0019409.

A new interacting capillary bundle model on the multiphase flow in micropores of tight rocks

Surfactants are widely used in the fracturing fluid to enhance the imbibition and thus the oil recovery rate. However, current numerical models cannot capture the physics behind capillary imbibition during the wettability alteration by surfactants. Although the interacting capillary bundle (ICB) model shows potential in characterizing imbibition rates in different pores during wettability alteration, the existing ICB models neglect the influence of wettability and viscosity ratio on the imbibition behavior, making it difficult to accurately describe the oil–water imbibition behavior within the porous media. In this work, a new ICB mathematical model is established by introducing pressure balance without assuming the position of the leading front to comprehensively describe the imbibition behavior in a porous medium under different conditions, including gas–liquid spontaneous imbibition and oil–water imbibition. When the pore size distribution of a tight rock is known, this new model can predict the changes of water saturation during the displacement process in the tight rock, and also determine the imbibition rate in pores of different sizes. The water saturation profiles obtained from the new model are validated against the waterflooding simulation results from the CMG, while the imbibition rates calculated by the model are validated against the experimental observations of gas–liquid spontaneous imbibition. The good match above indicates the newly proposed model can show the water saturation profile at a macroscopic scale while capture the underlying physics of the multiphase flow in a porous medium at a microscopic scale. Simulation results obtained from this model indicate that both wettability and viscosity ratio can affect the sequence of fluid imbibition into pores of different sizes during the multiphase flow, where less-viscous wetting fluid is preferentially imbibed into larger pores while more-viscous wetting fluid tends to be imbibed into smaller pores. Furthermore, this model provides an avenue to calculate the imbibition rate in pores of different sizes during wettability alteration and capture the non-Darcy effect in micro- and nano-scale pores.

Implementing pore size distribution into saturation height function modelling of reservoir rock types: A case study on a carbonate gas reservoir

The accurate determination of saturation-height functions for modeling multiphase fluid flow in porous media is critical for applications, such as hydrocarbon recovery and subsurface CO2/H2 storage. The challenges associated with water saturation distribution in carbonate reservoirs arise from their inherent heterogeneity and complex pore systems. Addressing such challenges, this study aims to introduce a robust saturation-height function model that considers a non-linear relationship between capillary pressure and saturation, leading to more reliable estimates of fluid saturations. To achieve this, modifications were performed on a saturation height model based on the relationship between porosity, permeability, and pore size distribution (PSD). First of all, the capillary pressure model implemented in the previously introduced PSD-based approach was replaced by a model suitable for heterogeneous reservoirs, fitting the available mercury injection capillary pressure (MICP) data with higher accuracy. Additionally, the derivation of the relations between the optimum pore throat radius and matching parameters of the capillary pressure model was conducted by finding the best correlation among all the available data in the previous approach. For the first time in this study, considering the resemblance in rock properties like capillary pressure and PSD within each rock type, individual correlations among these parameters were established for each reservoir rock type. The predicted saturation height model was cross-checked against the log and core-derived saturation heights, demonstrating a high level of consistency, particularly along the gas-saturated regions. The obtained results were also compared with the conventional saturation height models, including the Leverett J-Function, Johnson's method, and Cuddy's approach. The significance of the modifications was underscored through a comparison of results with those achieved by the previous approach in which the rock typing was ignored. Although the PSD method, which ignored rock types, exhibited high consistency with log data, our modifications yielded far better predictions by improving the coefficient of determination from 0.68 to 0.84.

Prediction of relative permeability from capillary pressure based on the fractal capillary bundle model

The accurate prediction of relative permeability is one of the most important issues in the study of multiphase flow in porous media and is involved in many fields, such as geothermal energy development and petroleum engineering. Traditional models such as the Purcell model and Burdine model for predicting relative permeability from capillary pressure usually assume that the wetting phase (WP) flows in small pores and that the nonwetting phase (NWP) flows in large pores, which is a limiting assumption, such that these models cannot describe the process of WP being displaced by NWP. In this study, we propose a generalized theoretical model for calculating relative permeability based on the fluid distribution characteristics and the fractal capillary bundle model. The relative location α of the interface between NWP and WP is introduced to characterize the transport of the two-phase interface in porous media. The developed model was validated with relative permeability experimental data of gas–water/oil and compared with the Li model and the Brooks–Corey model. The comparison results show that the new model provides an improved match to experimental data than the Li model and the Brooks–Corey model. The sensitivity analysis results of the model show that tortuosity and pore size distribution play a key role in predicting relative permeability from the capillary pressure curve. The relative permeability of wetting phase decreases significantly with increasing fractal dimension of tortuosity and fractal dimension of pore size distribution. The effect of parameter α, which reflects fluid transport characteristics, on relative permeability of wetting phase is more pronounced in porous media with complex structures and low/ultralow permeability.

Validating mechanistic models of fluid displacement during imbibition

Pore-scale modelling is an important tool to improve our understanding of multiphase flow in porous media. Slow fluid invasion is commonly modelled using quasi-static pore network models (PNM). These models simulate the invasion in a network of simplified pores and throats by invading network elements in order of the quasi-static “invasion” capillary pressure needed for the invading fluid to enter. Despite a multitude of studies that address the predictiveness of PNM, it remains unclear what the leading causes of errors in these methods are, particularly during imbibition. To address this, we developed a novel method to directly validate the invasion capillary pressure models that underlie quasi-static PNM for the first time. The new method compares these models to local capillary pressures measured during in-situ flow experiments visualized with 4D μCT. We applied this to two different open-source PNM extractions from a μCT dataset of a glass beads pack that underwent slow imbibition. This methodology is limited by the temporal resolution of the data, hence we tested assumptions regarding displacement sequences when individual displacements could not be resolved. To constrain the uncertainty on the input parameters, we used local contact angles measured from the μCT images. In the PNMs we investigated, the model-predicted invasion-Pc values were on average greater than the direct measurements made using curvatures from the μCT images. Important sources of mismatch were the difficulty to accurately describe the pore space of a beadpack as a network of pores and throats, as well as the relatively low temporal resolution of the μCT dataset. The method presented here can be used to direct the development of improved pore network models.

Investigating an extended multiphase flow model that includes specific interfacial area

Niessner and Hassnaizadeh (2008) proposed a set of governing equations to model multiphase flow in porous media based on first principles that includes fluid/fluid specific interfacial area as a state variable. Herein, we shed light on the lesser-discussed aspects of their proposed model, referred to as the extended model. Firstly, we show how the extended model facilitates real-time tracking of specific interfacial area. Secondly, we compare numerical solutions of the extended model to that of the traditional multiphase flow model with capillary dispersion and the analytical Buckley–Leverett solution. Thirdly, we provide a sensitivity analysis for the additional unknown parameters of the extended model - specific interfacial permeability and specific interfacial area generation. Lastly, a stability analysis is performed for the numerical solutions. As an auxiliary outcome, we provide an approach to solve the non-linear partial differential equations of the extended model by using torch.autograd as the automatic differentiation engine of PyTorch. Our results demonstrate that the extended model can provide saturation profiles similar to those generated by traditional models, but with the added benefit of real-time tracking of specific interfacial area. The generated specific interfacial area profiles were comparable to expected trends from previous numerical and experimental studies and highlighted the importance of the capillary pressure relationship and specific interfacial area generation term. The results also demonstrate an important balance between the permeability of the porous media and the interfacial permeability that must be maintained; otherwise, generated profiles become physically unrealistic. Overall, the extended model explains the evolution of specific interfacial area during multiphase flow at the cost of additional non-linearity and unknown parameters.

Effect of Rock Dissolution on Two-Phase Relative Permeabilities: Pore-Scale Simulations Based on Experimental Data

Relative phase permeability is an important characteristic of multiphase flow in porous media. Its assessment is an urgent issue when the pore structure changes due to rock dissolution. This article examines the effect of carbonate rock dissolution on two-phase flow based on images obtained by X-ray microcomputed tomography with a spatial resolution of ~18 µm. The characteristics of the two-phase flow were calculated through pore network modeling. The studies were conducted on 20 sub-volumes, which were extracted from cylindrical samples A and B with permeabilities of 0.72 and 0.29 D. HCl solutions (12% and 18%) were injected into samples A and B at a rate of 8 and 2 mL/min, respectively. Due to rock dissolution, the porosity and absolute permeability of the sub-volumes increased by 1.1–33% and 44–368%, respectively. Due to dissolution, the residual oil and water saturations decreased by 20–46% and 25–60%, respectively. These results showed that an increase in absolute permeability led to a significant reduction in residual oil and water saturations. These results also demonstrated that rock dissolution resulted in a change in the spatial heterogeneity of the relative phase permeabilities. The spatial heterogeneity increased in sample A after rock dissolution, while in sample B, it decreased.

Numerical simulation analysis of CH4 breakthrough pressure in partially saturated low-permeability rock sample under multiple P-T conditions

Breakthrough pressure of CH4 is an important parameter in shale gas exploitation and the evaluation of cap rocks. To date, many studies have been carried out to investigate CH4 breakthrough pressure based on experimental methods, meanwhile, some studies have also proposed numerical simulation theories on multiphase flow in porous media. However, there are few studies on numerical simulation methods for predicting CH4 breakthrough pressure on rock-core scale under various conditions. Therefore, in this study, we propose a numerical method that can be used to predict CH4 breakthrough pressure in partially saturated low-permeability rock sample under multiple P-T conditions based on our published experimental results. The simulative results show that both CH4 breakthrough pressure and breakthrough time are exponentially related to temperature and pressure conditions, moreover, CH4 breakthrough pressure and breakthrough time decrease with increasing temperature and pressure. Under the multiple P-T conditions in this study, the effect of pressure on numerical results is greater than that of temperature. By comparing the numerical results with the published experimental data, it has been validated that the numerical method proposed in this study is reasonable. Furthermore, we have parametrically swept 3 key properties in CH4-H2O-rock systems, namely, dynamic viscosity, density, and interfacial tension; the order of the effects of 3 properties on the CH4 breakthrough process is, dynamic viscosity > interfacial tension > density. The numerical method established in this study can provide an important reference for the prediction of gas breakthrough process in rock core and for related numerical studies and engineering practice.

Nonlinear parallel-in-time simulations of multiphase flow in porous media

As the number of processors on supercomputers has increased dramatically, there is a growing interest in developing scalable algorithms with a high degree of parallelism for extreme-scale reservoir simulation. However, traditional simulators and algorithms for such nonlinear problems are usually based on the family of time-marching methods, where parallelization is restricted to the spatial dimension only. In this paper, we propose a family of parallel-in-time (PinT) reservoir algorithms for solving multiphase flow problems in porous media to fully exploit the parallelism of supercomputers, in which the design of efficient nonlinear and linear space-time algorithms plays an essential role. More precisely, we first introduce a space-time mixed finite element method for the fully-implicit discretization. The nonlinear system arising at each parallel-in-time step is solved by a variant of bound-preserving Newton methods with a nonlinear elimination preconditioner, where the corresponding linear system is solved by the space-time restricted additive Schwarz (stRAS) method. Since the straightforward extension of one-level stRAS to multilevel does not work because of the pollution effects from the temporal direction, we accordingly present a nonstandard V-cycle multilevel stRAS method with a pollution-removing strategy to accelerate the convergence and improve the robustness. Numerical experiments are presented to demonstrate that the aforementioned parallel-in-time algorithm can not only achieve a high degree of parallelism in accurately resolving reservoir transport features in a heterogeneous medium, but also successfully circumvent the convergence and scalability issues associated with the constraint of large time steps and the boundedness requirement of the solution.

Systematic Study of Wettability Alteration of Glass Surfaces by Dichlorooctamethyltetrasiloxane Silanization-A Guide for Contact Angle Modification.

To investigate the effects of wettability on multiphase flow in porous media, glass bead packs or micromodels are commonly used. Their wettability can be altered by the surface treatment method-silanization. Although silanization is widely used for glass wettability modification, comparable systematic approaches over a large range of geometries, treatment conditions, and measurement systems are scarce. In this work, dichlorooctamethyltetrasiloxane (Surfasil) treatment was systematically investigated, resulting in a guide for achieving a wide range of contact angles. Initially, the influence of the Surfasil solvent, treatment time, and Surfasil-to-solvent ratio was investigated on glass plates using the sessile drop method. By varying these variables, it was possible to achieve a wide range of comparable, repeatable, and stable contact angles, from approximately 20-95° for air-water systems. Due to the linear increase of contact angle with larger Surfasil exposure, either due to the time or concentration, contact angle tuning is possible until the critical point. Beyond the critical point of exposure, a system-specific plateau value is reached, independent of the approach. After establishing a clear relationship between the parameters and contact angles, the same treatment parameters were applied to single beads, micromodels, and beadpacks with heptane as the chosen solvent. Optical image analysis was used for the microchips, and micro CT data analysis was used for the bead packs. The treatment appeared to be transferable to all geometries, resulting in similar wetting conditions within the limitations of the measurements. It is concluded that a glass plate can be used as an analogue for obtaining the contact angle alteration trends for more complex porous media with similar compositions. Data analysis methods and surface roughness could have an effect on the obtained contact angle spread.