A Semi-analytical Model For Multi-stage Fractured Horizontal Wells

Abstract

Abstract Multi-stage fractured horizontal wells are widely applied to develop tight reservoirs and shale gas reservoirs. Testing and evaluating well productivity are necessary in horizontal well multi-stage fracturing. Through analyzing the post-fracturing transient pressure data, key parameters affecting the productivity, such as effective fracture lengths, fracture conductivities, fracture skin factors and average formation permeability, can be estimated. This paper presents a semi-analytical model based on Green’s function and source/sink method to facilitate the transient pressure analysis for a multi-stage fractured horizontal well in a closed box-shaped reservoir. The fluid flow for a multi-stage fractured horizontal well includes the fluid flowing from the reservoir to fractures, the fluid directly from the reservoir to the horizontal wellbore, fluid flow inside the fractures and fluid flow inside the horizontal wellbore. Compared with previous models, fluid flow directly from the reservoir to the horizontal wellbore and pressure drop caused by pipe flow inside the wellbore are considered. In this model, fractures and horizontal wellbore are discretized into vertical plane segments and horizontal line segments, respectively. The fluid flow from the reservoir to fracture and that directly from the reservoir to the horizontal wellbore at each segment are modeled based on analytical solutions of vertical plane source and horizontal line source, respectively. The fluid flow inside the fracture is modeled based on 1-D linear flow. The fluid flow inside the horizontal wellbore is described with Penmatcha and Aziz’s model (1999). Then, the flow equations are coupled together by using the flux- and pressure-continuity conditions on the interfaces. The effects of the fracture lengths, fracture conductivities and fracture skin factors on the transient pressure behavior are studied and type curves are generated. The results suggested that in a tight or shale-gas reservoir, the transient pressure behavior during a testing period is mainly dominated by fracture stages, fracture lengths, conductivities and skin factors. The fluid flow directly from the reservoir into the horizontal wellbore reduces the pressure drop slightly. A field case is analyzed and reliable results are obtained. This model can be applied to optimize the fracture spacing and fracture length for a multistage fractured horizontal well.