Linear superposition time for variable-rate, variable-pressure production from a fractured tight gas well

Hydraulically fractured, tight gas wells produce under large pressure drawdowns, which may cause three-to ten-fold variations in the gas viscosity-compressibility product, particularly in the vicinity of the fracture, over the life of the production. Under such a large variation, the pseudo-pressure transformation cannot remove nonlinearity of the gas diffusion equation. The remaining nonlinearity makes the application of superposition principal questionable; specifically the linear superposition time based on linear flow, a dominant flow regime for hydraulically fractured tight gas reservoirs. Not accounting for the effect of large gas viscosity-compressibility product variations in pressure and rate transient analysis of fractured, tight gas well performances leads to misinterpretation of reservoir characteristics.