Applying macroscopic material balance to evaluate interplay between dynamic drainage volume and well performance in tight formations

This study presents a novel approach to predict the production performance and evaluate the efficiency of fracturing stimulation. Despite the great success of fracturing operation in production from unconventional oil/gas resources, prediction of well performance is yet to be understood.We develop a mathematical model relating dynamic drainage volume and well deliverability in extremely low permeable formations. As the pressure disturbance created at the production well starts propagating throughout the reservoir, it will shape an expanding drainage volume; the boundaries of drainage volume are pushed back expanding the size of productive region as production continues. We treat the expanding drainage volume as moving boundary problem. In our mathematical model, the weak (integral) form of mass balance equation is written for the productive region. Fluids and rock compressibility, desorption parameters (for shale gas), and production rates are controlling the speed at which the boundaries are advancing.The calculated well deliverability is used to determine optimal fracturing spacing for wells completed in one of the oil shale plays in the United States. Two approaches are studied: 1) keep the original horizontal length and change the number of fracture clusters; 2) keep the original fracture spacing and change the horizontal length.For the wells studied here, changing the fracture spacing and the horizontal length result in various level of performance enhancement. Through the study, we determine the optimal parameters: optimal fracture spacing and optimal well spacing.The ultimate drainage volume (effective stimulated reservoir volume) and optimal fracture spacing can be obtained by the proposed method; therefore, neither comprehensive inputs required for the strong form (differential) nor any pre-knowledge about the productive region (shape, size,…) are needed for the new approach.