Gas Slippage Research Articles

Fluid Performance in Coal Reservoirs: A Comprehensive Review

The fluids in coal reservoirs mainly consist of different gases and liquids, which show different physical properties, occurrence behaviors, and transport characteristics in the pore-fracture system of coal. In this study, the basic characteristics of fluids in coal reservoirs are firstly reviewed, consisting of coalbed methane (CBM) components and physical properties of CBM/coalbed water. The complex pore-fracture system mainly provides the enrichment space and flow path for fluids, which have been qualitatively and quantitatively characterized by various methods in recent years. Subsequently, this study has summarized CBM adsorption/desorption behaviors and models, the CBM diffusion-seepage process and models, and gas-water two-phase flow characteristics of coal reservoirs. Reviewed studies also include the effects of internal factors (such as coal metamorphism, petrographic constituents, macroscopic types, and pore structure) and external factors (such as pressure, temperature, and moisture content) on CBM adsorption/desorption and diffusion behaviors, and the relationship between three main effects (effective stress, gas slippage effect, and coal matrix shrinkage effect) and the CBM seepage process. Moreover, we also discuss in depth the implication of fluid occurrence and transport characteristics in coal reservoirs for CBM production. This review is aimed at proposing some potential research directions in future studies, which mainly includes the control mechanism of the microscopic dynamics of fluids on CBM enrichment/storage; enhancing CBM desorption/seepage rate; and the synergistic effect of multiple spaces, multilevel flow fields, and multiphase flow in coal reservoirs. From this review, we have a deeper understanding of the occurrence and transport characteristics of fluids in pore-fracture structures of coal and the implication of fluid performance for CBM production. The findings of this study can help towards a better understanding of gas-water production principles in coal reservoirs and enhancing CBM recovery.

Effect of Pore Structure on Slippage Effect in Unsaturated Tight Formation Using Pore Network Model

The gas slippage phenomenon under dry conditions has been investigated extensively both numerically and experimentally. However, very limited research has focused on gas slippage behavior under wet conditions. Unlike conventional formation, the influence of water on the gas transport process cannot be neglected in tight formations due to the comparable amount of thin water film attached along the rock surface. It is found experimentally that the gas slippage factor is positively related to water saturation if the water saturation is small, while it decreases with water saturation if it is larger than a critical value. Most of the existing models failed to capture the measured downtrend of the gas slippage factor with increasing water saturation, which resulted from water blocking or gas trapping phenomenon. In this work, a pore-scale network model is proposed to look at the water distribution characteristic and investigate the effect of water on the gas slippage factor. The proposed pore-scale model incorporates the capillary dominated multiphase fluid distribution, real gas effect, and gas transport mechanisms at pore scale. On the basis of our pore network model, the effect of pore structure characteristics including the frequency of mean pore radius, size of mean pore radius, aspect ratio, and coordination number on the gas slippage behavior are investigated and discussed in detail. Similar to previous experimental observations, the simulated gas slippage factor shows a non-monotonic increase trend with water saturation; it starts to decrease under high water saturation, and the critical water saturation depends on the pore structure factors. It increases with the mean pore radius and coordination number but decreases with the aspect ratio. We used the pore network model to investigate the effect of the water phase on the gas slippage behavior at the pore scale for the first time. It emphasized the predominance of water blocking and the gas trapping phenomenon in the estimation of the gas slippage factor at high water saturation.

Modeling and Simulation of Shale Fracture Attitude.

A large number of natural fractures are distributed in shale gas reservoirs. In-depth studying of the attitude of fractures is of great significance for the efficient development of shale gas. In previous studies, the complex three-dimensional discrete fracture networks (DFNs) and transport mechanisms were often not fully considered. In this study, the fully coupled multimechanism transport model and the complex discrete fracture networks (DFNs) model are developed to incorporate these complexities. The comprehensive transport model can couple multiple mechanisms such as slippage, diffusion, adsorption, and dissolution of shale gas. Moreover, the mechanisms of two-phase flow, reservoir deformation, real gas effect, and fracture closure are also considered. The three-dimensional DFN model can flexibly characterize the fracture attitudes, which means that the construction of the discrete fracture network is easier and faster. Under these frameworks, a series of partial differential equations (PDEs) were derived to describe transport mechanisms of shale gas in the shale fracture-matrix system. These PDEs were numerically discretized and solved by the finite element method. The proposed models are verified against gas production data from the field and validated against others’ solutions. This study numerically simulates the influence of different fracture attitudes on shale gas transport and analyzes the sensitivity of the model. The results and sensitivity analysis reveal that both fracture dip angle and strike direction will significantly affect the gas production, and the smaller the angle between the strike direction and the flow direction, the higher the shale gas production. The length, density, area, and shape of fractures also play important roles in shale gas transport. There is an ideal fracture density in the fracture network, and the suggested excessive fracturing is not economic. The shale fracture-matrix system modeling and simulation methods can improve the development of shale gas reservoirs and increase the gas production of wells.

Experimental study of pressure sensitivity in shale rocks: Effects of pore shape and gas slippage

The permeability and porosity significantly impact the flow and storage of fluids in shale reservoirs. In this work, permeability, porosity, gas slippage factors, and gas diffusion coefficients of different shale samples were systematically measured at varying confining pressures and pore pressures. Before the experiments, the scanning electron microscope (SEM), N2 adsorption, and X-Ray Diffraction (XRD) analyses were used to characterize the shale samples. Results indicate that while the pressure sensitivity coefficient is smaller than 1 for permeability, it is slightly larger than 1 for porosity. In addition, pore shape significantly impacts the pressure sensitivity of porosity and permeability. For cores with a large number of crack-like pores, the permeability was decreased by two to three orders of magnitude and the porosity was decreased by approximately 32%. However, for cores dominated by circular and irregular-shaped pores, the permeability varied by one order of magnitude, and the porosity was reduced by 14%–19%. Moreover, effective gas diffusion coefficients and slippage factors were measured at different pore pressure and confining pressure. The results show that gas diffusion coefficients varied from 0.95 to 3.17 × 10−7 m2/s, and gas slippage factors ranged from 0.64 to 1.25 MPa. While the gas diffusion coefficient decreased exponentially with confining pressure, it increased exponentially with rock intrinsic permeability (k∞). The gas slippage factor increased exponentially with confining pressure, however, it decreased and exhibited a power relationship with k∞. Those experimental results provide a comprehensive understanding of pressure sensitivity, gas slippage factors, and gas diffusion coefficients in shale rocks.

Quantitative visualization and characteristics of gas flow in 3D pore-fracture system of tight rock based on Lattice Boltzmann simulation

The geometric complexity of the 3D pore-fracture system of tight rock at the pore-scale is a primary challenge for the prediction of gas flow. In this paper, the 3D pore-fracture systems of tight rock are reconstructed based on the representation unit volume (REV) of the intact tight sandstone and fractal fracture. A 3D regularized lattice Boltzmann model that considered the gas slippage effect is employed to simulate gas flow in the 3D pore-fracture systems. Effects of the micro-fracture morphology and gas rarefaction effect on gas flow and permeability of the pore-fracture systems are examined and investigated. The simulation results indicate that the gas flow behaviors in the pore-fracture system are strongly related to the above two factors. Gas flow behaviors in the pore-fracture structure is more sensitive at the low-pressure condition and gas rarefaction effect are more sensitive to the pore-fracture system with the highly rough fracture or the low fracture connectivity.

An Open-Source Code for Fluid Flow Simulations in Unconventional Fractured Reservoirs

In this article, an open-source code for the simulation of fluid flow, including adsorption, transport, and indirect hydromechanical coupling in unconventional fractured reservoirs is described. The code leverages cutting-edge numerical modeling capabilities like automatic differentiation, stochastic fracture modeling, multicontinuum modeling, and discrete fracture models. In the fluid mass balance equation, specific physical mechanisms, unique to organic-rich source rocks, are included, like an adsorption isotherm, a dynamic permeability-correction function, and an Embedded Discrete Fracture Model (EDFM) with fracture-to-well connectivity. The code is validated against an industrial simulator and applied for a study of the performance of the Barnett shale reservoir, where adsorption, gas slippage, diffusion, indirect hydromechanical coupling, and propped fractures are considered. It is the first open-source code available to facilitate the modeling and production optimization of fractured shale-gas reservoirs. The modular design also facilitates rapid prototyping and demonstration of new models. This article also contains a quantitative analysis of the accuracy and limitations of EDFM for gas production simulation in unconventional fractured reservoirs.

Effective thermal conductivity changes of the hydrate-bearing quartz sands in depressurization and soaking

The effective thermal conductivity changes in the sediments during depressurization are significant for hydrate exploitation. But these changes cannot be measured directly because of the unavailable stable conditions during depressurization. In this work, in order to form the stable conditions for the measurements, soaking was designed to stabilize temperature and pressure in the sample after depressurization. Afterward, the effective thermal conductivity changes were measured by the transient hot-wire method. To define reasons for these changes, gas-water-hydrate distribution was inferred by the electrical resistance changes. The effective thermal conductivity changes were further analyzed from initial hydrate saturation, back pressure, water-gas production ratio, and gas-water-hydrate distribution, respectively. The results showed that the effective thermal conductivity changes were involved with hydrate dissociation closely. The effective thermal conductivity was increased with increasing initial hydrate saturation and back pressure. Moreover, the effective thermal conductivity was increased by the enlarged water distribution at the early period of hydrate dissociation and decreased by the enlarged gas distribution at the late period of hydrate dissociation. Gas slippage effect and gas-water gravity differentiation played important roles in these gas-water redistribution in the sample. Meanwhile, the sandy grain rearrangement was inferred to improve the contact quality among grains and thus also increased the effective thermal conductivity. Additionally, although there was hydrate dissociation rate of 0.36% during the measurements, the trends of the effective thermal conductivity were not supposed to change. This work may offer some reference to understand the mechanisms of heat transfer in the sediments during depressurization.

Second-order correction of Klinkenberg equation and its experimental verification on gas shale with respect to anisotropic stress

Shale is an extremely tight and fine-grained sedimentary rock with nanometer-scale pore sizes. The internal nanopore structure gives rise to not merely the ultra-low permeability of shale, but also the significant slip flow (non-Darcy) phenomenon. This study involves a second-order correction of the traditional Klinkenberg equation and its experimental verification, in consideration of the effect of anisotropic stress, using cube-sized shale samples sourced from a typical Chinese sedimentary basin. The effects of two gas slippage factors, Klinkenberg-corrected permeability, and anisotropic stress were also discussed. The results showed an increasing trend of apparent permeability with decreasing pore pressure when the pressures are relatively low, due to the gas slippage effect. The second-order model results in a lower Klinkenberg-corrected permeability compared with that from the traditional Klinkenberg equation and yields a better match with the experimental data. Analysis of the experimental data showed that both the first-order slippage factor A and the second-order slippage factor B rose as stress anisotropy increased, and that A was more sensitive to stress anisotropy compared with B. Interestingly, both A and B first increased slightly and then dramatically as the permeability declined. It is recommended that when the shale permeability is below 10−3 mD, the second-order approach should be taken into consideration. Darcy's law starts to deviate when Kn > 0.01 and is invalid at high Knudsen numbers. The second-order approach alleviates the problem of permeability overestimation compared with the traditional Klinkenberg equation. When subjected to effective stress, shale pores become constricted and the degree of this constriction decreases gradually as the effective stress continues to increase.

Experimental Investigation about Gas Transport in Tight Shales: An Improved Relationship between Gas Slippage and Petrophysical Properties

This study presents both experimental and theoretical investigations about gas transport in shales. Gas apparent permeability coefficients and Klinkenberg slippage factors were determined on Longmaxi shales using He, Ar, N2, CH4, and CO2. Then, a model was developed to interpret the experimentally determined gas slippage factor, considering the effects of intrinsic permeability, porosity, tortuosity, and gas physical properties. The proposed model is verified by correlating Klinkenberg-corrected permeabilities and gas slippage factors of shales probed by He, Ar, N2, CH4, and CO2 at different confining pressures. The model can quantitatively describe the gas dependence of slippage factors (He > Ar > N2 > CH4 > CO2). According to the model presented, the slippage factor increases proportionally to the ratio of the characteristic gas parameter (C=C1μπZRTM) to tortuosity. The model also leads to a practicable approach to determine the effective tortuosity of tight rocks at in situ reservoir stress state. Effective tortuosity of shales determined using helium slippage measurements are far larger than the generally assumed values. Another advantage of the model is its ability to quantitatively account for the variation in permeability values at similar gas slippage and the counterintuitive reduction in gas slippage during compaction observed in previous experiments. The proposed model correctly matches a set of gas slippage measurements and provides insight into gas transport in tight porous medium.

A Semi-Analytical Analysis of Gas Slippage Effect in Pressure Transient Behavior of Non-Condensate Gas Reservoirs with the Different Boundary Condition

The conventional models utilized to study flow behavior in a Non-Condensate gas reservoir did not consider the effects of gas slippage and different outer boundary conditions. For gas wells with a constant production flow rate in a bounded oil or gas reservoir, commonly, the outer boundary conditions are infinite boundary conditions or zero flux. In this study, the dimensionless pseudo pressure and dimensionless derivative of pseudo pressure in the presence of 4 different outer boundary conditions (infinite reservoir, constant pressure, exponential, and power-law) besides effects of gas slippage, wellbore storage, and skin factor are analyzed. To do this, the dimensionless pseudo pressure partial differential equation of radial flow was derived from the combination of continuity equation with Darcy’s law, the equation of state, compressibility equation, and dimensionless parameters. Then the derived partial differential equation is solved analytically in the Laplace domain. The obtained results of this work have important significance to understand the effects of different conditions on the transient pressure behavior of Non-Condensate gas reservoirs.

Semi-analytical Approach to Modeling Forchheimer Flow in Porous Media at Meso- and Macroscales

Darcy’s law (which states that a fluid flow rate is directly proportional to the pressure gradient) is shown to be accurate in a rather narrow range of flow velocities. Numerous studies show that at low pressure gradients gas slippage effect occurs, which gives overestimated flow rates compared to Darcy’s law. At higher flow rates, Darcy’s law is usually replaced by the Forchheimer equation which accounts for inertial forces including a quadratic term in the flow rate. Darcy’s and Forchheimer’s laws and the problem of detecting transitions between their ranges of applicability are discussed in this study. Analysis of experimental data shows that deviation from Darcy’s law is governed by the Forchheimer number, which is defined by the authors as a product of tortuosity and Reynolds number. The use of the Forchheimer number and semi-analytical approaches enables us to describe non-Darcy flow as a simple universal equation valid for any flow geometry. Comparison of the experimental data with predictions based on a semi-analytical model shows excellent agreement for a wide range of reservoir properties.

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.

Flow Characteristics of UBD Applied to Gas Reservoirs

Underbalanced drilling technology implemented in high pressure and low permeability gas reservoirs can better protect gas formation from drilling fluid damage, and can improve the drilling speed, but gas invade into the wellhole from the formation by the underbalanced pressure will make the borehole flow presented two-phase flow state. The gas phase compactness and slippage effect will increase the drilling of well control difficulty. In order to ensure the invaded gas is not appear violent slippage and rapid inflation, study the two-phase flow law is necessary to determine the size of the applied well backpressure, applying process of gas distribution law in borehole, and the bottom hole pressure, for the reasonable design of drilling fluid density, well backpressure design and the equipment selection. This paper applies the numerical difference method to two-phase flow one-dimensional equations were solved. Combined with an example of drilling, the gas void fraction distribution, migration and bottom-hole pressure change law is given, which provides theoretical basis for low permeability gas reservoirs in underbalanced pressure drilling borehole designing.

Recent Cryogenic Carbon Capture™ Field Test Results

Sustainable Energy Solutions (SES) has been developing Cryogenic Carbon Capture™ (CCC) since 2008. In that time, two processes have been developed, the External Cooling Loop and Compressed Flue Gas CCC processes (CCC-ECL and CCC-CFG, respectively). The CCC-ECL process cools the flue gas with an external refrigerant loop. This process currently captures up to 1 tonne of CO2 per day (TPD). SES has tested CCC-ECL on real flue gas slip streams from subbituminous coal, bituminous coal, biomass, natural gas, shredded tires, and municipal waste fuels at field sites that include utility power stations, heating plants, cement kilns, and pilot-scale research reactors. The CO2 concentrations from these tests ranged from 5 to 22% on a dry basis. CO2 capture ranged from 95-99+% during these tests. Several other condensable species were also captured including NO2, SO2 and PMxx at 95+%. NO was also captured at a modest rate. The CCC-CFG process has been scaled up to a 0.25 ton per day system. This system has been tested on real flue gas streams including subbituminous coal, bituminous coal, and natural gas at field sites that include utility power stations, heating plants, and pilot-scale research reactors. CO2 concentrations for these tests ranged from 5 to 15% on a dry basis. CO2 capture ranged from 95-99+% during these tests. Several other condensable species were also captured including NO2, SO2, and PMxx at 95+%. NO was also captured at 90+%. Hg capture was also verified and the resulting effluent from CCC-CFG was below a 1ppt concentration. This paper will focus on discussion of the capabilities of CCC generally, the results of CCC-ECL field testing, and future steps surrounding the development of this technology. Test results that will be presented have been collected during 9 months of testing at a commercial power plant under funding from the US Department of Energy (DOE) and the host utility. Testing of one of the systems at a commercial cement plant in the United States will also be discussed. During this testing, the system captured CO2 from the cement plant and stored the CO2 in pressurized tanks. These tanks were provided to a partner company that later used the CO2 in a CO2 utilization demonstration. The CO2 was utilized to cure concrete manufactured using cement from the same plant where the CO2 was captured. This integrated capture and utilization demonstration was the first time that the cement industry has shown in the field that it can sequester its CO2 emissions in its main product stream. This represents a potential game changing solution for industrial CO2 emissions. Operational data and host-site feedback indicate that the CCC process is ideally suited for deployment into a variety of commercial environments. A few areas of de-risking remain to make sure the technology can meet very strict industrial reliability standards. These areas of de-risking are identified and discussed. The product CO2 is shown to meet specification for many uses including industrial and merchant applications. The technology is nearing readiness for deployment at commercial scale and several initial target markets have been identified.

An advection-diffusion-mechanical deformation integral model to predict coal matrix methane permeability combining digital rock physics with laboratory measurements

This study proposed an advection-diffusion-mechanical deformation integral model to predict coal matrix methane permeability combining digital rock physics with laboratory measurements. The coal matrix pore network was first extracted from the segmented 3D digital coal image. Organic pore-controlled methane transport pathways and mineral-associated pore methane transport pathways were identified from the coal matrix pore network. Advection and Knudsen diffusion processes were considered for methane transport in the mineral associate pores and bulk methane transport in organic pores. To determine the adsorbed methane surface diffusion ability in organic pores, laboratory adsorption and desorption experiments were conducted to determine the desorption curve and critical desorption pressure. Pore shrinkage was considered for organic pores and mineral-associated pores whereas sorption-induced volumetric strain was also modeled for the organic pore system. The coal matrix methane permeability was calculated over a wide range of production pressures and the influences of reservoir and methane transport properties on coal matrix methane permeability were analyzed in detail. Results revealed that gas slippage and initial formation pressure dominate the coal matrix methane permeability more than other influencing factors. Coal matrix methane permeability was underestimated by at least 40% by using Darcy flow to describe methane flow in the coal matrix and the influence of organic matter bulk modulus variation on coal matrix methane permeability can be neglected at initial formation pressures less than 10 MPa.

Gas sorption-induced pore radius change and their impact on gas apparent permeability

Shale gas reservoirs contain small pore network that typically range from macro to nano meters and abundant gas storage as sorbed gas. In addition, the storage medium in such pore network varies and may be affected by physical parameters of shale matrix. This work presents the influence of gas sorption on pore radius and thickness at low and high pressure and analyzes the gas apparent permeability. Langmuir model is generally used to quantify the adsorbed layer thickness; however, such model undertakes mono-layer gas sorption on pore surfaces and provides poor results especially at high pressure. In this work, supercritical dubinin radushkevich (SDR) model, micropore-filling mechanism based, has been used to quantify the adsorbed layer thickness and their results have been compared with Langmuir model. The impact of adsorbed gas density on gas sorption and the impact of gas sorption crucial factors on pore radius were examined. At the end, gas slippage, geo-mechanical and adsorbed layers impacts were analyzed for evolution of gas apparent permeability. The proposed gas apparent permeability model was also validated with experimental data. The results show that assumed adsorbed gas density in Langmuir model is misleading the accurate measurement of gas sorption. The SDR model does not only provide an accurate adsorbed gas density but also its values are very close to the experimental at both low and high pressure. Gas sorption-induced pore radius based on SDR model was altered when gas sorption behavior alter at same pressure than Langmuir model-based. Gas apparent permeability changes due to gas slippage, geo-mechanical and gas adsorbed layers impacts. High gas adsorbed layer impact was observed when using proposed model as compared with Langmuir model especially at high pressure.

A Review of Gas Flow and Its Mathematical Models in Shale Gas Reservoirs

The application of horizontal wells with multistage hydraulic fracturing technologies has made the development of shale gas reservoirs become a worldwide economical hotspot in recent years. The gas transport mechanisms in shale gas reservoirs are complicated, due to the multiple types of pores with complex pore structure and special process of gas accumulation and transport. Although there have been many attempts to come up with a suitable and practical mathematical model to characterize the shale gas flow process, no unified model has yet been accepted by academia. In this paper, a comprehensive literature review on the mathematical models developed in recent years for describing gas flow in shale gas reservoirs is summarized. Five models incorporating different transport mechanisms are reviewed, including gas viscous flow in natural fractures or macropores, gas ad-desorption on shale organic, gas slippage, diffusion (Knudsen diffusion, Fick diffusion, and surface diffusion), stress dependence, real gas effect, and adsorption layer effect in the nanoshale matrix system, which is quite different from conventional gas reservoir. This review is very helpful to understand the complex gas flow behaviors in shale gas reservoirs and guide the efficient development of shale gas. In addition to the model description, we depicted the type curves of fractured horizontal well with different seepage models. From the review, it can be found that there is some misunderstanding about the essence of Knudsen/Fick diffusion and slippage, which makes different scholars adopt different weighting methods to consider them. Besides, the contribution of each mechanism on the transport mechanisms is still controversial, which needs further in-depth study in the future.

Non-equilibrium phenomena in gas mixture flow through a plane channel in near-continuum regime

Non-equilibrium phenomena in the flow of a binary gas mixture between two parallel plates, driven by gradients of the pressure, temperature and concentration, are studied. The phenomenological relationships that describe the energy and mass transfer in the flow of a gas mixture through a channel are analyzed by using methods of the non-equilibrium thermodynamics of discontinuous systems. The solution of the linearized moment equations in the 13-moments approximation of the Grad’s method and the relation for the slip velocity previously found in Zhdanov (Phys. Rev. E95 (2017), 033106) are applied to deduce the expression for the mass-average velocity of the mixture flowing in a plane channel in the near-continuum regime. Expressions for the diffusion and heat fluxes are determined from the initial third-order moment equations for the gas mixture, averaged over the channel cross-section, with the subsequent evaluation of several moments of the distribution function at the channel wall by using the modified Maxwell method. It is shown that the employed approach automatically ensures the validity of the reciprocal relations for the cross terms in the Onsager matrix. Analytical formulas for kinetic coefficients of the Onsager matrix, expressed in terms of known transport coefficients of the gas mixture and slip coefficients at the channel wall, are obtained. The results of calculations of the matrix coefficients for several binary mixtures of noble gases (Ne–Ar and He–Xe) and their comparison with the results of the numerical calculations on the basis of the linearized Boltzmann equation with the McCormack model are presented.

Experimental investigation and its analysis of gas holdup in a three-phase counter-current microstructured bubble column

The present work investigates the gas holdup in a three-phase counter-current microstructured bubble column with and without the presence of surfactant. The coal (specific gravity 1.4) was taken to prepare slurry (a mixture of water and coal) and Methyl Isobutyl Carbinol (MIBC) was used as a surfactant. The effects of the dispersed phase and continuous phase velocity, solid loading and solid size on gas holdup are studied. The result shows that the gas holdup is highly dependent on the operating variables and the solid loading, but only to a small extent on the size of the particles. The gas holdup is analyzed with a slip velocity model. The maximum gas holdup in the column is found to be 38.570% and 33.195% in the presence and absence of the surfactant, respectively. It has been found that increasing the concentration of solids reduces gas holdup. Moreover, increasing particle size and dispersed phase and continuous phase velocity increases gas holdup. A novel correlation has been developed to predict the gas holdup and slip velocity model parameters. Gas holdup data from the available literature and the current experimental values were compared to the recommended correlation. The results of the study show that the recommended correlations give a precise prediction of experimental values in the error range of ± 20%.

FRACTAL MODELS FOR GAS–WATER TRANSPORT IN SHALE POROUS MEDIA CONSIDERING WETTING CHARACTERISTICS

Complicated gas–water transport behaviors in nanoporous shale media are known to be influenced by multiple transport mechanisms and pore structure characteristics. More accurate characterization of the fluid transport in shale reservoirs is essential to macroscale modeling for production prediction. This paper develops the analytical relative permeability models for gas–water two-phase in both organic and inorganic matter (OM and IM) of nanoporous shale using the fractal theory. Heterogeneous pore size distribution (PSD) of the shale media is considered instead of the tortuous capillaries with uniform diameters. The gas–water transport models for OM and IM are established, incorporating gas slippage described by second-order slip condition, water film thickness in IM, surface diffusion in OM, and the total organic carbon. Then, the presented model is validated by experimental results. After that, sensitivity analysis of gas–water transport behaviors based on pore structure properties of the shale sample is conducted, and the influence factors of fluid transport behaviors are discussed. The results show that the gas relative permeability is larger than 1 at the low pore pressure and water saturation. The larger pore pressure causes slight effect of gas slippage and surface diffusion on the gas relative permeability. The larger PSD fractal dimension of IM results in larger gas relative permeability and smaller water relative permeability. Besides, the large tortuosity fractal dimension will decrease the gas flux at the same water saturation, and the surface diffusion decreases with the increase of tortuosity fractal dimension of OM and pore pressure. The proposed models can provide an approach for macroscale modeling of the development of shale gas reservoirs.