An Analytical Solution of the Pseudosteady State Productivity Index for the Fracture Geometry Optimization of Fractured Wells

Hui Gao, Yule Hu, Longchen Duan and Kun Ai
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Hui Gao: Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
Yule Hu: Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
Longchen Duan: Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
Kun Ai: Faculty of Engineering, China University of Geosciences, Wuhan 430074, China

Energies, 2019, vol. 12, issue 1, 1-22

Abstract: The pseudosteady state productivity index is very important for evaluating the production from oil and gas wells. It is usually used as an objective function for the optimization of fractured wells. However, there is no analytical solution for it, especially when the proppant number of the fractured well is greater than 0.1. This paper extends the established fitting solution for proppant numbers less than 0.1 by introducing an explicit expression of the shape factor. It also proposes a new asymptotic solution based on the trilinear-flow model for proppant numbers greater than 0.1. The two solutions are combined to evaluate the pseudosteady state productivity index. The evaluation results are verified by the numerical method. The new solution can be directly used for fracture geometry optimization. The optimization results are consistent with those given by the unified fracture design (UFD) method. Using the analytical solution for the pseudosteady state productivity index, optimization results can be obtained for rectangular drainage areas with arbitrary aspect ratios without requiring any interpolation or extrapolation. Moreover, the new solution provides more rigorous optimization results than the UFD method, especially for fractured horizontal wells.

Keywords: asymptotic solution; pseudosteady state productivity index; fractured wells; proppant number; fracture geometry optimization (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
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