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Energies 2019, 12(1), 176; https://doi.org/10.3390/en12010176

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

1,* , 1
,
1
and
1,2
1
Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
2
Downhole Operation Company, Sinopec North China Petroleum Bureau, Zhengzhou 450042, China
*
Author to whom correspondence should be addressed.
Received: 13 November 2018 / Revised: 16 December 2018 / Accepted: 30 December 2018 / Published: 6 January 2019
(This article belongs to the Section Energy Sources)
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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. View Full-Text
Keywords: asymptotic solution; pseudosteady state productivity index; fractured wells; proppant number; fracture geometry optimization asymptotic solution; pseudosteady state productivity index; fractured wells; proppant number; fracture geometry optimization
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Gao, H.; Hu, Y.; Duan, L.; Ai, K. An Analytical Solution of the Pseudosteady State Productivity Index for the Fracture Geometry Optimization of Fractured Wells. Energies 2019, 12, 176.

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