A HYBRID NUMERICAL/ANALYTICAL MODEL OF TRANSIENT SEEPAGE FOR VERTICAL FRACTURED WELL IN TIGHT GAS RESERVOIR BY USE OF FRACTAL THEORY AND CONFORMAL MAPPING METHOD

Qianchen Cui, Yulong Zhao, Chengzhong Bu, Jian Zheng, Haoran Hu and Liehui Zhang
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Qianchen Cui: State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China
Yulong Zhao: State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China
Chengzhong Bu: ��Shale Gas Project Manager Department, Chuanqing Drilling Company, Chengdu, Sichuan 610051, P. R. China
Jian Zheng: ��Sichuan Changning Natural Gas Development Co., Ltd., Chengdu, Sichuan 610056, P. R. China
Haoran Hu: �Shale Gas Research Institute, PetroChina Southwest Oil & Gasfield Company, Chengdu, Sichuan 610051, P. R. China
Liehui Zhang: State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 08, 1-17

Abstract: Insufficient consideration of the complex morphology of hydraulic fractures (HF) and heterogeneous physical properties of fractured reservoirs in seepage models can result in unreliable well testing analyses. The fractal porosity and permeability (FPP) model provides an effective method for characterizing reservoir heterogeneity in the near-wellbore zone. However, its application to scenarios involving irregularly-shaped hydraulic fracture networks and multiple fracture clusters is challenging due to the lack of spatial symmetry. To address this issue, this paper proposes a combined approach of FPP and conformal mapping (FPP-CM) to transform the region of fractured formation into the exterior of the unit disk domain using numerical conformal mapping. The transient seepage flow model of the vertical fracture well (VFW) is then established by coupling it with the FPP model. The typical curve of pressure transient behavior with the division of flow stages was plotted, and the model verification and sensitivity analysis of parameters were conducted. The results indicate that the fractal dimension primarily affects the formation linear flow stage and its subsequent flow stages; with a decrease in fractal dimension resulting in an increase in the position of the typical curve. For VFW with multiple HF wings, a decrease in the included angle of fracture wings causes an increase in the heterogeneity distribution of microfracture physical properties, resulting in an increase in the position of the pseudo-pressure derivative curve during the late flow stage.

Keywords: Vertical Fractured Well; Transient Seepage Model; Fractal Theory; Conformal Mapping Method; Dual-Porosity Medium (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401801

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