A Simple Analytical Model for Predicting Productivity of Multifractured Horizontal Wells

Horizontal wells drilled in the direction of the minimum horizontal stress allow multiple transverse fractures to be hydraulically created for enhancing well productivity in low-permeability oil and gas reservoirs. Dominating factors affecting the productivity of the multifractured horizontal wells vary with reservoir and fracture properties, and with well trajectories. A simple and accurate mathematical model for evaluating and optimizing productivity of this type of well is not available and is highly desirable to reservoir engineers. This paper fills the gap. After a case study with existing analytical models that were derived for multifractured wells, the authors found that these models cannot describe the performance of oil wells with acceptable accuracy. We then formulated a simple analytical model that describes the productivity of multifractured horizontal wells better. The new model couples the radial flow in the nonfractured region of reservoir, the linear flow toward the fractures in the fractured region, the linear flow in the fracture, and the radial flow in the fracture toward the horizontal wellbore. It can model pseudosteady-state flow of reservoir fluids in reservoir sections of any shape, with the fractured region being located at any area in the reservoir. The difference between the production rate given by the new model and the actual production rates was found to be less than 5% in the two cases studied. This paper provides reservoir engineers a simple and accurate tool for predicting, evaluating, and optimizing the performance of multifractured horizontal oil and gas wells.