Process-based machine learning for multi-physics and chemistry in geothermal applications: parameter estimation and optimization under uncertainties

RWTH Publications (RWTH Aachen)

Abstract

Geothermal energy, the heat from the Earth, offers a clean and sustainable alternative for transitioning away from fossil-fuel based energy and addressing climate change. Given that this energy resource is located underground and sparse measurement data are available for its characterization, designing an efficient and safe extraction process must rely on numerical simulations. The numerical simulations should also address uncertainties associated with inaccurate characterization caused by sparse measurement data, ensuring robustness and reliability. This poses a significant computational challenge, demanding numerous model runs to solve inverse and optimization problems. In this dissertation, I present an efficient method to enable these inverse and optimization problems under multi-physics and chemistry settings, which is not feasible using the current state-of-the-art numerical methods, such as finite element and finite volume methods. Recently, machine learning methods, such as Neural Networks, have been widely employed to accelerate numerical simulations for performing costly inverse and optimization tasks in geothermal applications. A machine learning model represents a numerical model by learning its input-output relationship, a data-driven approach. However, since data-driven machine learning models are not inherently based on physics and chemistry laws, they can often produce inaccurate predictions. Consequently, achieving higher prediction accuracy requires many training samples, leading to exhaustive sample generation. Therefore, integrating the knowledge of physical and chemical processes into the construction of machine learning models, namely process-based machine learning methods, is essential to ensure accurate predictions and the efficiency of machine learning models. There are several process-based machine learning methods, such as the non-intrusive reduced-basis method and the Physics-Informed Neural Network. However, not all process-based machine learning methods are suitable for dealing with the multi-physics and chemistry settings in geothermal applications. Using two multi-physics problems, hydro-mechanical (HM) benchmark problems used in geothermal applications, I compare the non-intrusive reduced-basis method, the Physics-Informed Neural Network, and data-driven machine learning methods. The results indicate that the non-intrusive reduced-basis method provides the most accurate approximations with the smallest number of training samples. The non-intrusive reduced-basis method also demonstrates a more substantial speedup compared to both the Physics-Informed Neural Network and data-driven machine learning methods. This finding is crucial for addressing real-world geothermal cases, where numerical models are often high-dimensional and non-linear, requiring significant computational resources for generating training samples. This convinced me to implement the non-intrusive reduced-basis method for real-world, multi-physics geothermal cases, such as the The Hague case. I conduct an assessment of the heat extraction process in The Hague, Netherlands, utilizing the non-intrusive reduced-basis method. This allows me to efficiently perform uncertainty quantification to address producer placement, enhancing the understanding of the transient thermo-hydraulic (TH) process in The Hague from the perspective of entropy production, and designing optimum operating conditions while considering uncertainties and safety. Notably, the non-intrusive reduced-basis method demonstrates an impressive six to seven orders-of-magnitude speedups compared to the use of the finite element method. Furthermore, this work marks the first implementation of the non-intrusive reduced-basis method for addressing chemistry (C) problems, such as reactive transport problems and chemical equilibrium calculations. These problems are known for their nonlinearity and the presence of 'shock' features. Capturing these 'shock' features poses a significant challenge when utilizing data-driven machine learning methods, which are, up to now, the most used approaches within the geochemistry communities. I show that the non-intrusive reduced-basis method can capture the "shock" features with a smaller number of training samples, compared to the data-driven machine learning methods. This result opens up possibilities for future inverse and optimization involving chemistry in real-world geothermal cases, which are computationally expensive.

Authors 1

1. Ryan Santoso corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen