History-Matching of Historical Pressures from Naturally Fractured Reservoirs

Summary In this study, we developed the equation for calculating equivalent dual-media pressure for comparison to historical pressure from Naturally Fractured Reservoirs (NFR) during history-matching. Dual-Porosity Dual-Permeability (DPDP) approach is the most popular approach used for modeling NFRs, however, commercial DPDP simulators calculate individual rather than the equivalent dual-media pressure, leading to uncertainties during history-matching. Using the DPDP representation of NFRs, the compressibility equation was used to derive a mathematical model for deriving the equivalent dual-media pressure from the simulated matrix and fracture pressures. By applying the compressibility equation to each media, we obtained an expression containing both equivalent dual-media compressibility and pressure-change. Using the known dual-media pressure at the start of a time-step and the pressure-change during the time-step, we obtained the dual-media pressure at the end of the time-step. The resulting mathematical model is a storativity-weighted function of the simulated matrix and fracture pressures. A synthetic dataset shows the relationship between the simulated individual media, and the derived dual-media pressures, under different scenarios. In reservoirs with low matrix permeability, and high fracture-to-matrix porosity and permeability ratios, large uncertainties may arise when the simulated matrix pressures are compared to historical pressure data. In an application example, using dual-media pressure instead of the simulated matrix pressure resulted in better history-matching of pressure prior to model's property modifications. The history-matching of pressure is a non-unique process, this study provides a new degree of freedom that can be explored during such a process in NFRs. Prior to modifying model properties to obtain a history-match, the dual-media pressure rather than the individual matrix pressure should be the basis of comparison to observed pressure data. This study is the first to demonstrate the uncertainty associated with using simulated matrix pressure to history-match historical pressure in NFR. The findings could be incorporated into commercial simulators to improve the history-matching process, and ensure that model property modifications are not used as compensation for the mis-match between incomparable elements. Statements and Declarations The authors have no financial interests, ethical considerations or competing interests to declare relating to the contents of this work.