Diagnosis of nonlinear reservoir behaviour for correctly applying the superposition principle and deconvolution

• Wavelet transform is applied to diagnose nonlinear reservoir behaviour.
• The diagnostic function is constant in a linear system and time-varying in a nonlinear reservoir system.
• This novel nonlinearity diagnostic method and sliding window technique can ensure deconvolution is correctly applied.

The superposition principle is the fundamental theory of pressure-transient analysis. Many pressure analysis methods, such as pressure build-up analysis and deconvolution, are based on the superposition principle. Deconvolution, which can provide the equivalent constant-rate pressure response from variable-rate pressure data, has become more popular in recent years. Mathematically, the superposition principle is only valid in a linear system. However, many reservoir behaviours can make the system nonlinear and the superposition principle invalid, such as the time-dependent skin factor and permeability, multiphase flow and non-Darcy flow. Erroneously applying the superposition principle and related methods will lead to incorrect analysis results and inappropriate production decisions. To reduce the analysis uncertainties and obtain the correct reservoir information, diagnosing the nonlinear reservoir behaviour and selecting the appropriate pressure analysis method are important. In this paper, nonlinear reservoir behaviours are diagnosed from transient pressure data with the wavelet transform. A defined diagnosis function can effectively diagnose the nonlinear reservoir behaviours. As studies have proved, the diagnosis function is constant in the linear system and time varying in the nonlinear system. Based on the diagnosis result, the nonlinear system can be linearized in a short time period using the sliding window technique, and the superposition principle and related methods can be correctly applied.