Drawdown Induced Changes in Permeability of Coalbeds: A New Interpretation of the Reservoir Response to Primary Recovery

A model for pore pressure-dependent cleat permeability is presented for gas-desorbing, linear elastic coalbeds under uniaxial strain conditions experienced in producing reservoirs. In the model, changes in the cleat permeability of coalbeds, which are idealised to have a bundled matchstick geometry, is controlled by the prevailing effective horizontal stresses normal to the cleats. Variations in the effective horizontal stresses under uniaxial strain conditions are expressed as a function of pore pressure reduction during drawdown, which includes a cleat compression term and a matrix shrinkage term that have competing effects on cleat permeability. A comprehensive analysis has revealed that the shape of the stress – pore pressure curve is predominantly determined by the magnitude of recovery pressure and rebound pressure relative to the initial reservoir pressure. A total of five possible scenarios have been identified with regard to response of the horizontal stress function to reservoir drawdown. When applied to four coalbed wells at two separate sites in the fairway of the San Juan basin, the model predictions at one site, where the three wells have shown increased absolute permeability during gas production, are in excellent agreement with the published pore pressure dependent permeability changes that were obtained independently from history matching the field production data. At a separate site the model correctly predicts, at least qualitatively, a strong permeability rebound at lower drawdown pressures that has been inferred through history matching the production data. An analysis of the effects of initial reservoir pressure on the response of effective horizontal stress to drawdown was carried out, with reference to the range of pressure likely to be encountered in the San Juan basin. The implications of this in terms of pore pressure dependent permeability are discussed.     

A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.     

An Alternative Approach to Predicting Reservoir Performance in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Coalbed methane (CBM) reservoirs contain gas molecules in adsorbed state into the solid matrix of coal. The pressure depletion in CBM reservoir causes the matrix gas to desorb into the cleat system which leads to matrix shrinkage. The pore volume of the cleat network changes as coal matrix shrinks. Consequently, cleat porosity and permeability of reservoir change as reservoir pressure depletes. The change in cleat porosity and permeability due to shrinkage of coal matrix with depletion of reservoir pressure invalidates the underlying assumptions made in the derivation of diffusivity equation. Under the conditions of changing porosity and permeability, the utility of the standard method of inflow performance relationship (IPR), paired with \(\frac{P}{Z^{*}}\) method suggested by King (in: SPE Annual Technical Conference and Exhibition, New Orleans, 1990), for performance prediction diminishes. In this paper, an effort has been made to predict reservoir performance of such CBM reservoirs with an alternative approach. The method suggested by Upadhyay and Laik (Transp Porous Media, 2017. doi: 10.1007/s11242-016-0816-6) has been leveraged to describe pseudo-steady-state flow in the form of a new equation that relates stress-dependent pseudo-pressure function with time. The analytical equation derived in this paper is useful in predicting reservoir pressure and flowing bottom hole pressure of a CBM well under the situation when coal matrix shrinks below desorption pressure. The paper aims to predict production performance of CBM reservoirs producing under the influence of matrix shrinkage effect with an approach alternative to conventional IPR approach paired with \(\frac{P}{Z^{*}}\) method. The results of this analytical solution have been validated with the help of numerical simulator CMG–GEM as well as in-field production data. The equations and workflow suggested in this paper can be easily implemented in spreadsheet applications like Microsoft Excel tools.     

Flow of Coal-Bed Methane to a Gallery

Coal-seam methane reservoirs have a number of unique feature compared to conventional porous or fractured gas reservoirs. We propose a simplified mathematical model of methane movement in a coal seam taking into account the following features: a relatively regular cleat system, adsorptive methane storage, an extremely slow mechanism of methane release from the coal matrix into cleats and a significant change of permeability due to desorption.Parameters of the model have been combined into a few dimensionless complexes which are estimated to an order of magnitude. The simplicity of the model allows us to fully investigate the influence of each parameter on the production characteristics of the coal seam. We show that the reference time of methane release from the coal matrix into cleats – the parameter which is most poorly investigated – may have a critical influence on the overall methane production.     

Impact of CO<Subscript>2</Subscript> Injection on Flow Behavior of Coalbed Methane Reservoirs

On the basis of observations at four enhanced coalbed methane (ECBM)/CO₂ sequestration pilots, a laboratory-scale study was conducted to understand the flow behavior of coal in a methane/CO₂ environment. Sorption-induced volumetric strain was first measured by flooding fresh coal samples with adsorptive gases (methane and CO₂). In order to replicate the CO₂–ECBM process, CO₂ was then injected into a methane-saturated core to measure the incremental “swelling.” As a separate effort, the permeability of a coal core, held under triaxial stress, was measured using methane. This was followed by CO₂ flooding to replace the methane. In order to best replicate the conditions in situ, the core was held under uniaxial strain, that is, no horizontal strain was permitted during CO₂ flooding. Instead, the horizontal stress was adjusted to ensure zero strain. The results showed that the relative strain ratio for CO₂/methane was between 2 and 3.5. The measured volumetric strains were also fitted using a Langmuir-type model, thus enabling calculation of the strain at any gas pressure and using the analytical permeability models. For permeability work, effort was made to increase the horizontal stress to achieve the desired zero horizontal strain condition expected under in situ condition, but this became impossible because the “excess” stress required to maintain this condition was very large, resulting in sample failure. Finally, when CO₂ was introduced and horizontal strain was permitted, permeability reduction was an order of magnitude greater, suggesting that the “excess” stress would have reduced it significantly further. The positive finding of the work was that the “excess” stresses associated with injection of CO₂ are large. The excess stresses generated might be sufficient to cause microfracturing and increased permeability, and improved injectivity. Also, there might be a weakening effect resulting from repeated CO₂ injection, as has been found to be the case with thermal cycling of rocks.     

A New Coal-Permeability Model: Internal Swelling Stress and Fracture–Matrix Interaction

We have developed a new coal-permeability model for uniaxial strain and constant confining-stress conditions. The model is unique in that it explicitly considers fracture–matrix interaction during coal-deformation processes and is based on a newly proposed internal swelling stress concept. This concept is used to account for the impact of matrix swelling (or shrinkage) on fracture-aperture changes resulting from partial separation of matrix blocks by fractures that do not completely cut through the whole matrix. The proposed permeability model is evaluated using data from three Valencia Canyon coalbed wells in the San Juan Basin, where increased permeability has been observed during CH₄ gas production, as well as using published data from laboratory tests. Model results are generally in good agreement with observed permeability changes. The importance of fracture–matrix interaction in determining coal permeability, demonstrated in this study using relatively simple stress conditions, underscores the need for a dual-continuum (fracture and matrix) mechanical approach to rigorously capture coal-deformation processes under complex stress conditions, as well as the coupled flow and transport processes in coal seams.     

Simulation of Pressure Transient Behavior for Asymmetrically Finite-Conductivity Fractured Wells in Coal Reservoirs

Based on Fick’s law in matrix and Darcy flow in cleats and hydraulic fractures, a new semi-analytical model considering the effects of boundary conditions was presented to investigate pressure transient behavior for asymmetrically fractured wells in coal reservoirs. The new model is more accurate than previous model proposed by Anbarci and Ertekin, SPE annual technical conference and exhibition, New Orleans, 27–30 Sept 1998 because new model is expressed in the form of integral expressions and is validated well through numerical simulation. (1) In this paper, the effects of parameters including fracture conductivity, coal reservoir porosity and permeability, fracture asymmetry factor, sorption time constant, fracture half-length, and coalbed methane (CBM) viscosity on bottomhole pressure behavior were discussed in detail. (2) Type curves were established to analyze both transient pressure behavior and flow characteristics in CBM reservoir. According to the characteristics of dimensionless pseudo pressure derivative curves, the process of the flow for fractured CBM wells was divided into six sub-stages. (3) This paper showed the comparison of transient steady state and pseudo steady state models. (4) The effects of parameters including transfer coefficient, wellbore storage coefficient, storage coefficient of cleat, fracture conductivity, fracture asymmetry factor, and rate coefficient on the shape of type curves were also discussed in detail, indicating that it is necessary to keep a bigger fracture conductivity and fracture symmetry for enhancing well production and reducing pressure depletion during the hydraulic fracturing design.     

Dual Porosity and Dual Permeability Modeling of Horizontal Well in Naturally Fractured Reservoir

This article is the first investigation on the dual permeability flow issue for horizontal well-production in a naturally fractured dual-porosity reservoir. Based on the inter-porosity flow from matrix system to fracture system and treating the media directly connected with horizontal wellbore as matrix and fracture systems, we established a model of horizontal well-production and then solved the model using some modern mathematical methods, such as Laplace integral transformation, separation of variables, eigenvalue, and eigenfunction. Later in the article, we obtained the standard log–log type curves using numerical simulation and analyzed the transient flow behavior thoroughly, which showed it is dual porosity and dual permeability flow behavior. The numerical simulation results showed that there are obvious differences between dual permeability and single permeability models. The dual permeability flow behavior accelerates energy supplement during production and reduces the classical matrix-fracture (V-shaped) response. We also showed that type curves characteristics are affected by external boundary conditions, the parameter κ, ω _f and λ _mf, etc. The research results show that our model would be a good semi-analytical model supplied to users. Because the single permeability modeling ignores the direct fluid supply from matrix to wellbore, we recommend using the dual permeability modeling to make well testing and rate decline interpretation in real case studies.     

Impact of Effective Stress and Matrix Deformation on the Coal Fracture Permeability

The permeability of coal is an important parameter in mine methane control and coal bed methane exploitation because it determines the practicability of methane extraction. We developed a new coal permeability model under tri-axial stress conditions. In our model, the coal matrix is compressible and Biot’s coefficient, which is considered to be 1 in existing models, varies between 0 and 1. Only a portion of the matrix deformation, which is represented by the effective coal matrix deformation factor $f_\mathrm{m}$ , contributes to fracture deformation. The factor $f_\mathrm{m}$ is a parameter of the coal structure and is a constant between 0 and 1 for a specific coal. Laboratory tests indicate that the Sulcis coal sample has an $f_\mathrm{m}$ value of 0.1794 for $\hbox {N}_{2}$ and $\hbox {CO}_{2}$ . The proposed permeability model was evaluated using published data for the Sulcis coal sample and is compared to three popular permeability models. The proposed model agrees well with the observed permeability changes and can predict the permeability of coal better than the other models. The sensitivity of the new model to changes in the physical, mechanical and adsorption deformation parameters of the coal was investigated. Biot’s coefficient and the bulk modulus mainly affect the effective stress term in the proposed model. The sorption deformation parameters and the factor $f_\mathrm{m}$ affect the coal matrix deformation term.     

Prediction of Porosity and Permeability of Caved Zone in Longwall Gobs

The porosity and permeability of the caved zone (gob) in a longwall operation impact many ventilation and methane control related issues, such as air leakage into the gob, the onset of spontaneous combustion, methane and air flow patterns in the gob, and the interaction of gob gas ventholes with the mining environment. Despite its importance, the gob is typically inaccessible for performing direct measurements of porosity and permeability. Thus, there has always been debate on the likely values of porosity and permeability of the caved zone and how these values can be predicted. This study demonstrates a predictive approach that combines fractal scaling in porous medium with principles of fluid flow. The approach allows the calculation of porosity and permeability from the size distribution of broken rock material in the gob, which can be determined from image analyzes of gob material using the theories on a completely fragmented porous medium. The virtual fragmented fractal porous medium so generated is exposed to various uniaxial stresses to simulate gob compaction and porosity and permeability changes during this process. The results suggest that the gob porosity and permeability values can be predicted by this approach and the presented models are capable to produce values close to values documented by other researchers.     

Adsorption and strain: The CO2-induced swelling of coal

Enhanced coal bed methane recovery (ECBM) consists in injecting carbon dioxide in coal bed methane reservoirs in order to facilitate the recovery of the methane. The injected carbon dioxide gets adsorbed at the surface of the coal pores, which causes the coal to swell. This swelling in confined conditions leads to a closure of the coal reservoir cleat system, which hinders further injection. In this work we provide a comprehensive framework to calculate the macroscopic strains induced by adsorption in a porous medium from the molecular level. Using a thermodynamic approach we extend the realm of poromechanics to surface energy and surface stress. We then focus on how the surface stress is modified by adsorption and on how to estimate adsorption behavior with molecular simulations. The developed framework is here applied to the specific case of the swelling of CO₂-injected coal, although it is relevant to any problem in which adsorption in a porous medium causes strains.     

Coal Permeability Evolution and Gas Migration Under Non-equilibrium State

Laboratory test of coal permeability is generally conducted under the condition of gas adsorption equilibrium, and the results contribute to an understanding of gas migration in the original coal seams. However, gas flow under the state of non-equilibrium, accompanied by gas adsorption and desorption, is more common in coalbed methane (CBM) recovery and \(\hbox {CO}_{2}\) geological sequestration sites. Therefore, research on gas migration under the non-equilibrium state has a greater significance with regard to CBM recovery and \(\hbox {CO}_{2}\) geological sequestration. However, most permeability models, in which only one gas pressure has been considered, cannot be used to study gas flow under the non-equilibrium state. In this study, a new mathematical model, which includes both fracture gas pressure and matrix gas pressure, and couples the gas flow with the coal deformation, has been developed and verified. With the developed model, the spatial and temporal evolution of gas flow field during gas adsorption and desorption phases has been explored. The results show that the gas pressures present nonlinear distributions in the coal core, and the matrix gas pressure is generally lower than the fracture gas pressure during adsorption, but higher than the fracture gas pressure during desorption. For gas flow during adsorption, the main factor controlling permeability varies at different points. At the initial time, the permeability is dominated by the effective stress, and at the later time, the permeability in the part close to the gas inlet is mainly controlled by the matrix swelling, whereas that in the part close to the gas outlet is still dominated by the effective stress. For gas flow during desorption, from the gas inlet to the gas outlet, the permeability deceases at the initial time, and when the time is greater than 10,000 s, it shows a decreasing and then an increasing trend. The reason is that at the initial time, the permeability is dominated by the increased effective stress caused by the sharp decrease of the fracture gas pressure. Later, desorption of the adsorbed gas results in matrix shrinkage, which further leads to an increase of the permeability.     

Pressure Dependent Properties of a Compressible Polymer

This paper deals with the investigations of a porous carbon black-filled rubber, tested with regard to its pressure and tension behaviour. In the tension range only uniaxial tests are performed while in the pressure range uniaxial as well as hydrostatic tests are performed. The uniaxial experiments are carried out in a custom-made uniaxial device and the hydrostatic tests in a pressure chamber which is specially developed for this application. The construction and use of the pressure chamber is clearly described in this paper. All experiments are related to the basic elasticity of the material. The viscoelastic behaviour is completely disregarded at this point. Not only the experiments are discussed, also the modelling of the material is looked at. The tested cellular rubber is composed of an incompressible solid phase and a compressible gas phase. For that reason a so-called structural compressibility is observed. The compressible behaviour of cellular rubber is an important property. So the main focus of the paper is on the pressure tests and the simulation of these. The existing material models for rubber like materials only deal with incompressible rubber structures. To represent the compressible behaviour, the Theory of Porous Media is used. The constitutive model is based on a polynomial approach for an incompressible material. This is complemented by a volumetric expansion term with a point of compaction to model the structural compressibility.     

Approximate Solutions for Non-stationary Gas Permeability Tests

Full and approximate models describing changes in gas pressure for non-stationary single- and double-reservoir methods of testing of gas permeability of porous materials were formulated. The models include effects of compressibility and slip of gas. For derivation of the approximate models it was assumed that a transient mass flux of gas is constant along the tested sample (spatially homogeneous). The assumption allowed finding analytical solutions for evolution of reservoir pressures as well as the transient spatial distributions of pore pressure in tested samples. The full model was solved with help of the finite element method and the results were compared with the derived approximations. The comparison shows very good agreement of predictions of both models. Parametric studies have given the evaluation of the role of selected material parameters (permeability, porosity and slip factor) and parameters of the experimental system (initial pressure, volume of reservoirs), especially important from the point of view of identification procedures of the material parameters.     

综放极限平衡区顶煤渗透性的计算模型

基于放顶煤开采中顶煤渗透率对工作面安全生产的重要性, 对煤壁前方极限平衡区内顶煤渗透率的变化规律进行了研究. 应用损伤力学和数理统计方法对顶煤垂直和水平应变进行了研究分析, 并建立了数学模型. 以甲烷气体为渗流体, 应用自制三轴实验机对煤样体积应变与渗透率的关系进行了试验研究, 并利用多项式拟合方法对试验结果进行了分段拟合. 结果表明：根据所建立的顶煤应变计算模型, 可以求出综放顶煤内任意点的体积应变, 且顶煤的水平应变与其距底板的高度无关. 依据试验及拟合所得到的煤体体积应变与渗透率的函数关系, 可以求得顶煤内任意点渗透率. 最后对计算模型进行了实践检验.     

Modeling Reservoir Gas Permeability Tests for Cylindrical and Spherical Geometry

Approximate analytical models of non-stationary single and double reservoir gas permeability tests with radial flow through hollow cylindrical or hemispherical samples are developed and compared with numerical solutions of full models. The effects of compressibility and slip of gas are included. The approximate solutions are obtained assuming that the total transient mass flux is spatially homogeneous, i.e., it has constant value in direction of flow (along radius in cylindrical or spherical coordinate system). The evolutions of reservoir pressures and transient spatial distributions of pore pressure are determined and apply both for pumping and suction tests. The solutions of full model were obtained with help of the finite element method and served as references to evaluate the approximate models.     

Pore Volume and Porosity Changes under Uniaxial Strain Conditions

Expressions for the changes that occur in the pore volume and the porosity of a porous rock, due to changes in the pore pressure, overburden stress, and temperature, are derived within the context of the linearised theory of poroelasticity. The resulting expressions are compared to the commonly used equations proposed by Palmer and Mansoori, and it is shown that their expressions are consistent with the exact expressions if their factor f is identified with \((1+\nu )/3(1-\nu )\), where \(\nu \) is the Poisson’s ratio of the porous rock. Finally, the first derivation is given, within the context of the fully coupled linearised theory of poroelasticity, that under uniaxial strain, the partial differential equation that governs the evolution of the pore pressure is a pure diffusion equation, with a total compressibility term that (exactly) equals the sum of the fluid compressibility and the uniaxial pore volume compressibility.     

The reference shrinkage curve of clay soil

The objective of this work is to develop and validate a model that predicts the reference soil shrinkage curve, that is one without crack volume contribution, as a necessary preliminary step in future estimation of soil crack volume from soil shrinkage data. Current soil shrinkage models are based on the approximation of soil shrinkage data by some a priori taken mathematical expressions and justified by the fitting of their parameters to the data. However, the crack volume entering the data is not single valued and depends on shrinkage conditions. Unlike that the reference shrinkage curve is single valued. For soils with sufficiently high clay content when there are no large pores (lacunar pores) inside the intra-aggregate clay, the reference shrinkage curve is derived from the assumption of the rigid superficial (interface) layer of aggregates with changed pore-size range and distribution compared with the intra-aggregate matrix. This consideration is based on accounting for contributions of the interface aggregate layer and intra-aggregate matrix to the soil volume and water content during shrinkage. The reference shrinkage curve is predicted by eight fundamental physical immediately measured parameters of (i) the intra-aggregate matrix (including clay content); (ii) the aggregate structure; and (iii) the mean silt-sand grain size or mean interface layer thickness. The model was validated using the data for eight soils. In addition to the major potential application for estimating a soil crack volume, the model explains differences between the observed shrinkage curves of soil and pure clay, and it can have other numerous applications.     

Morphology of horizontal cracks in swelling soils

Horizontally formed cracks in the network of cracked swelling soils tend to influence water and solute transport. An approach is suggested for estimating the mean width and volume of horizontal cracks. It is assumed that the nearly horizontal cracks appear as a result of inhomogeneous soil subsidence caused by rapid drying and shrinkage of thin layers at the walls of vertical cracks. Compared with the moist soil matrix, at the same soil depth, horizontal cracks originate as ruptures in stretched layers of the drying walls of vertical cracks. A characteristic of the average inhomogeneity of soil subsidence, i.e., the mean potential relative subsidence (MPRS) depending on the soil depth is defined. It is calculated on the basis of linear shrinkage in the clay soil matrix and at the walls of vertical cracks of different depths, and on two geometrical parameters of crack networks. They are namely the maximum crack depth and the thickness of the upper intensive-cracking layer. The absolute value and sign of the derivative of the MPRS function with respect to soil depth determine the specific volume of horizontal cracks (horizontal-cracks porosity), and their mean width as functions of depth. Model predictions are obtained using published data on variation of linear shrinkage with depth in 19 soil profiles. For lack of data specific to horizontal-crack characteristics model, predictions were compared with data on vertical cracks and subsidence at the soil surface. Satisfactory agreement was obtained for all soil depths up to the maximum crack depth.     

Pore-Scale Numerical Investigation on Chemical Stimulation in Coal and Permeability Enhancement for Coal Seam Gas Production

Permeability is a controlling factor for gas migration in coal seam reservoirs and has invariably been the barrier to economically viable gas production in certain deposits. Cleats are the main conduits for gas flow in coal seams though cleat mineralisation is known to significantly reduce permeability. Cleat demineralisation by the use of acids may enhance the effective cleat aperture and therefore permeability. This modelling study examines how acids transport through coal subject to reactive cleat mineralisation, and develops a fundamental understanding of the mechanisms controlling permeability change from pore scale to sample scale. A novel Lattice Boltzmann Method (LBM)-based numerical model for the simulation, prediction, and visualisation of the reaction transport is proposed to numerically investigate relationships between physio-chemical changes and permeability during coal stimulation. In particular, the work studies the interaction of acidic fluids (HCl) with reactive mineral (e.g. calcite) and assumed non-reactive mineral (e.g. coal) surfaces, mineral dissolution and mass transfer, and resultant porosity change. The reaction of a calcite cemented core sub-plug from the Bandanna Formation of Bowen Basin (Australia), is used as a study case. LBM simulations revealed a permeability enhancement (27.15 times of the pre-flooding permeability) along the x-axis after 20 min HCl flooding of a \(5.3~\hbox {cm} \times 5.3~\hbox {cm} \times 1.3~\hbox {cm}\) sub-section. The analysis and evaluation of the 4D permeability evolution is conducted as a contribution work for the fluid flow modelling in the subsurface petrophysical conditions, at the micron to centimetre scales. The simulation results demonstrate the proposed algorithm is capable for studies of multiple mineral reactions with disparate reaction rates.