Analytic solutions for finite-conductive vertical fractured reservoirs are developed based on bilinear1,2  and trilinear3  fracture flow models for constant-pressure and constant-rate cases with and without boundaries. These solutions include effects of linear skin on the fracture, fracture conductivity, fracture to formation height ratio, wellbore and fracture storage, fracture to formation hydraulic diffusivity ratio, and wellbore phase segregation.

A simple method for solving these calculations is used to extend the transient fracture solutions to pseudoradial flow regime for various fracture parameters. Characteristic curves relating the effective wellbore radius for different fracture conductivities, skin and wellbore storage values are presented to facilitate the transition to the pseudoradial solutions.

The provided type curves identify fracture linear, storage linear, bilinear, formation linear, and pseudoradial flow regimes. Example problems are analyzed using type curve methods, and parameters are optimized with a Levenberg-Marquardt4  regression technique.

Keywords:
complete set, flow period, laplace transform, fracture, fracture storage, machine learning, linear flow, formation linear, conductivity, fracture conductivity
Subjects:
Hydraulic Fracturing, Formation Evaluation & Management, Pressure transient analysis, Drillstem/well testing
Copyright 1990, Society of Petroleum Engineers
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