Apparent Gas Permeability Research Articles

Macroscopic modeling of gas permeability in hierarchical micro/nanoporous media: A unified characterization of rarefaction using Klinkenberg theory and equivalent diameter

Estimating gas transport through a hierarchical micro/nanoporous system is challenging due to non-equilibrium gas dynamics. The primary difficulty lies in determining the rarefaction level, because identifying a representative flow dimension in a complex porous system with multiple pore scales is not straightforward. Our study performed a pore-level analysis for gas permeability in dual-scale porous media with varying porosity, throat size, and secondary pore size under different rarefaction conditions. We found that secondary porosity negatively affects permeability due to increased friction forces, with this influence growing as the secondary pore size and porosity increase until the secondary pore becomes comparable to the throat. However, rarefaction reduces the effects of secondary pores due to boundary slip. Traditional Knudsen number (Kn) calculations based on Darcy-defined height failed to accurately describe the rarefaction effects on gas permeability. Instead, we introduced an equivalent diameter to calculate the Kn, which provided an accurate normalization of apparent gas permeability independent of pore geometry. The extended Kozeny–Carman–Klinkenberg model developed in our previous study successfully yielded a macroscopic model for apparent gas permeability in hierarchical micro/nanoporous systems as a function of the traditional Darcy height and porosity.

Analysis of Influence of Sand Matrix on Properties of Moulding Compounds Made with Furan Resin Intended for 3D Printing

Binder jetting (BJ) sand printing is a 3D printing process in which a sand mould or sand core is produced from an STL file. A single layer of a sand matrix consisting of one or more grains in height of sand is applied to a worktable, and then a liquid resin or binder is applied to bond the grains together. This process is repeated until the final result matches the CAD model. The sand matrix is the main component of ceramic cores and moulds. The present study aims to demonstrate the influence of the matrix used on the properties of the resulting moulding sand. Three types of sand matrices were selected for the study. The first was a quartz matrix for 3D printing with binder jetting; this is characterised by a sharp geometry that allows for proper layering during printing. Ordinary quartz sand was also used for the study; this type of sand is usually used for the production of sand cores in the hotbox process, among other things. The shape of this sand is irregular. The last matrix to be tested was Cerabeads sand; this was selected because its spherical geometry clearly distinguishes it from the other two matrices. The matrices were analysed for their grain sizes. Scanning electron microscope images were also taken to compare the geometries and chemical compositions of the respective matrices. In presented research utilises a sand matrix for the production of self-curing compounds with furan resin dedicated for binder jetting 3D printing. The moulding masses were produced in a laboratory circulation mixer. The laboratory moulds were produced with wooden core boxes and pre-compacted by vibration. The samples from the matrix for the 3D printing were produced using the binder jetting method. The samples were produced to determine the flexural strength, tensile strength, gas permeability, hot distortion, and apparent density. It was not possible to carry out tests for the Cerabeads sand, as the obtained moulds were too brittle to perform adequate tests. Tests with the other matrices have shown that the shape and size of the matrix affect the apparent density and gas permeability.

A 3D FRACTAL MODEL COUPLED WITH TRANSPORT AND ACTION MECHANISMS TO PREDICT THE APPARENT PERMEABILITY OF SHALE MATRIX

The permeability of shale controls gas transport in shale gas reservoirs. The shale has a complex pore structure at the nanoscale and its permeability is affected by multiple transport and action mechanisms. In this study, a 3D fractal model for predicting the apparent gas permeability of shale matrix is presented, accounting for the effects of the transport mechanisms (bulk gas transport and adsorption gas diffusion) and action mechanisms (gas adsorption, real gas properties, water film, stress dependence, and total organic carbon (TOC) content). The proposed model is validated with the published experimental data. A series of sensitivity analyses are performed to investigate the influence of fractal characteristics and action mechanisms on the apparent permeability caused by each transport mechanism. The results show that the real gas properties, water film, and stress dependence cause different effects on the total apparent permeability of shale under different fractal characteristics. The maximum pore diameter is inversely proportional to the effects of these action mechanisms, and the porosity is positively proportional to the effects of real gas properties and water film but inversely proportional to the effects of stress dependence. An increase in TOC content can cause an improvement in the total apparent permeability. Furthermore, the effects of action mechanisms on the apparent permeability caused by different transport mechanisms are differently affected by the fractal characteristics. Changes in fractal characteristics mainly affect the apparent permeability caused by slip flow in the real gas effect, slip flow and Knudsen diffusion in the water film effect, and all transport mechanisms in the stress dependence effect.

Highly rarefied gas flows in rough channels of finite length

Highly rarefied gas flows through a rough channel of finite length with small bumps appended to its surfaces are investigated, by varying the accommodation coefficient alpha in Maxwell’s diffuse-specular boundary condition, the characteristic size and position of the bumps, and the channel length. First, we study the influence of the surface bumps and consider the rarefied gas flow in a unit channel with periodic boundary conditions to remove the end effect. It is found that the surface bumps have a significant impact on the flow permeability. When alpha is very small (i.e., nearly specular reflection of gas molecules at the channel surface), the apparent gas permeability is dramatically reduced, even in the presence of small bumps, to a value that is almost comparable to the one when fully diffuse gas-surface scattering is assumed. This impact can be taken into account through an effective accommodation coefficient, i.e., the permeability of the rough channel is taken equivalently as that of a smooth channel without bumps but having gas-surface scattering under the effective accommodation coefficient. Second, we study the end effect by connecting a smooth channel of length L_0 to two huge gas reservoirs. It is found that (i) the end correction length is large at small alpha. Consequently, the mass flow rate barely reduces with increasing L_0 rather than scales down by a factor of 1/L_0 as predicted by the classical Knudsen diffusion theory; and (ii) the end correction is related to the channel’s aspect ratio. Finally, based on the effective accommodation coefficient and end correction, we explain the exotic flow enhancement in graphene angstrom-scale channels observed by Geim’s research group (Keerthi et al, Nature 558:420–424, 2018).

A pore network-based multiscale coupled model for rapid permeability prediction of tight sandstone gas

Tight sandstone has multiscale pore structures. Gas transport in tight sandstones involves several length scales and the complicated physics. Gas transport characteristics in tight sandstone can be represented by apparent gas permeability. Microstructure-based accurate and efficient calculation of gas permeability is challenging. By combining CT and SEM images along with statistical analysis, we present a novel pore network-based multiscale coupled model (MCPNM) to rapidly predict the apparent gas permeability. CT images are adopted to extract the large-scale pore network (LPNM) and the clay component, and SEM image is used to get the properties of small-scale pores. Upscaled model (UM) of small-scale pores is built via statistical analysis and then assigned to the clay domains. The LPNM and UM are coupled as MCPNM by the cross-scale connection structure with variable diameter. The pore spaces at several length scales and the flow characteristics in them are included in the MCPNM. We validate the MCPNM by comparing the calculated apparent gas permeability to the results of available multiscale pore network models and the experimental data. Compared with the available multiscale pore network models, MCPNM solves the accuracy/efficiency trade-off of tight gas permeability prediction. The effects of pressure, temperature, and gas type on gas permeability are studied. The MCPNM simplifies the permeability calculation process and can accurately and rapidly predict tight sandstone gas permeability.

An improved transport model in shale nanopores based on advection diffusion method

As an unconventional oil and gas resource, shale gas plays a very important role in global energy supply. A breakthrough in efficient exploitation of shale gas is how to accurately describe the percolation mechanism of shale gas in nano-pores. In this article, a new shale gas apparent permeability model is established on the basis of advection diffusion model and considering adsorption stress effect and gas viscosity correction. On this basis, the influence factors of apparent permeability, the comparative difference between stress effect or not and viscosity correction or not, and the contribution of gas flow mechanism are studied. The results show that: the apparent permeability decreases with the increase of pressure, increases with the increase of pore radius, and increases with the increase of temperature; when the pore radius increases, the difference caused by stress correction becomes obvious; when the pressure decreases, the difference caused by viscosity correction becomes obvious. The results can provide some new ideas and methods for the study of gas flow mechanism in microscopic nano-pores.

Shale gas transport model considering gas adsorption and desorption

The gas migration mechanism and apparent permeability in shale reservoirs are significantly different from those in conventional gas reservoirs, which is mainly caused by nanoscale phenomena and organic matter as gas storage and supply media. However, in shale reservoirs, gas flow behavior plays an important role in well performance, so it is necessary to develop a new apparent permeability model considering gas transport mechanism. Therefore, in order to study the change of matrix permeability under different pressures in the development process of shale adsorption layer, combined with previous studies, considering the seepage mechanism of stress sensitivity, real gas effect and adsorption, a new model of apparent permeability is created by combining multiple gas transmission mechanisms. The sensitivity analysis of the new model is carried out by changing the corresponding parameters, and the corresponding conclusions are drawn. In this work, the established model can accurately calculate the apparent permeability of viscous flow, Knudsen diffusion and desorption, which makes us have a more accurate understanding of the transmission mechanism of shale gas and contributes to the efficient and sustainable development of shale gas.

Minireview on Lattice Boltzmann Modeling of Gas Flow and Adsorption in Shale Porous Media: Progress and Future Direction

As an important unconventional resource, shale gas reservoirs have unique characteristics different from conventional oil and gas reservoirs. The ultrasmall pore sizes in shale induce the nanopore confinement effect on shale gas flow. In addition, shale rocks are rich in organic matter, which has strong interactions with gas molecules and results in gas adsorption. The lattice Boltzmann method (LBM) for micro- and nanoscale gas flow, which is originally designed for micro-electro-mechanical systems (MEMS), has been modified to simulate gas flow and adsorption in shale rocks. This work reviews four types of lattice Boltzmann models developed recently for shale gas flow/adsorption: (1) the slip-velocity-based LBM, (2) high-order LBM, (3) diffusion-based LBM, and (4) REV-scale LBM. Among these models, the slip-velocity-based LBM is widely used for shale gas modeling, which incorporates the slip boundary condition and Knudsen number (Kn)-determined relaxation time to simulate the nanopore confinement effect. To model the gas adsorption, the fluid–solid interaction force is introduced into the model, and the magnitude of this interaction force is usually obtained from the molecular level simulations. LBMs have been regarded as an efficient numerical tool to estimate the shale gas apparent permeability, to describe the pore-scale flow behaviors, and to address the influence of gas adsorption on shale gas storage and transport. Nevertheless, some challenges exist in current applications of LBMs for shale gas flow and adsorption simulations that are discussed in this minireview as well.

Characterization of the Knudsen Number and Gas Transport in Shale Reservoirs: Coupling the Microfracture Network and Capillary Network

An accurate understanding of gas seepage mechanisms in shale reservoirs would have a positive impact on promoting shale gas development. Shale is a complex dual-porosity medium composed of a microfracture network and capillary network. However, most shale dual-porosity permeability models have usually ignored the influence of key mechanisms, such as effective stress and gas adsorption. In addition, the depiction and analysis of the Knudsen number has not been fully discussed in previous studies. In this study, the inner relationship between intrinsic permeability and porosity has been taken to be a bridge, with the fracture width including the pore radius being quantified, leading to a modification of the Knudsen number in the microfracture network and capillary network. Based on the modified Knudsen number, a dual-porosity permeability model has been developed for typical shale reservoirs that considered real gas effect, flow regimes, effective stress, and gas adsorption. The reliability of the new model has been validated by published experimental data under different conditions and through comparisons with the existing theoretical models. Finally, the evolution law relating to gas apparent permeability and the Knudsen number in the microfracture network and capillary network has been discussed, and the effects of different factors concerning apparent permeability and the Knudsen number have been quantified. Based on the results, the relationships between the coupled effects relating to the rock deformation field, the microfracture network seepage field, the capillary network seepage field, and the Knudsen number have been proposed. Moreover, the mechanisms relating to the internal swelling coefficient and gas rarefaction coefficient, including different pore network occupancies on total gas transport capacity, have been presented. The research results will provide a basis for the accurate numerical simulation for shale gas and will be of great significance to the economic development of shale gas in the future.

Transport Behavior of Methane Confined in Nanoscale Porous Media: Impact of Pore Evolution Characteristics

As a key technical aspect contributing to shale gas development, nanoconfined methane flow behavior has received tremendous research interest, which remains challenging to understand clearly. The majority of previous contributions put emphasis on the mechanism model for methane confined in a single nanopore; at the same time, the other part focusing on an upscaling approach fails to capture the spatial pore-network characteristics as well as the way to assign pressure conditions to methane flow behavior. In light of the current knowledge gap, pore-network modeling is performed, in which a pore coordination number, indicating the maximum pores a specified pore can connect, gas flow regimes classified by Knudsen numbers, as well as different assigned pressure conditions, are incorporated. Notably, the pore-network modeling is completely self-coded, which is more flexible in adjusting the spatial features of a constructed pore network than a traditional one. In this paper, the nanoconfined methane flow behavior is elaborated first, then the pore network modeling method based on the mass conservation principle is introduced for upscaling, and in-depth analysis is implemented after that. Results show that (a) as for porous media with pore sizes ranging from 5~80 nm, dramatic advancement on apparent gas permeability takes place while pressure is less than 1 MPa; (b) apparent gas permeability evaluated at a specified pressure shall be underestimated by as much as 31.1% on average compared with that under the pressure-difference condition; (c) both a large pore size and a high coordination number are beneficial for strong gas flow capacity through nanoscale porous media, and the rising ratio can reach about 6 times by altering the coordination number from 3 to 7, which is quantified and presented for the first time.

Study on Apparent Permeability Model for Gas Transport in Shale Inorganic Nanopores

Inorganic nanopores occurring in the shale matrix have strong hydrophilicity and irreducible water (IW) film can be formed on the inner surface of the pores making gas flow mechanisms in the pores more complex. In this paper, the existence of irreducible water (IW) in inorganic pores is considered, and, based on the Knudsen number (Kn) correction in shale pores, a shale gas apparent permeability model of inorganic nano-pores is established. The effect of the Kn correction on the apparent permeability, the ratio of flow with pore radius and the effect of IW on the apparent permeability are assessed. The main conclusions are as follows: (1) at low pressure (less than 10 MPa) and for medium pore size (pore radius range of 10 nm–60 nm), the effect of the Kn correction should be considered; (2) considering the effect of the Kn correction, bulk phase transport replaces surface diffusion more slowly; considering the existence of IW, bulk phase transport replaces surface diffusion more slowly; (3) with increase in pressure, the IW effect on gas apparent permeability decreases. Under low pressure, the IW, where pore size is small, promotes fluid flow, while the IW in the large pores hinders fluid flow. In conditions of ultra-high pressure, the IW promotes gas flow.

Mechanical and Durability Properties of High-Performance Concrete Incorporating Fibers and Algerian Natural Pozzolans in Chloride Attack

This study aims to assess the effect of sodium chloride attack on the mechanical and durability properties of high-performance concrete (HPC) based on fibers and natural pozzolans. The resistance of specimens against chemical attack is determined by the unit weight, compressive strength, splitting-tensile strength, chloride ion permeability, apparent gas permeability, and visual inspection after 28, 90, 180, and 365 days of testing. A total of three types of concrete are assessed: reference concrete (RC), HPC, and high-performance fiber-reinforced concrete (HPFRC) stored in tap water and aggressive water (i.e., a 10% NaCl solution). The test results demonstrate that the presence of fibers negatively affects the permeability of HPC. However, HPC and HPFRC remain stable and are not influenced by the NaCl solution compared to RC. The natural pozzolans attenuate the side effect of fibers by occupying voids (i.e., the filler effect) and generating denser products (i.e., the pozzolanic reaction) in the cement matrix.

Study on the two-component gas apparent permeability model in shale nanopores considering Knudsen number correction

At present, the technology of carbon dioxide flooding shale gas is a hot topic for scholars. The numerical simulation of shale gas driven by carbon dioxide is inseparable from the accurate understanding of gas percolation mechanism and the construction of two-component gas motion equation. During the flooding process, the gas apparent permeability and the Knudsen number both change with time and space. However, this has not been fully discussed in previous studies. In this paper, the percolation mechanisms of two-component gas are discussed. On this basis, the calculation formula of Knudsen number in porous media is modified, and the transport equation of two-component gas is established. According to the derivation of apparent permeability, the two-component gas apparent permeability model is deduced. Then, the correction effect of Knudsen number and the related properties of two-component apparent permeability are analyzed. The results show that: (1) the effect of Knudsen number correction is significant at low pressure. Under high pressure, that is, when the pressure is greater than 10 MPa, the effect can be ignored; (2) the effect of Knudsen number correction is mainly significant in the range of medium pores, which is generally 10 nm–60 nm. And the peak value range decreases with the increase of pressure; (3) for the relative component apparent permeability curve, it has the properties of both relative permeability and apparent permeability. Based on the data in this paper, for the pressure change, it can be concluded that the maximum change rate of methane is 47.79% and that of carbon dioxide is 51.36%. For the change of pore size, it can be concluded that the maximum change rate of methane is 223.45% and that of carbon dioxide is 106.19%. It can be shown that the relative permeability of carbon dioxide is sensitive to pressure and the relative permeability of methane is sensitive to pore size.

Image-based model for dynamic apparent gas permeability in Organic-rich shales

Current shale gas apparent permeability models often fail to integrate morphological properties of multiple storage spaces and various transport mechanisms. To deal with this, we propose a comprehensive model for estimating the dynamic apparent gas permeability (DAGP) during depressurization based on a representative model. First, dual fractal characteristics of organic matter (OM) particles and inorganic matter (IOM)/OM pores along with morphological information of OM particles from scanning electron microscope (SEM) images are considered to establish the representative model conditioned to a total organic carbon (TOC) content. Next, multiple transport mechanisms and a pore size change due to a poromechanical response and desorption-induced volumetric strain are incorporated in the DAGP calculation. Results reveal that the controlling factor of the DAGP comes from pore size shrinkage owing to a poromechanical response to gas transport mechanisms during depressurization at a high Young’s modulus, while the DAGP is totally controlled by a poromechanical response at a low Young’s modulus. The critical TOC content is determined to be about 5% at which the influence of the degree of OM pore development can be neglected. This work provides a practical method to estimate the DAGP from both geostatistical and petrophysical perspectives, which effectively decreases the uncertainty during productivity prediction in shale gas reservoirs and other unconventional reservoirs.

Permeability of High-Performance Fiber Reinforced Concrete Immersed in High Concentration Sodium Chloride Solution

This paper aims to study the permeability of High-Performance Concrete containing natural pozzolan and reinforced with fibers in high concentration sodium chloride solution. Optimized finely ground natural pozzolan was employed as 6% of partial substitution of the cement. Polypropylene fibers with 6 mm and 12 mm lengths were introduced individually for a volume fraction of 0.1% and 0.15% respectively. Then, in combination with a total fiber content of 0.25%. The effect of sodium chloride attack on the performance of concretes was assessed through the measurement of the compressive strength, splitting tensile strength, sorptivity, rapid chloride permeability test, apparent and intrinsic gas permeability, and visual inspection at various testing ages (28, 90, 180, and 365 days). A total of four (04) types of concretes were cast: one (01) High-Performance Concrete (HPC), and three (03) High-Performance Fiber Reinforced Concrete (HPFRC) stored in tap water and sodium chloride environment. From the experiments performed, it can be concluded that the polypropylene fibers introduction into HPC favorably affect its chemical resistance to chloride attack and long-term durability. The difference in the permeability of HPC and HPFRC stored in tap water and chloride environment is not significant. Furthermore, the visual investigation of HPFRC after 365 days of immersion in sodium chloride environment showed no sign of degradation. Based on the results obtained in this study, we recommend the use of hybrid fiber-reinforced concrete (F0-0.25%) as a low permeable material in a severe chloride environment.

A Model for the Apparent Gas Permeability of Shale Matrix Organic Nanopore Considering Multiple Physical Phenomena

The flow of shale gas in nano scale pores is affected by multiple physical phenomena. At present, the influence of multiple physical phenomena on the transport mechanism of gas in nano-pores is not clear, and a unified mathematical model to describe these multiple physical phenomena is still not available. In this paper, an apparent permeability model was established, after comprehensively considering three gas flow mechanisms in shale matrix organic pores, including viscous slippage Flow, Knudsen diffusion and surface diffusion of adsorbed gas, and real gas effect and confinement effect, and at the same time considering the effects of matrix shrinkage, stress sensitivity, adsorption layer thinning, confinement effect and real gas effect on pore radius. The contribution of three flow mechanisms to apparent permeability under different pore pressure and pore size is analyzed. The effects of adsorption layer thinning, stress sensitivity, matrix shrinkage effect, real gas effect and confinement effect on apparent permeability were also systematically analyzed. The results show that the apparent permeability first decreases and then increases with the decrease of pore pressure. With the decrease of pore pressure, matrix shrinkage, Knudsen diffusion, slippage effect and surface diffusion effect increase gradually. These four effects will not only make up for the permeability loss caused by stress sensitivity and adsorption layer, but also significantly increase the permeability. With the decrease of pore radius, the contribution of slippage flow decreases, and the contributions of Knudsen diffusion and surface diffusion increase gradually. With the decrease of pore radius and the increase of pore pressure, the influence of real gas effect and confinement effect on permeability increases significantly. Considering real gas and confinement effect, the apparent permeability of pores with radius of 5 nm is increased by 13.2%, and the apparent permeability of pores with radius of 1 nm is increased by 61.3%. The apparent permeability model obtained in this paper can provide a theoretical basis for more accurate measurement of permeability of shale matrix and accurate evaluation of productivity of shale gas horizontal wells.

Rarefied gas transport in heterogeneous shale matrix using a practical apparent permeability model and fuzzy statistical method

A new shale gas transport model is derived to characterize the matrix structural heterogeneity impact on the gas apparent permeability (AP). The developed analytical model is built upon two steps: first, the homogeneous AP model is formulated by assigning the Knudsen-number-parameterized weight coefficients to flow mechanisms based on the analyses of representative rarefied gas transport models; then, the homogeneous model is improved to the heterogeneous model with the help of fuzzy statistical method to assess the structural heterogeneity influences. More specifically, the homogeneous AP model incorporates the multilayer adsorption, surface diffusion, real gas effect, and pore confinement effect. The physical terms in the apparent permeability including the rarefaction coefficient and multilayer adsorption model are simplified to facilitate the large-scale simulation. Meanwhile, the heterogeneous AP model is quantified by the distribution of porosity, tortuosity, and pore size. It is demonstrated that the developed AP model can reproduce the experimental and numerical experiments for five types of gases. It is concluded that the rarefaction in nanopores could be reasonably characterized by the weighted Knudsen diffusion and viscous flow mechanisms. Moreover, it is noticed that the surface diffusion and Knudsen diffusion cannot be ignored in nanopores with radius smaller than 3 nm at low reservoir pressures. In contrast, the viscous flow plays a significant role in shale gas transport in nanopores with radius larger than 75 nm. In addition, the fuzzy statistical method in the proposed heterogenous model provides the indicators to evaluate the impact of structural heterogeneity on the AP. It is observed that the heterogeneous model can accurately predict the realistic apparent permeability as the heterogeneity increases to σ = 0.15. However, the accuracy decreases when the matrix heterogeneity increases.

Pore pressure dependent gas flow in tight porous media

Gas flow in micro-porous media is more complex than liquid flow, partially because of the gas compressibility storage effect, and because of that, permeability as a function describing the flow efficiency for liquid might not apply to gas, but gas pressure diffusivity concept taking into account the effect of gas compressibility might do. However, verifying this supposition in conventional reservoirs at the core scale is challenging because the gas flow process finishes almost instantly. In comparison, gas flow time in unconventional tight cores is longer, and pulse-decay experiments are frequently used to estimate permeability, which requires a period to be finished. Therefore, theoretically, the supposition could be tested. In this study, pulse-decay experiments were performed on one shale core plug under different pore pressures with different pulse magnitudes to explore the relationship between gas permeability/diffusivity with experiment durations. We put forward a novel approach to determining the intrinsic permeability and gas slippage factor through a single pulse-decay experiment, which requires running multiple experiments by the conventional approach. We verified that gas pressure diffusivity instead of the permeability is the appropriate measure of the efficiency of gas propagating through the porous media, given the fact that the ratio of pulse size over diffusivity is roughly proportional to the experiment duration. Consistent results were obtained using different empirical models to obtain the intrinsic permeability, gas slippage factor, and pressure-dependent apparent gas permeability simultaneously. Results in this study also verified that pulse size affects the permeability determination more under a lower pore pressure in a pulse-decay experiment.

Permeability measurements using rate-transient analysis (RTA): Comparison with different experimental approaches

Reservoir engineers commonly apply rate-transient analysis (RTA) and pressure-transient analysis (PTA) methods to analyze multi-fracture horizontal wells (MFHWs) completed in unconventional reservoirs quantitatively for reservoir and hydraulic fracture properties. Data from core analysis techniques are commonly used to provide important input for RTA-PTA models. However, conventional laboratory techniques (i.e., steady-state and non-steady-state fluid flow) do not reproduce the operating conditions that MFHWs are subjected to in the field. In the current work, laboratory techniques that better reproduce these boundary conditions are explored and compared to more traditional core analysis methods.For this study, RTA methods are applied to gas produced from core plugs and PTA methods are applied to gas injection-fall-off data at the start of the core test before gas production. While the RTA method has been previously described by the authors, the application of the PTA method to provide an early, and fast, estimate of permeability is unique to this study. Further, our previous experimental setup for performing RTA was modified to accommodate not only the use of both RTA/PTA methods, but also the use of conventional core analysis methods (steady-state and non-steady-state methods) to allow for direct comparison of all methods.For both RTA and PTA core tests, the observed flow-regime sequence is transient linear flow followed by boundary-dominated flow, which is the same sequence that is commonly observed in the field for MFHWs producing from low-permeability and shale reservoirs. Two independent permeability values were estimated using the slope of the square root time plot and the time at the end of linear flow for each test. The pore volume of the samples were also estimated using the RTA method. Permeability and pore volume values obtained from the RTA method, referred to as ‘RTAPK’ previously, were in good agreement with those obtained from more conventional core testing methods (average coefficient of variation = 8%). The derived permeabilities from the time at the end of linear flow during the fall-off test were close to other permeabilities. In contrast, the square root time plot (fall-off) resulted in significantly higher permeabilities attributed to the experimental artifact caused by substantial dead volume in the injection port. The primary advantage of the RTA core analysis method is the accelerated test-time. For samples with permeability values ranging between 0.1 and 3 mD, the apparent gas permeabilities can be estimated in less than 3 to 10 minutes using both fall-off and production data.

A novel Monte Carlo simulation on gas flow in fractal shale reservoir

The apparent gas permeability (AGP) is one of the key parameters in shale gas exploitation, which is difficult to determine due to the mutliscale structure of shale formation. In this paper, a fractal probability law and Monte Carlo technique are used to predict the rarefied gas flow through shale reservoir, since from the adsorption-desorption experiments it is known that the distribution of pore size follows the fractal scaling law. The results indicate that the AGP increases with the increment of Knudsen number, and it grows linearly with Knudsen number when Knudsen number is larger than 0.1. When the porosity is fixed, increased pore fractal dimension reduces the AGP and the intrinsic permeability, but enhances the permeability ratio (ratio of AGP to intrinsic permeability). However, when the pore size limit is fixed, the permeability ratio can be reduced by increasing pore fractal dimension. While the increment of tortuosity fractal dimension can lower both AGP and intrinsic permeability, it has marginal effect on the permeability ratio. The proposed fractal Monte Carlo model is an efficient and economic method to predict the AGP, which bridges the microscale structures and macroscale gas flow properties of shale reservoir.