scholarly journals Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3381 ◽  
Author(s):  
Qiang Wang ◽  
Yongquan Hu ◽  
Jinzhou Zhao ◽  
Lan Ren ◽  
Chaoneng Zhao ◽  
...  
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Clear Understanding ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Shale Gas Transport

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.

A FRACTAL PERMEABILITY MODEL FOR REAL GAS IN SHALE RESERVOIRS COUPLED WITH KNUDSEN DIFFUSION AND SURFACE DIFFUSION EFFECTS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050017 ◽  
Author(s):  
TAO WU ◽  
SHIFANG WANG
Keyword(s):  
Fractal Dimension ◽  
Surface Diffusion ◽  
Shale Gas ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Real Gas ◽  
Shale Reservoirs

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

scholarly journals A non-empirical model for gas transfer through circular nanopores in unconventional gas reservoirs

2021 ◽  
Vol 11 (5) ◽  
pp. 2217-2232
Author(s):  
Jiangtao Li ◽  
Jianguang Wei ◽  
Liang Ji ◽  
Anlun Wang ◽  
Gen Rong ◽  
...  
Keyword(s):  
Gas Flow ◽  
Gas Transport ◽  
Transport Model ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Gas Reservoirs ◽  
Permeability Model ◽  
Proposed Model ◽  
Unconventional Gas Reservoirs ◽  
Empirical Coefficients

AbstractIt is difficult to predict the flow performance in the nanopore networks since traditional assumptions of Navier–Stokes equation break down. At present, lots of attempts have been employed to address the proposition. In this work, the advantages and disadvantages of previous analytical models are seriously analyzed. The first type is modifying a mature equation which is proposed for a specified flow regime and adapted to wider application scope. Thus, the first-type models inevitably require empirical coefficients. The second type is weight superposition based on two different flow mechanisms, which is considered as the reasonable establishment method for universal non-empirical gas-transport model. Subsequently, in terms of slip flow and Knudsen diffusion, the novel gas-transport model is established in this work. Notably, the weight factors of slip flow and Knudsen diffusion are determined through Wu’s model and Knudsen’s model respectively, with the capacity to capture key transport mechanism through nanopores. Capturing gas flow physics at nanoscale allows the proposed model free of any empirical coefficients, which is also the main distinction between our work and previous research. Reliability of proposed model is verified by published molecular simulation results as well. Furthermore, a novel permeability model for coal/shale matrix is developed based on the non-empirical gas-transport model. Results show that (a) nanoconfined gas-transport capacity will be strengthened with the decline of pressure and the decrease in the pressure is supportive for the increasing amplitude; (b) the greater pore size the nanopores is, the stronger the transport capacity the nanotube is; (c) after field application with an actual well in Fuling shale gas field, China, it is demonstrated that numerical simulation coupled with the proposed permeability model can achieve better historical match with the actual production performance. The investigation will contribute to the understanding of nanoconfined gas flow behavior and lay the theoretical foundation for next-generation numerical simulation of unconventional gas reservoirs.

scholarly journals Prediction of Production Performance of Refractured Shale Gas Well considering Coupled Multiscale Gas Flow and Geomechanics

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21 ◽  
Author(s):  
Zhiqiang Li ◽  
Zhilin Qi ◽  
Wende Yan ◽  
Zuping Xiang ◽  
Xiang Ao ◽  
...  
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Stress Sensitivity ◽  
Production Performance ◽  
Design Parameters ◽  
Production Loss ◽  
Apparent Permeability ◽  
Gas Well ◽  
The Matrix

Production simulation is an important method to evaluate the stimulation effect of refracturing. Therefore, a production simulation model based on coupled fluid flow and geomechanics in triple continuum including kerogen, an inorganic matrix, and a fracture network is proposed considering the multiscale flow characteristics of shale gas, the induced stress of fracture opening, and the pore elastic effect. The complex transport mechanisms due to multiple physics, including gas adsorption/desorption, slip flow, Knudsen diffusion, surface diffusion, stress sensitivity, and adsorption layer are fully considered in this model. The apparent permeability is used to describe the multiple physics occurring in the matrix. The model is validated using actual production data of a horizontal shale gas well and applied to predict the production and production increase percentage (PIP) after refracturing. A sensitivity analysis is performed to study the effects of the refracturing pattern, fracture conductivity, width of stimulated reservoir volume (SRV), SRV length of new and initial fractures, and refracturing time on production and the PIP. In addition, the effects of multiple physics on the matrix permeability and production, and the geomechanical effects of matrix and fracture on production are also studied. The research shows that the refracturing design parameters have an important influence on the PIP. The geomechanical effect is an important cause of production loss, while slippage and diffusion effects in matrix can offset the production loss.

The Calculation of Apparent Permeability for Shale Gas Considering Adsorption and Flow Patterns

2014 ◽  
Vol 1073-1076 ◽  
pp. 2305-2309
Author(s):  
Wen Xu She ◽  
Jun Bin Chen ◽  
Jie Zhang ◽  
Bo Wei ◽  
Han Qing Wang ◽  
...  
Keyword(s):  
Pore Size ◽  
Flow Pattern ◽  
Shale Gas ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Great Influence ◽  
Flow Patterns ◽  
Apparent Permeability ◽  
Longmaxi Formation ◽  
Shale Reservoirs

The flow pattern is unique in a certain range of pore size divided by the Knudsen number. In order to characterize permeability of nanopore in shale gas reservoir more accurately, the formulas of nanopore permeability are put forward considering the influence of adsorption gas and flow patterns. After the calculated results were compared and analyzed, the conclusions are obtained as follows: (1) Pore size is the main factor to determine the flow pattern; (2) There are three main flow pattern in the nanopore of Longmaxi formation shale reservoirs, slip flow, Fick diffusion and transition diffusion, meanwhile Darcy percolation and Knudsen diffusion do not exist; (3) Flow pattern has great influence on apparent permeability and adsorption has a greater impact in a high pressure condition (greater than 20MPa).

A slip-flow model for multi-component shale gas transport in organic nanopores

2019 ◽  
Vol 12 (5) ◽  
Author(s):  
Fengrui Sun ◽  
Yuedong Yao ◽  
Guozhen Li ◽  
Xiangfang Li
Keyword(s):  
Shale Gas ◽  
Flow Model ◽  
Gas Transport ◽  
Slip Flow ◽  
Shale Gas Transport

A Novel Multiphysics Multiscale Multiporosity Shale Gas Transport Model for Geomechanics/Flow Coupling in Steady and Transient States

SPE Journal ◽  
2021 ◽  
pp. 1-13
Author(s):  
Zihao Li ◽  
Yuntian Teng ◽  
Ming Fan ◽  
Nino Ripepi ◽  
Cheng Chen
Keyword(s):  
Pore Pressure ◽  
Shale Gas ◽  
Gas Transport ◽  
Model Parameters ◽  
Apparent Permeability ◽  
Transient States ◽  
Effective Stresses ◽  
Microscale Model ◽  
Model Component ◽  
Shale Gas Transport

Summary A novel multiphysics multiscale multiporosity shale gas transport (M3ST) model was developed to investigate shale gas transport in both transient and steady states. The microscale model component contains a kerogen domain and an inorganic matrix domain, and each domain has its own geomechanical and gas transport properties. Permeabilities of various shale cores were measured in the laboratory using a pulse decay permeameter (PDP) with different pore pressure and confining stress combinations. The PDP-measured apparent permeability as a function of pore pressure under two effective stresses was fitted using the microscale M3ST model component based on nonlinear least squares fitting (NLSF), and the fitted model parameters were able to provide accurate model predictions for another effective stress. The parameters and petrophysical properties determined in the steady state were then used in the transient-state,continuum-scale M3ST model component, which performed history matching of the evolutions of the upstream and downstream gas pressures. In addition, a double-exponential empirical model was developed as a powerful alternative to the M3ST model to fit laboratory-measured apparent permeability under various effective stresses and pore pressures. The developed M3ST model and the research findings in this study provided critical insights into the role of the multiphysics mechanisms, including geomechanics, fluid dynamics and transport, and the Klinkenberg effect on shale gas transport across different spatial scales in both steady and transient states.

A New Unified Gas-Transport Model for Gas Flow in Nanoscale Porous Media

SPE Journal ◽  
2019 ◽  
Vol 24 (02) ◽  
pp. 698-719 ◽  
Author(s):  
Di Chai ◽  
Zhaoqi Fan ◽  
Xiaoli Li
Keyword(s):  
Viscous Flow ◽  
Pore Size ◽  
Surface Diffusion ◽  
Gas Flow ◽  
Gas Transport ◽  
Transport Model ◽  
Knudsen Diffusion ◽  
Apparent Permeability ◽  
Real Gas ◽  
Reservoir Conditions

Summary A new unified gas-transport model has been developed to characterize single-component real-gas flow in nanoscale organic and inorganic porous media by modifying the Bravo (2007) model. More specifically, a straight capillary tube is characterized by a conceptual layered model consisting of a viscous-flow zone, a Knudsen-diffusion zone, and a surface-diffusion zone. To specify the contributions of the viscous flow and the Knudsen diffusion to the gas transport, the virtual boundary between the viscous-flow and Knudsen-diffusion zones is first determined using an analytical molecular-kinetics approach. As such, the new unified gas-transport model is derived by integrating the weighted viscous flow and Knudsen diffusion, and coupling surface diffusion. The model is also comprehensively scaled up to the bundles-of-tubes model considering the roughness, rarefaction, and real-gas effect. Nonlinear programming methods have been used to optimize the empirical parameters in the newly proposed gas-transport model. Consequently, the newly proposed gas-transport model yields the most accurate molar fluxes compared with the Bravo (2007) model and four other analytical models. One of the advantages of the new unified gas-transport model is its great flexibility, because the Knudsen number is included as an independent variable, which also endows the newly proposed model with the capability to cover the full-flow regimes. In addition, the apparent permeability has been mathematically derived from the new unified gas-transport model. A series of simulations has been implemented using methane gas. It is found through sensitivity analysis that apparent permeability is strongly dependent on pore size, porosity, and tortuosity, and weakly dependent on the surface-diffusivity coefficient and pore-surface roughness. The increased viscosity can reduce the total molar flux in the inorganic pores up to 66.0% under the typical shale-gas-reservoir conditions. The viscous-flow mechanism cannot be neglected at any pore sizes under reservoir conditions, whereas the Knudsen diffusion is found to be important when pore size is smaller than 2 nm and pressure is less than 35.0 MPa. The contribution of surface diffusion cannot be ignored when the pore size is smaller than 10 nm and the pressure is less than 15.0 MPa.

scholarly journals An Apparent Gas Permeability Model for Real Gas Flow in Fractured Porous Media with Roughened Surfaces

Polymers ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 1937
Author(s):  
Tao Wu ◽  
Qian Wang ◽  
Shifang Wang
Keyword(s):  
Porous Media ◽  
Gas Flow ◽  
Chemical Engineering ◽  
Gas Permeability ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Fractured Porous Media ◽  
Permeability Model ◽  
Real Gas ◽  
Apparent Gas Permeability

The investigation of gas transport in fractured porous media is essential in most petroleum and chemical engineering. In this paper, an apparent gas permeability model for real gas flow in fractured porous media is derived with adequate consideration of real gas effect, the roughness of fracture surface, and Knudsen diffusion based on the fractal theory. The fractal apparent gas permeability model is obtained to be a function of micro-structural parameters of fractured porous media, relative roughness, the pressure, the temperature, and the properties of gas. The predictions from the apparent gas permeability model based on the fractal theory match well with the published permeability model and experimental data, which verifies the rationality of the present fractal apparent gas permeability model.

A NEW FRACTAL TRANSPORT MODEL OF SHALE GAS RESERVOIRS CONSIDERING MULTIPLE GAS TRANSPORT MECHANISMS, MULTI-SCALE AND HETEROGENEITY

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850096 ◽  
Author(s):  
WEIPENG FAN ◽  
HAI SUN ◽  
JUN YAO ◽  
DONGYAN FAN ◽  
KAI ZHANG
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Transport Mechanisms ◽  
Apparent Permeability ◽  
Multi Scale ◽  
Inorganic Systems ◽  
Inorganic Matter ◽  
Fractal Characteristics

Duo to different transport mechanisms and gas storage in organic and inorganic systems, a new triple-continuum model coupling Discrete Fracture Model (DFM) was established to investigate gas flow in shale gas reservoir. Considering the multi-scale and heterogeneity of shale matrix, fractal theory was used to calculate the apparent permeability of organic and inorganic systems while multiple gas transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, gas absorption/desorption effect and real gas effect were incorporated. This coupled mathematical model was solved by Finite Element Method (FEM) and the presented fractal apparent permeability model was validated with the experimental data. The results show that fractal characteristics of shale matrix have great impact on gas reservoir performance. The model without considering the influence of fractal characteristics could lead to underestimate gas production by approximately 17%. Viscous flow is the dominate transport mechanisms of shale gas and Knudsen diffusion has an impact on gas flow when the pressure declines. Surface diffusion should be only considered in organic systems and can be ignored. Then the results of sensitivity analysis show that the characteristic parameters of inorganic matter have a greater impact than those of organic matter and establishing a triple-continuum model with considering comprehensive effect of organic and inorganic matter is necessary. In addition, gas production would decrease as the pore fractal dimension and tortuosity fractal dimension increase, which results from the increasing number of small pores and more tortuous path for gas flow.

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