Application of semi-analytical multiphase flow models for the simulation and optimization of geological carbon sequestration

Abstract

Geological carbon sequestration (GCS) has been identified as having the potential to reduce increasing atmospheric concentrations of carbon dioxide (CO2). However, a global impact will only be achieved if GCS is cost effectively and safely implemented on a massive scale. This work presents a computationally efficient methodology for identifying optimal injection strategies at candidate GCS sites having caprock permeability uncertainty. A multi-objective evolutionary algorithm is used to heuristically determine non-dominated solutions between the following two competing objectives: 1) maximize mass of CO2 sequestered and 2) minimize project cost. A semi-analytical algorithm is used to estimate CO2 leakage mass rather than a numerical model, enabling the study of GCS sites having vastly different domain characteristics. The stochastic optimization framework presented herein is applied to a case study of a brine filled aquifer in the Michigan Basin (MB). Twelve optimization test cases are performed to investigate the impact of decision maker (DM) preferences on heuristically determined Pareto-optimal objective function values and decision variable selection. Risk adversity to CO2 leakage is found to have the largest effect on optimization results, followed by degree of caprock permeability uncertainty. This analysis shows that the feasible of GCS at MB test site is highly dependent upon DM risk adversity. Also, large gains in computational efficiency achieved using parallel processing and archiving are discussed. Because the risk assessment and optimization tools used in this effort require large numbers of simulation calls, it important to choose the appropriate level of complexity when selecting the type of simulation model. An additional premise of this work is that an existing multiphase semi-analytical algorithm used to estimate key system attributes (i.e. pressure distribution, CO2 plume extent, and fluid migration) may be further improved in both accuracy and computational efficiency. Herein, three modifications to this algorithm are presented and explored including 1) solving for temporally averaged flow rates at each passive well at each time step, 2) using separate pressure response functions depending on fluid type, and 3) applying a fixed point type iterative global pressure solution to eliminate the need to solve large sets of linear equations. The first two modifications are aimed at improving accuracy while the third focuses upon computational efficiency. Results show that, while one modification may adversely impact the original algorithm, significant gains in leakage estimation accuracy and computational efficiency are obtained by implementing two of these modifications. Finally, in an effort to further enhance the GCS optimization framework, this work presents a performance comparison between a recently proposed multi-objective gravitational search algorithm (MOGSA) and the well-established fast non-dominated sorting genetic algorithm (NSGA-II). Both techniques are used to heuristically determine Pareto-optimal solutions by minimizing project cost and maximizing the mass of CO2 sequestered for nine test cases in the Michigan Basin (MB). Two performance measures are explored for each algorithm, including 1) objective solution diversity and 2) objective solution convergence rate. Faster convergence rates by the MOGSA are observed early in the majority of test optimization runs, while the NSGA-II is found to consistently provide a better search of objective function space and lower average cost per kg sequestered solutions.