Gas Slippage Effect Research Articles

Pore-scale modeling of rarefied gas flow in fractal micro-porous media, using lattice Boltzmann method (LBM)

Due to the widespread use of rarefied gas flow in micro-porous media in industrial and engineering problems, a pore-scale modeling of rarefied gas flow through two micro-porous media with fractal geometries is presented, using lattice Boltzmann method. For this purpose, square- and circular-based Sierpinski carpets with fractal geometries are selected due to their inherent behavior for real porous media. Diffusive reflection slip model is used and developed for these porous media through this study. With this respect, the planar Poiseuille flow is selected as a benchmark and validated with the literature. The effect of Knudsen number (Kn) on the permeability is investigated and compared in each geometry. It is shown that as Knudsen number increases, the permeability will increase due to the gas slippage effect on the solid blocks. In addition, it is observed that the permeability is more sensitive to the gaseous flow behavior at the slip and beginning of transition flow regimes. At last, the permeability relationship with Knudsen number is presented with a higher coefficient of determination for both fractal geometries, showing that this relation is logarithmic.

Water saturation-driven evolution of helium permeability in Carboniferous shale from Qaidam Basin, China: An experimental study

Permeability is an important parameter for describing the transport properties of gas shales. This study investigates the effects of water saturation on stress-dependent permeability and the slip factor of Carboniferous shales in the Qaidam Basin, China. To analyze correlations between water saturation, effective stress, helium permeability, and slip factor, helium permeability of 12 shale samples with different water saturation at pore pressures up to 6.89 MPa and effective stresses up to 27.58 MPa at 25 °C is measured. Subsequently, shale characteristics, including mineral composition, total organic carbon (TOC) content, thermal maturity, vitrinite reflectance, and pore structure distribution (PSD; pore volume and type), are determined. The analyses reveal a consistent (exponential) relation between apparent effective gas permeability (at 6.89 MPa) and effective stress. The apparent effective helium permeability (at 4.13 MPa) decreases exponentially with increasing water saturation, particularly in shale samples with a high intrinsic permeability. The critical water saturation value of shale is 30%–40%. Two different modes of gas–water two-phase flow are observed. When water saturation is ∼30%, helium permeability decreases sharply and gas–water flow in the shale samples appear as channel flow. However, when water saturation is >40%, helium permeability slowly decreases, gas–water flow in the shale samples appear as funicular flow, gas and water simultaneously flow in all capillaries, and thin films of structured water on mineral surfaces reduce the pore-throat diameter. Thus, increased water films in narrow flow paths increase the gas slippage effect. Furthermore, the slip factor initially decreased with increasing water saturation before increasing. Helium permeability exhibits a negative correlation with TOC and clay contents and a positive correlation with quartz content. The micropores and mesopores in samples with high clay content and TOC are favorable to gas adsorption but not to gas transport. Permeability measurements of humidity oven–dried samples reveal a power–law relation between the gas slip factor and Klinkenberg-corrected permeability; the slope of the resulting curve (−0.29) is lower than that obtained for low-permeability gas sands. This study provides practical information for further studies of shale gas migration and the gas slippage effect in certain gas–water flows.

Effect of Water Saturation on Pressure-Dependent Permeability of Carboniferous Shale of the Qaidam Basin, China

Permeability is the most important parameter that describes gas flow characteristics in shale. Water saturation and effective pressure have a considerable effect on shale permeability. This paper presents the results of a laboratory study of the effects of water saturation and effective pressure on gas permeability in Carboniferous shales of the Qaidam Basin, China. The permeability of shale samples with varying water saturation (0–33 wt%) was measured at effective pressure of 6.9 to 27.59 MPa and at low mean pore pressure (< 6.89 MPa) at room temperature, using a pressure pulse decay permeameter. The results indicate that the water saturation and the effective pressure are the main factors affecting the shale permeability. Permeability of sample C034, which has a high clay content and is dominated by nanoscale slit-shaped pores, shows a large decrease (up to 90%) with increasing water saturation (from 0 to 31.7 wt%), depending on the effective pressure. A much larger permeability reduction with increasing water saturation fraction is associated with the swelling of clay minerals. For each sample with varying water saturation, our analyses revealed a consistent line relationship between log permeability and effective pressure variation. The impact of effective pressure on the measured permeability becomes more significant as water saturation increases. With increasing water saturation, the gas slippage factor decreases and calculated effective pore size increases, and gas–water flow in the shale samples occurs as channel flow. This study provides practical information for further studies of stress-dependent permeability of shale with water and the gas slippage effect in two-phase, gas–water flow.

A mechanism for generating the gas slippage effect near the dewpoint pressure in a porous media gas condensate flow

This paper presents an experimental study of gas condensate flow in porous media at pressures above the dewpoint pressure. Experimental studies of steady-state flows show that the gas flow rate starts to increase when the pressure significantly exceeds the dewpoint pressure (P = 1.74 Pс). The gas flow rate reaches its peak and is almost 30% higher than that near the critical point (P=Pc) at P = 1.5 Pс. Furthermore, the dependence of the gas flow rate on the pressure is non-monotonic and increased flow rates are reached when P = 1.4–1.74 Pс. The effect of wettability on the steady-state flow is considered. Changes in wettability do not increase the gas flow rate in the oleophobic porous media. A significant reduction of the hydraulic diffusivity of the porous medium occurs during unsteady-state flow when the pressure decreases. The observed effects are thought to be driven by formation of stable subcritical condensate nuclei, along with a slippage effect and changes in compressibility. The mechanism of stabilization of subcritical nuclei via combined action of the surface and electrical forces is considered and mathematical models that describe the experimental results are proposed.

Laboratory investigations of inert gas flow behaviors in compact sandstone

The seepage evolution behavior of compact rock is significant for the stability and safety of many engineering applications. In this research, both hydrostatic and triaxial compression tests were conducted on compact sandstone using an inert gas, namely argon. A triaxial compression test with a water permeability measurement was carried out to study the difference between the gas permeability and water permeability evolutions during the complete stress–strain process. Based on the experimental data, the hydrostatic stress-dependent gas permeability was discussed firstly. A second-order function was proposed to predict and explain the gas slippage effect. The mechanical properties and crack development of the sandstone samples were discussed to better understand the permeability evolution with crack growth during the complete stress–strain process. The results show that the gas permeability evolution can be divided into five stages according to the different crack growth stages. Then, the permeability changes in the crack closure stress $$ \sigma_{\text{cc}} $$, crack initiation stress $$ \sigma_{\text{ci}} $$, crack damage stress $$ \sigma_{\text{cd}} $$ and peak stress $$ \sigma_{\text{p}} $$ with confining pressures were analyzed. Finally, we found that the difference between the corrected gas permeability and water permeability can be attributed to the interaction between the water and sandstone grains.

Impact of non-linear transport properties on low permeability measurements

The results of modeling nonlinear transport properties on a plug scale for steady state, unsteady state, pulse decay and sinusoidal pressure measurements are presented. We include the gas slippage (Klinkenberg corrections) and pressure dependent density effects.To validate the modeling, we compare it to analytical calculations based on an assumption of constant mass flow once the transients have dissipated for steady state models. Validation of the other measurement protocols is performed by comparison to finite difference calculations.For low permeability samples, significant pressure drops must be modeled to obtain large enough flow rates to allow accurate measurement in the laboratory. We limited ourselves to 100 psi pressure differences because of the large influence of effective stress on gas density that would be present for larger pressure differences. Flowing pressures of this magnitude imply significant pressure dependent density effects, which reduce the flow rates. In contrast, gas slippage increases the transport of gas. The result is that nearly identical fits are obtained for widely varying magnitudes of permeability and gas slippage. This result is obtained for all of the modeled measurement protocols. We introduce a new technique to interpret the modeled data, the ”k0-b plot”. The method allows the values of k0 and b to be extracted if multiple measurements are performed at different mean pressures. The technique is also compared to laboratory data to demonstrate that the effects occur in the measurements.The influence of the non-linearities predicted on the measured chamber pressures are presented for each of the measurement protocols (other than steady state in which there are no chambers). In particular, sinusoidal pressure variation of the upstream chamber results in an increased average downstream chamber pressure and the introduction of harmonic distortion. These effects have not been discussed in the literature and give a motivation for development of this measurement for low permeability samples.The modeling indicates that plug scale measurements are practical, but multiple mean pressures must be used to separate the competing effects of permeability and gas slippage. We recommend performing unsteady state measurements at reservoir stress at multiple mean pressures, supplemented with sinusoidal pressure and pulse decay to calibrate the nonlinear and adsorption effects.

Effects of nano-pore wall confinements on rarefied gas dynamics in organic rich shale reservoirs

The advancements in horizontal well drilling and multistage hydraulic fracturing technology enabled us to unfold major sources of hydrocarbon trapped in ultra-tight formations such as organic rich shales. Tremendous gas production from these reservoirs has transformed today’s energy landscape [1]. Even though multi-stage hydraulic fracturing stimulation provides high permeability paths to transfer gas to the wellbore, however, most of the gas is stored in nano-organic pores of the ultra-low permeability shale matrix that needs to be transferred to the hydraulic fractures to be able to be produced. Studies using advanced imaging technologies such as FIB/SEM and low temperature adsorption measurements show that in the organic rich shale gas reservoirs, Kerogen, the finely dispersed organic nano-porous material with an average pore size of less than 10 nm holds bulk of the total gas in place (GIP). The molecular level interactions between fluid–fluid and fluid–solid organic pore walls govern the transport and storage in these organic nano-pores.To understand the high gas production rates from these ultra-tight formations, the objective of this study is to advance our understanding of non-ideal gas dynamics in multiscale pore structure of organic rich shale matrix (i.e., gas storage and transport influenced by adsorption and adsorbed gas transport) and develop a model to quantify these effects under wide range of reservoir conditions. Among different methods used to model gas dynamics in organic nano-pores such as the multi-continuum, molecular dynamics and Monte Carlo, the lattice Boltzmann method (LBM) is more effective method with much less computational cost relative to other techniques. In this study we focus on rarefied gas dynamics in Kerogen organic nano-tubes under wide range of reservoir pressure and temperature conditions using a two dimensional LBM model.In this model the Langmuir-slip boundary condition at capillary walls, convection or darcy flow and diffusive transport (slippage of free gas molecules and surface transport of adsorbed molecules combined) are considered to model gas transport. Different transport mechanisms and their contribution in gas transport is investigated in a large range of Knudsen numbers from continuum flow to transition flow regime under different reservoir conditions. The deviation from classical theory of fluid flow in micro channels such as Knudsen’s minimum in the mass flow rate is investigated and the effect of gas slippage and double slippage on Knudsen minimum is discussed in details. Finally the results are compared with analytical, and semi analytical solutions available in the literature.The LBM model results displays a clear indication that the gas transport in the capillary tube is highly depends on the pore width size, pressure and temperature. The relative impact of pore size, pressure and temperature on maximum gas velocity and gas wall velocity differs at different flow regime conditions. A critical Knudsen number exists at different reservoir conditions, where the anticipated parabolic fluid velocity profile in organic nano-pores alters and shows higher flow rate as capillary widths reduces due to the underlying effect of molecular phenomena of double slippage and the wall confinement. The comparison with traditional continuum Hagen-Poiseuille law, Klinkenberg slip theory, and recent modified versions of Klinkenberg slip flow equations show that the previous models are valid only in the continuum flow regime, however, they fail to capture high gas flow rates at high Knudsen number and transition flow regimes which is the case in most of the shale organic nano-pore conditions [2].This work is not only important for the advancement of shale gas flow simulators, but also for organic rich shale characterization.

An improved productivity model in coal reservoir and its application during coalbed methane production

Permeability of coal reservoir is a key parameter affecting coalbed methane (CBM) productivity. The dynamic variation of permeability depends on the effect of effective stress, coal matrix shrinkage and gas slippage during CBM well drainage. On the basis of S-D stress-permeability model, a dynamic prediction model of coal reservoir permeability considering effective stress, coal matrix shrinkage and gas slippage effect (is called “three effects”) is established. The dynamic change of permeability in CBM development is revealed. It shows that permeability initially drops and then rises. An improved CBM productivity model considering “three effects” is derived, and the influence law of “three effects” on CBM production during CBM well drainage is revealed. The results of the theoretical model are compared with the field data, and the reliability of the theoretical model is further verified. During CBM production, with the decrease of reservoir pressure, the effective stress increases. Before reservoir pressure reaches the critical desorption pressure, the effective stress effect is dominant and the permeability of coal reservoir declines; after the reservoir pressure declines to below the critical desorption pressure, the coal matrix shrinkage effect will play a dominant role in the permeability variation, and the permeability will start to increase at lower pressure. It is critical not only to avoid too much initial pressure drawdown, which decreases well productivity; but also to ensure matrix shrinkage effect improve the permeability and productivity of coal reservoirs in longer term.

Characteristics of shale nanopore system and its internal gas flow: A case study of the lower Silurian Longmaxi Formation shale from Sichuan Basin, China

The gas flow in shale nanopores undergoes a transition from continuum-transition flow regimes to Knudsen diffusion, rather than the traditional Darcy flow, due to the dynamic properties of shale gas. Thus, becoming the premise in understanding gas flow regime within the shale nanopores to further investigate how shale permeability evolves during gas depletion as well as to predict gas production. The microstructure features of Longmaxi Formation shale (Longmaxi Shale), characterized by SEM imaging, MICP, and gas adsorption, are dominated by micropores and mesopores that are less than 10 nm in size on average. Judging from the pore sizes of Longmaxi Shale and the general reservoir pressures, the gas flow inside shale matrix is determined as slip flow and transition flow regimes by Knudsen number. About the investigation of the Barnett Shale, a second-order slip model is superior to the first-order slip model in describing apparent permeability of Longmaxi Shale. Then and there, the velocity profile and volumetric flow rate in Longmaxi Shale are discussed with a second-order slip model. The gas velocity on the pore walls becomes larger as pressure decreases. The gas production enhancement due to gas slippage effect brings about a higher yield than that of Darcy's Law. However, shale itself is highly heterogeneous in pore geometry. Therefore, the model construction of gas flow simulation must be based on refined shale pore models.

Experimental simulation on dynamic variation of the permeability of high-rank coal reservoirs

In terms of the coal reservoir permeability of effective stress, coal matrix shrinkage and gas slippage, we conduct the tests of gas permeability under constant confining pressure and effective stress, as well as illustrate the cumulating method of permeability increment caused by the effects of gas slippage and coal matrix shrinkage. The results show that under the constant confining pressure, gas slippage affecting coal permeability changes to effective stress affecting it mainly. The change point increases with the increase of the confining pressure. The gas slippage effect leads to high permeability under low confining pressure, but coal matrix expansion results in the low value as confining and gas pressures increase. Combined with the drainage process of coalbed methane (CBM) well, the permeability is divided into four change stages based on the above analysis about the three effects, which can improve the change regulation understanding. Four stages are the downward phase under effective stress, the conversion phase of effective stress-coal matrix contraction effect (mainly based on effective stress), the rising stage of the effective stress-coal matrix contraction effect (mainly based on coal matrix contraction effect) and the rising phase of coal matrix contraction-slippage effect (mainly based on slippage effect). Permeability of coal reservoir during the process of drainage and production goes through four stages.

Relationship between pressure drop and face velocity for electrospun nanofiber filters

Nanofiber filters are typically fabricated using the electrospinning technique, which can reach high particle removal efficiency with relatively low air resistance because of the gas slip effect. They have a great potential for applications in the filtration units of heating, ventilation, and air-conditioning (HVAC) systems to reduce the fan energy consumption. This study systematically examined the relationship between pressure drop and face velocity for electrospun nanofiber filters. Experimental data of 122 nanofiber filters were collected from the literature to validate the theory regarding pressure drop for nanofiber filters proposed in previous studies. The linear regressions between pressure drop and face velocity showed that 89% of the tested nanofiber filters had an R2 value greater than 0.9. Therefore, the pressure drop can be confidently regarded as being proportional to the face velocity for nanofiber filters. This conclusion was further confirmed by additional experimental measurements conducted in this study. After confirming the theory, the air resistance coefficients of nanofiber filters were calculated and compared with that of commercial HVAC filters. The comparison showed that the air resistances of nanofiber filters with careful design could be lower than that of the commercial filters with similar particle removal efficiency.

An analytical model for relative permeability in water-wet nanoporous media

A relative permeability model for gas-water two phase flow in water-wet nanoporous media is proposed based on the continuity equation with modified non-slip boundary in a single nanotube and the pore size distribution (PSD) of the media. The present model takes into account the nanoscale effects including gas slippage in the entire Knudsen range, multilayer sticking (near-wall structural water film) and the quantified thickness of water film. The flow model in single nanotube and relative permeability model in nanoporous media have been validated by comparing with the various molecular simulations, experimental data, and analytical models. The results show the nanoscale effects play an extremely significant role in determining both the gas and water phase relative permeability in nanoporous media: the gas phase relative permeability increases dramatically due to the gas slippage effect, especially at low water saturation; the multilayer sticking of the water film will reduce the water phase relative permeability as well as slightly decrease gas phase relative permeability; the flow of water film has a negative impact on both the gas and water phase relative permeability. Additionally, logarithmic normal distribution function is adopted to characterize PSD, and the sensitivity analysis of PSD on the relative permeability are examined as well.

Impact of Stress-Dependent Matrix and Fracture Properties on Shale Gas Production

Unconventional shale gas production is often characterized by a short period of high production followed by a rapid decline in the production rate. Given the high costs of hydraulic fracturing and horizontal drilling, it is critical to identify the mechanisms behind the production loss. The existing shale gas production models often assume constant matrix permeability. However, laboratory observations show that matrix permeability can decrease significantly with increasing effective stress, which highlights the necessity of considering the stress-dependent properties of shale matrix in production analysis. Moreover, the compaction of pore space will also increase the matrix permeability by enhancing the gas-slippage effect. In this paper, a matrix permeability model which couples the effect of pore volume compaction and non-Darcy slip flow is derived. Numerical simulations are conducted to understand the role of matrix permeability evolution during production. Changes of fractures’ permeability and contact area during depletion process are also taken into account. The results indicate that the loss of fracture permeability has a greater impact at the early stage of the depletion process, while matrix permeability evolution is more important for the long-term production.

Effect of gas slip on the behavior of the aerostatic guideway

PurposeThis paper aims to better understand the dynamic characteristics of an aerostatic slider caused by a gas film, and the impact of a gas film slip on the load capacity, stiffness and dynamic stiffness of the guideway is studied.Design/methodology/approachIn theory, the Navier velocity slip model is introduced for fluid continuous flow equation to calculate the flow state in the micro-state; in experimental techniques, the stiffness experiment of the guideway by digital inductance meter is performed under different loadings, which are used to inspect the simulation results.FindingsThe maximum value of bearing stiffness in the condition of considering that the gas slip is larger than that of not considering the gas slip, and the gas film clearance of maximum bearing stiffness in the condition of considering the gas slip is less than that of not considering the gas slip. This is verified by the measurement of the stiffness of the guideway.Originality/valueThis paper mostly studies the influence of the gas slip effects on the performance of the aerostatic guideway, which will make a certain contribution to the guideway stability and the machining precision of the machine tool.

Experimental Study on Gas Slippage of Tight Gas Sands in Kirthar Fold Belt Sindh, Pakistan

The laboratory experiments on samples from Kirthar fold belt of lower Indus basin Sindh Pakistan were carried out to investigate the effect of gas slippage under varying conditions of pore pressures and overburden stress. The samples were dried in an oven at temperature of 600C and were randomly selected for measurement of permeability and porosity. Permeability was measured using nitrogen gas, while the porosity measurements were made using helium gas expansion porosimeter. The bulk volume was determined by measuring sample diameter and length with caliper. The permeability results suggest that gas slippage increases as if low pore pressures are used, which leads to higher measured permeability than intrinsic permeability of samples. An attempt was also made to estimate the permeability using existing correlations and found that there is large scatter in predicted permeability and measured data. This large amount of scatter in the predicted permeability values concludes that unless absolutely necessary, such correlations should not be used where accurate absolute permeability values are needed. Moreover, the permeability and porosity were plotted together to develop a relation between two properties; the power law fitting of the data well explains the relation between permeability and effective porosity.

Experimental investigation on the coupled effect of effective stress and gas slippage on the permeability of shale

Permeability is one of the most important parameters to evaluate gas production in shale reservoirs. Because shale permeability is extremely low, gas is often used in the laboratory to measure permeability. However, the measured apparent gas permeability is higher than the intrinsic permeability due to the gas slippage effect, which could be even more dominant for materials with nanopores. Increasing gas pressure during tests reduces gas slippage effect, but it also decreases the effective stress which in turn influences the permeability. The coupled effect of gas slippage and effective stress on shale permeability remains unclear. Here we perform laboratory experiments on Longmaxi shale specimens to explore the coupled effect. We use the pressure transient method to measure permeability under different stress and pressure conditions. Our results reveal that the apparent measured permeability is controlled by these two competing effects. With increasing gas pressure, there exists a pressure threshold at which the dominant effect on permeability switches from gas slippage to effective stress. Based on the Klinkenberg model, we propose a new conceptual model that incorporates both competing effects. Combining microstructure analysis, we further discuss the roles of stress, gas pressure and water contents on gas permeability of shale.

Apparent permeability of gas shales – Superposition of fluid-dynamic and poro-elastic effects

The permeability of low-permeable gas shales is affected by both, fluid-dynamic (slip flow) and poro-elastic effects over a large pore pressure range. To analyse and separate the influence of these superposed effects, an apparent permeability model has been set up. The model’s poro-elastic and fluid-dynamic parameters were adjusted simultaneously to match own experimental data for an intact Bossier Shale (“matrix”) sample, a fractured Haynesville Shale sample and previously published literature data.The effective stress-permeability relationship can only be described by a modified effective stress law:σ′=Pc-χPpHere the fitted permeability effective stress coefficients χ, were consistently ≤1, indicating that pore pressure has a lesser influence on effective stress than confining pressure. Fluid-dynamic gas slippage effects were found to be significant up to pore pressures of 20MPa in low permeable (<10μD) matrix samples.Pitfalls in the separation of fluid-dynamic and poro-elastic effects are wrong a priori assumptions. These are neglecting gas slippage above a certain pore pressure and assuming effective stress conditions to be constant in the Klinkenberg evaluation. Ignoring gas slippage in the evaluation of stress effects results in underestimation of χ values whereas undetected stress effects (by wrong a priori χ values) lead to incorrect predictions of the fluid-dynamic effects with increasing pore pressures.The predictions of the apparent permeability model were validated and checked for consistency and plausibility by (1) visualization in a k(Pp, Pc) diagram, (2) preparation of Klinkenberg plots over large pore pressure ranges (>10MPa) and (3) analysis of the different slippage behaviour of He and Ar.The apparent permeability model predicts that during depletion of a shale gas reservoir apparent permeability passes through a minimum in the pressure range from 2 to 10MPa due to the transition from a poro-elastic to a fluid-dynamic dominated realm.

Shale gas apparent permeability model coupling the transport mechanisms in matrix and natural fractures

Shale gas reservoirs exist micropores, nanopores and natural fractures. The mode of gas occurrence and the transports mechanisms vary with the change of type pores. In this paper, a new shale gas apparent permeability model coupling the gas transport mechanisms in matrix pores and natural fractures is presented on the basis of the quantitative characterization of the natural fractures. The model is derived based on the permeability tandem-parallel model and considers the gas slippage effect, diffusion effect in nanopores and the flow characteristics in natural fractures. Sichuan Basin Niutitang group shale sample with natural fractures are used to verify the theoretical model. The results show that the analytical solution of the apparent permeability model not only can match the measured value in lab, but also accurately describes the flow features of interaction in matrix pores and natural fractures in the core internal. In short, the natural fractures quantitative characterization of shale gas reservoirs and the apparent permeability model considering the flow characteristics in the micropores, nanopores and natural fractures not only provides a new approach to the modeling of complex fractures network, but also further promotes the shale gas reservoirs discrete fracture network model numerical simulation for the industrial application.

A Numerical Study of Factors Affecting Fracture-Fluid Cleanup and Produced Gas/Water in Marcellus Shale: Part II

Summary Horizontal wells combined with successful multistage-hydraulic-fracture treatments are currently the most-established method for effectively stimulating and enabling economic development of gas-bearing organic-rich shale formations. Fracture cleanup in the stimulated reservoir volume (SRV) is critical to stimulation effectiveness and long-term well performance. However, fluid cleanup is often hampered by formation damage, and post-fracture well performance frequently falls to less than expectations. A systematic study of the factors that hinder fracture-fluid cleanup in shale formations can help optimize fracture treatments and better quantify long-term volumes of produced water and gas. Fracture-fluid cleanup is a complex process influenced by multiphase flow through porous media (relative permeability hysteresis, capillary pressure), reservoir-rock and -fluid properties, fracture-fluid properties, proppant placement, fracture-treatment parameters, and subsequent flowback and field operations. Changing SRV and fracture conductivity as production progresses further adds to the complexity of this problem. Numerical simulation is the best and most-practical approach to investigate such a complicated blend of mechanisms, parameters, their interactions, and subsequent effect on fracture-fluid cleanup and well deliverability. In this paper, a 3D, two-phase, dual-porosity model was used to investigate the effect of multiphase flow, proppant crushing, proppant diagenesis, shut-in time, reservoir-rock compaction, gas slippage, and gas desorption on fracture-fluid cleanup and well performance in Marcellus Shale. The research findings have shed light on the factors that substantially constrain efficient fracture-fluid cleanup in gas shales, and we have provided guidelines for improved fracture-treatment designs and water management.

Gas flow in a layer of chains formed from permeable clusters of nanoparticles

The Stokes–Brinkman flow field has been calculated in a model deposit, i.e., a row of parallel chains formed from porous spherical clusters of nanoparticles and oriented perpendicularly to the gas flow direction. The force of drag to an air flow has been calculated for the row of chains taking into account their permeability and the distance to neighboring chains. The drag forces have been found for nanodendrites composing clusters with allowance for the gas slip effect. Corresponding approximation formulas have been derived. A method has been proposed for calculating the pressure drop across a highly porous deposit of clusters of aerosol nanoparticles deposited onto a filter.