non-Darcy Effects Research Articles

Estimating of Non-Darcy Flow Coefficient in Artificial Porous Media

This study conducted a radial flow experiment to investigate the existence of non-Darcy flow and calculate the non-Darcy “inertia” coefficient; the experiment was performed on seven cylindrical perforated artificial porous media samples. Two hundred thirty-one runs were performed, and the pressure drop was reported. The non-Darcy coefficient β was calculated and compared with available in the literature. The results showed that the non-Darcy coefficient decreased nonlinearly and converged on a value within a specific range as the permeability increased. Nonetheless, it was found that the non-Darcy flow exists even in the very low flow rate deployed in this study. In addition, it has been found that the non-Darcy effect is not due to turbulence but also the inertial effect. The existence of a non-Darcy flow was confirmed for all the investigated samples. The Forchheimer numbers for airflow at varied flow rates are determined using experimentally measured superficial velocity, permeability, and non-Darcy coefficient.

Productivity model with mechanisms of multiple seepage in tight gas reservoir

The productivity model with unilateral threshold pressure gradient, real gas effect or non-Darcy effect has been documented in the research of tight gas reservoir. However, the multiple seepage mechanisms are poorly addressed in a productivity model, especially the application of gas-water relative permeability curve changing with the displacement pressure. A novel productivity model of multi-stage fractured horizontal wells with mechanisms of multiple seepage was proposed the present study. Results show that the stress effect has a negative effect on the effective permeability, while the Knudsen diffusion effect of gas has a positive effect. The water flow can inhibit the gas flow in the tight gas reservoir, whose effect is more significant with larger displacement pressure differences. The higher initial water saturation and reservoir temperature, whereas the lower gas well productivity, contribute to a high gas well productivity in the reservoir of high pressure.

Two-phase Flow Model and Productivity Evaluation of Gas and Water for Dual-Medium Carbonate Gas Reservoirs

Fluid flow in the dual-medium carbonate gas reservoir is characterized by stress sensitivity and non-Darcy flow effect. In order to accurately describe the unsteady flow of gas and water in the dual-medium gas reservoir, a two-phase flow model of gas and water is built. First, reservoir space and fluid flow characteristics of carbonate gas reservoirs are investigated, and the flow model that considers both the stress sensitivity and non-Darcy flow is built based on the fundamental flow theory, after fully investigating the reservoir space and fluid flow characteristics of carbonate gas reservoirs. Then, the perturbation theory is introduced, and the model is solved in the Laplace space, after which the obtained Laplace space analytical solution is converted into the real-space solution. Finally, the productivity evaluation model for the dual-medium gas reservoir with the gas-water two-phase flow is built, based on the flowing material balance method and Newton iteration. The presented productivity evaluation model is applied to analyze the effects of stress sensitivity and non-Darcy flow on the two-phase flow model of gas and water for the dual-medium gas reservoir and the reservoir productivity. The results indicate that a higher stress sensitivity coefficient is demonstrated to indicate higher stress sensitivity and accelerated production decline of the reservoir, while a lower non-Darcy flow effect coefficient represents a stronger non-Darcy effect and boosted drop of initial production of the reservoir. Hence, it is not reasonable to neglect the effects of stress sensitivity and non-Darcy flow during the evaluation of the productivity of a dual-medium carbonate gas reservoir. The model presented in this research provides important references for improving the recovery performance of dual-medium gas reservoirs.

Research on stimulation of injection and production capacity for single well in underground gas storage

Underground gas storage is the best choice for natural gas resource reserve and peak value. Storage capacity of underground gas storage and single well injection and production capacity are the key indicators of shaving capacity. This paper focuses on research of expansion of gas storage and the stimulation of injection and production capacity of single well of a basin in Western China. Firstly, based on the study of two-phase seepage law of gas and water, a numerical simulation model coupling high velocity non-Darcy effect and gas-water two phase seepage is established; Secondly, the influencing factors of single well injection and production capacity are analysed. Finally, acidizing can effectively improve the single well injection and production capacity of well. The numerical simulation result shows that the injection and production differential pressure is reduced by 70%, and gas injection and production volume are increased by 14.8% and 26.9%.

Injection-production optimization of fault-karst reservoir\u2014considering high-speed non-Darcy effect

Fault-karst reservoirs are featured by complex geological characteristics, and accurate and fast simulation of such kind of reservoirs using traditional simulator and simulation methods is pretty hard. Herein, we tried to discrete the complex fault-karst structures into one-dimensional connected units connecting the well, fracture and cave based on reservoir static physical parameters and injection-production dynamics. Two characteristic parameters, conductivity and connected volume, are proposed to characterize the inter-well connectivity and material basis. Meanwhile, the high-speed non-Darcy seepage term is introduced into the material balance equations for well-fracture-cave connected units to describe the actual seepage characteristics within the fault-karst reservoirs, and to better simulate the oil/water production dynamics. Based on this method, a fracture reservoir model of 1 injection-3 production was established. The change of oil–water action law in different injection and extraction systems under two production regimes of fixed production rate and fixed pressure is analyzed. A case study was conducted on S fault zone, where the flow of oil and gas did not follow the Darcy seepage rule and with a β value of 103–104, the single well flow pressure and oil production were perfectly matched with the real data. In addition, connected units with more prominent high-speed non-Darcy features were found to have better connectivity, which might shed light on the more accurate prediction of inter-well connectivity. Moreover, an improved injection-production well pattern and was proposed based on connectivity prediction model and reservoir engineering method to solve the problems of insufficient natural energy supply and overhigh oil production rate in Block S. Furthermore, the injection/production rate as well as the timing and cycle of water injection was predicted and optimized so as to better guide to site operations.

Estimation of aquitard hydraulic conductivity and skeletal specific storage considering non-Darcy flow

Darcy's law has been widely used to study the groundwater drainage process within an aquitard. However, non-Darcy flow is frequently encountered in laboratory and in situ investigations. With consideration of a sudden drop in boundary hydraulic heads, aquitard compaction characteristics and their sensitivities to the non-Darcy flow control variables were analyzed. The non-Darcy flow was found to retard groundwater drainage, and the retardation effects were much more significant at early-to-intermediate time points. Under this specific boundary condition, the time–compaction curve in a log–log graph at early time points was found to be close to a straight line, whose slope can be used to indirectly evaluate the extent of the non-Darcy effect. A non-Darcy flow-based type curve method was developed for estimating aquitard hydraulic conductivity (K) and skeletal specific storage (Ss), and this method was used to interpret the time–compaction data recorded in a laboratory experiment. The tested aquitard was determined to be associated with non-Darcy flow due to the fact that the time–compaction curve deviated from the Darcy's law-based theoretical curve. Darcy's law resulted in an underestimated K. In contrast, the estimated Ss was almost unaffected by the flow state, if the observation lasted long enough to reach final steady compaction.

Modeling transient flow behavior with the high velocity non-Darcy effect in composite naturally fractured-homogeneous gas reservoirs

A gas reservoir with composite properties contains two distinct regions, where one develops natural fractures and the other does not. To investigate the pressure transient behavior of the non-Darcy flow in composite naturally fractured-homogeneous gas reservoirs, a radial bi-zonal composite non-Darcy flow model was developed based on Izbash's equation. The inner region was considered as a dual-porosity medium to simulate the non-Darcy flow, whereas the outer region was considered as a homogeneous medium to simulate the Darcy flow. This model was solved using the Laplace transform, linearization and Stehfest numerical inversion. Then, the standard bi-logarithmic characteristic curves of the non-Darcy flow model were plotted. The flow stages were recognized and the influence of vital characteristic parameters on the transient behavior was analyzed and discussed in detail, such as the empirical constant, radius of the non-Darcy region, storage ratio, crossflow coefficient, etc. It is found that the values of the empirical constant n have a significant influence on the pressure transient behavior of the non-Darcy region. Moreover, three reduced models of the model proposed in this study were analyzed and discussed. Finally, it was found from the field application that this model had an excellent agreement between the measured and simulated pressure responses. The research results can be a helpful guide for researchers in the related fields when studying the transient behavior of high-velocity non-Darcy gas flow in composite naturally fractured-homogeneous gas reservoirs.

Pressure-dependent flow characteristics of proppant pack systems during well shut-in and the impact of fines invasion

Near-wellbore screenouts during the shut-in stage due to the development of compact proppant clusters is an issue reported in several fracturing treatments for Coal Seam Gas (CSG) reservoirs. The usual solutions to counter this issue implemented in deep rocks such as Shale and Siltstone do not solve for coal reservoirs due to its geological characteristics. Therefore, the development of proppant packs is an expected outcome during CSG extraction, and the permeability in the proppant pack could decide the overall gas productivity. This study investigates the permeability of proppant packs prepared using the Under-compaction method to simulate compact proppant clusters experienced in near-wellbore screenouts. In this regard, two commonly used proppant types are selected; sand and ceramic, and a series of tri-axial permeability tests were conducted under various effective stresses relevant to CSG environments. According to the experimental outcomes, interestingly, both proppant packs exhibited non-Darcy and Darcy flow regimes, while the non-Darcy effect was more profound at low confining pressures due to its high packing porosity. Results showed that the permeability through the compact proppant pack depends on both the reservoir pressure and the type of proppants selected. The sand proppant pack (SPP) showed 1–2 orders higher than the permeability values of the ceramic proppant pack (CPP) until a threshold pressure is reached (10 MPa), after which the ceramic proppants produced higher permeability values. We also investigate the potential impact of the invasion of coal fines into the proppant packs and the corresponding pore blockings. The impact of fines invasion on CPP permeability was more potent compared to the fines induced SPP permeability. The shape of the ceramic particles, the polar effect of the α-Al2O3 atoms, and the attraction of the oxygen functional groups of the coal fines to these polar sites increase the likelihood of fines clogging in a ceramic proppant pack.

A semi-analytical solution for shale gas production from compressible matrix including scaling of gas recovery

The aim of this work is to present semi-analytical solutions for shale gas production from a 1D porous medium, where constant pressure is assumed at one side and a no-flow boundary at the other. Adsorbed gas is modeled by a Langmuir isotherm, the gas and rock are compressible, porosity reduction reduces intrinsic permeability and apparent permeability further depends on the Knudsen number.The partial differential equation describing this system can be formulated as a nonlinear diffusion equation in terms bulk gas density M. This system is comparable to a form described for spontaneous imbibition with semi-analytical solutions regardless of the shape of the diffusion coefficient as function of the conserved property, in that case fluid saturation. Semi-analytical solutions are thus obtained that can give spatial profiles, at given times, of pressure, adsorption, porosity and apparent permeability, in addition to time profiles of gas recovery. These solutions are valid until the no-flow boundary is encountered (the critical time). Late time behavior is investigated using numerical solutions. The roles of system length, adsorption isotherm, rock compressibility, porosity-permeability relations and non-Darcy effects are examined.It is shown that gas recovery follows a square root of time profile before the critical time. Scaling yields full overlap of recovery curves until their critical time. The square root of time solution is valid for recoveries around 12–22%, but is a good approximation until obtainable recoveries of 35–50% for typical shale cases. Cases where the diffusion coefficient increases more steeply with M leave the square root profile at lower recovery values and obtain slower recovery with time systematically according to the steepness of the coefficient.

Study on unsteady seepage characteristics and production decline of tight channel sandstone gas reservoirs

Tight channel sandstone gas reservoirs are mainly characterized by low porosity and permeability to ultra-low porosity and permeability, strong heterogeneity, and slow energy supply rate in the later stage, resulting in small gas well control reserves, and fast decline rate of gas well pressure and production. Therefore, it is urgent to carry out targeted research on production decline. In this paper, from the perspective of percolation mechanics, a mathematical model of low-velocity non-Darcy unstable percolation in tight channel sandstone gas reservoir is established, a diagram of the relationship between non-Darcy effect, flow boundary characteristics, and dynamic bottom-hole flow is established, and the dynamic influencing factors of bottom hole flow are analyzed. From a seepage mechanics point of view, this paper establishes a tight sandstone gas reservoir river unstable low-speed non-darcy seepage flow mathematical model of non-darcy effect and flow boundary characteristics and the relationship between the bottom hole flow dynamic chart and analysis of bottom hole flow dynamic influence factors, research shows that start-up pressure gradient, skin factor, the closed boundary of tight sandstone gas reservoir river bottom hole flow dynamic effect is bigger, The research content of this paper has certain guiding significance for realizing the effective development of tight channel sandstone gas reservoir.

Seepage and Heat Transfer Characteristics of Gas Leakage under the Condition of CAES Air Reservoir Cracking

The contradiction between supply and demand of energy leads to more and more attention on the large-scale energy storage technology; Compressed Air Energy Storage (CAES) technology is a new energy storage technology that is widely concerned in the world. The research of coupled heat transfer and seepage in fractured surrounding rocks is the necessary basis to evaluate the operation safety and effectiveness of CAES. Current studies point to the possibility of cracking in concrete liner seals, but the thermodynamic processes and leakage characteristics of compressed air in the presence of cracking and the heat transfer characteristics of seepage have not been addressed and reported. In order to investigate the leakage, the gas seepage and heat transfer law in fractured rock when the hard rock CAES gas reservoir seal cracks, the COMSOL fracture Darcy module, and the non-Darcy Forchheimer model are used as the constitutive seepage. The global ODE is used to calculate the thermodynamic process of compressed air in gas storage with coupled seepage and heat transfer process. The pressure and temperature of compressed air are obtained as the unsteady boundary of the seepage heat transfer model. A program for calculating the seepage and heat transfer characteristics of fractured surrounding rock in the CAES gas reservoir is established. On this basis, with the proposed Suichang CAES cavern as the background, the seepage and heat transfer characteristics of the fractured surrounding rock of the gas storage are studied. The results showed that when there are fewer cracks in the lining and surrounding rock of the air reservoir, the air pressure decreases due to a small amount of air leakage after 30 operation cycles, and the leakage rate of each cycle is 0.7% of the gas storage capacity, but it still meets the engineering requirements. If the plant is operating under these conditions, the charging rate will need to be increased by 1.2 kg/s per cycle charging stage. In the discharging and power generation phase, the high-pressure air that previously percolated into the rock mass cracks could flow back into the air storage through the lining cracks. Therefore, it is incorrect and unreliable to consider the gas which flows out from the inner surface of the lining as unusable. When the lining crack width is less than 0.3 mm, the seepage flow is Darcy flow and the non-Darcy effect can be ignored; when the lining crack width is greater than 0.5 mm, the non-Darcy effect of seepage cannot be ignored. The gas velocity in the surrounding rock fracture medium is on the order of 0.01 m/s with an influence range of over 100 m, and the gas velocity in the pore medium is on the order of 10-6 m/s with an influence range of 50 m. The findings of this study contribute to a better understanding of the interaction between the thermodynamic properties of compressed air and the seepage heat transfer process in compressed air storage underground reservoirs, as well as the gas leakage process in the event of liner seal cracking.

A Novel Mathematical Model Considering Real Gas PVT Behavior to Estimate Inflow Performance Relationship of Gas Well Production

Inflow performance relationship (IPR) is one of the most important methods for the analysis of the dynamic characteristics of gas reservoir production. The objective of this study was to develop a model to improve the accuracy of the IPR for evaluating and predicting the production of gas reservoirs. In this paper, a novel mathematical model, taking into account the real gas PVT behavior, is developed to accurately estimate the inflow performance relationship. By introducing a pseudo-pressure function and a real gas properties database, this model eliminates the error caused by the linearization method and improves the calculation accuracy. The results show that more than 90% of the energy in the flow field is consumed by inertial forces, which leads to significant high-velocity non-Darcy effects in the gas reservoir. The reservoir permeability, original reservoir pressure, stress sensitivity coefficient, and skin factor have a great impact on the inflow performance relationship of gas reservoir production. This model predicts gas IPR curves with excellent accuracy and high efficiency. The high-precision gas well inflow performance relationship lays a solid foundation for dynamic production analysis, rational proration, and intelligent development of the gas field.

Non-Darcy thermal-hydraulic-mechanical damage model for enhancing coalbed methane extraction

Under the thermal-hydraulic-mechanical coupling conditions, structural change of the damaged coal and rock mass will affect its thermodynamic properties, permeability characteristics, and even the flow state. This study proposes a nonlinear (Non-Darcy) thermal-hydraulic-mechanical damage model based on the equivalent matrix scale and dynamic diffusion (EDN-THMD), which is solved via the finite element method combined with programming. The model is validated with field data and compared with different coupled models. The influence of different factors on gas extraction promoted by fracturing is analyzed. The results show that ad/desorption thermal effect dramatically influences the temperature field. The gas production is underestimated if ignoring equivalent matrix scale, especially after fracturing, but overestimated without considering water effect and dynamic diffusion. Consistency of direction between the fracture hole centerline and the maximum principal stress contributes to damage propagation, and the key to fracture-enhanced extraction is whether damage connection across the hole. The Non-Darcy factor evolution is tortuous, and the Non-Darcy effect is the most significant in the dehydration period which can reduce the extraction volume by 0.04–1.7%, and is directly proportional to Non-Darcy flow coefficient.

Investigation on the effect of metal foam properties on the PCM melting performance subjected to various heat fluxes

The purpose of this paper is to analyze the effects of structural and mechanical characteristics of metal foam on the melting behavior of phase change materials under the influence of different heat fluxes. To this aim, a two dimensional numerical model considering the non-equilibrium thermal factor, non-Darcy effect and local natural convection was used. The governing equations of PCM and metal foam are discretized using a finite volume method with a collocated grid arrangement. To simulate the melting of PCM, the enthalpy-porosity method is applied which computes the liquid fraction at each iteration, based on the enthalpy balance. The effect of metal foam characteristics (porosity, pores size and base material) and wall heat flux on the PCM melting time were investigated. The result showed that for both wall heat fluxes (4000 W m-2 and 8000 W m-2), foam structure and its mechanical properties have significant influence on the PCM melting time which these effects should be considered.

Transient behaviour of heat transfer with complete evaporation process in Porous Channel with localised heating using non-Darcian flow and LTNE model

This study numerically presents the transient behaviour of complete evaporation process inside porous channel. Based on the modified enthalpy formulation under non-Darcy flow and Local Thermal Non-Equilibrium (LTNE) conditions, solutions have been obtained utilizing the finite volume method for various relevant parameters. The results have been validated with the experiments and they show good agreement between them. The results demonstrate that LTNE model should be employed while modelling the transient complete evaporation process in porous media. The non-Darcy effects have considerable influences on the locations of the initiation and termination of the phase change processes as compared to Darcy flow model. Therefore, the behaviours of the two-phase and the superheated vapour zones, when the steady-state solutions is reached, are substantially changed for non-Darcy flow as compared to Darcy model due this assumption provides an additional mechanism for heat transfer that represented by the heat exchange between the solid and fluid phases. It has been observed that the two-phase zone is considerably extended in the axial direction and this zone has not been occupied a large size towards transverse direction due to the axial velocity is noticeably higher than the transverse velocity, caused by reducing the diffusive energy through the two-phase region. The results indicate that non-Darcian effects leads to considerably extend the size of superheated region towards the outlet of the channel, which is not the case for Darcy model. The non-Darican effects become more pronounced for high Reynolds number and heat flux. The influences of varying in Reynolds number, heat flux, porosity, and solid thermal conductivity are substantial near the heated surface, whereas Darcy number has a minor impact on the solution of complete evaporation process. It can be emphasised from the present predictions that the non-Darcy flow along with LTNE condition is indispensable model for the complete evaporation process, especially under high mass flowrate as well heat flux.

Improving two-phase mass transportation under Non-Darcy flow effect in orientated-type flow channels of proton exchange membrane fuel cells

Orientated-type flow channels of proton exchange membrane fuel cells cause non-Darcy effect occurring in flow regions. Therefore, the species transportation is affected by inertial effect. However, how the inertial force affects convection and diffusion of different species has not been discussed before. Thus, a modified two-dimensional, non-isothermal, two-phase and steady state model considering non-Darcy effect is employed in this study, and reactants and products transportations through diffusion and convection under inertial effects are quantitatively analyzed for the first time. Simulation results reveal that the convective transportation of reactants increases more under the influence of inertial force; water vapor transportation through convection increases the water content in porous regions. At the same time, liquid water expels more rapidly from gas diffusion layers under baffle regions, and enlarging baffle volumes increases the regions where the liquid water is rapidly removed under the inertial effect.

Two-Dimensional Numerical Analysis of Non-Darcy Flow Using the Lattice Boltzmann Method: Pore-Scale Heterogeneous Effects

Abstract This study simulates pore-scale two-dimensional flows through porous media composed of circular grains with varied pore-scale heterogeneity to analyze non-Darcy flow effects on different types of porous media using the lattice Boltzmann method. The magnitude of non-Darcy coefficients and the critical Reynolds number of non-Darcy flow were computed from the simulation results using the Forchheimer equation. Although the simulated porous materials have similar porosity and representative grain diameters, larger non-Darcy coefficients and an earlier onset of non-Darcy flow were observed for more heterogeneous porous media. The simulation results were compared with existing correlations to predict non-Darcy coefficients, and the large sensitivity of non-Darcy coefficients to pore-scale heterogeneity was identified. The pore-scale heterogeneity and resulting flow fields were evaluated using the participation number. From the computed participation numbers and visualized flow fields, a significant channeling effect for heterogeneous media in the Darcy flow regime was confirmed compared with that for homogeneous media. However, when non-Darcy flow occurs, this channeling effect was alleviated. This study characterizes non-Darcy effect with alleviation of the channeling effect quantified with an increase in participation number. Our findings indicate a strong sensitivity of magnitude and onset of non-Darcy effect to pore-scale heterogeneity and imply the possibility of evaluating non-Darcy effect through numerical analysis of the channeling effect.

Efficient thermal management of the photovoltaic/phase change material system with innovative exterior metal-foam layer

This research proposes an innovative configuration for modifying the thermal management system of the photovoltaic (PV) panel, integrated with a phase-change material (PCM) with an attached exterior metal-foam layer to the rear part of the PCM container. The configuration enables faster heat dissipation from the system leading to longer thermal-management duration for the PV panel during the energy storage (PCM charging) mode. Also, it supports faster energy recovery (PCM discharging) rate by decreasing the amount of heat trapped in the melted part of the PCM during the solidification mode. The effects of the foam-layer inclusion, PCM thickness, and PV tilt angle are numerically simulated and revealed. A mathematical model that accounts for natural convection effects of the melted PCM and non-Darcy effects of the metal foam, is formulated and validated via previous experiments. The results show that inclusion of an exterior foam layer could increase the PCM melting time, and the corresponding PV thermal-management duration, by up to 32% and 55% respectively, depending on the PCM thickness and PV tilt angle. The results also show that reducing the tilt angle from 90° to 30° increases the melting time by about 18%. Thus, a superior PCM-based thermal management is achieved. Moreover, utilizing PCM of thickness in the range of 20–30 mm lengthens the melting time by up to 54%, enhancing the potential for improved thermal management of PV panels.

Transition from linear to nonlinear flow in single rough fractures: effect of fracture roughness

A series of laboratory experiments on water flow through rough fractures was performed using self-designed experimental devices to investigate the effect of fracture roughness on the flow behavior. Nine models of single rough fractures—with three joint roughness coefficients (JRCs) of 0–2, 8–10 and 18–20, and three apertures for each JRC—were prepared using three-dimensional printing technology. In the flow experiments, the values of Reynolds numbers ranged widely from less than 10 to around 10,000. According to the experimental data, the fracture roughness has an obvious influence on the hydraulic properties of fractures. A parametric expression for the Forchheimer equation was proposed to quantitatively describe the influence of fracture roughness on the flow behaviour in the fractures. The relations between the parameters for nonlinear flow (such as critical Reynolds number, non-Darcy effect coefficient and friction factor) and the JRCs were obtained. It was found that the critical Reynolds number decreased significantly from 566 to 67 as the JRC increased from 2 to 20. The increase in fracture roughness causes more extra energy losses and enhances the degree of flow nonlinearity in single fractures.

Pore network extraction for shale gas flow in nanoporous media

Most of pore network models were originally designed for conventional porous media (e.g. sandstone), where pore size is at micron-scale and the dominant flow is Darcy-flow. However, those models could be inapplicable for shale (a typical unconventional porous media), since plenty of nanopores exist therein and therefore the non-Darcy effects can no longer be ignored. In this contribution, the details of shale gas flow were analyzed, and it was found that flow resistance could be misestimated by previous models. For this reason, we propose a pore network model that takes into account the influences of non-Darcy effects on pore structure. In the model, pore/throat radius and throat length are not constant but change with pressure, which is distinguishable from previous models where parameters are independent of pressure. The proposed model and previous models are defined as apparent pore network (APN) and intrinsic pore network (IPN), respectively. A shale sample, imaged by focused ion beam-scanning electron microscope, was used to extract APN and IPN, and then, their network structures were compared in the terms of throat length and throat radius. Under different pressure conditions (ranging from 0.1 MPa to 48 MPa) and image resolutions (5 nm, 10 nm, 20 nm, 50 nm, and 100 nm), shale gas flow was simulated through APN and IPN, respectively. Numerical results show that apparent permeability is likely to be erroneously predicted by IPN, while APN provides a relatively reasonable solution.