Production from previously uneconomic tight/shale formations has become feasible by constructing multifractured horizontal wells. Rate‐transient analysis of these wells is commonly performed with the assumption of homogeneous‐reservoir models, which might not be valid in reality. During hydraulic fracturing, secondary fractures might be formed in the reservoir. Because of the limited energy of hydraulic fracturing, the quality of secondary fractures decreases with the distance from the main fracture. This would negate the assumption of a homogeneous reservoir.
In this paper, we present practical solutions that include reservoir heterogeneity in rate‐transient analysis of multifractured wells. The solutions are developed for transient linear flow, which is a dominant‐flow regime in many tight/shale reservoirs. In addition to forward solutions, inverse solutions are also developed that would ease the analysis procedure and reduce the uncertainty of estimation. The solutions are presented in simple formats and can be easily applied. We first developed the solutions such that they can be applied for any arbitrary permeability profile. We further considered special formats for the permeability/distance relationship and developed the relevant models. For a homogeneous system, the well‐known square‐root‐of‐time (time to the power of 0.5) plot is used. For the case of heterogeneity, however, the power of time should be greater than 0.5 and less than unity to produce a straight‐line plot. We mathematically demonstrate this for a recognized format of the permeability/distance relationship.
The presented solutions are verified with the numerical simulation of synthetic examples. Comparison of the results reveals the accuracy of the analytical solutions. Two field examples are also analyzed to indicate the practical applicability of the analytical solutions. The permeability/distance profiles for these field examples are derived using the inverse solutions.