A Five-Linear Anomalous-Diffusion Model for Fractured Horizontal Well in Fractal Tight Oil Reservoir

Abstract

Multi-stage fractured horizontal well is currently the most effective way to exploit tight oil reservoirs. The stimulated reservoir volume in the Multi-stage fractured horizontal well can be regarded as fractal porous media. Anomalous diffusion models have been proposed to investigate pressure transient behaviors in fractal porous media. However, these models pay little attention to the effect of the unstimulated reservoir volume. An anomalous diffusion model based on five flow region model for multi-stage fractured horizontal wells in tight oil reservoirs is presented in this paper. Execpt the extending from trilinear anomalous-diffusion to five-linear anomalous-diffusion model, this model also considers the effect of threshold-pressure gradient (TPG) in unstimulated reservoir volume. The Laplace transform is applied to obtain the Laplace space solution of a single crack at a closed boundary under fixed production conditions. Through the Stehfest numerical inversion calculation, the bottom hole pressure and pressure derivative values of the volume fracturing horizontal well are obtained. The differences and similarities of dimensionless wellbore pressure and pressure derivative curves between our solution and the classical trilinear dual-porosity model are delineated. Effect of fractional derivative of time and TPG on tight oil transient behavior are investigated. The model is tested with field cases and verified that the five-linear anomalous-diffusion model presented in this paper is useful for performance predictions and pressure transient analysis of fractured horizontal wells in tight oil reservoirs, which is of great significance for fracturing construction effect analysis and reservoir understanding.KeywordsRactal theoryVolume-fractured horizontal wellFive-linear flow modelParameter inversion