Diagnosis and Quantification of Stress-Sensitive Reservoir Behaviour from Pressure and Rate Transient Data

Classical analytical and numerical techniques for simulation of fluid flow in petroleum reservoirs typically assume permeability is independent of pressure. In naturally fractured and low permeability systems the reservoir permeability may depend on the stress state of the reservoir which means the diffusivity equation that governs single phase flow in the reservoir becomes nonlinear. Stress-sensitive behaviour is particularly relevant to the development of tight gas and other unconventional resources. This work develops a set of tools to diagnose and quantify stress sensitivity through analysis of transient pressure or flow rate data. The work builds on analytical solutions for radial flow in a stress-sensitive medium presented by Friedel and Voigt (SPE 122768, 2009), and for the linear flow case presented by Archer (AFMC 17, 2010). The radial flow solution uses the Boltzmann transform whereas the linear flow solution is based on the use of the Cole-Hopf transform. High resolution numerical solutions are also used to complement these analytical solutions. Where appropriate pseudo-pressures are used to take account of the pressure dependence of gas properties on pressure. This paper considers both transient pressure and rate solutions and develops a range of type curve formats to demonstrate how production from stress-sensitive reservoirs differs from conventional reservoirs when plotted in traditional well test format (log-log plot of pressure and pressure derivative), as a p/z plot (for the gas case), as a rate versus cumulative plot, and as “Blasingame” type curves in the including the normalised rate, rate-integral, and rate-integral-derivative formats. This suite of tools can be used in a diagnostic manner to identify whether stress-sensitive behaviour is occurring, to quantify the errors that may be made in permeability estimates if stress-sensitive behaviour is ignored, and to estimate the impact of stress-sensitivity on ultimate recovery from a well.