Two-phase Displacement Research Articles

Percolation without trapping: How Ostwald ripening during two-phase displacement in porous media alters capillary pressure and relative permeability.

Conventional measurements of two-phase flow in porous media often use completely immiscible fluids, or are performed over timescales of days to weeks. If applied to the study of gas storage and recovery, these measurements do not properly account for Ostwald ripening, significantly overestimating the amount of trapping and hysteresis. When there is transport of dissolved species in the aqueous phase, local capillary equilibrium is achieved: this may take weeks to months on the centimeter-sized samples on which measurements are performed. However, in most subsurface applications where the two phases reside for many years, equilibrium can be achieved. We demonstrate that in this case, two-phase displacement in porous media needs to be modeled as percolation without trapping. A pore network model is used to quantify how to convert measurements of trapped saturation, capillary pressure and relative permeability made ignoring Ostwald ripening to account for this effect. We show that conventional measurements overestimate the amount of capillary trapping by 20-25%.

Numerical pore-scale investigation of two-phase displacement with non-Newtonian defending fluid

In the petroleum engineering and chemical industries, fluids engaging in displacement often have non-Newtonian properties, even though many former studies assume constant viscosities in the defending fluid. In this study, the computational fluid dynamics approach was performed in a two-dimensional model with uniformly distributed disks. This arrangement helps reveal the phenomenon and mechanics of how non-Newtonian characteristics of defending fluid affect two-phase displacement in porous media. Both global (in the whole medium) and regional (in the pore throat) studies revealed that shear-thinning makes capillary force and the pressure in the invading fluid decisive and leads to a uniform pattern. Meanwhile, the shear-thickening causes fingering due to the pressure drop in the defending fluid that becomes decisive. Cases of increasing injection rates were investigated to verify their ability to improve efficiency. The results verified that increased injection rates are effective in shear-thinning cases but energy-intensive when it comes to costs in shear-thickening cases. Finally, the viscosity ratio and capillary number (M-Ca) diagram were extended by plotting non-Newtonian cases as lines to consider viscosity variation. An estimation method was presented, which calculates the characteristic viscosity and locates non-Newtonian cases on an M-Ca diagram. This work can serve as a reference for enhanced oil recovery method development and microfluidic manipulation.

Effect of Wettability and Permeability on Pore-Scale of CH4–Water Two-Phase Displacement Behavior in the Phase Field Model

Hydraulic measures such as hydraulic slotting and hydraulic fracturing are commonly used in coal seam pressure relief and permeability enhancement. Two-phase flow patterns of CH4–water in pore-sized coal seams after hydraulic measures are critical to improve gas extraction efficiency. The phase field module in COMSOL Multiphysics™ 5.4 and the classical ordered porous media model were used in this paper. The characteristics of CH4–water two-phase immiscible displacement in coal seams under different capillary numbers (Ca) and viscosity ratios (M) were simulated and quantitatively analyzed. By changing the contact angle of the porous media, the flow patterns of CH4–water two-phase in coal with different wettability were simulated. Results show that wettability significantly affects the displacement efficiency of CH4. Additionally, by constructing a dual-permeability model to simulate the varying local permeability of the coal, the flow patterns of different Ca and M in dual-permeability media were further investigated. It is found that CH4 preferentially invades high-permeability regions, and the displacement efficiency in low-permeability regions increases with higher Ca and M, providing a reference for gas extraction from coal seams after hydraulic measures.

Influence of cationic surfactants on two-phase air–liquid displacement in porous media

The displacement efficiency of leaching agent solution in orebody pores is the key factor affecting the leaching rate of rare earth ions. To improve the displacement efficiency, cationic surfactants were added to the solution as the invading phase fluid, and microfluidic visualization experiments were carried out. Based on the experimental results, the effects of cationic surfactants on air-liquid two-phase displacement and its mechanism were analyzed. The results show that cationic surfactants can change the capillary fingering to stable displacement mode. Moreover, the closed air clusters are significantly reduced, and the displacement efficiency is greatly improved, up to 96.75 %. In addition, displacement efficiency is negatively correlated with the porosity of the porous media. Cationic surfactants primarily affect the displacement by changing the interfacial properties of the solution. The research results provide theoretical guidance for the efficient mining of ionic rare earths.

Influence of binder content on gas-water two-phase flow and displacement phase diagram in the gas diffusion layer of PEMFC: A pore network view

Understanding the gas-water flow dynamics in the gas diffusion layer (GDL) is one of the keys to improving the proton exchange membrane fuel cell's (PEMFC) overall performance and avoiding water flooding. Yet, the relationship between the two-phase flow and micro-scale GDL structures (including binder, PTFE, and fiber skeleton) is not well understood. In this study, three-dimensional GDL structures with different fractions of binder contents (φb=0%∼50%) and a fixed porosity of 75.6 % are confidently reconstructed based on high-resolution images from the confocal microscope, implying that the addition of binder will increase the number of large pores and cause a bimodal throat size distribution through morphology analysis. Thereafter, drainage simulations are performed under a wide range of capillary number (−9 < log Ca <0) and viscosity ratio (−3 < log M < 2) by the pore network model (PNM), which robustly predicts the displacement phase diagram of viscous fingering, capillary fingering, stable displacement, and transitional regime. In the viscous fingering and stable displacement regime, the nonwetting phase saturation (Snw) is nearly the same for different φb, implying the fluid invading pathway does not change much with the addition of binder. However, in the capillary fingering regime (refer to the actual operating conditions), Snw increases rapidly with φbat the breakthrough time and its transient value continues to increase until the steady state, which may be attributed to the increased fractions of pores above the capillary threshold attributed by the bimodal throat size distribution. In addition, the effective water permeability increases sharply with φb, whereas the gas permeability remains almost constant, which means such pore structure alteration by adding the binder is beneficial to water disposal in PEMFC. This research provides insights into delineating the effect of pore and throat size distribution alteration by adding binder on two-phase dynamics in GDL.

Study on two-phase displacement law considering mass transfer and diffusion

The influence of channeling on viscous fingering instability of CO2 miscible displacement is studied in the paper. Due to the viscous fingering not easily observed in porous media, channeling is used to simplify the viscous fingering instability. We adopted nonlinear simulation to investigate the development of viscous fingering instability during the displacement of Newtonian fluids in a channel by miscible fluids, and the influence of different Pe and different viscosity ratio R was studied. Under homogeneous conditions, when R is the same, the larger the Pe is, the more obvious the convection in the process of CO2 displacement is, the earlier the viscous fingering occurs, and the shorter the time for the finger to break through to the right boundary is. When Pe is the same, the larger the R is, the more unstable the contact area of miscible displacement becomes. More finger structures appear, and more complex fingering phenomena occur. The larger the R is, the earlier the fingering phenomenon appears, and the earlier it breaks through to the right boundary. In addition, we studied the change in Relative Mixing Length (RML) during the diffusion process quantitatively. Finally, our investigation delved into the impact of heterogeneity on viscous fingering. We observed that under significant heterogeneity, viscous fingering tends to manifest preferentially in the direction of increasing permeability.

Deep learning-based pore network generation: Numerical insights into pore geometry effects on microstructural fluid flow behaviors of unconventional resources

Pore-scale transport behaviors and mechanisms of rock reservoirs are still not well understood to increase unconventional resource production. This work mainly focuses on proposing a deep learning-based method to rapidly construct optimal pore network with different pore types, and deeply analyze its effects on pore-scale transport behaviors and mechanisms. The pore-scale variables reservoir evaluation indexes are defined to quantitatively evaluate pore geometry effects on the properties and production of rock reservoirs. The two-phase displacement simulations in pore network are conducted to study microstructural flow behaviors and transport mechanisms. Results suggest that the deep learning-based digital labeling algorithm (DL-DLA) has excellent abilities to rapidly construct pore network with errors less than 5%, compared with the classical algorithms. Square pores and circle throats are suggested as the optimal pore network assembly, considering the fluid phase drainage efficiency and production rate. The microstructural transport mechanisms are concluded as the pore-throat drainage, pore-filling, fluid phase mixing and fluid phase equilibrium processes. The novel theoretical relation between fluid phase drainage and microscopic production indexes provides effective tools to estimate rock reservoir production with errors all less than 10%, which are helpful for the technique developments to increase the production of unconventional resources in rock reservoirs.

Does backflow occur in forced imbibition into a dual-permeability pore network?

Backflow is a typical flow phenomena in two-phase displacement, but it is rarely studied in the forced imbibition and it remains unknown if the backflow occurs in forced imbibition into a porous medium. In this paper, we focus on the forced imbibition and investigate the backflow behavior in pore doublet (PD) models and in dual-permeability pore networks. Inspired by Gu et al. (2021) and Shan et al. (2023), a general mathematical model is first developed to predict the evolution of the penetration length of wetting fluid in a PD with arbitrary initial interface locations. Based on the analytical predictions and numerical simulations, we then study the influence of initial interface location, capillary number, viscosity ratio, and channel width ratio on the backflow. Results show that the backflow in a PD is mainly attributed to high flow rate in narrow channel, driven by the dominant capillary force. To supplement the insufficiency of inlet flow rate, the fluid in wide channel has to flow backwards to fill the narrow channel. The backflow strengthens with the decrease of capillary number or viscosity ratio, but it exhibits non-monotonic variation with initial interface location and channel width ratio. Moreover, the phase diagrams showing the critical conditions for the occurrence of backflow are established in terms of capillary number, viscosity ratio and channel width ratio. Finally, numerical simulations are conducted to explore the occurrence of backflow in three different dual-permeability pore networks. It is found that the backflow does not occur in dual-permeability pore networks due to the low flow rate caused by overlap event and pronounced tortuosity in the low permeability zone, or occurs only in the early stage when the capillary valve effect does not work.

Study on Numerical Simulation of Gas–Water Two-Phase Micro-Seepage Considering Fluid–Solid Coupling in the Cleats of Coal Rocks

The increasing demand for natural gas energy will promote unconventional natural gas, such as coal seam gas and shale gas, to play a key role in future energy development. The mechanical properties of coal seams are weaker compared with conventional natural gas reservoirs. The fluid–solid coupling phenomenon exists widely at the pore scale and macro scale of coal seams, and runs through the whole process of coalbed gas exploitation. The objective of this study is to establish a microscale gas–water flow model for coalbed methane considering fluid structure coupling. Frist, this study used scanning electron microscopy (SEM) to obtain microscopic pore images of coal rocks. Then, we constructed a numerical model to simulate the movement of coalbed methane and water within the scale of coal cleats based on the Navier–Stokes equation, phase field method, and solid mechanics theory. Finally, we analyzed the effects of injection pressure and wettability on the microscopic two-phase seepage characteristics and displacement efficiency of coal. Our research shows that when the injection pressure is increased from 60 kPa to 120 kPa, the displacement completion time is shortened from 1.3 × 10−4 s to 7 × 10−5 s, and the time is doubled, resulting in a final gas saturation of 98%. The contact angle increases from 45° to 120°, and the final gas saturation increases from 0.871 to 0.992, an increase of 12.2%.

Pore-scale investigation on the effect of capillary barrier on two-phase displacement in dual-structure porous media

Although immiscible fluid–fluid displacement in porous media has received extensive attention, understanding the dynamics behavior within complex structures remains elusive. This study utilizes the direct numerical simulation by solving the Navier–Stokes equations and coupling with the volume of fluid method to examine oil–water flow in porous media across various contact angles θ and capillary number Ca. Three kinds of artificial porous media were generated with designed opening angle β, including single-structure and dual-structure models. A theoretical analysis of the capillary barrier phenomenon, as well as its occurrence conditions, is identified under water-wet conditions. Generally, when θ + β &amp;lt; 90°, the capillary force consistently drives oil displacement from throats to pores. Conversely, if θ + β &amp;gt; 90°, the direction of the capillary force can move toward the water phase side and prevent the fluid interface from continuing to move. For a single-structure porous medium, the dynamics behavior of fluids is controlled by the capillarity, wettability, and geometric structures. The greatest efficiency occurs when the condition θ + β = 90° is met, particularly at an intermediate Ca. For a dual-structure porous medium with smaller opening angles inside, the water phase tends to infiltrate the embedded pore structure due to weaker capillary barrier effects. Conversely, larger opening angles within the embedded structure lead to stronger capillary barrier effects, hindering water entry into the interior porous medium. This obstruction forces the water phase to bypass and traverse longer flow paths, resulting in the formation of a large amount of residual oil.

Effect of the capillarity and viscosity on the change of flow paths during two-phase displacement in porous media

Pore-scale direct numerical simulations were conducted to explore the changes of flow paths and dynamic distribution of water-oil phases during two-phase displacement in porous media. Three contact angles, i.e., 45°, 90°, and 135°, correspond to water-wet, intermediate-wet, and oil-wet rock surfaces, respectively. The medial axis within complex pore channels is obtained using a grid-based method. Subsequently, a novel particle tracking-based approach is proposed to extract the flow paths during two-phase displacement. The results show that when water enters a porous medium filled with oil, the distribution of oil phase flow paths is uniform, indicating that all oil phases are movable. As water continues to be injected, some water-oil interfaces stop at pores or throats due to capillary force, causing the flow paths through these locations to disappear. In oil-wet and intermediate porous media, capillary forces always act as resistance; therefore, the water-oil interfaces stop at the throat channels. Interestingly, under water-wet conditions, the water-oil interface can reverse, and the capillary force presents resistance, resulting in the interfaces being blocked at enlarging areas, usually from throats to pores. Once breakthrough occurs, preferential flow paths for pure water are established, resulting in a rapid decrease of flow paths with moving water-oil interfaces under oil-wet and intermediate-wet conditions, while movement continues in a water-wet medium. Due to the typically lower viscosity of water than oil, the viscous force decreases as water saturation increases. As water injection continues, the water in some channels gradually displaces oil, resulting in differences in flow rates between oil-filled and water-filled channels. This study provides a method for identifying the changes in flow paths during two-phase displacement in porous media and gives potential benefits for designing strategies to improve oil recovery.

Effects of displacement velocity on interfacial reconstruction events during immiscible two-phase displacement

During the two-phase fluid displacement in porous media, with the increase in capillary number Ca, different wettability effects are suppressed; however, its potential control mechanism has not been clarified. Therefore, in this study, we have analyzed the pore scale process related to interface reconfiguration events in detail and profoundly clarified the nature of a series of interface reconfiguration events being suppressed. Based on typical pore throat, we elaborated and confirmed that the development and evolution direction of fluid displacement mode always follow the principle of minimum operating power. That is to say, in order to avoid extra work, the system will compare all the potential moving meniscus at the displacement front and always choose the local path with the minimum operating power (Po=ΔpQ) of the system for displacement. Under this theory, a series of interface reconfiguration events are considered energy favorable self-regulation events derived by the system in order to avoid extra energy consumption. However, the appearance and disappearance of interface reconstruction events are considered to be the result of the mechanism of “self-regulation of surface energy change rate” and “self-regulation of viscosity dissipation rate” in order to approach the minimum operating power. This study provides us with a sufficient physical explanation to understand the nature of the wettability effect being suppressed.

Estimation of relative permeability curves in fractured media by coupling pore network modelling and volume of fluid methods

The relative permeability of porous and fractured media is an important concept for various technological applications including hydrocarbon recovery, CO2 sequestration, hydrogen storage, hydrology, and microfluidics. In pore-scale simulations, relative permeability curves can be obtained either by pore-network modelling or direct numerical simulations (e.g., Navier–Stokes based and Lattice Boltzmann methods). While pore network models rely on several conceptual mathematical and geometric simplifications compared to more rigorous direct numerical methods, pore network modelling is often the only option to conduct the fast numerical simulation at a core-scale and regular desktop PC within a reasonable time frame. In this study, we analyse the ability of the developed hybrid pore network modelling and volume of fluid methods (VOF–PNM) model to accurately predict the two-phase flow displacement in a ramified system of fractures. This is done by conducting a number of 2D and 3D two-phase flow simulations with different viscosity ratios, contact angles, and capillary numbers. The VOF–PNM output with respect to history-matched relative permeability and capillary pressure curves is then compared to the reference conventional VOF simulations using a range of validation metrics. Such benchmarking allows concluding that the developed VOF–PNM solver can model flow through a system of fractures with an acceptable accuracy compared to the widely used VOF method. In turn, the conventional dynamic PNM algorithm failed to match the relative permeability and capillary pressure when compared to the reference VOF simulations. In terms of computational time, the non-parallelised hybrid VOF–PNM model is at least two orders of magnitude faster than parallelised VOF simulation and only one order of magnitude slower than the conventional dynamic PNM algorithm. The findings are beneficial for simulating two-phase flow through a fractured system at a core scale, as a design tool for microfluidic devices, and for further evolution of the VOF–PNM model into a comprehensive tool for transient multi-scale multi-physics simulations in coal.

Gas–Water Two-Phase Displacement Mechanism in Coal Fractal Structures Based on a Low-Field Nuclear Magnetic Resonance Experiment

In this paper, the gas–water two-phase seepage process under a real mechanical environment is restored by a nuclear magnetic resonance experiment, and the gas–water two-phase distribution state and displacement efficiency in coal with different porosity under different gas injection pressures are accurately characterized. The fractal dimension of liquid phase distribution under different gas injection pressures was obtained through experiments, and the gas–water two-phase migration law is inverted according to it. Finally, the gas–water two-phase migration mechanism inside the fractal structure of coal was obtained. The results are as follows: 1. Gas will first pass through the dominant pathway (the composition of the dominant pathway is affected by porosity) and it will continue to penetrate other pathways only when the gas injection pressure is high. When the gas injection pressure is low, the displacement occurs mainly in the percolation pores. With the increase in gas injection pressure, the focus of displacement gradually shifts to the adsorption pore. 2. As the gas injection pressure increases, the displacement efficiency growth rate is relatively uniform for the high-porosity coal samples, while the low-porosity coal samples show a trend of first fast and then slow growth rates. When the gas injection pressure reaches 7 MPa, the displacement efficiency of high-porosity coal samples exceeds that of low-porosity coal samples. 3. With the increase in gas injection pressure, the fractal dimension of the adsorption pore section and the seepage pore section shows an increasing trend, but the fractal dimension of the adsorption pore section changes faster, indicating that with the increase in gas injection pressure, gas–water two-phase displacement mainly occurs in the adsorption pore section.

Modeling pore-scale CO2 plume migration with a hypergravity model

Understanding site-scale carbon dioxide migration in saline aquifers is crucial for storage safety. High time and economic costs make establishing a full-scale model of this long-term and large-scale process difficult. Hypergravity model shortens the length and time scale, which has been applied to physical modeling of two-phase immiscible displacement. To evaluate the feasibility of hypergravity modeling two-phase displacement in porous media at pore scale, CO2 migration in saline aquifer is a suitable and classic problem. We used the phase field method to simulate the vertical displacement of brine by carbon dioxide due to buoyancy and pressure at the pore scale. The pore-scale phenomena of the two-phase displacement process were obtained by assessing different flow rates with or without gravity. We systematically analyzed the feasibility of the hypergravity model to evaluate CO2 migration in the geological domain by evaluating the hypergravity effect and using dimensionless analysis. We provide suggestions for performing the hypergravity model to evaluate and predict immiscible displacement in two-phase system.

Representative elementary volumes for various characteristics of two-phase flows in porous media: A statistical approach

This article presents a systematic study of the influence of two-phase flowpatterns on the representative elementary volume for various displacement characteristics. This paper considers both drainage and imbibition regimes and related patterns such as compact displacement, viscous, and capillary fingering. As two-phase flow characteristics, the displacement efficiency and interfacial contact areas between the invaded fluid and the displaced fluid, as well as between the invaded fluid and solid particles, are considered. Not limited to displacement patterns, we study the effect of capillary number on the minimum REV size. The findings of this paper are based on numerical simulations performed in two-dimensional artificially created porous structures using the Monte-Carlo movement algorithm. The main conclusions are validated on 3D X-ray computed tomography images of natural sandstones. Two-phase immiscible displacement in a porous medium is modeled using the lattice Boltzmann equations with the multi-relaxation time collision operator in combination with the color-gradient method describing interfacial phenomena and wetting effects. Minimum REV sizes have been identified using statistical data collected from a large number of numerical simulations in two-dimensional samples. Coefficient of variation and average value of the investigated property have been used to identify REV. The results show that REV for two-phase flow in porous media depends on the displacement pattern. Minimum REV sizes for viscous fingering and compact displacement are close. The accuracy of predicting the displacement efficiency for viscous fingering and compact displacement modes is much higher than for capillary fingering. Minimum REV sizes for interfacial contacts are lower than for displacement efficiency.

Effects of Cassie-Wenzel wetting transition on two-phase flow in porous media

Wettability is one of the most important factors affecting multiphase flow in porous media. In this study, effects of the dynamic wetting process on two-phase flow displacement are investigated at the pore scale. A time-dependent Cassie-Wenzel wetting transition model is improved and incorporated into the pseudopotential multiphase multicomponent lattice Boltzmann model. With the Cassie-Wenzel wetting transition considered, two-phase flow displacement is simulated in Voronoi porous media with structural disorder and layered characteristics under different capillary number and wetting transition characteristic time. The simulation results show that the wetting transition promotes cooperative pore filling and weakens the effect of nonuniformity of capillary resistance. Under different capillary number, increased wetting transition rate improves the wettability of invading fluid, and thus the saturation of invading fluid is increased. The results also show that the layered structure with decreased pore size along the flow direction compacts the displacement pattern and weakens the viscous fingering, leading to higher displacement efficiency. While in this layered structure, effects of the wetting transition are suppressed due to lower interfacial length between the invading fluid and solid surface. The simulation results provide new insights of the influence of the dynamic wetting transition and on fluid displacement in porous media.

Pore-scale modeling of gravity-driven superheated vapor flooding process in porous media using the lattice Boltzmann method

In this work, a hybrid method combining interparticle-potential multiphase LBM, finite difference method and characteristic-line wetting scheme, is developed for pore-scale simulation of superheated vapor displacing liquid, driven by gravity, in a porous geometry. The influence of injected vapor superheat, surface wettability and gravity on two-phase displacement and heat transfer processes is investigated. Results show that in thermal displacement, the vapor-liquid interface is unstable and trapped liquid blobs gradually evaporate into vapor. At low vapor superheat degrees, the displacement efficiency, as compared to isothermal displacement, is significantly improved, but it reduces as the vapor superheat degree rises due to the shift of displacement patterns. At all contact angles considered, the displacement always exhibits viscous fingering, although vapor flowpaths become wider with increasing surface wettability. The final vapor saturation is insensitive to surface wettability, but reducing contact angle leads to a less even temperature distribution inside vapor and a decrease in final average vapor temperature. In addition, increasing gravity is found to reduce vapor front temperature, but it almost has no effect on final average vapor temperature because the final average vapor temperature does not only depend on specific interfacial length but also on fingering number and inlet flow rate.

Influence of Different Redevelopment Measures on Water–Oil Immiscible Displacement and Mechanism Analysis

Understanding the two-phase displacement behaviors of oil and water in porous media under different reservoir development modes for enhanced oil recovery is essential. In this paper, the influence of development measures, such as increasing the injection rate, changing the inlet/outlet position, increasing the water viscosity, and reducing the surface tension coefficient, on oil–water dynamic behaviors was studied using a numerical simulation based on the study of the formation of a high-water-cut channel by water flooding at different injection rates. The results show that blockage and restart occur during displacement in the pore–throat channel and during staggered displacement in different pore channels. With an increase in the injection rate, the recovery increases first and then decreases. All the different development measures can increase the swept area and recovery factor. The recovery factor increases significantly by reducing the surface tension coefficient at medium/high injection rates (≥0.01 m/s) and by increasing the viscosity of the water at low injection rates (&lt;0.01 m/s). The numerical simulation study preliminarily revealed the influence of different development measures on displacement behaviors in the pore model. It thus provides theoretical support for understanding the law of oil and water movement in reservoirs.

Effects of macro-scale heterogeneity on the kinetic interface-sensitive tracer test for measuring the fluid–fluid interfacial area in dynamic two-phase flow in porous media

A novel reactive smart tracer method, termed the kinetic interface-sensitive (KIS) tracer test, has been demonstrated in laboratory column experiments to enable measurement of the specific capillary-associated fluid–fluid interfacial area in dynamic two-phase flow displacement processes in porous media. Development of the tracer method towards effective application in real field conditions requires investigation of the influence of the porous media heterogeneity on the front size and the specific interfacial area, and, consequently, in how far a kinetic interface-sensitive tracer experiment, and the corresponding breakthrough curves, are affected. This study employs a two-dimensional Darcy-scale two-phase flow reactive transport model to investigate numerically the KIS tracer transport in heterogeneous porous media. Simulations were carried out for the primary drainage process in a domain formed of fine and coarse porous media. Various heterogeneity patterns, having different numbers of inclusions and different geometrical distributions, were studied. It is shown that the shape of the breakthrough curves can be used as an indicator for quantifying the displacement front roughness, the specific interfacial area in the domain, and the domain heterogeneity, e.g., the existence of preferential flow pathways inside the porous media. The results indicate that when the displacement front roughness is small, the concentration breakthrough curves exhibit a linear increase. The slopes of the breakthrough curves linearly depend on the fraction of the bulk volume occupied by the low-permeability sand inclusions. The volume-averaged specific interfacial area and the size of the transition zone can be determined from the slopes of the breakthrough curves.