Applying Method of Characteristics to Determine Pressure Distribution in 1D Shale-Gas Samples

SPE Journal ◽  
2013 ◽  
Vol 19 (03) ◽  
pp. 361-372 ◽  
Author(s):  
R. Ghanbarnezhad Moghanloo ◽  
F.. Javadpour
Keyword(s):  
Pressure Distribution ◽  
Shale Gas ◽  
Gas Flow ◽  
Method Of Characteristics ◽  
Continuum Approximation ◽  
Apparent Permeability ◽  
Reservoir Performance ◽  
Pressure Profiles ◽  
Slippage Effect ◽  
Gas Expansion

Summary This paper examines application of the method of characteristics (MOC) to determine pressure distribution in a 1D matrix of shale gas. Because of gas expansion and local desorption in shale gas, pressure distribution changes during production. We developed a semianalytic MOC solution of gas flow in shale by use of the analogous-continuum approximation (apparent permeability). The MOC solution is derived with the inclusion of compressibility, gas-slippage effect, and desorption. Through quantitative comparison of pressure profiles and history plots, we used a simulation approach to verify the accuracy of the analytic solution. Results suggest that the simulation results are consistent with our MOC solution, which can also be used to evaluate impacts of different parameters on pressure distribution. Prediction of pressure distribution over time will greatly enhance approximation of reservoir performance.

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 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.

Rarefaction Effect on Gas Flow in Microchannels with Various Aspect Ratios

2016 ◽  
Vol 33 (1) ◽  
pp. N1-N6 ◽  
Author(s):  
C.-Y. Huang ◽  
J.-S. Li
Keyword(s):  
Pressure Distribution ◽  
Gas Flow ◽  
Narrow Channel ◽  
Maximum Deviation ◽  
Pressure Sensitive Paint ◽  
Pressure Data ◽  
Aspect Ratios ◽  
Pressure Sensitive ◽  
Rarefaction Effect ◽  
Pressure Profiles

AbstractThis study investigated the effect of rarefaction on microchannel gas flow by measuring pressure profiles in microchannels with various aspect ratios. Pressure-sensitive paint (PSP) was applied in rectangular microchannels to obtain the global flow field by using detailed pressure data. The effect of rarefaction on the microchannel gas flow was clearly observed in the microchannels through the pressure data obtained using PSP measurements. A nonlinear pressure distribution was observed inside the microchannels, and this distribution decreased as the Knudsen number (Kn) increased because of the rarefaction effect. The dimensionless pressure deviation from the linear assumption dropped from 0.25 to 0 when the outlet Kn number increased to 0.066 in the 100-μm-wide microchannel, and the dimensionless location of the maximum deviation moved upstream because of the gaseous slip at the wall. The nonlinear pressure distribution also decreased in the 50-μm-wide microchannel as the outlet Kn number increased; however, the peak of the maximum deviation could no longer be identified because of the characteristic of the narrow channel.

scholarly journals A Mathematical Pressure Transient Analysis Model for Multiple Fractured Horizontal Wells in Shale Gas Reservoirs

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Yan Zeng ◽  
Qing Wang ◽  
Zhengfu Ning ◽  
Hongliang Sun
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Horizontal Wells ◽  
Analysis Model ◽  
Fracture Permeability ◽  
Gas Reservoirs ◽  
Apparent Permeability ◽  
Matrix Permeability ◽  
Fractured Horizontal Wells ◽  
Half Length

Multistage fractured horizontal wells (MFHWs) have become the main technology for shale gas exploration. However, the existing models have neglected the percolation mechanism in nanopores of organic matter and failed to consider the differences among the reservoir properties in different areas. On that account, in this study, a modified apparent permeability model was proposed describing gas flow in shale gas reservoirs by integrating bulk gas flow in nanopores and gas desorption from nanopores. The apparent permeability was introduced into the macroseepage model to establish a dynamic pressure analysis model for MFHWs dual-porosity formations. The Laplace transformation and the regular perturbation method were used to obtain an analytical solution. The influences of fracture half-length, fracture permeability, Langmuir volume, matrix radius, matrix permeability, and induced fracture permeability on pressure and production were discussed. Results show that fracture half-length, fracture permeability, and induced fracture permeability exert a significant influence on production. A larger Langmuir volume results in a smaller pressure and pressure derivative. An increase in matrix permeability increases the production rate. Besides, this model fits the actual field data relatively well. It has a reliable theoretical foundation and can preferably describe the dynamic changes of pressure in the exploration process.

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.

The Seepage Pressure Distribution and the Capacity of Low-Permeability Reservoirs Gas

2013 ◽  
Vol 734-737 ◽  
pp. 1317-1323
Author(s):  
Liang Dong Yan ◽  
Zhi Juan Gao
Keyword(s):  
Mathematical Model ◽  
Pressure Distribution ◽  
Low Permeability ◽  
Flow State ◽  
Klinkenberg Effect ◽  
Gas Reservoirs ◽  
Gas Well ◽  
Seepage Pressure ◽  
Slippage Effect ◽  
Low Permeability Reservoirs

Low-permeability gas reservoirs are influenced by slippage effect (Klinkenberg effect) , which leads to the different of gas in low-permeability and conventional reservoirs. According to the mechanism and mathematical model of slippage effect, the pressure distribution and flow state of flow in low-permeability gas reservoirs, and the capacity of low-permeability gas well are simulated by using the actual production datum.

A permeability model for gas flow in coal considering the water content and slippage effect

2020 ◽  
Vol 3 (4) ◽  
pp. 305
Author(s):  
Jianhua Li ◽  
Bobo Li ◽  
Jiang Xu ◽  
Zhihe Wang ◽  
Zheng Gao ◽  
...  
Keyword(s):  
Water Content ◽  
Gas Flow ◽  
Permeability Model ◽  
Slippage Effect
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