Stress-dependent Permeability Research Articles

Impact of stress regime change on the permeability of a naturally fractured carbonate buildup (Latemar, the Dolomites, northern Italy)

Abstract. Changing stress regimes control fracture network geometry and influence porosity and permeability in carbonate reservoirs. Using outcrop data analysis and a displacement-based linear elastic finite-element method, we investigate the impact of stress regime change on fracture network permeability. The model is based on fracture networks, specifically fracture substructures. The Latemar, predominantly affected by subsidence deformation and Alpine compression, is taken as an outcrop analogue for an isolated (Mesozoic) carbonate buildup with fracture-dominated permeability. We apply a novel strategy involving two compressive boundary loading conditions constrained by the study area's NW–SE and N–S stress directions. Stress-dependent heterogeneous apertures and effective permeability were computed in the 2D domain by (i) using the local stress state within the fracture substructure and (ii) running a single-phase flow analysis considering the fracture apertures in each fracture substructure. Our results show that the impact of the modelled far-field stresses at (i) subsidence deformation from the NW–SE and (ii) Alpine deformation from N–S increased the overall fracture aperture and permeability. In each case, increasing permeability is associated with open fractures parallel to the orientation of the loading stages and with fracture densities. The anisotropy of permeability is increased by the density and connectedness of the fracture network and affected by shear dilation. The two far-field stresses simultaneously acting within the selected fracture substructure at a different magnitude and orientation do not necessarily cancel each other out in the mechanical deformation modelling. These stresses affect the overall aperture and permeability distributions and the flow patterns. These effects – potentially ignored in simpler stress-dependent permeability – can result in significant inaccuracies in permeability estimation.

Rate Transient Analysis for Multi-Fractured Wells in Tight Gas Reservoirs Considering Multiple Nonlinear Flow Mechanisms

Making rate transient analysis (RTA) and formation evaluation for multi-fractured tight gas wells has always been a difficult problem. This is because the fluid flow in the formation has multiple nonlinear flow mechanisms, including gas-water two-phase flow, gas slippage, low-velocity non-Darcy flow, and stress-dependent permeability. In this paper, a novel RTA method is proposed for multi-fractured wells in tight gas reservoirs incorporating nonlinear flow mechanisms. The RTA method is based on an analytical model, which is modified from the classical trilinear flow model by considering all the nonlinear flow mechanisms. The concept of material balance time and normalized rate is used to process the production data for both water and gas phases. The techniques of approximate solutions in linear/bilinear flow regimes and type curve fitting are combined in the proposed RTA method. After that, the rate transient behaviors and influencing factors of multi-fractured tight gas wells are analyzed. A field case from Northwestern China is used to test the efficiency and practicability of the proposed RTA method. The results show that six flow regimes for both gas and water production performances are exhibited on the log-log plots of normalized production rate against material balance time. The rate transient responses are sensitive to the nonlinear flow mechanisms, and formation and fracture properties. The medium flow regimes are significantly affected by fracture number, fracture conductivity, fracture half-length, stress-dependent permeability, gas-water two-phase flow, and formation permeability, which should be considered in making RTA of fractured tight gas wells. The field case shows that both gas and water production performances can be well-fitted using the proposed RTA method. The major innovation of this paper is that a novel RTA method is proposed for fractured tight gas wells considering multiple nonlinear flow mechanisms, and it can be used to make reasonable formation and fracturing evaluations in the field.

Experimental investigation on the stress-dependent permeability of post-failure sandstone under loading–unloading conditions

Experimental investigation on the stress-dependent permeability of post-failure sandstone under loading–unloading conditions

Numerical study of the impact of stress concentration on shale gas production

Predicting the production amounts has great significance for exploitation of oil and gas resources. The flow–geomechanical coupling effect plays an important role in predicting production. Shale rocks and the stress-dependent permeability model are critical for representing this coupling effect. The pore network of shale rock is not abundant like that of coal rock, and the matrix blocks of shale rock are not completely separated by the pore network. There is stress concentration around the pores when shale rock is deformed. Based on previous studies, the stress-dependent permeability model considering the impact of stress concentration is used in this study to build a numerical simulation model for flow–geomechanical coupling in a shale gas reservoir and validation using field data. Sensitivity studies are conducted to discuss the difference in production prediction between the new and common models. The main conclusions of this study are as follows: 1) The new model can fit both the field and experimental data well; the average error in daily production rate between the numerical solution and field data is 8%, which indicates that the new model can be used to predict shale gas production. 2) Under the geomechanical condition of a real reservoir, the difference in predicted production between models with and without stress concentration can be large and increase with the ratio of a to b. If this ratio is less than 50, the impact of stress concentration is not significant. Otherwise, the impact of stress concentration on production increases sharply and can exceed 20%. 3) The adsorption-induced strain enhances the impact of stress concentration on production. When the Langmuir pressure exceeds 1 MPa and Langmuir strain exceeds 0.01, the impact magnitude of stress concentration can exceed 10%.

On the stress-dependent tight-rock permeability under anisotropic stress conditions

Permeability is a key parameter for characterizing an unconventional tight-rock reservoir and predicting hydrocarbon production from the reservoir. Because of the technical difficulty in accurately measuring extremely low tight-rock permeability, the permeability measurements have been commonly made in laboratory under hydrostatic (or isotropic stress) conditions. For unconventional reservoirs, stress distributions, however, are generally anisotropic. This paper presents a theoretical and experimental study on stress-dependent tight-rock permeability under anisotropic stress conditions. The theoretical development is based on the concept of effective stress and expresses rock permeability as an exponential function of the effective stress defined in this paper. The laboratory permeability data obtained under anisotropic stress conditions support the usefulness of the theoretical model for the stress-dependent permeability and demonstrate the importance of stress anisotropy in determining rock permeability. Considering that the effective stress is the only independent variable for determining the relationship between rock permeability and stress, we further propose a workflow to convert tight-rock permeability data collected under hydrostatic stress conditions to those for anisotropic stress conditions that are more realistic for field applications. A theoretical relation for upscaling a parameter characterizing the impact of stress anisotropy on local-scale permeability is also discussed as the first step to address this important upscaling issue.

Asymptotic-Poroelastic Model for Reservoir Compaction Damage Management in Fractured Oil Wells with Stress-Dependent Permeability

Asymptotic-Poroelastic Model for Reservoir Compaction Damage Management in Fractured Oil Wells with Stress-Dependent Permeability

A GENERALIZED FRACTAL-BASED APPROACH FOR STRESS-DEPENDENT PERMEABILITY OF POROUS ROCKS

The pore geometry of porous rocks is fundamental for accurate description of stress dependence of effective permeability, which is an important parameter of mass transfer in porous rocks. An important physical assumption that porous rocks contain numerous elliptical or spherical pores has been shown to be successfully applied to many aspects of hydromechanical coupling properties of porous rocks. To investigate the detailed description of pore structures on the degree of effect on the coupled hydromechanical process, in this work, a generalized stress-dependent model for permeability of porous rocks has been proposed based on fractal geometry theory and mechanics of porous rock. The proposed model is expressed as a nonlinear function of pore structure parameters, such as aspect ratio ([Formula: see text]), the fractal dimensions ([Formula: see text] and [Formula: see text]) for tortuosity, the initial fractal dimension ([Formula: see text]), and initial porosity ([Formula: see text]) as well as matrix elastic constants ([Formula: see text] and [Formula: see text]) of porous rocks without any empirical parameter. The validity of the proposed models is verified by the good agreements between available experimental data and theoretical predictions of stress-dependent permeabilities of porous rocks. Detailed discussions of the essential effects of pore structures parameters and material elastic constants of porous rocks on the dimensionless stress-dependent permeabilities are performed. It is found that the stress parameters ([Formula: see text] and [Formula: see text]) have remarkable effects on the dimensionless stress-dependent permeabilities compared with other parameters ([Formula: see text] and [Formula: see text]). The proposed model may contribute to a better quantitative understanding of the coupled hydromechanical properties of porous rocks.

A novel method to estimate the Stress-Dependent Kozeny-Carman constant of Low-Permeability, clastic sedimentary rocks

The stress-dependent permeability of low-permeability sedimentary rocks has seized attention because of the growing need for fossil fuels, geological carbon sequestration, and radioactive waste disposal. The Kozeny-Carman equation (K-C equation) is a well-known model for predicting the permeability of sedimentary rocks. The Kozeny-Carman constant (K-C constant, ckc) in the K-C equation accounts for the shape of the pores and the complexity of the pore conduit geometry in rocks. The pore structure of rocks varies owing to compaction at different burial depths. Therefore, the ckc is stress-dependent, a key parameter for understanding the stress-dependent permeability of rocks. However, measuring the stress-dependent ckc in low-permeability rocks is challenging. The present study proposes a novel approach for measuring the stress-dependent ckc of low-permeability rocks. The key elements of the proposed approach are (1) utilizing the Klinkenberg slip factor to evaluate the pore structure of rocks under stress, and (2) measuring rock porosity and permeability simultaneously under stress. This study amended the existing apparatus to fulfill the aforementioned purpose. Silty sandstone and clayey siltstone were selected to illustrate the novel ckc measurement method. The measured ckc values were compatible with the measurement results of documented sandstones and mudstones (most stress-independent). Interestingly, the ckc increased with increasing effective confining stress but started to decrease when the applied stress exceeded a certain critical value. Finally, we provide a synthetic case demonstrating the importance of considering stress-dependent ckc for permeability prediction under stress. If we neglect the stress dependence of ckc, the prediction of permeability using the K-C equation can induce errors up to several orders of magnitude.

Modelling of the impact of stress concentration on permeability in porous medium based on machine learning method

The behavior of stress-dependent permeability has been an important research topic for oil/gas production. The majority of permeability models for porous media have been proposed based on porelasticity theory. The matrix is assumed to be thoroughly separated by pores in the models and the pore compressibility is used to represent the stress-dependent behavior of permeability. However, matrix could not be separated by pores thoroughly and the impact of stress concentration around pores on pore deformation and permeability should be considered. In this study, the impact of stress concentration on permeability was illustrated by numerical simulation. In addition, the mechanism of stress-dependent behavior of permeability was analyzed. Since it is difficult to establish theoretical permeability models involving stress concentration effect caused by the complex pore structure, machine learning was applied in this paper. One of the four capable machine learning methods was selected and the corresponding machine learning model was validated through both numerical and experimental data. Moreover, the different performance of permeability prediction between the conventional model and the proposed one was discussed. The results indicate that the stress-dependent behavior of permeability results from stress concentration rather than the pore bulk modulus. Therefore, the stress-dependent permeability model with the impact of stress concentration is more accurate, compared with the numerical results and experimental data. In addition, the stress concentration increases the pore deformation and induces strong stress-dependent behavior of permeability, which is sensitive to pore shapes and related to the pore shape complexity. Specifically, the impacts of pores with different shapes on permeability are similar if the complexity index of pore shape is under 0.6 or over 0.9 and distinct for the value in between. Furthermore, the alteration in the magnitude and orientation of the stress affects stress dependency of permeability, which increases with the pore shape complexity. If the complexity index of pore shape exceeds 0.96, the alteration of permeability induced by change in stress orientation can be over 64%.

Study on influencing factors and mechanism of pore compressibility of tight sandstone reservoir—A case study of upper carboniferous in ordos basin

A series of studies were carried out on 11 tight sandstone samples of Upper Carboniferous in Ordos Basin. Firstly, the deposit composition and pore structure characteristics are investigated based on analysis and experiments including cast thin section scanning electron microscope high-pressure mercury intrusion and nuclear magnetic resonance Then, combined with DP-P test, the stress-dependent permeability change and pore compressibility characteristics of sandstone reservoirs were studied to reveal the influencing factors and mechanism of reservoir pore compressibility. The detrital particles of the sandstone reservoir in the study area are mainly quartz (75.8%–89%), followed by fragments (3%–16.1%), and almost no feldspar. The content of interstitial materials is 6.5%–11.2%. The type I reservoirs mainly consist of mesopores and macropores, accounting for 60.57% and 32.84% respectively. Mesopores are dominated in Type II reservoirs, accounting for 78.98% of the total pore volume. There are almost no macropores, while a similar proportion of mesopores, micro mesopores and micropores in the type Ⅲ reservoirs. The study of pore compressibility shows that the pore compressibility coefficient decreases with the increase of effective stress, and the reduction rate shows the two-stage characteristics of rapid in the early stage and slow in the later stage. The pressure turning point is between 3 and 10 MPa. The average pore compressibility coefficient increases from type I to type Ⅲ reservoirs. The compressibility coefficient is directly proportional to the changing rate of the pore volume. The higher the content of rigid detrital particles, quartz and carbonate cement in sandstone, the smaller the pore compressibility coefficient, while the higher the content of ductile components such as soft rock fragments and clay minerals, the greater the pore compression coefficient. The pore-throat structure is closely related to the pore compressibility, reservoirs with low displacement pressure, T2glm value, and large average pore-throat radius show lower compressibility coefficient. In addition, the compressibility coefficient of the reservoir is positively correlated with DL (dimension of large pores such as mesopores and macropores), and negatively correlated with DS (the fractal dimension of micropores and micro mesopores). It is considered the pore compression of sandstone including two stages, viscoplastic destructive deformation of ductile components for the first and then the small-scale non-ideal elastic deformation on rigid particles.

STRESS-DEPENDENT MODELS FOR PERMEABILITY AND POROSITY OF FRACTURED ROCK BASED ON FRACTAL THEORY

The hydro-mechanical coupling behavior of the fractured rock is constitutive in accurately modeling the seepage properties such as permeability and porosity. In this work, the stress-dependent models for permeability and porosity of the fractured rock are proposed by employing the fractal geometry theory and the two-part Hooke’s model (TPHM). The proposed models for the permeability and porosity are related to the effective stress and the microstructures of fractures, such as the fractal dimension ([Formula: see text] and [Formula: see text], the maximum fracture length [Formula: see text], and fracture orientations ([Formula: see text] and [Formula: see text] as well as porosities ([Formula: see text] and [Formula: see text]. The validity of the proposed permeability model coupled with stress is validated by comparison with the available experimental data. The model predictions agree well with the experimental data. The effects of microstructures of fracture networks in fractured rock on the dimensionless stress-dependent permeability and porosity as well as the fractal dimension for fracture areas are also discussed in detail. The proposed models may shed much light on the fundamental behavior of coupled hydro-mechanical properties of fractured rock.

Wellbore cement fracture permeability as a function of confining stress and pore pressure

Cemented annulus fractures are a major leakage path in a wellbore system, and their permeability plays an important role in the behavior of fluid flow through a leaky wellbore. The permeability of these fractures is affected by changing conditions including the external stresses acting on the fracture and the fluid pressure within the fracture. Laboratory gas flow experiments were conducted in a triaxial cell to evaluate the permeability of a wellbore cement fracture under a wide range of confining stress and pore pressure conditions. For the first time, an effective stress law that considers the simultaneous effect of confining stress and pore pressure was defined for the wellbore cement fracture permeability. The results showed that the effective stress coefficient (λ) for permeability increased linearly with the Terzaghi effective stress (σ-p) with an average of λ=1 in the range of applied pressures. The relationship between the effective stress and fracture permeability was examined using two physical-based models widely used for rock fractures. The results from the experimental work were incorporated into numerical simulations to estimate the impact of effective stress on the interpreted hydraulic aperture and leakage behavior through a fractured annular cement. Accounting for effective stress-dependent permeability through the wellbore length significantly increased the leakage rate at the wellhead compared with the assumption of a constant cemented annulus permeability.

Experimental study on stress-dependent permeability of coal samples with different salinities of water in coal

The stress sensitivity and water sensitivity of coals are key factors restricting the productivity of coalbed methane (CBM) wells. In this study, stress sensitivity experiments with different salinities and X-ray diffraction (XRD) tests were conducted with coal samples from the Zhaozhuang (ZZ), Sihe (SH), and Xishan coalmine (XS) in the Qinshui Basin to analyse the correlation between permeability and the coupling of salinity and effective stress. To reveal the revolution of coal permeability under the coupling of salinity and stress, the permeability damage rate (PDR), the stress sensitivity coefficient (αk), and the water sensitivity index (IW) were introduced to evaluate the stress sensitivity and water sensitivity. The results showed that the permeability varied with the effective stress following a negative exponential function and was positively correlated with salinity within a certain range. When the salinity increased from 0 ppm to 5000 ppm, the stress sensitivity decreased; when the salinity increased from 5000 ppm to 10,000 ppm, the stress sensitivity remained constant, and the water sensitivity increased with increasing effective stress. Finally, a mathematical model for predicting coal permeability that considered the impacts of stress and salinity was established, and the control mechanism of stress and salinity on permeability was revealed.

The Role of Heterogeneity on Deformation and Flow in Fractured Coal Slopes

The fractures in brown coal influence fluid flow and deformation in these materials. These fractures display highly heterogeneous characteristics in the distributions of their apertures, separations and orientations. While discrete fracture models have previously been used to analyse the effects of fractures, such models are not feasible for the scales encountered in many brown-coal mines. Instead, here a continuum permeability model is used to capture the effects of the fracture heterogeneity on fractured coal. This paper presents an analysis of the fracture heterogeneity of brown coal at the AGL Loy Yang coal mine in Latrobe Valley and its influence on the fluid flow, dispersion and rock stability. A stress dependent fracture permeability is considered and captures the effects of heterogeneity in the fracture aperture and orientation. Numerical simulations conducted with multiple plasticity models present different flow paths and potential failure modes depending on the the implemented boundary conditions.

Performance of a tight reservoir horizontal well induced by gas huff–n–puff integrating fracture geometry, rock stress-sensitivity and molecular diffusion: A case study using CO2, N2 and produced gas

This work provides a comprehensive workflow with practical guidelines for integrating fracture-geometry, rock stress-sensitivity, and gas molecular diffusion to evaluate the performance of a tight reservoir horizontal well induced by gas Huff–n–Puff (HnP). The laboratory measurements and field results were integrated in numerical simulation. The stress-sensitivity led the permeabilities of the matrix and fractures to significantly decrease during primary depletion and HnP stages, thereby impairing well productivity. Rigorous characterizations of fracture-geometry and rock stress-sensitivity are crucial for history-matching and oil recovery simulation. During produced gas HnP, the cumulative oil production was reduced by 4.6% original oil in place (OOIP) because of the stress-dependent permeability. The hysteresis in fracture-permeability noticeably decreased the transport of mass and pressure but hardly affected the short-term production owing to the rapid closure of fractures during puff stage. The final oil recoveries induced by gas diffusion were 0.4%, 0.04% and 0.35% OOIP by CO2, N2 and produced gas HnP, respectively. The produced gas HnP process produced the highest efficiency of enhanced oil recovery than CO2 and N2 owing to its significant pressurizing effect and lower gas-oil ratio. Minimum-miscibility-pressure should not be the primary consideration for gas HnP in tight reservoirs.

Hydro-thermal impacts on near-field flow and transport in a shale-hosted nuclear waste repository

Performance of geologic radioactive waste repositories depends on near-field and far-field processes, including km-scale flow and transport in engineered and natural barriers, that may require simulations of up to 1 M years of regulatory period. For a relatively short time span (less than 1000 years), the coupled thermo-hydro-mechanical–chemical (THMC) processes caused by heat from the waste package will influence near-field multiphase flow, chemical/reactive transport, and mechanical behaviors in the repository system. This study integrates the heat-driven perturbations in THM characteristics into THC simulations using PFLOTRAN to reduce dimensionality and improve computational efficiency by implementing functions of stress-dependent permeability and saturation-temperature-dependent thermal conductivity. Our reduced-order THMC simulation of a single waste package in a shale-hosted repository reveals three physical mechanisms associated with heat pulse emitted from the waste package: (1) increase of liquid mobility that accelerates the inflow and solute transport from the fully saturated host rock, (2) production of thermal gradients that results in outward flow within the buffer and disturbed rock zone (DRZ) nearest the waste package, and (3) reduction of thermal conductivity that confines heat within the engineered barrier system (EBS). These combined hydro-thermal mechanisms influence the rate of re-saturation process and transport/exchange of corrosive species in the repository system.

Poro-Mechanical Coupling for Flow Diagnostics

Accounting for poro-mechanical effects in full-field reservoir simulation studies and uncertainty quantification workflows using complex reservoir models is challenging, mainly because of the high computational cost. We hence introduce an alternative approach that couples hydrodynamics through existing flow diagnostics simulations with poro-mechanics to screen the impact of coupled poro-mechanical processes on reservoir performance without significantly increasing computational overheads. In flow diagnostics, time-of-flight distributions and influence regions can be used to characterise the flow field in the reservoir, which depends on the distribution of petrophysical properties that are altered due to production-induced changes in pore pressure and effective stress. These extended flow diagnostics calculations hence enable us to quickly screen how the dynamics in the reservoirs (e.g. reservoir connectivity, displacement efficiency, and well allocation factors) are affected by the complex interactions between poro-mechanics and hydrodynamics. Our poro-mechanically informed flow diagnostics account for steady-state and single-phase flow conditions based on the poro-elastic theory and assume that the reservoir does not contain fractures. Fluid flow and rock deformation calculations are coupled sequentially. The equations are discretised using a finite-volume method with two-point flux-approximation and the virtual element method, respectively. The solution of the coupled system considers stress-dependent permeabilities. Due to the steady-state nature of the calculations and the effective proposed coupling strategy, these calculations remain computationally efficient while providing first-order approximations of the interplay between poro-mechanics and hydrodynamics, as we demonstrate through a series of case studies. The extended flow diagnostic approach hence provides an efficient complement to traditional reservoir simulation and uncertainty quantification workflows and enable us to assess a broader range of reservoir uncertainties.

The influence of confining stress and pore pressure on effective stress coefficient for permeability: A novel Discretized Clay Shell Model for clayey sandstone

The effective stress coefficient α determines the effective stress and dominates the permeability of rocks. This study proposes a novel theoretical model called the Discretized Clay Shell Model (DCSM) that modifies the Clay Shell Model (CSM) by incorporating the stress-dependent elastic modulus of clay into a discretized multi-layer clay domain to depict the relationship between α, pore pressure, and confining stress. The proposed model was successfully used to provide insights into the stress-dependent α of clayey sandstones. We found that α always decreased with increasing pore pressure and could decrease or increase with increasing confining stress. The modelling trends, which are also observed in the previous laboratory tests, can be well explained using two effects due to the heterogeneity of radial stress within clay domain, that is, the bulk and differential clay hardening effects. The bulk clay hardening effect generates a decreasing trend in α with increasing pore pressure, while the differential clay hardening effect competes with the bulk clay hardening effect and yields a reverse trend, that is, α first decreases with increasing confining stress and then decreases when the confining stress reaches a certain critical value. This study provides synthetic cases to quantify the influence of stress-dependent α evaluated by the DCSM on the evaluation of the permeability-depth relation. Based on the laboratory testing data, the calibrated parameters of the stress-dependent permeability model assuming α=1 are significantly overestimated, and the prediction model yields overestimated permeability up to three to four orders of magnitude. Meanwhile, the synthetic in-situ case shows that the predicted permeability could be underestimated by up to one third, and the errors due to laboratory analysis that neglect the stress dependency of α will propagate to and amplify the errors of prediction for the in-situ permeability-depth relation.

Dewatering Optimization of Coal Seam Gas Production Wells: A Review and Future Perspectives

Coal seam gas (CSG), as a type of unconventional gas resource, is playing an increasingly important role in energy generation and transition to renewables, as the world takes action to meet the climate change challenge. To produce CSG, the reservoir first needs to be dewatered, but unreasonable dewatering rates can lead to various unfavorable outcomes, such as a reduction in productivity, capillary trapping, borehole instability, excessive coal fines generation, and frequent production well workovers due to particle-induced damage to pumps. Determining the optimum dewatering strategy is currently in a very primitive stage of development, and CSG operators rely on empirical and instinctive approaches to deal with this problem. This paper conducts a comprehensive literature review to (i) explain why dewatering rate optimization remains a great challenge for the CSG industry, (ii) illustrate the complexity and nature of the issue through a conceptual model, and (iii) investigate four key factors that dominate the dewatering optimization design, borehole stability, stress-dependent permeability, gas–water two-phase flow, and generation of coal fines. A detailed summary of current dewatering optimization practices in CSG reservoirs is then presented, focusing on the employed theories, methodology, key learnings, and limitations of each practice. Finally, the remaining knowledge gaps are highlighted, and recommendations for further future work are provided.

Modelling anisotropic adsorption-induced coal swelling and stress-dependent anisotropic permeability

To investigate the anisotropy of coal swelling, this study proposes an effective stress model for saturated, adsorptive fractured porous media by considering gas adsorption induced surface stress change on solid-fluid interface. The effective stress model can be used to capture the anisotropic swelling of coal combining anisotropic mechanical properties and to link with the anisotropic permeability. Direction dependent fracture compressibility is used to describe the evolution of anisotropic stress-dependent permeability behaviour. Particularly, the impact of gas adsorption on fracture compressibility is considered in the model. The proposed models were tested against experimental results and compared to relevant existing models available in literatures. The model predicts that the coal swelling in the direction perpendicular to the bedding plane, is greater than that in the parallel plane. Coal permeability in each direction can be affected by the stress changes in any directions. The permeability parallel to the bedding plane is more sensitive to change in stresses than in perpendicular to the bedding due to higher fracture compressibility. The cleat compressibility could increase with gas adsorption, especially for carbon dioxide. Permeability loss in the direction parallel to the bedding plane is more significant than that in the direction perpendicular to the bedding plane. The presented models provide a tool for quantifying gas adsorption-induced anisotropic coal swelling and permeability behaviours.