Klinkenberg Effect Research Articles

Experimental study on ultrasonic irradiation for enhancing coalbed methane recovery

The present study proposes the use of a new ultrasonic irradiation method to enhance permeability and desorption for gas recovery from low-permeability coal reservoirs. A triaxial stress ultrasonic irradiation test apparatus was developed specifically for coal, considering the properties of gas adsorption, migration, and sound intensity, and providing a simultaneous measurement of gas flux, to investigated the deformation and temperature of coal samples obtained from the Fuxin coal field by permeability and desorption experiments. With the ultrasonic irradiation duration, the permeability of coal improved gradually with unequal variation, accompanied by the Klinkenberg effect where it decreased rapidly and then increased slowly with increasing gas pressure. The ability to desorb coal was enhanced by higher sound intensity ultrasound irradiation, and the volume of gas desorption was much greater than that of the sample without mange, the temperature and strain were demonstrated as a “J shaped” curve. An X-ray computer tomography (CT) technique was used to visualise the meso- or macro-cracks in the coal sample at pre- and post- ultrasonic irradiation, consequently, fractures expanded under the irradiation of ultrasonic waves. A permeability and desorption model was developed to describe the improvement of coal seam gas production capacity under ultrasonic irradiation, which introduced effective sound pressure.

Deformation behavior and damage-induced permeability evolution of sandy mudstone under triaxial stress

The mechanic and permeability behavior in sandy mudstone is crucial to hazard prevention and safety mining. In this study, to investigate the evolution and characteristic of permeability and mechanical properties of sandy mudstone subjected to loading of in-site stress, a series of triaxial compression–seepage experiments are performed. The increase in permeability and decrease in mechanical strength gradually transformed to the decrease in permeability and increase in mechanical strength responding to the increase in confining stress from 5 to 15 MPa, which corresponds to the transformation from brittleness to ductility in sandy mudstone, and the transformation threshold of 10 MPa confining stress was determined. The penetration shear fracture generated at brittle regime, while plastic flow behavior presented at semibrittle and ductile state. The critical value of the yielding stage in axial strain increases with the increase in confining stress. The relatively higher permeability corresponds to the higher pore pressure during the increase in confining stress. The increase in confining stress promoted the increase in volumetric strain, while increased pore pressure reduced the volumetric strain, and the lower permeability occurred at higher volumetric strain. In addition, an improved permeability model was developed to describe the loading-based permeability behavior considering the Klinkenberg effect.

The Method of Determining Layer in Bottom Drainage Roadway Taking Account of the Influence of Drilling Angle on Gas Extraction Effect

The pre-drainage of coalbed methane through boreholes in the bottom drainage roadway (BDR) is the key measure to prevent and control coal and gas outburst. Different arrangement layers in the BDR will make a difference in the range of drilling angle and affect the gas extraction effect. In this paper, the mathematical model of the rock loose circle area around elliptical drilling was constructed. Meanwhile, the fluid–solid coupling model is constructed by using COMSOL software, the dynamic response of coal permeability and volumetric strain with gas pressure and the Klinkenberg effect of gas are considered, and the effect of the change of the elliptical drilling angle on the pressure relief effect of the coal seam is studied. The results showed that the distance between the layer in the BDR and the pre-drainage coal seam would decrease, and the effective extraction length at the same point of gas extraction in the coal seam increases. The area of the rock loose circle and permeability around the drilling decayed negatively and exponentially with the increase in drilling angle. As the drilling angle decreased, the stress in the major axis of the ellipse at the drilling cross-section increased, so the drilling was prone to collapse, and the gas extraction was hindered. Finally, an optimal method of determining the layer in the BDR under the coupling effect of multiple factors was established by combining the measured ground stress. Through field measurement, the drilling extraction rate of the optimized scheme is 60% higher than that of the original scheme.

The slippage effect of concrete gas permeability and the influence of its microstructure

Klinkenberg effect has a significant influence on the test results of gas permeability. To study the gas slippage effect of concrete and its microscopic mechanism, five kinds of concrete with different w/c ratios were designed, and the gas permeability coefficients were measured at seven additional gas pressures and five saturation degrees according to the Cembureau method, the effects of w/c ratio, saturation degree and additional gas pressure on slippage effect were investigated by the Grey Correlation Analysis (GCA) method. Meanwhile, based on the nuclear magnetic resonance (NMR) method, the influences of microstructure parameters on gas intrinsic permeability and slippage factor were studied. Results show that w/c ratio which reflects the microstructure characteristics of concrete, is the most important factor affecting the slippage effect. Moreover, a larger porosity indicates a more obvious slippage effect. The pores in concrete with size of 100–200 nm, have the greatest influence on the gas slippage effect.

CBM exploration: Permeability of coal owing to cleat and connected fracture

Coalbed methane (CBM) resources cannot be efficiently explored and exploited without a robust understanding of the permeability of fracture-size heterogeneities in coal. In this study, two sister coal samples were imparted with pre-developed cleat and connected fractures, and the permeability of the coal samples was measured under different conditions of controlled confining and gas pressures. Furthermore, the implications of the results for CBM exploration and exploitation were discussed. The permeability of coal with cleat development ranged from 0.001–0.01 mD, indicating ultra-low permeability coal. The gas migration in this coal changed from a linear flow to a non-linear flow, with the increase in gas pressure (>1 MPa). Thus, the permeability of the coal initially increased and then decreased. However, the Klinkenberg effect does not exist in this ultralow-permeability coal. For the coal sample with connected fracture, permeability ranged from 0.1–10 mD, which is larger by hundred orders of magnitude than that of the sample with cleat. For this coal, with a decrease in gas pressure (<1 MPa), the Klinkenberg effect significantly increased the permeability of the coal. With an increase in the applied confining pressure, both the Klinkenberg coefficient and permeability of the coal presented a decreasing trend. It is suggested that field fracture investigation is a prerequisite and indispensable step for successful CBM production. The coal beds that cleat network is well conductive to the connected fracture can be an improved target area for CBM production. During CBM production, a variety of flow regimes are available owing to the decrease in CBM reservoir pressure. In particular, under the low CBM reservoir pressure and low in situ geo-stress conditions, the gas migration in the CBM reservoir with connected facture development exhibits remarkable free-molecular flow. Thus, the reservoir permeability and predicted CBM production will be enhanced.

Advanced understanding of gas flow and the Klinkenberg effect in nanoporous rocks

Gas flow in nanoporous rocks is closely relevant to several globally important energy and environmental issues, such as shale-gas production and CO2 subsurface sequestration. The Klinkenberg effect is critical to an understanding of gas flow, yet many specifics are unclear for nanoporous rocks. Here we investigated gas flow and the Klinkenberg effect in nanoporous rocks on the basis of a systematic study of gas permeability and diffusivity under a range of pore pressures and varying water saturations. We invalidated the use of the Klinkenberg equation for determination of intrinsic permeability and the Klinkenberg slippage factor on the basis of measurements in current laboratory conditions and propose a modified Klinkenberg equation for a more reliable determination of the slippage factor. We show that gas relative permeability is higher at higher pore pressures and that the Klinkenberg effect is more important in lower water saturations than in higher ones. The underlying mechanism of increased pore size after saturation was elucidated through neutron imaging on water distribution. In addition, we demonstrate that gas diffusivity better characterizes the diffusive gas flow than gas permeability and can be higher at higher pressures in either dry or partly saturated conditions. Finally, a characteristic pore-diameter index was derived on the basis of a new form of porosity–permeability relationship and was found to have a good correlation, which was previously lacking, with the Klinkenberg slippage factor for nanoporous rocks. Collectively, these new insights can advance the understanding of gas flow in nanoporous rocks and will have important implications on industrial applications.

A Novel Multiphysics Multiscale Multiporosity Shale Gas Transport Model for Geomechanics/Flow Coupling in Steady and Transient States

Summary A novel multiphysics multiscale multiporosity shale gas transport (M3ST) model was developed to investigate shale gas transport in both transient and steady states. The microscale model component contains a kerogen domain and an inorganic matrix domain, and each domain has its own geomechanical and gas transport properties. Permeabilities of various shale cores were measured in the laboratory using a pulse decay permeameter (PDP) with different pore pressure and confining stress combinations. The PDP-measured apparent permeability as a function of pore pressure under two effective stresses was fitted using the microscale M3ST model component based on nonlinear least squares fitting (NLSF), and the fitted model parameters were able to provide accurate model predictions for another effective stress. The parameters and petrophysical properties determined in the steady state were then used in the transient-state, continuum-scale M3ST model component, which performed history matching of the evolutions of the upstream and downstream gas pressures. In addition, a double-exponential empirical model was developed as a powerful alternative to the M3ST model to fit laboratory-measured apparent permeability under various effective stresses and pore pressures. The developed M3ST model and the research findings in this study provided critical insights into the role of the multiphysics mechanisms, including geomechanics, fluid dynamics and transport, and the Klinkenberg effect on shale gas transport across different spatial scales in both steady and transient states.

Research and Optimization of Gas Extraction by Crossing-Seam Boreholes from Floor Roadway

Deep coal seams are characterized by large stress, high gas pressure, and low permeability. The gas disaster threatens the safe production of coal mine seriously. Gas extraction by crossing-seam boreholes from floor roadway (GECMBFR) can reduce the pressure and content of coal seam gas, which is the main measure to prevent gas disaster. Considering the Klinkenberg effect, governing equations of gas adsorption/desorption-diffusion, gas seepage, and stress fields within the coal seam are established to form the seepage-stress coupling model. The governing equations are embodied into a finite element driven software to numerically simulate gas migration and fluid-solid coupling law in coal seam. On this basis, the process of gas extraction under different borehole spacings and diameters is simulated. The effects of these two key parameters on coal seam gas pressure, gas content, and gas permeability were analyzed. The borehole spacing and diameter were determined to be 5 m and 0.09 m, respectively. Combined with the actual situation of a mine, the process of gas extraction from floor roadway with different cross-sectional schemes, ordinary drilling boreholes and punching combined drilling boreholes, is comparatively analyzed. The results show that the gas extraction effect by ordinary drilling boreholes is lower than that of the punching combined drilling boreholes, and the extraction is uneven and makes it difficult to meet the standard. Hydraulic punching was carried out, and coal was washed out of the borehole, which expanded the contact area between the borehole wall and coal seam. The coal seam around the punching borehole is unloaded, which improves coal permeability and accelerates gas migration towards the borehole, thus promoting the efficiency of gas extraction. It is more reasonable to use punching combined drilling borehole scheme when implementing the GECMBFR technology.

The dependence of shale permeability on confining stress and pore pressure

We examined the permeability behavior of two Marcellus Shale samples and two Eagle Ford Shale samples using argon gas under multiple confining stresses (PC = 13.8–68.9 MPa) and pore pressures (PP = 1.6–28.2 MPa). We corrected our measured permeability values for the Klinkenberg effect and contoured permeability as a function of PP and PC to obtain the effective stress coefficient for permeability (nk), which scales the influence of PP on permeability relative to PC. We explored the underlying mechanisms controlling nk using two idealized models of a cylindrical capillary tube consisting of low and high compressibility material to model the unique pore structure present in our samples. Finally, we investigated the impact of PP reduction on permeability during production. We show that the permeability is stress-dependent and that nk is formation-dependent. Marcellus Shale samples, with predominantly organic matter hosted pores, have a Klinkenberg-corrected permeability of 11.0 to 1.9 nD (PC - PP = 5.3–33.8 MPa) and nk value of 1.11 and 1.60, respectively. In contrast, Eagle Ford Shale samples, with predominantly inter-particle pores, have Klinkenberg-corrected permeability of 33.6 to 2.0 nD (PC - PP = 13.3–40.8 MPa) and nk value of 0.96 and 0.84, respectively. We infer that the PP change produces considerable pore wall strain relative to the PC change in the Marcellus Shale organic matter pores resulting in nk > 1. In contrast, we infer a smaller pore wall strain for the same PP and PC changes in the Eagle Ford Shale inter-particle mineral pores giving in nk < 1. Our findings will inform models to predict production behavior of reservoirs and may be used to improve recovery efficiency by adopting the best production strategy in unconventional shale reservoirs.

Automatic fracture optimization for shale gas reservoirs based on gradient descent method and reservoir simulation

In shale gas reservoir development, determination of hydraulic fracture geometry for horizontal wells is a demanding yet challenging task. One type of approach for hydraulic fracture optimization is based on reservoir simulation. To improve optimization efficiency and accuracy, an automatic and robust procedure integrating the gradient descent method with gas reservoir simulation has been developed. Fractured reservoir models were constructed using the “Multiple INteracting Continua” method, whereby an in-house shale gas reservoir simulator was implemented to model multiple gas transport mechanisms including non-Darcy flow, gas desorption, Klinkenberg effect, and geomechanical effect. The optimization procedure was first validated against two ideal cases and then applied to two realistic cases to optimize fracture spacing, half-length, and dimensionless fracture conductivity. It showed that the optimization results depend on optimization objective, reservoir property, natural fractures, economics and termination criteria. This gradient descent assisted fracture optimization procedure can achieve significant computational reduction and high prediction accuracy for various shale gas reservoir cases. Cited as : Chen, J., Wang, L., Wang, C., Yao, B., Tian, Y., Wu, Y.-S. Automatic fracture optimization for shale gas reservoirs based on gradient descent method and reservoir simulation. Advances in Geo-Energy Research, 2021, 5(2): 191-201, doi: 10.46690/ager.2021.02.08

Experimental Study on Gas Transport in Shale Matrix with Real Gas and Klinkenberg Effects

Gas transport in shale matrix is complex due to multiple mechanisms and is difficult to be investigated by macroscopic experiment. For Gas Research Institute (GRI) method, which is the most accepted one for gas transport investigation in shale matrix, the apparatus was modified by adding an automatic gas supplement and pressurization (AGSP) system, and a numerical model considering the variation of real gas property and the Klinkenberg effect was established for data interpretation. Then, the intrinsic permeability and Klinkenberg coefficient were effectively obtained by maintaining high expanding speed of gas in apparatus and eliminating the negative effect of low filling degree of sample. By analysis, the ideal gas transports faster than real gas due to the viscosity difference at low pressure and the deviation factor difference at high pressure. For Wufeng-Longmaxi shale matrix, the positive influence of Klinkenberg effect on gas transport would attenuate with increasing pressure and is more powerful than bulk shale sample with fractures. Therefore, the gas transport in real shale matrix could be well known, which is meaningful to production forecast and evaluation in oil and gas fields.

The Partial Transformational Decomposition Method for a Hybrid Analytical/Numerical Solution of the 3D Gas-Flow Problem in a Hydraulically Fractured Ultralow-Permeability Reservoir

SummaryThe analysis of gas production from fractured ultralow-permeability (ULP) reservoirs is most often accomplished using numerical simulation, which requires large 3D grids, many inputs, and typically long execution times. We propose a new hybrid analytical/numerical method that reduces the 3D equation of gas flow into either a simple ordinary-differential equation (ODE) in time or a 1D partial-differential equation (PDE) in space and time without compromising the strong nonlinearity of the gas-flow relation, thus vastly decreasing the size of the simulation problem and the execution time.We first expand the concept of pseudopressure of Al-Hussainy et al. (1966) to account for the pressure dependence of permeability and Klinkenberg effects, and we also expand the corresponding gas-flow equation to account for Langmuir sorption. In the proposed hybrid partial transformational decomposition method (TDM) (PTDM), successive finite cosine transforms (FCTs) are applied to the expanded, pseudopressure-based 3D diffusivity equation of gas flow, leading to the elimination of the corresponding physical dimensions. For production under a constant- or time-variable rate (q) regime, three levels of FCTs yield a first-order ODE in time. For production under a constant- or time-variable pressure (pwf) regime, two levels of FCTs lead to a 1D second-order PDE in space and time. The fully implicit numerical solutions for the FCT-based equations in the multitransformed spaces are inverted, providing solutions that are analytical in 2D or 3D and account for the nonlinearity of gas flow.The PTDM solution was coded in a FORTRAN95 program that used the Laplace-transform (LT) analytical solution for the q-problem and a finite-difference method for the pwf problem in their respective multitransformed spaces. Using a 3D stencil (the minimum repeatable element in the horizontal well and hydraulically fractured system), solutions over an extended production time and a substantial pressure drop were obtained for a range of isotropic and anisotropic matrix and fracture properties, constant and time-variable Q and pwf production schemes, combinations of stimulated-reservoir-volume (SRV) and non-SRV subdomains, sorbing and nonsorbing gases of different compositions and at different temperatures, Klinkenberg effects, and the dependence of matrix permeability on porosity. The limits of applicability of PTDM were also explored. The results were compared with the numerical solutions from a widely used, fully implicit 3D simulator that involved a finely discretized (high-definition) 3D domain involving 220,000 elements and show that the PTDM solutions can provide accurate results for long times for large well drawdowns even under challenging conditions.Of the two versions of PTDM, the PTD-1D was by far the better option and its solutions were shown to be in very good agreement with the full numerical solutions, while requiring a fraction of the memory and orders-of-magnitude lower execution times because these solutions require discretization of only the time domain and a single axis (instead of three). The PTD-0D method was slower than PTD-1D (but still much faster than the numerical solution), and although its solutions were accurate for t &amp;lt; 6 months, these solutions deteriorated beyond that point.The PTDM is an entirely new approach to the analysis of gas flow in hydraulically fractured ULP reservoirs. The PTDM solutions preserve the strong nonlinearity of the gas-flow equation and are analytical in 2D or 3D. This being a semianalytical approach, it needs very limited input data and requires computer storage and computational times that are orders-of-magnitude smaller than those in conventional (numerical) simulators because its discretization is limited to time and (possibly) a single spatial dimension.

Multiscale characterization of shale pore-fracture system: Geological controls on gas transport and pore size classification in shale reservoirs

A sound understanding of the pore-fracture system across all scales provides an in-depth look at the intricate gas transport mechanisms in shale reservoirs. We performed a comprehensive multiscale characterization analysis on the Longmaxi shale samples using five complementary techniques: low-temperature gas (N2) adsorption (LTGA), mercury intrusion porosimetry (MIP), nuclear magnetic resonance (NMR), field emission scanning electron microscopy (FE-SEM), and X-ray computed tomography (CT) scanning. For pore size distribution (PSD) determination, LTGA (N2) analysis can detect small pores (2–300 nm sized), while MIP analysis is suitable for large pores or fractures (> 300 nm). NMR can reveal full-scale PSD characteristics of shale. Combining NMR with LTGA or MIP is recommended, since NMR alone would over- or under-estimate the pore size. The Longmaxi shale pores observed by FE-SEM imaging are of good connectivity and, by and large, are tens of nanometers sized. The scale-dependent analysis shows that the representative elementary volume (REV) for porosity of the Longmaxi shale based on FE-SEM imaging is almost 600 μm. As evident from the CT scanning, the connectivity of the entire shale pore-fracture system increased significantly after saturating the sample with water. The gas slippage (Klinkenberg) effect is significant at relatively low pressures. A second-order model would better estimate the intrinsic permeability compared with the traditional Klinkenberg equation. Microfractures manifest preferred orientation or alignment parallel to the shale bedding plane and are the dominant pathways for gas transport in shale. Finally, we proposed a new pore size classification of shale considering gas transport mechanisms: adsorption pores (pore size < 10 nm), slippage pores (10 nm < pore size < 1000 nm), and seepage pores or fracture-pores (pore size > 1000 nm). Although slippage pores dominate in terms of the total volumetric contribution of the Longmaxi shale, with a clear presence of adsorption pores, overall gas transport in shale is predominantly controlled by the seepage pores (fracture-pores), which constitute a very small portion of the total volume.

A new stress-damage-flow coupling model and the damage characterization of raw coal under loading and unloading conditions

Coalbed methane, as a gas in coal seam, is a kind of potential clean energy with high reserves. At present, there are two main types of coalbed methane extraction in China, one is extracting coalbed methane by ground drilling, the other is coal and gas (coalbed methane) simultaneous extraction in coal mine underground. In the process of coal and gas simultaneous extraction, the migration of gas may not only cause coal and gas outburst, gas gushing and other disasters, but also cause the greenhouse effect. Therefore, in order to achieve the goal of safe simultaneous extraction of coal and gas and reducing greenhouse gas emissions, it is particularly important to understand the flow properties of gas and the damage characteristics of raw coal in the process of coal seam mining. In this paper, the mechanical properties and seepage characteristics of raw coal samples under loading and unloading conditions are studied experimentally by using the laboratory-fabricated ‘thermal-hydro-mechanical coupled with triaxial servo controlled seepage apparatus for gas-containing coal’. At the same time, X-ray tomography is carried out on the raw coal samples before and after the experiment. The deformation, damage and seepage characteristics of raw coal samples in the experimental process are recorded and analyzed. On the basis of the above, based on the information entropy theory, the change rate of information entropy is proposed as a damage characterization parameter, and its feasibility is verified by the comparison and analysis with the change rate of porosity. Finally, according to the basic definition of porosity, combined with statistical damage model, considering the gas adsorption expansion and Klinkenberg effect, the evolution model of permeability under loading and unloading conditions is developed. The model can better reflect the permeability evolution law of raw coal under loading and unloading conditions.

Gas Seepage Under Continuous and Step Loading Based on True Triaxial Seepage Test Apparatus

The conventional triaxial loading in gas seepage studies does not reflect the actual stressing state in the coal seam. Thus, a true triaxial seepage experimental apparatus is developed before seepage tests are conducted with it. The first group of tests is carried out with continuous axial loading under uniform lateral constrain on moulded coal specimen: one test under constant-velocity axial loading, two tests under monotonic variable-velocity axial loading, and two tests under single-cycle variable-velocity axial loading. The tests reflect the multi-step, discontinuous, stressing condition with variable-loading rate and strength in a coal seam. The law of coal deformation and gas permeability variation under constant-velocity and variable-velocity axial loading is obtained. Then, the multi-step seepage tests under different non-uniform lateral pressures are conducted, focusing on permeability variation under different triaxial stresses versus gas pressure and intermediate principal stress. The permeability increase with gas pressure decrease is confirmed and interpreted. Moreover, the turning point between Klinkenberg effect and gas wedging effect in the coal seam is determined. A simplified concept of average effective stress is put forward, and the dominant influence of this average effective stress on coal seam permeability is identified based on the concept.

Numerical Investigation of the Effect of Partially Propped Fracture Closure on Gas Production in Fractured Shale Reservoirs

Nonuniform proppant distribution is fairly common in hydraulic fractures, and different closure behaviors of the propped and unpropped fractures have been observed in lots of physical experiments. However, the modeling of partially propped fracture closure is rarely performed, and its effect on gas production is not well understood as a result of previous studies. In this paper, a fully coupled fluid flow and geomechanics model is developed to simulate partially propped fracture closure, and to examine its effect on gas production in fractured shale reservoirs. Specifically, an efficient hybrid model, which consists of a single porosity model, a multiple porosity model and the embedded discrete fracture model (EDFM), is adopted to model the hydro-mechanical coupling process in fractured shale reservoirs. In flow equations, the Klinkenberg effect is considered in gas apparent permeability, and adsorption/desorption is treated as an additional source term. In the geomechanical domain, the closure behaviors of propped and unpropped fractures are described through two different constitutive models. Then, a stabilized extended finite element method (XFEM) iterative formulation, which is based on the polynomial pressure projection (PPP) technique, is developed to simulate a partially propped fracture closure with the consideration of displacement discontinuity at the fracture interfaces. After that, the sequential implicit method is applied to solve the coupled problem, in which the finite volume method (FVM) and stabilized XFEM are applied to discretize the flow and geomechanics equations, respectively. Finally, the proposed method is validated through some numerical examples, and then it is further used to study the effect of partially propped fracture closures on gas production in 3D fractured shale reservoir simulation models. This work will contribute to a better understanding of the dynamic behaviors of fractured shale reservoirs during gas production, and will provide more realistic production forecasts.

Experimental research on stress-dependent permeability and porosity of compact sandstone with different moisture saturations

In this paper, compact sandstone with different moisture saturation from 0% to 73.60% was prepared. Subsequently, gas permeability and porosity of the prepared rock specimens under different pore pressure during confining pressure loading and unloading was measured. The experimental results indicate that, for rock specimen with moisture saturation 0%, 9.63%, 22.10%, 33.60%, and 42.30%, gas permeability rises with the increase of pore pressure due to Klinkenberg Effect, while for rock specimens with moisture saturation 54.36% and 73.60%, the opposite phenomenon was observed because the flow rate of gas has the dominant influences on the gas permeability than that of Klinkenberg Effect. The quadratic equation has better performance in describing the Klinkenberg Effect than that of Klinkenberg equation. Klinkenberg Effect enhances with the increase of moisture saturation and confining pressure, respectively, due to the decrease of equivalent pore radius for gas flow. With the rise of moisture saturation, the decreasing rate of intrinsic permeability under low moisture saturation is low than that under high moisture saturation. The intrinsic permeability of rock specimens with high moisture saturation is more sensitive to loading and unloading than that with low moisture saturation. The relationship between intrinsic permeability/porosity of rock specimens and confining pressure can be described correctly by adopting the exponential function model and power function model, respectively. Additionally, the gradual increase in moisture content in rock specimens revealed significant decrease on intrinsic permeability. This was attributed to clay swelling which contributed to blockage of seepage paths.

Predicting the permeability and specific surface area of compressed and uncompressed fibrous media including the Klinkenberg effect

In this study a geometric anisotropic two-strut model is presented to predict the permeability of fibrous porous media subject to compression. A further novelty of this study is the inclusion of the Klinkenberg effect in the permeability prediction of the two-strut model and existing three-strut model. The specific surface area of the anisotropic models are predicted by making use of two approaches, i.e. a geometric approach and a combined kinematic-geometric approach. The Klinkenberg effect has also been introduced into the non-compressed models. The model predictions are compared to a variety of available experimental data for non-woven fibre media and metal foams from the literature and the correspondence proves to be satisfactory. The analytical modelling approach presented adds value to the empirical studies in the literature which comprises of curve fitting procedures together with the introduction of empirical coefficients into the Forchheimer or Ergun equations to obtain correlation with experimental data.

Research on anisotropic permeability and porosity of columnar jointed rock masses during cyclic loading and unloading based on physical model experiments

In this paper, the permeability and porosity of self-prepared artificial columnar jointed rock masses (CJRM) with different columnar dip angles under different pore pressures during cyclic loading-unloading of confining pressure were measured. The experimental results indicate that the gas permeability of the artificial CJRM gradually decreases with the rise of pore pressure due to the existence of Klinkenberg effect, and Klinkenberg effect gradually decreases with the rise of columnar dip angle. The existence of it improves significantly the intrinsic permeability. Besides, the intrinsic permeability and porosity of artificial CJRM are more sensitive to the first loading than that of the intact cement mortar specimen. The permanent deformation of pores in the specimens mainly appears in the first cycle, and the subsequent cycles have smaller effects on the intrinsic permeability and porosity. The permanent deformation results in the intrinsic permeability, and porosity in the loading process is always higher than those in the unloading process. The intrinsic permeability gradually increases with the growth of columnar dip angle, exhibiting obvious permeability anisotropy. Under high confining pressure, the permeability anisotropy of artificial CJRM is less than that under low confining pressure. Meanwhile, under the same confining pressure, during the repeated loading-unloading cycles, the permeability anisotropy decreases gradually. The existence of a representative element volume (REV) for CJRM is verified; thus, the equivalent continuum media model can be utilized to analyse the seepage characteristics of CJRM.

A Comparison of Gas and Water Permeability in Clay‐Bearing Fault and Reservoir Rocks: Experimental Results and Evolution Mechanisms

AbstractTo better understand the discrepancy between gas and water permeability and the mechanism of permeability in response to the presence of water in clay‐bearing rocks, we performed transport property experiments on synthetic quartz‐clay mixtures and natural fault gouge, as well as clay‐bearing sandstones for comparison purpose. The experiments were performed on a fluid flow apparatus with effective pressures (Pe) cycling between 5 and 105 MPa. Each sample was subjected to nine Pe cycles, along which permeability and porosity of either the gas‐saturated (nitrogen) or water‐saturated samples were measured. The results show that the permeability of all samples investigated decreases with increasing Pe. Gas permeability exhibits strong pore pressure dependence, which can be explained by the slippage (Klinkenberg) effect. Permeability results measured by water are commonly lower than the gas results. The decrease in permeability after the addition of water can be generally explained by the evolution of porosity, as can be determined from the bulk volume and solid mineral volume measurement results. The loss of permeability is associated with the hydration expansion of clay minerals that causes the reduction of porosity. A conceptual model for the evolution of porosity that incorporates clay expansion and grain rearrangement is proposed to describe the mechanism for water permeability in clay‐bearing rocks. Based on these results, we discuss the effect of clay hydration on fluid transport and mechanical behaviors in clay‐bearing fault zones and reservoir formations following fluid injection.