Low-permeability Rocks Research Articles

Experimental and Numerical Simulation Studies on the Synergistic Design of Gas Injection and Extraction Reservoirs of Condensate Gas Reservoir-Based Underground Gas Storage

The natural gas industry has developed rapidly in recent years, with gas storage playing an important role in regulating winter and summer gas consumption and ensuring energy security. The Ke7010 sand body is a typical edge water condensate gas reservoir with an oil ring, and the construction of gas storage has been started. In order to clarify the feasibility of synergistic storage building for gas injection and production, the fluid characteristics during the synergistic reservoir building process were investigated through several rounds of drive-by experiments. The results show that the oil-phase flow capacity is improved by increasing the number of oil–water interdrives, and the injection and recovery capacity is improved by increasing the number of oil–gas interdrives; the reservoir capacities of the high-permeability and low-permeability rock samples increase by about 4.84% and 7.26%, respectively, after multiple rounds of driving. Meanwhile, a numerical model of the study area was established to simulate the synergistic storage construction scheme of gas injection and extraction, and the reservoir capacity was increased by 7.02% at the end of the simulation period, which was in line with the experimental results. This study may provide a reference for gas storage construction in the study area.

Effect of temperature on permeability of mudstone subjected to triaxial stresses and its application

In order to prevent leakage of pyrolysed oil and gas and the release of contaminants from the top and bottom strata, it is essential to carry out a comprehensive study of the seepage behaviour of these strata under high temperature triaxial stress conditions. The findings of this study will contribute to the development of effective strategies for the containment and integrity monitoring of subsurface reservoirs and storage environments. Mudstone, serving as both the upper and lower strata, offers an effective barrier due to its inherently low permeability. In order to explore the change rule of mudstone sealing performance under high temperature triaxial stress, an air-heated low permeability rock mass air permeability measurement system is used to measure the ground stress buried 500 m deep and the temperature variation characteristics of mudstone permeability on the roof and floor of Jimsar oil shale in Xinjiang under 100 °C. It was found that the permeability of stressed mudstone decreased with the temperature rising up to 100 °C. The primary factor influencing the outcome was the thermal expansion of the mudstone. The magnitude of the drop value was contingent upon the triaxial stresses that could potentially be induced by the application of significant tensile forces, resulting in a relatively minor drop value. The average hydraulic radius of pore in the mudstone was also calculated, which also exhibited continuous reduction as heating up to 100 °C and the degree of reduction could reach 68%. The capacity, that prevent oil & gas and contaminant from moving cross strata as a barrier, would be strengthened when the mudstone strata from roof and floor experienced the temperature low than 100 °C. The barrier performance of mudstone as a pollutant migration barrier layer to gas pollutant migration during in-situ heat injection mining of oil shale was further evaluated.

A conceptual and numerical model of fluid flow and heat transport in the Topusko hydrothermal system

Comprehensive understanding of hydrothermal systems is often obtained through the integration of conceptual and numerical modelling. This integrated approach provides a structured framework for the reconstruction and quantification of fluid dynamics in the reservoir, thereby facilitating informed decision-making for sustainable utilisation and environmental protection of the hydrothermal system. In this study, an updated conceptual model of the Topusko hydrothermal system (THS; central Croatia) is proposed based on structural, geochemical, and hydrogeological analyses. The stratigraphic sequence and the structural framework of the THS were defined based on geological maps and field investigations. As depicted by hydrochemical and isotope analyses, thermal waters in Topusko (temperatures of up to 65 °C) are of meteoric origin and circulate in a carbonate aquifer. The THS receives diffuse recharge approximately 13 km S from Topusko, where Triassic carbonates crop out. Gravity-driven regional groundwater circulation is favoured by regional thrusts that tectonically uplifted Palaeozoic low permeable rocks. These structures confine the fluid flow in the permeable, fractured and karstified, Triassic carbonates favouring the northward circulation of the water. A regional anticline lifts the aquifer closer to the surface in Topusko. Open fractures in the anticline hinge zone increase the fracturing and permeability field of the aquifer promoting the quick upwelling of the thermal water resulting in the Topusko thermal springs. Numerical simulations of fluid flow and heat transport corroborate the proposed conceptual model. In particular, a thermal anomaly was modelled in the Topusko subsurface with temperature values of 31.3 °C and 59.5 °C at the surface and at the base of the thermal aquifer, respectively, approaching the field observations. These findings showed that the circulation of Topusko thermal water is influenced by regional and local geological structures suggesting that the enhanced permeability field in the discharge area enables the formation of the natural thermal springs.

Gas transport mechanisms, mathematical models, and impact factors in low-permeability rocks: A critical review

Gas transport mechanisms, mathematical models, and impact factors in low-permeability rocks: A critical review

THE ROLE OF OIL-IN-WATER EMULSION COMPONENTS ON SANDSTONES PERMEABILITY

This work studies the stability of oil-in-water emulsions and proposes a new methodology to evaluate the impact of different emulsion's components (sodium chloride, surfactant, and oil) on permeability decline during the injection into natural rocks. Stable emulsions were obtained by varying surfactant and oil concentrations and stirring speed. Emulsions, proven to be stable for more than 24h, were used in coreflooding tests. First, coreflooding experiments were conducted by injecting brine, which provided a permeability reduction of 7% and 20% in rocks measuring approximately 20mD and 120mD, respectively. Then, a surfactant solution was injected, resulting in a decline in permeability from 17 to 23% in the studied scenarios. Finally, emulsions with 0.05 and 0.01wt% oil concentrations were injected, and permeability was reduced to around 65% of its original value in low permeability rocks. Results show that damage due to oil droplets retention was intensive in the scenarios studied.

Shear-induced fluid localization, episodic fluid release and porosity wave in deformable low-permeability rock salt

Understanding fluid distribution and migration in deformable low-permeability rock salt is critical for geologic disposal of nuclear waste. Field observations indicate that fluids in a salt formation are likely compartmentalized into relatively isolated patches and fluid release from such a formation is generally episodic. The underlying mechanism for these phenomena remains poorly understood. In this paper, a hydrological-mechanical model is formulated for fluid percolation in a rock salt formation under a deviatoric stress. Using a linear stability analysis, we show that a porosity wave (a train of alternating high and low porosity pockets) can emerge from positive feedbacks among intergranular wetting, grain boundary weakening and shear-induced material dilatancy. Fluid localization or episodic release can be viewed as a stationary or propagating porosity wave respectively. Fluid pockets transported via a porosity wave remain relatively isolated with minimal mixing between neighboring pockets. We further show that the velocity of fluid flow can be significantly enhanced by the emergence of a porosity wave. The concept and the related model presented in this paper provide a unified consistent explanation for the key features observed in fluid flow in rock salt. The similar process is expected to occur in other deformable low-permeability media such as shale and partially molten rocks under a deviatoric stress. Thus, the result presented here has an important implication to hydrocarbon expulsion from shale source rocks, radioactive waste isolation in a tight rock repository, and caprock integrity of a subsurface gas (CO2, H2 or CH4) storage system. It may also help develop a new engineering approach to fluid injection into or extraction from unconventional reservoirs.

Implicit hydromechanical representation of fractures using a continuum approach

Fractures control fluid flow, solute transport, and mechanical deformation in crystalline media. They can be modeled numerically either explicitly or implicitly via an equivalent continuum. The implicit framework implies lower computational cost and complexity. However, upscaling heterogeneous fracture properties for its implicit representation as an equivalent fracture layer remains an open question. In this study, we propose an approach, the Equivalent Fracture Layer (EFL), for the implicit representation of fractures surrounded by low-permeability rock matrix to accurately simulate hydromechanical coupled processes. The approach assimilates fractures as equivalent continua with a manageable scale (≫1 μm) that facilitates spatial discretization, even for large-scale models including multiple fractures. Simulation results demonstrate that a relatively thick equivalent continuum layer (in the order of cm) can represent a fracture (with aperture in the order of μm) and accurately reproduce the hydromechanical behavior (i.e., fluid flow and deformation/stress behavior). There is an upper bound restriction due to the Young's modulus because the equivalent fracture layer should have a lower Young's modulus than that of the surrounding matrix. To validate the approach, we model a hydraulic stimulation carried out at the Bedretto Underground Laboratory for Geosciences and Geoenergies in Switzerland by comparing numerical results against measured data. The method further improves the ability and simplicity of continuum methods to represent fractures in fractured media.

A heat mining strategy for the potential Enhanced Geothermal System of the Acoculco Caldera Complex, Puebla (Mexico): A numerical approach based on Multiple Interacting Continua

As the world faces a transition to low-carbon electricity, energy markets have witnessed a fast expansion of Variable Renewable Energy, such as solar and wind power. In contrast, the installed capacity of geothermal electricity has increased with at a much lower rate. Continuous innovation is required to maintain geothermal electricity as a cost-competitive technology that helps building flexible power generation systems. Here we propose a heat mining setup for the promissory Enhanced Geothermal System (EGS) of the Acoculco caldera complex, which hosts a heat source in low permeability rocks. The conceptual model of the EGS reservoir consists of a fractured-porous layer between impermeable confining beds. An injection-production triplet is located in line with a fault plane that intersects the model area. Under the assumption of hydraulic stimulation to the fault zone, flow of the injection-production system restricts to a fracture network with secondary and variable permeability. Mass and heat transport is modeled following the Multiple Interacting Continua method with the software TOUGH2. We evaluate the performance of the heat mining system considering water and CO2 as working fluids for a given flow rate. We also evaluate the impact of fracture spacing in the reservoir performance. Results show that for a reservoir temperature of 300 °C, the CO2-based system experiences considerable adverse flow conditions that demands a higher pressure differential between the producer and injector (about 60 bar higher than the water-based reservoir). Likewise, the low heat capacity of CO2 imply a considerable limitation for heat mining. While for the water-based reservoir the cooling front extends throughout the entire reservoir at 30 yr of operation, for CO2 this happens in only about 60%. Additionally, the energy extracted per unit time in the water-based reservoir results more than twice the energy extracted with CO2. Finally, our numerical results show that fracture spacings in the range of 10 to 75 m behave similarly in terms of heat mining performance; decreasing the heat exchange area by increasing the fracture spacing from 10 to 75 m produces a minor impact under the assumption of high permeability fractures. Additional constrains for the fracture network, such as geometry, effective porosity and permeability of both fractures and rock matrix, have to be investigated in future research to better understand the possible performance of the production system.

Constant-Head Step-Injection Tests Using a Conventional Straddle-Sliding-Packer System for Investigating the Shear Capabilities of Minor Faults

Low-permeability rock is suitable as the host rock of an underground repository for radioactive waste disposal; however, minor faults might develop there. Investigating the shear capability (= shear compliance) of those faults is crucial because they could be elastically sheared by the thermal effect of the waste to damage the waste’s engineered barriers. This study performed constant-head step-injection tests along with a recently developed packer-pressure-based extensometer method for assessing the applicability of this method to investigate the shear capability of minor faults. Herein, two neighboring minor faults (A and B) in siliceous mudstone were evaluated. The results showed that fault A, with centimeter-thick fault breccia, exhibited high shear capability, whereas fault B, with millimeters or less-thick fault breccia, displayed low shear capability despite containing an incohesive fault rock. An elastic shear displacement occurred for fault A during injection and reached 15–66 mm when the test-section pressure increased from 4.1 to 4.3 MPa. Here, the shear capability was 101 mm/MPa or more. Conversely, fault B had cohesion, and no shear displacement was detected even when the test-section pressure increased from 4.0 to 6.0 MPa. In this case, the shear capability was 10−1 mm/MPa or less. The estimated shear capabilities were consistent with the results from previous shear experiments, and therefore, the applied method helps investigate the shear capabilities of minor faults.

Experimental Study on the Gelling Properties of Nano-Silica Sol and Its Spontaneous Imbibition Grouting Mudstone

The low-permeability argillaceous rock mass is an unfavorable geological body commonly found in the construction process of underground engineering conditions such as roadways and tunnels. Due to the compact structure and low permeability of the rock mass, grouting with conventional materials cannot effectively seal the micro-cracks of the rock mass. Based on the low efficiency of high-pressure grouting of nano-silica sol, this paper preliminarily explores the regularities and mechanism of grouting and pore sealing of low-permeability rock mass under the action of silica sol imbibition from the aspects of gelling properties of silica sol, core pore structure, imbibition law, and pore sealing characteristics. The results show the following: (1) The increase in particle size during the gel process reduced the injectability and wettability of the silica sol. The imbibition properties of silica sol were time-varying, and the deterioration inflection points of injectability and wettability appeared at 10 h and 9 h, respectively. (2) Catalyst, temperature, gel process, and rock mass permeability will affect the law of core imbibition, and the injectability and capillary force of the grouting material and rock mass will jointly affect the imbibition process of silica sol. (3) Silica sol imbibition changed the pore size distribution of the core, the pore volume above 50 nm decreased, and the pore volume below 50 nm increased. Silica sol has multiple effects such as filling, adsorption, and percolation in the imbibition process of the micro-pores of rock mass, and the adsorption and percolation of silica are related to the nano micro-pores.

Advances in enhanced geothermal systems: Integrating laboratory, numerical and field insights

An enhanced geothermal system is a designed and engineered thermal reservoir that has been deliberately stimulated to extract economically viable amounts of heat from geothermal resources having no natural permeability. Enhanced geothermal system projects are typically initiated to meet the industrial production standards, usually via techniques such as chemical stimulation, hydraulic fracturing, or thermal processes to enhance the permeability of the reservoir. The main aim of this study is to evaluate the current advancements in enhanced geothermal system through a comprehensive examination of laboratory experiments, numerical simulation, and fieldwork investigations from numerous studies that are insufficient captures and combined by current open literature. This study highlighted the critical importance of precisely developing fracture systems, whether natural or artificially induced, in ensuring the effectiveness of such projects. Notably, hydraulic fracturing techniques have been proven instrumental in enhancing the performance of enhanced geothermal systems. On the contrary, research conducted through numerical simulations has demonstrated consistent findings that it is beneficial to enhance the permeability of low-permeability rock for the efficient use of enhanced geothermal systems. Additionally, this study has highlighted the intricate and expensive nature of designing enhanced geothermal systems due to uncertainties in subsurface conditions especially from projects that are in initial stages of development. This study enables researchers and operators to improve the efficiency and safety of geothermal energy extraction, paving the way for more sustainable enhanced geothermal system projects in the future.

Effect of Hydrothermal Treatment and Prolonged Extraction on the Generation of Hydrocarbons from High-Carbon Low-Permeability Rocks from Domanik Deposits

Effect of Hydrothermal Treatment and Prolonged Extraction on the Generation of Hydrocarbons from High-Carbon Low-Permeability Rocks from Domanik Deposits

Study on the evolution of permeability properties of limestone under different stress paths

Abstract Stress path change has a great relationship with the effect of deformation and strength of rock. However, the underground rock body is in the engineering environment where the stress field, seepage field, and other fields are coupled to change, the law of fluid flow in the rock body is complex and variable. The change in the stress field has an important effect on the seepage characteristics of rock body; therefore, it is necessary to study the pattern of rock permeability evolution pattern by different stress paths. This study is based on the study of limestone, conducting triaxial unloading seepage mechanics experiments, the evolution of permeability properties of limestone specimens was analyzed based on the test results. The results show that in the conventional triaxial loading seepage test, the permeability of the limestone decreases before the rock stress reaches the peak intensity and increases after that. Increasing axial pressure unloading surrounding pressure compression section, permeability loss rate and effective stress are in line with the changing law of Gaussian distribution function. Under the action of constant axial pressure unloading surrounding pressure, with the increase in unloading amount, the permeability rate of change appears to increase slowly, and in the late stage of unloading section, the permeability rate of change appears to surge. Unloading section permeability change rate and cumulative unloading amount are in line with the law of change of the exponential function. Creep unloading pressure seepage test found that unloading pressure stage strain-time and permeability-time evolution characteristics are in line with the exponential rule of change. The experimental results of this study can provide an important experimental and theoretical basis for the permeability analysis of low-permeability rock body under complex stress conditions in underground engineering.

Chemical enhanced oil recovery under Harsh conditions: Investigation of rock permeability and insights from NMR measurements

Injecting surfactant into a hydrocarbon reservoir stands out as a highly effective method for EOR due to its ability to reduce water/oil IFT and alter rock wettability in certain cases. However, the efficiency of this process is compromised in heterogeneous reservoirs, especially carbonates, characterized by significant permeability variations. This study presents findings from three core flooding experiments on heterogeneous carbonate core samples with different permeabilities. The experiments were conducted under representative reservoir conditions of 100 °C, pressures higher than 3000 psi, and seawater salinities and formation water of 57,745 ppm and 213,768 ppm, respectively. In each experiment, seawater was continuously injected followed by continuously injecting a 2500-ppm solution of in-house synthesized Gemini surfactant. Results revealed that the recovery factor was highest in low-permeability rocks and lowest in high-permeability rocks for both seawater and surfactant floods. Surfactant floods yielded additional recoveries of 31%, 23%, and 19% for low, medium, and high-permeability samples, respectively. Nuclear magnetic resonance (NMR) analysis on short analogous core plugs at different flooding stages confirmed these results. Effluent analysis on the produced aqueous phase indicated that dynamic retention was highest (0.467 mg/gm-rock) in the lowest permeability and lowest (0.146 mg/gm-rock) in the highest permeability rock. NMR analysis suggested that the surfactant's recovery performance and dynamic retention were influenced by the larger surface area of low-permeability rocks, facilitating increased contact with the surfactant. Utilizing NMR monitoring in this work enhances EOR insights through integrated studies and coreflooding experiments and establishes a novel framework for complex reservoir conditions.

Subsurface hydrogen storage controlled by small-scale rock heterogeneities

Subsurface porous rocks hold significant hydrogen (H2) storage potential to support an H2-based energy future. Understanding H2 flow and trapping in subsurface rocks is crucial to reliably evaluate their storage efficiency. In this work, we perform cyclic H2 flow visualization experiments on a layered rock sample with varying pore and throat sizes. During drainage, H2 follows a path consisting of large pores and throats, through a low permeability rock layer, substantially reducing H2 storage capacity. Moreover, due to the rock heterogeneity and depending on the experimental flow strategy, imbibition unexpectedly results in higher H2 saturation compared to drainage. These results emphasize that small-scale rock heterogeneity, which is often unaccounted for in reservoir-scale models, plays a vital role in H2 displacement and trapping in subsurface porous media, with implications for efficient storage strategies.

Permeability Modeling of Pore Shapes, Compaction, Sorption, and Molecular Diffusivity in Unconventional Reservoirs

Summary Shale and ultratight gas reservoirs are multiscale, containing organic matter (OM) and inorganic minerals in multiple pore compartments of different pore shapes and scales. Selecting a suitable model to describe the multiscale transport mechanisms requires a minimum understanding of the inherent pore shape, OM content, typical pore size, and inherent flow regime. Interestingly, during gas production and associated pressure depletion, some mechanisms, such as pore compressibility, pore diffusion, and diffusion of sorbed gas molecules, become significant at lower pressure. In this study, multiscale and multiphysics permeability models are introduced that couple the effects of poroelasticity (especially in slit-shaped pores with <1.0 aspect ratio) and sorbed gas diffusion, Fick diffusion, transition diffusion, or Knudsen diffusion, depending on the pore structural properties at multiscale for shale and ultratight gas applications. Shale here refers to organic-rich low-permeability rock with >1–2 wt% OM, while ultratight gas has negligible organic content with <1.0 wt%. These experimentally and computationally validated models could be combined with Gaussian pressure transient solutions to effectively understand the uncertainty in multiphysics gas permeability in addition to the hydraulic and natural fracture parameters for large-scale flow simulation of hydraulically fractured unconventional reservoirs.

Simulation Analysis of the Characteristics of Layered Cores during Pulse Decay Tests

The permeability of low-permeability cores is generally measured using a pulse decay method. The core of low-permeability rocks, such as shale, often has a layered structure. The applicability of pulse decay testing for layered cores is not clear. In this study, the performance of the pulse decay method on layered cores was comprehensively investigated. Numerical simulations were conducted to investigate the influence of the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers on the pulse decay pressure and pressure derivative curves, as well as the permeability obtained from pulse decay testing. The results revealed that the pressure curves of layered cores exhibit distinct differences from those of homogeneous cores if the upstream permeability is larger than the downstream one. The pressure derivative curve shows more inclined or horizontal straight-line segments than in the homogeneous case. The shapes of the pressure and pressure derivative curves are affected by the upstream and downstream positions of the core, but the tested permeability is not affected. The tested permeability differs from the equivalent model permeability, with an error of up to 22%. If the number of layers is not less than 10, the permeability obtained from the pulse decay test is consistent with that of the equivalent model. These differences are influenced by the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers. To improve the accuracy of permeability analysis in pulse decay testing for layered cores, curve fitting using the characteristics of the pressure derivative curve can be employed.

Phase-Field Modeling of Coupled Thermo-Hydromechanical Processes for Hydraulic Fracturing Analysis in Enhanced Geothermal Systems

Abundant geothermal energy can be harvested from deep, low-permeability rocks using an enhanced geothermal system (EGS) that relies on an artificially created permeable fracture network through cold water injection. In this study, a two-way coupling technique for thermo-hydromechanical modeling was used to simulate hydraulic fracture propagation in an EGS. The transient heat and fluid flow in porous media were modeled using the finite volume method, while hydraulic fracture propagation and interaction with natural fractures were modeled using the variational phase-field method. Our findings underscore the importance of poroelastic and thermoelastic effects on fracture propagation in naturally fractured reservoirs. The results of this study demonstrate that thermo-hydromechanical processes are crucial elements in simulating and optimizing an enhanced geothermal reservoir system.

Laboratory studies of induction of flow using vibratory wave draining in carbonate low-permeability reservoirs

The object of the study is a laboratory unit for inducing flow to the well using vibration wave draining in carbonate low-permeability reservoirs. Vibratory wave draining is a method used to stimulate flow draining to the well. The method is based on the fact that mechanical waves generated in the soil can cause the opening of microcracks and pores, which leads to an increase in the fluid flow. Vibratory wave scouring can be effectively used to increase fluid flow in low-permeability carbonate reservoirs. Carbonate reservoirs are a common type of reservoir in the oil and gas industry. They often have low permeability, which makes it difficult to extract fluid. With the help of the plunger device developed in the work, a fluid disturbance was created, thereby creating elastic waves in the conventional well (plastic pipe), which were measured using a manual contact vibrometer. This demonstrated the effectiveness of the vibratory method to increase the well productivity and helped to improve the permeability of the rocks, providing better access to challenge the influx of hydrocarbon products. It is shown that with a significant decrease in the permeability of the formation well zone (FWZ), the flow induction should be started only after the restoration works. Otherwise, the well will be significantly hydrodynamically imperfect due to the quality of the reservoir opening, and the flow of production into the well will occur only through a few separate areas of the reservoir with relatively high permeability, which will lead to uneven production of the reservoir and low return of hydrocarbons. Therefore, it is advisable to use the developed method of influencing the productive layer in low-permeability rocks, such as carbonates with layers of clay, siltstones, argillites, and others, with low formation pressures. The obtained results are based on the generation of vibrations that are transmitted to the wellbore. These vibrations can help break up contaminants and fines in carbonate rocks, facilitating the release of hydrocarbon products and improving permeability.

Extended analysis of benchmarks for gas phase appearance in low-permeable rocks

This manuscript presents a comprehensive study on the numerical simulation of gas transport in clay rock using the finite-element method, with a specific focus on the transition of the transport regime from single-phase to two-phase conditions. Our code demonstrates the capability to cover this transition seamlessly, without relying on common approaches such as the use of persistent primary variables or the switching of primary variables. In our simulations, the primary variables are gas pressure, capillary pressure, temperature, and displacement of the solid phase. To validate our approach, two benchmark tests were conducted. The first benchmark replicates a well-known scenario in the field of radioactive waste disposal, where gas injection induces a transition from single-phase to two-phase flow. The second benchmark simulates a core drilling experiment, where the mechanical unloading of a fully saturated domain results in the appearance of a gas phase. In addition to analyzing primary quantities, a comprehensive set of secondary variables was introduced to gain deeper insights into the model’s operation and enhance understanding of the underlying processes. By plotting these secondary variables alongside the primary quantities, a comprehensive understanding of the system’s behavior during the transition of flow regimes was obtained. The primary objective of this work is to improve our understanding and confidence in the model used for simulating large repository systems, particularly in the context of nuclear waste disposal and CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} storage. By successfully capturing the transition from single-phase to two-phase gas transport, our study provides valuable insights into the behavior of gas in clay rock. This enhanced understanding lays the groundwork for utilizing the model effectively in large-scale repository simulations, contributing to the advancement of the field of gas transport in clay rock.