Research on optimization of perforation parameters for formation fractures based on response surface optimization method

Abstract

For staged multi-cluster fracturing, methods for controlling perforation friction to adjust the flow distribution of each cluster can effectively promote the uniform extension of multiple fractures but lacks a fast and quantitative optimization method for different perforation parameters of each cluster. By establishing a numerical model of single-stage three-cluster flow-limited fracturing under stress-seepage coupling, and based on the response surface optimization method, fully considering the impact of perforation parameters interaction among three perforation clusters, according to the regression equation fitted under the global response, the rapid optimization of perforation parameters of segmented multi-cluster fracturing model is realized. The results show that: in determining the three factors of the study, it is found that there is an obvious interaction between the number of intermediate cluster perforations and the number of cluster perforations on both sides, the number of cluster perforations on both sides and the diameter of intermediate cluster perforations, the response surface optimization method gives the optimal perforation parameter combination of three clusters of fractures under global response; When the perforation parameters were combined before optimization, the fracture length difference was 32.550m, and the intermediate perforation cluster evolved into invalid perforation cluster, when the perforation parameters were combined after optimization, the fracture length difference was 0.528m, the three perforation clusters spread uniformly, and there are no invalid clusters. At the same time, the regression equation under the response is optimized before and after the comparison between the predicted value of the equation and the actual simulation value. It is found that the estimated deviation rate of the equation before optimization is 1.2%, and the estimated deviation rate after optimization is 0.4%. The estimated deviation rates are all less, and the response regression equation based on the response surface optimization method can quickly optimize the perforation parameters. The response surface optimization method is suitable for the multi parameter optimization research of formation fracturing which is often affected by many geological and engineering factors. Combining with the engineering practice and integrating more factors to optimize the hydraulic fracturing parameters, it is of great significance to improve the success rate of hydraulic fracturing application.

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“…The functional expression between the system response Y after design of experiments and the design variable x can be expressed as [ 30 , 31 ]: …”