Study on flow model of multi-stage fracturing horizontal well in stress-denpendent dual medium reservoir

Abstract

Often with abundant of natural fracture, Carbonate reservoirs are characterized with the stress sensitive and dual media. Mostly, its flow model solved by numerical method. In this paper, the semi-analytical solution for this problem is presented: firstly, the point source function considering stress sensitivity in infinite dual medium reservoir is obtained in Laplace space by Perturbation Transformation and Laplace Transformation; Secondly, the Laplace space solution of multi-stage fracturing horizontal well in infinite plate reservoir is obtained by Image Principle and Superposition Principle; Finally, the spacial solution of multi-stage fracturing horizontal well is obtained by Stehfest numerical inversion and perturbation inverse transformation. The calculation results show that the flow regime of multi-stage fracturing horizontal well can be divided into six stages: Ⅰ- linear flow, Ⅱ-first radial flow, Ⅲ-double radial flow, Ⅳ-radial flow of natural fracture system, Ⅴ-channeling flow regime and Ⅵ-radial flow of the whole system. The impact of stress sensitivity of formation permeability on linear flow is lower, and mainly affecting the last five flow regimes, and the dimensionless pressure drop derivative curve tends to rise in the later stage of development, showing the characteristics of closed boundary. In this paper, when the reservoir stress sensitivity is not considered, the calculation results will produce a large error, and the wrong well test interpretation will be obtained.