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

Abstract

Abstract An analytical solution is presented for pressure- and rate-transient behavior of an array of, parallel, 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. Properties of hydraulic fractures and stimulated reservoir volumes may vary from well to well. Different properties may also be assigned to unstimulated reservoir section between wells. Natural fractures in the stimulated and unstimulated reservoir volumes are accounted for by the transient dual-porosity idealization. Flow domain is divided into blocks of one-dimensional flow under the trilinear flow assumption. Analytical solution for each block is obtained by the appropriate Green's function and coupled with the neighboring blocks by the continuity of pressure and flux at the block interfaces. 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 time-domain numerically. Results are robust and reasonably accurate for most practical applications of single-phase oil and gas production from multiple wells in an unconventional reservoir. The solution provides an efficient tool to assess well interference effects for different well completion designs and varying reservoir characteristics. The speed of calculations is convenient for pressure-transient and production-data analysis, as well as for the initial calibration and verification of more complex numerical models. The closed analytical form of the solution enables assessment of flow regime diagnostics under well-interference.