Multi-objective optimization under uncertainty of geothermal reservoirs using experimental design-based proxy models

Geothermal energy has a high potential to contribute to a more sustainable energy system if the associated economic risks can be overcome in the design process. The development planning of deep geothermal reservoirs (over 1000 m depth) relies on computer models to forecast and then optimize system design. Optimization is easy where all the objective's (e.g. NPV) optimization parameters and, most importantly, the geology are considered as known, but this is almost always not the case. Where the complex engineering design (e.g. well placement) meets significant geological uncertainty every development option should be tested using an expensive simulation against the range of geological possibilities. The impracticality of simulating so many models results in a limited exploration of geological uncertainties and development options. Consequently, the risk of improper system design cannot be properly assessed. This paper presents an approach to understand the trade-offs in maximizing heat extraction while minimizing energy usage in re-injection for a new geothermal reservoir development while considering the uncertainty from 18 different geological models. Our approach is computationally feasible because we apply multi-objective particle swarm optimization (MOPSO), to an ensemble of response surface models, built using Gaussian process regression (GPR), for each and every geological scenario. MOPSO explores the trade-off surface for the competing objectives using the mean reservoir responses (covering the geological uncertainty). Our results highlight the impact of geological uncertainty on the optimal well placement and show the need to consider geological uncertainties adequately in optimization. The work demonstrates the shortcomings of using only one geological model of a geothermal reservoir and/or a single objective in optimization. We additionally demonstrate the practicalities of using response surface models in this way for geothermal systems. We anticipate that our work raises awareness for the scope of optimization of geothermal reservoir design under geological uncertainty