Decision making and efficient surrogate-assisted optimisation techniques under uncertainty: application to CO2 sequestration

Abstract

One promising proposal to mitigate the effect of climate change as a result of high atmo- spheric CO2 concentrations is carbon capture and storage. Deep saline aquifers provide the most storage capacity for CO2 storage. However, their geological characteristics are often poorly defined, which makes it difficult to design CO2 sequestration operations. This thesis considers how CO2 sequestration can be performed effectively and efficiently under geological uncertainty by allocating injection rates among injectors to maximise economic performance criteria and simultaneously minimise the risk of CO2 leakage. To this end, we consider the following four challenges in this thesis. 1.) Optimisation of CO2 injection strategies is a time-consuming operation since it re- quires multiple evaluations of expensive black-box functions. This computational cost increases rapidly when accounting for the impact of geological uncertainty. In this thesis, we propose the use of adaptive sparse grid interpolation (ASGI) to speed up the CO2 optimisation process. Based on numerical results, the ASGI is an efficient surrogate technique and will be used throughout the thesis. 2.) Injection designs for CO2 sequestration is difficult when the geology of the storage formation is not well-defined. In the thesis, we propose a utility function to find the injection strategy that is insensitive to the impact of geological uncertainty. Numeri- cal results show potential benefits of using the utility function for the optimisation of CO2 under geological uncertainty. 3.) Optimisation of CO2 sequestration for several conflicting criteria is a challenging task. In the thesis, we use a non-dominated sorting genetic algorithm (NSGA-II) coupled with the ASGI surrogate to maximise both economic performance and sweep efficiency of CO2 flooding while simultaneously minimising the risks of CO2 leakage. Solutions obtained from the NSGA method help decision makers to manage multiple conflicting criteria for CO2 sequestration. 4.) The ASGI surrogate is an efficient surrogate-assisted optimisation technique for a small to moderate number of input variables, but for problems with 10s of control parameters, it suffers from the curse of dimensionality — the computational time increases exponentially with the number of input variables. In the thesis, we develop a high-dimensional model representation (HDMR) technique to efficiently map the input-output relationship of a function. Several numerical examples show that the HDMR approach is suitable for CO2 storage optimisation with many input variables.