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.

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.

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

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Bo-ning Zhang ◽  
Xiao-gang Li ◽  
Yu-long Zhao ◽  
Cheng Chang ◽  
Jian Zheng
Keyword(s):  
Mathematical Models ◽  
Shale Gas ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Model Description ◽  
Transport Mechanisms ◽  
Gas Reservoirs ◽  
Flow Process ◽  
Type Curves ◽  
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.

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.

EDFM-based Multi-Continuum Shale Gas Simulation with Low Velocity Non-Darcy Water Flow Effect

2021 ◽  
Author(s):  
Yu Jiang ◽  
John Killough ◽  
Linkai Li ◽  
Xiaona Cui ◽  
Jin Tang
Keyword(s):  
Water Flow ◽  
Shale Gas ◽  
Gas Flow ◽  
Early Stage ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Darcy Flow ◽  
Low Velocity ◽  
Water Imbibition ◽  
The Impact

Abstract The exploitation of shale gas has attracted extensive attention in industry and academia. Multi-scale gas transportation mechanisms in matrix and fractures have been well studied. However, due to the presence of water originating from both fracking fluids and connate water, shale gas production is also greatly affected by water imbibition and flowback, of which the processes have not been thoroughly analyzed. This paper aims at presenting a comprehensive multi-continuum multi-component model to characterize the complicated shale gas flow behaviors as well as the impact of non-Darcy water flow on shale gas production. A two-phase numerical simulator is built up with multi-continuum settings. Shale matrix is split into organic and inorganic matters while natural and hydraulic fractures are modeled using an embedded discrete fracture model (EDFM). Fracture closure and elongation are modeled using a dynamic gridding approach. Different transportation mechanisms are considered to describe gas flow in shale, including Knudsen diffusion, ab/desorption, and convection. The low-velocity non-Darcy flow of water is used in inorganic pores to analyze the effect of water flow. A pre-stage model based on pumping history is simulated firstly before production starts. This serves as an initialization step to model fracking fluid imbibition and early-stage water flowback. This pre-stage simulation gives out more precise pressure and saturation profiles than the conventional non-equilibrium initialization method, especially in enhanced pore volumes and fractures. Based upon simulation results from the production period, Langmuir isotherm absorption has shown a massive impact on gas flow in shale, and Knudsen diffusion weights highest among transport mechanisms. Water non-Darcy flow better benefits in simulating both early-stage water flowback and production process compared with Darcy flow, which gives us a new explanation on the low flowback efficiency in real shale gas operations. Studies on early-stage water flowback also show that the flowback affects saturation distribution, which has a strong relationship with gas production and shall not be ignored. This work establishes a novel method to simulate and analyze shale gas production. It considers multiple and complex flow mechanisms and gives out better estimates of water flux. It is also used to initialize a model for pumping water imbibition and early-stage flowback, which can be used as technical resources for analyzing and simulating unconventional plays.

scholarly journals Gas Multiple Flow Mechanisms and Apparent Permeability Evaluation in Shale Reservoirs

2019 ◽  
Vol 11 (7) ◽  
pp. 2114 ◽  
Author(s):  
Xuelei Feng ◽  
Fengshan Ma ◽  
Haijun Zhao ◽  
Gang Liu ◽  
Jie Guo
Keyword(s):  
Pore Size ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Stress Sensitivity ◽  
Gas Production ◽  
Apparent Permeability ◽  
Matrix Shrinkage ◽  
Gas Seepage ◽  
Flow Mechanisms ◽  
Shale Reservoirs

Gas flow mechanisms and apparent permeability are important factors for predicating gas production in shale reservoirs. In this study, an apparent permeability model for describing gas multiple flow mechanisms in nanopores is developed and incorporated into the COMSOL solver. In addition, a dynamic permeability equation is proposed to analyze the effects of matrix shrinkage and stress sensitivity. The results indicate that pore size enlargement increases gas seepage capacity of a shale reservoir. Compared to conventional reservoirs, the ratio of apparent permeability to Darcy permeability is higher by about 1–2 orders of magnitude in small pores (1–10 nm) and at low pressures (0–5 MPa) due to multiple flow mechanisms. Flow mechanisms mainly include surface diffusion, Knudsen diffusion, and skip flow. Its weight is affected by pore size, reservoir pressure, and temperature, especially pore size ranging from 1 nm to 5 nm and reservoir pressures below 5 MPa. The combined effects of matrix shrinkage and stress sensitivity induce nanopores closure. Therefore, permeability declines about 1 order of magnitude compare to initial apparent permeability. The results also show that permeability should be adjusted during gas production to ensure a better accuracy.

scholarly journals Numerical Simulation of Shale Gas Multiscale Seepage Mechanism-Coupled Stress Sensitivity

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Xun Yan ◽  
Jing Sun ◽  
Dehua Liu
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Gas Transport ◽  
Sensitivity Coefficient ◽  
Stress Sensitivity ◽  
Gas Production ◽  
Molecular Flow ◽  
Adsorption Phenomenon ◽  
Gas Seepage ◽  
The Impact

The complexity of the gas transport mechanism in microfractures and nanopores is caused by the feature of multiscale and multiphysics. Figuring out the flow mechanism is of great significance for the efficient development of shale gas. In this paper, an apparent permeability model which covers continue, slip, transition, and molecular flow and geomechanical effect was presented. Additionally, a mathematical model comprising multiscale, geomechanics, and adsorption phenomenon was proposed to characterize gas flow in the shale reservoir. The aim of this paper is to investigate some important impacts in the process of gas transportation, which includes the shale stress sensitivity, adsorption phenomenon, and reservoir porosity. The results reveal that the performance of the multistage fractured horizontal well is strongly influenced by stress sensitivity coefficient. The cumulative gas production will decrease sharply when the shale gas reservoir stress sensitivity coefficient increases. In addition, the adsorption phenomenon has an influence on shale gas seepage and sorption capacity; however, the effect of adsorption is very weak in the early gas transport period, and the impact of later will increase. Moreover, shale porosity also greatly affects the shale gas transportation.

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.

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