Klinkenberg Effect Research Articles

Mathematical model of permeability evolution of liquid CO2 pressurized coal

To examine the permeability alterations in coal seams induced by liquid CO2 injection, we employed COMSOL simulations to recreate the flow, force, and temperature fields, along with the corresponding physical parameters of the geological formation. We established a mathematical model to track the evolution of the coal body’s permeability, enabling us to capture the phase distribution of CO2, the dynamics of fluid transportation, and the coal body’s mechanical responses during the liquid CO2 injection process. Our findings revealed that the coal seam undergoes significant changes due to low-temperature freezing and shrinkage, gas-liquid phase transitions, and expansion impacts from solid-liquid phase changes. These factors collectively modify the pore structure, subsequently influencing the coal seam’s permeability. Notably, the coal body’s permeability, influenced by the pore structure and the Klinkenberg effect, increases logarithmically with rising injection pressure and falling temperatures. The structural changes in the coal body are markedly impacted by seepage and phase change pressures, with the permeability enhancement from secondary phase changes being 2.28 times greater than that from primary phase changes, and five times greater than in scenarios without phase change.

A permeability model considering the dynamic effect of stress on gas adsorption under discontinuous compression.

With the continuous advance of coal mining, the normal stress in front of coal seams will continue to increase, resulting in changes of internal structure and permeability of coal seams. During the continuous advance of mining face, the increase of vertical stress somewhere in front of coal seams may not be a transient process, but a gradual change process. Therefore, this paper carried out the seepage test of gas-containing coal under discontinuous loading axial stress. The stress, deformation and permeability of coal specimens were measured and recorded during the test, and the influence of discontinuous loading axial stress on the deformation, internal structure and seepage properties of coal specimens were discussed. On this basis, considering the influence of stress on the gas adsorption state, Klinkenberg effect and other factors, combined with Shi-Durucan permeability model, a new permeability model considering the dynamic adsorption state of coal specimens was developed.

Thermodynamic modeling of coal-gas interactions and desorption temperature analysis

This research developes an innovative thermodynamic coupling model for gas-bearing coal, improving temperature change simulations during coalbed methane desorption. The model distinctively integrates adsorption/desorption heat effects, free gas expansion, dynamic diffusion, the Klinkenberg effect, and moisture influence, offering a more comprehensive perspective of thermodynamic behavior. Comparisons with empirical data and previous models demonstrate that the predicted temperature changes closely match experimental results, indicating superior accuracy. The investigation finds a 23.51 % increase in desorption temperature as gas pressure rises from 0.4 MPa to 1.2 MPa, with temperature changes following the sequence CO2 > CH4 > N2, in the ratio ΔT(CO2): ΔT(CH4): ΔT(N2) = 1.76: 1.35: 1. Adsorbed gas desorption and free gas expansion are recognized as the primary drivers, especially near 0.5 MPa, where adsorbed gas contributes nearly 70 %. Sensitivity to variables such as gas pressure, adsorption heat, and permeability diminishes over time, with moisture exerting minimal impact. The study highlights a close thermodynamic connection between temperature changes and gas outbursts, proposing temperature variation as an reliable indicator for predicting and evaluating outburst risks. These findings enhance understanding of coalbed methane desorption and provide new theoretical foundations for efficient resource development and disaster prevention.

Analysis of dynamic characteristics and influencing factors of CO2 low-permeability coal reservoir sequestration

ABSTRACT Abandoned coal seams can be an important carrier for CO2 geological storage. Considering the gas seepage-diffusion and physical adsorption coupling characteristics in the process of CO2 adsorption and storage in coal and rock, a two-dimensional model of coupled flow-solidity for geological storage of CO2 in low-permeability reservoir with double voids was established by introducing the Zhang Hongbin model algorithm and adding the Klinkenberg effect and the compression effect of the rock skeleton in coal reservoirs in the controlling equation for rock deformation. The coupled flow-solid model was solved by using the PDE equation of COMSOL Multiphics program, and the simulation results difference between the new model and the traditional model in terms of sequestration dynamics were compared. The dynamic characteristic of reservoir gas pressure, formation stress, permeability and sequestration density in the process of CO2 geologic sequestration and injection were analyzed, and the influences of injection pressure and injection well diameter on the amount of CO2 sequestration were explored. The results show that the new model is more reasonable for calculating reservoir gas pressure and permeability compared with the Palmer-Mansoori model (PM model), and can simulate the free-state seepage movement of CO2 in the fracture system as well as its physical adsorption process compared with the single-heavy pore medium model. With continuous CO2 injection, the maximum sequestration density was raised to a limit value of about 1000 kg/m3 after 1 year. The date of reaching the limit of the sequestration volume was advanced by about 45 d when the positive pressure of the injected gas was increased from 10 kPa to 50 kPa. This model can reproduce the main parameters including, when affecting the effect, and realize the calculation of parameters such as CO2 density reaching the limit value, sealing limit day, sealing limit amount, which can provide a theoretical basis for further deep understanding of CO2 geological sealing law and scientific development of gas injection scheme.

Thermomechanical coupling seepage in fractured shale under stimulation of supercritical carbon dioxide

As a waterless fracturing fluids for gas shale stimulation with low viscosity and strong diffusibility, supercritical CO2 is promising than the water by avoiding the clay hydration expansion and reducing reservoir damage. The permeability evolution influenced by the changes of the temperature and stress is the key to gas extraction in deep buried shale reservoirs. Thus, the study focuses on the coupling influence of effective stress, temperature, and CO2 adsorption expansion effects on the seepage characteristics of Silurian Longmaxi shale fractured by supercritical CO2. The results show that when the gas pressure is 1–3 MPa, the permeability decreases significantly with the increase in gas pressure, and the Klinkenberg effects plays a predominant role at this stage. When the gas pressure is 3–5 MPa, the permeability increases with the increase in gas pressure, and the influence of effective stress on permeability is dominant. The permeability decreases exponentially with the increase in effective stress. The permeability of shale after the adsorption of CO2 gas is significantly lower than that of before adsorption; the permeability decreases with the increase in temperature at 305.15 K–321.15 K, and with the increase in temperature, the permeability sensitivity to the temperature decreases. The permeability is closely related to supercritical CO2 injection pressure and volume stress; when the injection pressure of supercritical CO2 is constant, the permeability decreases with the increase in volume stress. The results can be used for the dynamic prediction of reservoir permeability and gas extraction in CO2-enhanced shale gas development.

Experimental study on the Klinkenberg effect for gas permeability in carboniferous shales, Eastern Qaidam Basin, China

It is crucial to understand the conditions and influencing mechanisms of shale gas slip effect for predicting the productivity of shale gas reservoirs. This study focuses on the Carboniferous Hurleg Formation shales in the eastern Qaidam Basin and conducts gas permeability tests using different gases (He/N2), as well as geochemical and pore-structure tests. The slip behavior of different gases in micro- and nanopores as well as the anisotropy of gas permeability were analyzed and discussed. The results show that helium permeability is 1.81–3.56 times higher than nitrogen permeability, with a greater difference at lower pore pressures. These permeability differences are attributed to variations in gas molecule size and slip effects. Specifically, the slip effect of helium gas has a greater contribution to permeability at lower pore pressures, with a helium slip factor averaging 2.79 times that of nitrogen. The effective pore size of shale, calculated based on the helium slip factor, is 0.74 to 1.51 times larger than when nitrogen is used, with an average of 1.67 times. Helium molecules have smaller diameters and longer average molecular free paths, resulting in a more pronounced slip effect compared to nitrogen. While helium does not adsorb, nitrogen exhibits some adsorption, causing radial expansion during gas penetration. Furthermore, when testing with different gases, the horizontal permeability (S043∥; S052∥) is higher than the vertical permeability (S043⊥; S052⊥). The anisotropy of permeability is controlled by the pore system formed by the arrangement and combination of minerals. Calcium-rich samples (S052) tend to exhibit higher anisotropy compared to calcite-rich samples (S043). The effective pore size in the vertical sample is larger than that in the parallel sample, and the gas slip effect is significantly greater in the vertical sample. These findings provide valuable data for future studies on shale gas slip effects and productivity prediction.

The direct Monte Carlo simulation of microchannel flows for a large Knudsen number range

In recent years, porous materials containing micro- and nano-scale pores have found widespread applications. As the pore size decreases in such materials, rarefaction effects become significant in the pore flow, making the study of flow characteristics under higher Knudsen number conditions particularly crucial. In this work, through a direct simulation Monte Carlo (DSMC) method, an in-depth investigation is conducted into the gas flow characteristics and Klinkenberg effect in porous media with pore sizes ranging from 1 nm to 50 μm and Knudsen numbers spanning from 0.02 (slip flow) to 1200 (free molecular flow). The feasibility of using the DSMC method to simulate an internal free molecular flow in a porous medium under extreme rarefaction conditions with a Knudsen number of 1200 is validated. Furthermore, the impact of the gas pressure and porous medium pore size on the permeability is examined. The results reveal that with an increase in the Knudsen number, the dominant forces in the flow field transition from viscous forces to Knudsen diffusion, leading to a gradual increase in permeability. A comparative analysis reveals that existing apparent permeability models only provide satisfactory descriptions under certain Knudsen number conditions. Re-fitting the coefficient of the Kawagoe model and incorporating viscosity corrections leads to an apparent permeability model that can provide good predictions over a broader range of Knudsen numbers.

Experimental Study on Permeability and Gas Production Characteristics of Montmorillonite Hydrate Sediments Considering the Effective Stress and Gas Slippage Effect

Summary Gas permeability in hydrate reservoirs is the decisive parameter in determining the gas production efficiency and gas production of hydrate. In the South China Sea (SCS), the gas flow in tight natural gas hydrate (NGH) silty clay reservoirs is significantly affected by the gas slippage effect and the effective stress (ES) of overlying rock. To improve the effectiveness of hydrate exploitation, it is necessary to understand the influence of gas slippage in hydrate reservoirs on the permeability evolution law. For this paper, the gas permeability characteristics and methane production of hydrate montmorillonite sediments were studied at different pore pressures and ESs. Experimental data revealed that the gas permeability of montmorillonite samples before methane hydrate (MH) formation is seriously affected by the Klinkenberg effect. The gas permeability of montmorillonite sediments before hydrate formation is generally smaller than that after hydrate formation, and the gas slippage effect in the sediments after hydrate formation is weaker than that before hydrate formation. With the change in ES, the intrinsic permeability of sediment has a power law relationship with the simple ES. The ES law coefficient n was determined using the response surface method to eliminate the influence of gas slip on gas permeability. As pore pressure decreases and MH decomposes, montmorillonite swelling seriously affects gas permeability. However, the gas slippage effect has a good compensation effect on the permeability of montmorillonite sediments after MH decomposition under low pore pressure. The multistage depressurization-producing process of MH in montmorillonite sediments is mainly 3 MPa depressurization-producing stage and 2 MPa depressurization-producing stage. In this paper, the influence mechanism of gas slippage effect of hydrate reservoir is studied, which is conducive to improving the prediction accuracy of gas content in the process of hydrate exploitation and exploring the best pressure reduction method to increase the gas production of hydrate in the process of exploitation.

Experimental and molecular dynamics studies on the multiscale permeability properties of various gases in salt rock

To respond to the challenges posed by the intermittent nature of renewable energy sources, salt caverns are considered as ideal storage sites for energy such as hydrogen, compressed air, etc., as well as various other gases such as methane, helium, CO2, etc., due to their unique properties. However, the microfractures of salt rock are characterized by multiscale features and the microscopic flow properties of different gases in them are not yet clear. Here, we combine experiments and molecular dynamics simulations to investigate the multiscale flow of the above gases in salt rocks. First, the permeability of six gases has been evaluated to elucidate the microscopic mechanisms underlying the Klinkenberg effect. Second, based on the adsorption and flow characteristics of the gas, a multiscale permeability curve (ranging from 10−9∼10−3 m) was obtained for the salt rock slit. Furthermore, a fast method for predicting the permeability of salt rock samples was proposed, with predictions in the same order of magnitude as the experimental results. Finally, the storage requirements for different gases in salt caverns were discussed. This work provides multiscale insights into gas storage in salt caverns, which can guide the construction of salt cavern gas storage reservoirs and the assessment of leakage risk.

Experimental investigation on the effects of confining pressure and pore pressure on gas/water transport properties of COx argillite

As a preferred host rock for the disposal of high-level long-lived radioactive waste in France, Callovo-Oxfordian (COx) argillite inevitably undergoes gas and water intrusion during long-term sealing. In this study, a series of gas and water permeability tests have been performed on dry, partially saturated, and fully saturated COx argillite to investigate the effects of confining pressure and pore pressure on transport properties of this material. It is first found that gas permeability is very sensitive to the sample damage state for dry samples. Due to the presence of microcracks, the relationship between porosity and gas permeability is not evident, while the Klinkenberg effect is clearly observed in intact samples. Moreover, gas permeability of partially saturated samples is very sensitive to water saturation, especially for highly saturated samples. This indicates that the material has a good gas sealing capacity after the host rock is resaturated during the long-term sealing process. For both low- and highly saturated samples, confining pressure and gas pressure have very different effects on gas permeability of partially saturated argillite. Water permeability of argillite varies between 10−20–10−21 m2 (Kw), suggesting a good water-sealing capacity. The evolution of Kw is more sensitive to the change of pore pressure than to the change of confining pressure, indicating that the effective stress coefficient for water permeability is greater than 1. The intrinsic permeability of this low-permeable clayey rock is discussed at the end of this work.

Alterations in coal mechanical properties and permeability influenced by liquid CO2 phase change fracturing

Liquid CO2 phase change fracturing (LCPCF) is a promising approach for stimulating coal reservoirs and enhancing gas drainage efficiency of low-permeability coal seams. In this work, low pressure CO2/N2 adsorption, CH4 permeability measurements and UCS tests are combined to quantitatively analyze the changes in coal mechanical properties and permeability before and after LCPCF treatment. The results show that the axial peak strain is increased and ductile failure takes place in treated specimens after 1.26 L of liquid CO2 was used to conduct physical blasting. The UCS and elastic modulus after LCPCF are reduced by 10.82–25.78% and 12.92–28.57%, respectively. Muti-scale pore structures within coal are altered to varying degrees. After LCPCF treatment, mesopore volume and macropore volume are increased by 11.33–41.57% and 33.82–67.5%, respectively, while micropores are slightly affected. Due to the adsorption swelling and Klinkenberg effect, CH4 permeability of all the specimens is reduced with the increase of injection pressure. Comparative analysis of gas permeability has been made between the raw coal and treated specimens. Coal permeability is enhanced by 14.48-29.43% and 10.54-24.82% after LCPCF treatment at the injection pressure of 0.5 MPa and 1.4 MPa, respectively. During the LCPCF process, shock waves and stress waves trigger tensile damage to coal mass, and a large number of new macropores/fractures are generated within coal. This provides more accessible paths for gas flow and coal permeability are greatly promoted. Crack propagation is accelerated by the released high-pressure CO2, and both coal porosity and pore connectivity are further enhanced to facilitate gas seepage in coal seams.

Numerical Simulation of Effective Extraction Radius of Pre-Drainage Borehole Based on Coal Damage Model

Borehole pre-drainage is an important technical means to control a coal mine gas disaster. In order to determine the optimal pre-drainage parameters of Dashucun mine, a coal damage permeability evolution model was established based on coal damage deformation, considering gas adsorption and desorption and the Klinkenberg effect, and a damage fluid-structure coupling model of coal seam containing gas was established by combining the coal seam deformation equation and the mass conservation equation. COMSOL software was used to simulate the influence of factors such as the initial permeability of coal seam, negative pumping pressure, aperture and pumping time on the effective pumping radius of pre-drainage borehole. The results show that the effect of negative pressure on the effective extraction radius can be ignored. The effect of borehole aperture, initial permeability of coal seam and extraction time on effective extraction radius is great, which conforms to the power function relationship, and the coefficient correlation value is high. The optimal extraction parameters of Dashucun mine are determined as borehole diameter 113 mm, coal seam permeability 1 × 10−17 m2, negative extraction pressure 30 kPa and extraction time 180 d. The research results can provide theoretical reference for the pre-drainage of gas in Dashucun mine.

The influence mechanism of effective stress, adsorption effect and Klinkenberg effect on coal seam permeability

Permeability is an important parameter in the process of coalbed methane exploitation. To improve the production efficiency of coalbed methane and explore the control mechanism of the gas flow law in coal, the permeability of helium and nitrogen in the same coal sample was tested under different effective stress (the difference between external stress and pore pressure of coal mass) and pressure by using the seepage device. Based on the gas flow theory, the interaction mechanism of effective stress, adsorption effect and Klinkenberg effect in controlling the permeability has been analyzed. Increasing the gas pressure will enhance the adsorption and deformation ability of coal, causing the reduction of pore size, while it will also cause the reduction of effective stress and stress deformation. There is a certain competition between them under the same external stress condition, which will lead to the change of pore and then affect the permeability of coal seam. The Klinkenberg effect will lead to more complex change factors of permeability, especially in laboratory experiments. Both adsorption deformation and stress deformation will affect the pore structure of coal body, which will also lead to changes in the influence degree of Klinkenberg effect on apparent permeability. Under the influence of adsorption effect, the Klinkenberg effect may be a variable. The experimental results in this work elaborate the microscopic control mechanism of gas permeability change in coal. It can not only provide important guidance for gas injection technology, but also enrich the theory of coal seam gas flow.

Study on Effective Extraction Radius of Directional Long Borehole and Analysis of the Influence Mechanism.

To accurately determine the effective extraction radius of directional long drilling, the influence of the negative pressure of the hole mouth, the drilling diameter, and the drilling length of the hole on the effective extraction radius of a directional long drilling hole is simulated by establishing a coal-to-gas gas-structure coupling model considering the Klinkenberg effect. Finally, the reliability of the numerical simulation is verified through field testing in Yuxi Coal Mine. The results reveal that the attenuation of negative pressure in a directional long borehole along a long hole has a significant influence on the gas extraction effect. The radial gas pressure of the extraction drilling hole is distributed in a "V" shape when the negative pressure of the extraction decays along the direction of the hole length. The higher the negative pressure and the longer the diameter of the drilling hole, the higher is the gas extraction effect. The effective extraction radius is exponentially related to the drilled hole depth when the negative pressure of extraction is attenuated along the long hole direction. The negative pressure of the hole and the diameter of the borehole are linearly related to the effective extraction radius at the depth of drilling hole of 430 m. Through field tests, while extracting for 180 days based on the stubble pressing effect, the effective extraction radius of the directional long borehole of the No. 3 coal seam of Yuxi Coal Mine is 5.7 m, and the absolute error between the numerical simulation is 0.1 m. In addition, the gas pressure obtained from different sampling points is consistent with the numerical simulation. The relative error is 0.3-4.1%. The results provide a theoretical basis for the rational layout of directional drilling.

Exact solutions for flow through porous media with the Klinkenberg effect

The effect of gas compressibility during flow through a porous medium modifies the governing equation for pressure, and for low pressures, this leads to the so-called Klinkenberg effect. Darcy’s law remains unchanged, and accounting for the equation of state leads to a parabolic governing equation for pressure. The increased flow rate at low pressure modifies the nonlinearity of this governing equation. We present two broad approaches for constructing exact solutions to the steady state problem. First, geometric reduction is employed to construct exact solutions in Cartesian and polar coordinates. Next, the governing equation is interpreted so that a stream function exists for the flow, and this is used to demonstrate that solutions can only be found when the flow is irrotational. A second, rather broad, class of exact solutions is thus constructed from potential flows and their generalization for variable permeability cases. The latter leads to a non-constant coefficient problem, and we provide both an algorithm illustrating how to use an existing linear numerical solver to solve the nonlinear problem and an explicit exact solution for an annular domain.

Summary of research methods for porosity and permeability of coalbed methane reservoir

In order to serve the research on the physical properties of coalbed methane reservoirs and improve the prediction effect of porosity and permeability of coal reservoirs, this paper, based on a large number of literature research, summarizes the concepts, influencing factors and prediction methods of coal seam porosity and permeability. The research shows that the main factors affecting the porosity of coalbed methane reservoir are coal petrographic composition, metamorphic degree, coal body structure and buried depth, compaction, tectonism, etc; The main influencing factors of permeability include component content, coal rank, coal body structure and in-situ stress, buried depth of coal seam, natural fracture of coal seam, matrix shrinkage, Klinkenberg effect, etc. The porosity prediction of coalbed methane reservoir generally adopts true and apparent relative density method, in addition, there are multiple regression method based on logging information, nuclear magnetic resonance logging method, etc; The measurement methods of CBM reservoir permeability mainly include the calculation method based on conventional logging, triaxial stress experimental research method, joint prediction method of nuclear magnetic resonance and electrical imaging logging, dynamic data analysis method and numerical simulation method. The development of coal seam porosity and permeability prediction technology needs innovative breakthroughs in hardware and software.

Assessment of polydisperse substrate flow in a fermentor for computational fluid dynamics modelling

In this paper study results of selected production methods for agricultural biogas are shown and technical and technological aspects of these methods are described for monosubstrate bioreactors. Based on the available literature, modelling of mixing in bioreactors using computational fluid dynamics (CFD) was is demonstrated. As part of the research, the numerical simulation method was used with a tool that contains CFD codes. The model k-ε is used to simulate the mean flow characteristics under turbulent flow conditions. This is a two-equation model that gives a general description of turbulence. The work presents the results of numerical studies that make it possible to understand the characteristics of fluid flow in the adhesive bed used for the production of agricultural biogas. The tests showed that in the core of the adhesive bed there is a flow of 0.19 m∙s –1, while in the outer part of the bed there is a flow in the range 0.01–0.02 m∙s –1. Taking into account the substrate inflow of 0.17 m∙s –1 (in the upper part of the fermentor), it was observed that the Klinkenberg effect for autocyclic movement (from bottom to top) takes place. The novelty in the article is the observation of the dominant flow in the core of the bed and the autocyclic flow in the opposite direction in the peripheral areas of the adhesive bed.

Experimental study on stress-dependent gas permeability and porosity of artificially cracked cement mortar

In this paper, gas permeability and porosity for the prepared cement mortar samples with diverse numbers of internal cracks under diverse pore pressure during confining pressure loading and unloading was measured. According to the outcomes of experiments, the following findings were obtained: Klinkenberg correction is appliable to the modification on gas permeability of cement mortar samples containing different number of internal cracks to obtain the intrinsic permeability, with the quadratic equation (Coefficient of Determination R2 is above than 0.92) having a better performance than that of Klinkenberg equation; Owing to the increase in the equivalent pore radius of seepage passages, Klinkenberg Effect of the cement mortar samples reduces when the number of internal cracks rises. When the number of internal cracks rises from 0 to 12, the slippage factor decreases over 90 %; When the number of internal cracks is high, the same changing extent in the number of internal cracks can lead to higher influence on the intrinsic permeability than that when the number of internal cracks is low. The variation magnitude of intrinsic permeability when the number of internal cracks increases from 6 to 12 is around 3–10 times higher than that when the number goes up from 0 to 6; When confining pressure increases, the sensitivity of intrinsic permeability to the changes in confining pressure reduces. The variation magnitude of intrinsic permeability when confining pressure is loaded from 0 MPa to 25 MPa is 5–10 times higher than that when confining pressure is loaded from 25 MPa to 45 MPa; Owing to the permanent deformation of pores and cracks, under the same confining pressure, the intrinsic permeability and porosity during the unloading stage are less than those during the loading stage, respectively; The sub-cubic law (R2 is above than0.90) is able to describe gas seepage in cement mortar specimens with different number of internal cracks more precisely compared to the cubic law.

A Comparative Study on Water and Gas Permeability of Pervious Concrete

The water and gas permeability of pervious concrete play essential roles in rainwater infiltration and plant root respiration. In this study, the gas and water permeability of pervious concrete samples were measured and compared. The water permeability was tested using the constant water head method and several water heads were measured for inspection, in which the permeability varied with the application of the pressure gradient. The permeability of gas was measured using a new simple gas permeameter, which was specially manufactured for measuring the gas permeability of pervious concrete under a stable pressure difference. A series of different gas pressure gradients was applied to test whether the gas permeability was a function of the applied pressure. Both the gas and water permeability of pervious concrete were found to decrease with an increased applied pressure gradient, which did not conform to the Klinkenberg effect (gas slippage effect). When comparing the gas permeability and water permeability of pervious concrete, we found that the water permeability was 4–5 times larger than the gas permeability.

Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

Darcy’s law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure gradient is determined using non-equilibrium molecular dynamics, and the hydraulic conductivity and permeability are investigated. The transport coefficients are determined for single-phase flow in face-centered cubic lattices of solid spheres. The porosity changed from that in the closest packing of spheres to near unity in a pure fluid, while the fluid mass density varied from that of a dilute gas to a dense liquid. The permeability varied between 5.7 times {10^{-20}} hbox {m}^2 and 5.5 times {10^{-17}} hbox {m}^2, showing a porosity-dependent Klinkenberg effect. Both transport coefficients depended on the average fluid mass density and porosity but in different ways. These results set the stage for a non-equilibrium thermodynamic investigation of coupled transport of multi-phase fluids in complex media.