Reservoir simulations for CO2 sequestration are computationally expensive because they run for centuries or millennia. Shortened, cheaper simulation timelines prevent the observation of gas leakages that might occur over a longer duration. In the statistics community, the exclusion of these leakages is called censorship. We propose a fast simulator surrogate that captures these potentially unobservable long-term risks. The crux of our approach is survival analysis, a branch of statistics tailored to handle censored data.
Our proposed framework begins by sampling scenarios with varied injection and production rates from a number of geological and flow uncertainty realizations. The potentially censored time to gas leakage is recorded for each simulated scenario. We then leverage varied survival analysis methods, ranging from Kaplan-Meier to Random Survival Forests, to create a computationally cheap, and highly interpretable, simulator surrogate. The surrogate can predict the risk of CO2 leakage in new scenarios for significantly shorter simulations than usual in carbon sequestration studies, or no new simulations at all. This eases the computational burden of centuries-long, expensive simulations.
In order to validate our methodology, we constructed an exploratory case study with a shortened monitoring window. The proposed framework is implemented within a compositional simulation model where CO2 is injected into a saline aquifer. To assess the risk of leakage and caprock integrity, we simulated scenarios where we inject CO2 for permanent storage using 4 injector wells, while 5 producer wells are used for pressure maintenance. This model is run for 2000 days under varied permeability realizations to monitor CO2 breakthrough from the production wells. We then infer the occurrence of leakage in new scenarios and compare these results to full simulations via appropriate statistical metrics such as hypothesis testing, metrics tailored for the censored data context and usual prediction metrics. Initial results show that the proposed method predicts time to gas leakage with good accuracy without the need for any new simulations at all.
To the best of the authors’ knowledge, this is the first paper to approach the carbon storage optimization issue with survival analysis, a clear fit due to the presence of censored data coming from shortened simulations. Our unique, novel framework yields a simulator surrogate built with techniques never-before-seen in this context. Also, we fill the gap other approaches leave open by focusing on interpretability, a model quality that is paramount to decision-making under high uncertainty.
