The reservoir system in the real world is a dynamic system which the reservoir properties is changed with time. Considering the data in which PDGs record, one of the most defining characteristics is the inherent combination of short-term transients and long-term trendy. These characters permit dual application of these data to infer short-term effects (e.g., skin effect) and longer-term effects such as pressure depletion or changes in reservoir mechanism. The current approach to analyze the PDG data includes two directions. PDG data are analyzed with the traditional well testing approach to get the changed reservoir properties with respect to the transient character. With respect to the longer-term changes, PDG data are especially useful for history matching in the reservoir simulation.

Our approach tries to use the dual character of the PDG data. The transient character is mainly expressed in the log-log plot which is always used in traditional well testing. The long-term character is expressed in the Cartesian plot which is always used in the history matching of reservoir simulation. The numerical welltesting is approach to achieve the two direction. But the numerical well testing can not be used for the multi-rate pressure in dynamic system. Our idea is to linearize the nonlinear system to linear system with deconvolution. The deconvolution makes mistake to get the constant rate system response when the reservoir parameter changes because it can only be applied for linear system. This phenomena is used to diagnostic the critical point where the reservoir parameter changes. The critical points series divide the nonlinear system into different linear periods, and the numerical well testing is conducted to do forward modeling in every parts.


The traditional well testing approach can get the changed reservoir information from the separated BU. However, this information can not guide the long term reservoir information because the DD part of PDG data has not been analyzed. The numerical well testing approach can help to analyze the complex geological model. But, it still suffers from multi-rate and nonlinear data. Currently, the deconvolution approach is introduced. This approach can transfer the multi-rate pressure into unit-response of reservoir in the linear system. However, the reservoir system in the real world is a dynamic system in which the reservoir's properties changed with time. The PDG data recorded from nonlinear system can not analyzed with current approach because the theory of current approach is based on the linear system. There are two approaches to analyze the nonlinear system data. The first approach is to linearize the nonlinear system into separated linear system. The current approach can be applied in every linear part. The second approach is to build a nonlinear model for nonlinear system. This study considers the first approach because the nonlinear model is hard to build and is not easy to solve.

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