Fast-objective function estimators (FOFE) are often used to speed up reservoir management. This work presents a FOFE constructed with the parametric Dynamic Mode Decomposition (DMDp) method for a carbonate reservoir with WAG-CO2 injection. The FOFE results are then compared to simulation results to analyze the FOFE’s efficiency.
We present an example of how changes in the production strategy can affect reservoir behavior. The FOFE utilizes snapshots of gas and water saturation of numerical simulation runs with different sizes of WAG-CO2 cycles to predict the snapshots and fluid rates of a production strategy with a desired WAG-CO2 cycle size. The FOFE utilizes the DMDp method to calculate the saturation snapshots and material balance equations to calculate oil, water, and gas rates. Unlike the standard where snapshots are stacked up for multiple parameters, leading to increased computational costs, here we perform interpolation directly on the reduced Koopman operator. This leads to enhanced performance as the time eigenvalues are no longer shared between all parameters. The case study is the public access benchmark UNΊSFM-ΓV-2022, a carbonate reservoir model with characteristics of the Brazilian pre-salt. This model represents a developed reservoir with a WAG-CO2 recovery method for a compositional simulator with historical data.
For this work, the FOFE utilizes snapshots of two reservoir simulations, one with a WAG-CO2 cycle size of 6 months and the other with 18 months, to predict the states of a production strategy with 12 months of WAG-CO2 cycle. The FOFE results of gas, oil, and water are compared to a simulation result with the same production strategy. The comparisons for fluid dynamics are shown for reservoir conditions, and their curves with relative differences are provided. The FOFE can predict the states of a different field scenario, dispensing the necessity of extra numerical simulation runs. This result is promising for production optimization problems which require a significant amount of simulation runs to incorporate the many reservoir uncertainties, as it is observed in highly heterogeneous carbonate reservoirs.
The innovation of this work is the utilization of the DMDp in a highly heterogeneous reservoir with three-phase flow and WAG-CO2 injection utilizing commercial software. This FOFE can be utilized to reduce the time and computational effort necessary for the decision-making process involving the control variable of WAG-CO2 cycle size.