RETRACTED: Application of Symmetry Law in Numerical Modeling of Hydraulic Fracturing by Finite Element Method

Sun, Shanhui; Zhou, Meihua; Lu, Weicong; Davarpanah, Afshin

doi:10.3390/sym12071122

Cited by 49 publications

(19 citation statements)

References 37 publications

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“…The aperture b can be determined as ft(x) − fl(x) according to Equations (12) and (13). If thermal diffusion in the fluid is not considered, the boundary conditions in Equations (10) and 11are substituted into Equations (5) and 6; a temperature distribution equation of fluid can be expressed as:…”

Section: Heat Transport Modelmentioning

confidence: 99%

“…Geothermal energy, which is clean, renewable, and widespread, has been developed and utilized in many countries, and considerable attention has been given to exploiting thermal energy from hot dry rock (HDR) 3-10 km underground, using the enhanced geothermal system (EGS) to exchange and loop heat in/out of effectively connected systems of underground fractures [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For example, the Landau plant in Germany [15], the Soultz plant in France [16], and the recently commissioned Geodynamics Habanero pilot plant [17] demonstrate the feasibility of EGS running.…”

Section: Introductionmentioning

confidence: 99%

“…Temperature contour of fracture profile with different JRC(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20).…”

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confidence: 99%

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A Novel Procedure for Coupled Simulation of Thermal and Fluid Flow Models for Rough-Walled Rock Fractures

2021

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An enhanced geothermal system (EGS) proposed on the basis of hot dry rock mining technology has become a focus of geothermal research. A novel procedure for coupled simulation of thermal and fluid flow models (NPCTF) is derived to model heat flow and thermal energy absorption characteristics in rough-walled rock fractures. The perturbation method is used to calculate the pressure and flow rate in connected wedge-shaped cells at pore-scale, and an approximate analytical solution of temperature distribution in wedge-shaped cells is obtained, which assumes an identical temperature between the fluid and fracture wall. The proposed method is verified in Barton and Choubey (1985) fracture profiles. The maximum deviation of temperature distribution between the proposed method and heat flow simulation is 13.2% and flow transmissivity is 1.2%, which indicates the results from the proposed method are in close agreement with those obtained from simulations. By applying the proposed NPCTF to real rock fractures obtained by a 3D stereotopometric scanning system, its performance was tested against heat flow simulations from a COMSOL code. The mean discrepancy between them is 1.51% for all cases of fracture profiles, meaning that the new model can be applicable for fractures with different fracture roughness. Performance analysis shows small fracture aperture increases the deviation of NPCTF, but this decreases for a large aperture fracture. The accuracy of the NPCTF is not sensitive to the size of the mesh.

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Section: Heat Transport Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Novel Procedure for Coupled Simulation of Thermal and Fluid Flow Models for Rough-Walled Rock Fractures

2021

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“…A variety of mesh-generated techniques, such as the boundary element method [13], finite element method [14,15], finite volume method [16,17], and finite difference method [18,19], have been proposed to analyze heterogeneous layered porous media. In contrast with conventional mesh-generated techniques, meshfree approaches have attracted much attention in recent years because of their characteristics of simplicity, meshfree, and the capability to deal with engineering problems with complex geometry [20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

Hong

Liu

et al. 2021

Applied Sciences

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In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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“…In order to analyze production data and make long-term forecasts, analytical and numerical tools have been developed. Among them, a large number of numerical approaches [4][5][6][7][8], such as finite element method and boundary element method, are adopted to study the multiple flow mechanisms and fracture characteristics in shale gas reservoirs. Compared with the numerical models, the analytical models are simpler to set up and require fewer original data.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Model for Production Analysis of Hydraulically Fractured Shale Gas Reservoirs Considering Irregular Stimulated Regions

Qiu

2020

Energies

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Shale gas reservoirs are typically developed by multistage, propped hydraulic fractures. The induced fractures have a complex geometry and can be represented by a high permeability region near each fracture, also called stimulated region. In this paper, a new integrative analytical solution coupled with gas adsorption, non-Darcy flow effect is derived for shale gas reservoirs. The modified pseudo-pressure and pseudo-time are defined to linearize the nonlinear partial differential equations (PDEs) and thus the governing PDEs are transformed into ordinary differential equations (ODEs) by integration, instead of the Laplace transform. The rate vs. pseudo-time solution in real-time space can be obtained, instead of using the numerical inversion for Laplace transform. The analytical model is validated by comparison with the numerical model. According to the fitting results, the calculation accuracy of analytic solution is almost 99%. Besides the computational convenience, another advantage of the model is that it has been validated to be feasible to estimate the pore volume of hydraulic region, stimulated region, and matrix region, and even the shape of regions is irregular and asymmetrical for multifractured horizontal wells. The relative error between calculated volume and given volume is less than 10%, which meets the engineering requirements. The model is finally applied to field production data for history matching and forecasting.

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RETRACTED: Application of Symmetry Law in Numerical Modeling of Hydraulic Fracturing by Finite Element Method

Cited by 49 publications

References 37 publications

A Novel Procedure for Coupled Simulation of Thermal and Fluid Flow Models for Rough-Walled Rock Fractures

A Novel Procedure for Coupled Simulation of Thermal and Fluid Flow Models for Rough-Walled Rock Fractures

Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

An Analytical Model for Production Analysis of Hydraulically Fractured Shale Gas Reservoirs Considering Irregular Stimulated Regions

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