Investigations in Reducing the Computational Expense of Transient 3D Multi-Phase CO2 Wellbore Leakage Simulations: Time-Series Matching versus Multivariate Adaptive Regression Splines

Abstract:

Depleted oil and gas reserves have abandoned wellbore densities up to 10 per square kilometer (Crow, 2010). These locations are considered to have favorable geological structure and properties for CO2 sequestration. To understand the risk of CO₂ leakage along these abandoned wellbores requires the simulation of a comprehensive set of realizations encompassing the potential scenarios. The simulations must capture transient, 3D, multi-phase effects (i.e. supercritical, liquid, and gas CO₂ phases along with liquid reservoir and aquifer fluids), and include capillary and buoyant flow. Performing a large number of these simulations becomes computationally burdensome. In order to reduce this computational burden, regression approaches have been used to develop computationally efficient reduced order models to try to capture the general trends of the simulations. In these approaches, model inputs and outputs are collected from the transient simulations at each time step. Recognizing that many of the inputs to the regression approach come from time series (i.e. pressures and CO₂ saturations) and that all of the outputs are time series (i.e. CO₂ and brine flow rates), we develop a time-series matching approach. In this approach, CO2 and brine flow rate time series are estimated given input time series and parameters by averaging the flow rates of the collected simulations weighted by the similarity of their input time series and parameter. Similarity of both time series and parameters is calculated by the Euclidean distance. Euclidean distances are converted to a generalized likelihood metric, and used to weight the flow-rate time-series averages. We present a comparison of this time series matching approach to the MARS algorithm.