Pressure Desuperposition Technique for Improved Late-Time Transient Diagnosis (1990)

Diagnosing the reservoir model from a field data set is one of the main challenges in well test analysis. The log-log pressure and pressure derivative plot is now firmly established as a primary diagnostic tool. This paper provides a new derivative formulation that enhances model provides a new derivative formulation that enhances model diagnosis and addresses techniques for reducing noise in the derivative response.Transients initiated by a sufficiently large increase in the surface rate closely represent the ideal reservoir response. However, when a transient is initiated by a decrease in surface rate, distortions due to superposition effects from previous surface flow rate changes are frequently present previous surface flow rate changes are frequently present in the late-time derivative and can lead to incorrect characterization of reservoir boundaries.To improve the late-time response, the pressure data are corrected for effects of a variable surface rate history before differentiation. The resultant desuperposition derivative avoids assuming a model for the reservoir behavior by using the late-time character of a representative transient. The desuperposition derivative appears as an equivalent drawdown (injection) response regardless of the nature of the perturbation that was actually used to induce the particular transient. This technique is particularly useful in reservoir and limits tests designed to particularly useful in reservoir and limits tests designed to delineate heterogeneities or boundaries; it also applies to multirate and multilayer tests.Noise in the derivative can either mask or give a false impression of the true reservoir behavior. Overly smoothing noisy data may obscure the response and lead to erroneous model diagnosis. This study addresses logarithmic filtering and sampling techniques for reducing noise in the data.Introduction. From its inception, the log-log pressure derivative plot has played a fundamental role in reservoir model diagnosis. For tests where downhole flow rates are acquired, its counterpart is the convolution derivative. Experience with these diagnostic plots has shown that the shape of the classical derivative response depends on the overall well test sequence. These discrepancies typically occur in late time and can interfere with the correct characterization of boundary effects.Model diagnosis entails pattern recognition, during which the shape of the derivative of the transient test data is identified with a known reservoir model. The comparison may be achieved visually or automatically by applying artificial intelligence techniques.Since the late-time derivative shape can be influenced by the test sequence and the well flow rate history and may not necessarily match a shape in the lookup catalogue of theoretical drawdown responses, misdiagnosis of the reservoir model is a possibility. Misdiagnosis will likely be corrected during subsequent analytical modelling because the data are matched with a simulated reservoir model response that accounts for the entire rate history. However, a match might be obtained using an improper model resulting in incorrect reservoir characterization.Pressure and convolution derivatives are currently Pressure and convolution derivatives are currently computed by differentiating with respect to radial superposition and convolution time groups, respectively. This paper describes a desuperposition technique which paper describes a desuperposition technique which renders the derivative as an equivalent drawdown or injection response which can be directly compared with theoretical type curves. The desuperposition technique is explained for pressure, convolution, and deconvolution derivatives, and a simulated example shows its application.P. 201