Pressure- and Rate-Transient Model for an Array of Interfering Fractured Horizontal Wells in Unconventional Reservoirs

Abstract

An analytical solution is presented for pressure- and rate-transient behavior of an array of n parallel and fractured horizontal wells in an unconventional reservoir. Wells are of equal length but otherwise of unidentical properties. Each well has an arbitrary number of uniformly spaced identical, finite-conductivity fractures and is surrounded by a stimulated reservoir volume (SRV). The properties of hydraulic fractures (HFs) and SRVs may vary from well to well. Different properties may also be assigned to the unstimulated reservoir sections between wells. Natural fractures in stimulated and unstimulated reservoir volumes are accounted for by transient dual-porosity idealization. The flow domain is divided into blocks of 1D flow under the trilinear-flow assumption. Solution for each block is obtained analytically and coupled with the solutions for the neighboring blocks by the continuity of pressure and flux at the block interfaces. Drainage volumes of wells are adjusted based on the variation of well production rates because of moving no-flow boundaries between wells. The superposition principle is applied to consider variable-production conditions as well as nonsynchronous production and shut-in schedules of wells. The final solution is in the form of a matrix-vector equation in the Laplace transform domain and inverted into the time domain numerically. The model is robust and reasonably accurate for most practical applications of single-phase oil and gas production from multiple wells in an unconventional reservoir. It is an efficient tool to assess well interference effects for different well completion designs and varying reservoir characteristics. The speed of the model makes it useful for pressure-transient and production-data analysis, as well as for the initial calibration and verification of more complex numerical models.