The elastic boundary value problem of extended modified Bessel equation and its application in fractal homogeneous reservoir

Li, Shunchu; Guo, Hong; Zheng, Pengshe; Dong, Xiaoxu; Zhao, Chaochao; Gui, Q. M.

doi:10.1007/s40314-020-1104-1

Cited by 12 publications

(5 citation statements)

References 22 publications

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“…( 9), the general solution can be converted into: On substituting Eqs. (61) and (62) into the system of ordinary differential equations and using the differential property of linearly independent combination [4,23], The following equation is obtained:…”

Section: Appendix B (Derivation Details)mentioning

confidence: 99%

“…In recent three years, the elastic outer boundary conditions have been applied to the reservoir seepage model [3,4], replacing the three special outer boundary conditions commonly used before. The results show that the elastic outer boundary conditions can better reflect the real situation of the reservoir than the special outer boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The results show that the elastic outer boundary conditions can better reflect the real situation of the reservoir than the special outer boundary conditions. At the same time, the similar construction method used to solve the reservoir seepage model has also been greatly developed [3][4][5][6][7], and the simple algebraic method used to solve the seepage model has provided great convenience for scholars.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of flow characteristics of the dual media shale gas reservoir with the elastic outer boundary

Zheng

et al. 2021

SN Appl. Sci.

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In order to more accurately describe the seepage characteristics of shale gas reservoirs, in this paper, an elastic outer boundary condition is introduced, and a new dual-media shale gas seepage model is established to describe the seepage characteristics of shale gas reservoirs more accurately, while considering the adsorption and desorption process. Combining Laplace transformation and Similar Structure Method, the solution of the percolation model is obtained in Laplace space. Furthermore, the solutions are inverted into real space with the Stehfest numerical inversion method. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The results show that the conventional three kinds of outer boundary conditions (infinite, constant pressure and closed) are actually three special cases of elastic outer boundary. The introduction of elastic outer boundary conditions not only expands the scope of data interpretation, but also closer to the actual situation of the outer boundary of the reservoir. The theory of similar structure greatly simplifies the complex process of solving the model and will have a far-reaching impact on the development of well test analysis software in the future.

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Section: Appendix B (Derivation Details)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of flow characteristics of the dual media shale gas reservoir with the elastic outer boundary

Zheng

et al. 2021

SN Appl. Sci.

Self Cite

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“…The model solving steps were simplified, and the influence of different parameters on the dimensionless bottom hole pressure and its derivative was analyzed. In 2019, Li et al [21] aimed at the idealization of the external boundary conditions (infinite, constant pressure, closed) of the traditional fractal homogeneous reservoir model, introduced the elastic external boundary conditions, and the fractal homogeneous reservoir seepage model was established. It was found that the elastic external boundary is located between the three ideal state boundaries, which can more truly reflect the seepage law.…”

Section: Introductionmentioning

confidence: 99%

Studying on the solution of fractal composite reservoir seepage model with linear fault under elastic outer boundary

Jiang,

Zheng,

et al. 2023

Preprint

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In this paper, a fractal composite reservoir seepage model considering wellbore storage and skin factor is established for composite reservoirs with linear faults. The traditional three ideal external boundary conditions are generalized into elastic external boundary conditions. Through the dimensionless transformation and laplace transformation of the seepage model, combined with the mirror reflection method and the superposition principle, the similar structure solution of the dimensionless bottom hole pressure with the fault located in the inner zone and the mirror well located in the inner and outer zones is obtained by using the similar structure method. The Stehfest numerical inversion method is used to draw the typical characteristic curve of dimensionless bottom hole pressure and pressure derivative in real space, and the sensitivity analysis of the parameters is carried out. The results show that on the one hand, the distance between the fault and the production well has a great influence on the dimensionless pressure at the bottom of the well. On the other hand, the introduction of the elastic outer boundary can better describe the seepage characteristics of the reservoir and is more general. The research results are of great significance to the mining strategy of composite reservoirs, and also provide a new theoretical basis for further study of composite reservoirs with linearfaults.

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“…Several researchers studied the fluid flow characteristics of the reservoirs with the EOB. Li et al [65] studied the seepage model for the homogeneous reservoir by introducing the EOB, and Li et al [66] discussed an elastic boundary value problem of the extended modified Bessel equation introducing the elastic boundary value condition, established the seepage model for fractal homogeneous reservoirs with the EOB, and obtained its solution. Kim et al [67] built the well-testing model for the DPRs with the EOB 2 Geofluids considering skin and wellbore storage and introducing effective well radius, and Zheng et al [68] established the dualporosity media seepage model for shale reservoirs with the EOB taking the adsorption and desorption processes into account.…”

Section: Introductionmentioning

confidence: 99%

Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition

Kim,

Han,

Song

et al. 2023

Geofluids

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Stress sensitivity and the elastic outer boundary (EOB) condition have a great effect on the analysis of the characteristics of the fluid flow in a reservoir. When researchers analyzed the characteristics of the fluid flow, they have considered the stress sensitivity and the EOB condition separately but have not considered them simultaneously. Therefore, errors are inevitable during the analysis of well testing. The main object of this work is to present a well-testing model for stress-sensitivity dual-porosity reservoir (DPR) with EOB to improve the accuracy of the analysis of well-testing data. To this end, in this paper, we established a well-testing model for the DPR, considering the stress sensitivity and the EOB simultaneously, and presented its semianalytical solution. On the basis of the consideration of the EOB condition and stress sensitivity of permeability (SSP), a seepage model for the DPR with the EOB is built using the continuity equation, motion equation, state equation, and interporosity flow equation between matrix and fracture, which considers the stress sensitivity, wellbore storage, and skin. To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. Applying the Laplace transformation, an analytical solution in the Laplace space is obtained, and curves of pressure and pressure derivative (PPD) are drawn by numerically inverting them. The model is verified by comparing it with the EOB without consideration of SSP and using case data. The sensitivity of parameters on the curves of PPD is analyzed. This work may be significant for evaluating more accurately the parameters of wells and reservoirs using well testing.

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The elastic boundary value problem of extended modified Bessel equation and its application in fractal homogeneous reservoir

Cited by 12 publications

References 22 publications

Analysis of flow characteristics of the dual media shale gas reservoir with the elastic outer boundary

Analysis of flow characteristics of the dual media shale gas reservoir with the elastic outer boundary

Studying on the solution of fractal composite reservoir seepage model with linear fault under elastic outer boundary

Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition

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