Development and application of capacitance-resistive models to water/CO₂ floods

Quick evaluation of reservoir performance is a main concern in decision making. Time-consuming input data preparation and computing, along with data uncertainty tend to inhibit the use of numerical reservoir simulators. New analytical solutions are developed for capacitance-resistive models (CRMs) as fast predictive techniques, and their application in history-matching, optimization, and evaluating reservoir uncertainty for water/CO₂ floods are demonstrated. Because the CRM circumvents reservoir geologic modeling and saturation-matching issues, and only uses injection/production rate and bottomhole pressure data, it lends itself to rapid and frequent reservoir performance evaluation. This study presents analytical solutions for the continuity equation using superposition in time and space for three different reservoir-control volumes: 1) entire field volume, 2) volume drained by each producer, and 3) drainage volume between an injector/producer pair. These analytical solutions allow rapid estimation of the CRM unknown parameters: the interwell connectivity and production response time constant. The calibrated model is then combined with oil fractional-flow models for water/CO₂ floods to match the oil production history. Thereafter, the CRM is used for prediction, optimization, flood performance evaluation, and reservoir uncertainty quantification. Reservoir uncertainty quantification is directly obtained from several equiprobable history-matched solutions (EPHMS) of the CRM. We validated CRM's capabilities with numerical flow-simulation results and tested its applicability in several field case studies involving water/CO₂ floods. Development and application of fast, simple and yet powerful analytic tools, like CRMs that only rely on injection and production data, enable rapid reservoir performance evaluation with an acceptable accuracy. Field engineers can quickly obtain significant insights about flood efficiency by estimating interwell connectivities and use the CRM to manage and optimize real time reservoir performance. Frequent usage of the CRM enables evaluation of numerous sets of the EPHMS and consequently quantification of reservoir uncertainty. The EPHMS sets provide good sampling domains and reasonable guidelines for selecting appropriate input data for full-field numerical modeling by evaluating the range and proper combination of uncertain reservoir parameters. Significant engineering and computing time can be saved by limiting numerical simulation input data to the EPHMS sets obtained from the CRMs.