# Optimization methods for mathematical models for geophysical flows

Aachen : RWTH Aachen University (2020, 2021)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2020

Abstract

Regenerative energy resources such as wind, water, and sun are the sources of choice that are ecologically compatible and socially acceptable. Regenerative energy is considered to significantly contribute to sustainability because it does not involve combustion of fossil fuel and does not directly influence global warming. As the earthquake and tsunami disaster of Fukushima in 2011 showed us, nuclear power can no longer serve as a reliable source to overcome the rising demand for energy. Also, non-regenerative energy resources such as coal, oil, or gas are limited and may damage the environment massively. Here, we work with an essential sustainable resource - geothermal energy.To find a suitable location of geothermal reservoirs drilling, we need to generate a rough model of the subsurface and to drill different exploratory holes at locations that deliver as much information as possible from the measured data. This data can then be passed to a numerical simulation of the subsurface to understand the characteristics of suitable rocks in more detail. It can also be used to determine the optimal position of the boreholes that will be used in production mode. The geothermal reservoir development includes deep drilling boreholes, which is extremely expensive and risky. So, to work out the details of suitable borehole locations in progress has great importance. Also, we give a set of existing boreholes and demonstrate how a sophisticated numerical technique helps to find a location of an additional exploratory borehole that reduces risk and, ultimately, saves cost. This work is devoted to mathemetical aspects of the reservoir development.A core part of the work is optimal experimental design (OED) methodology and its application on the geothermal reservoirs. Today, despite high significance and relevance to geothermal engineering, it is not at all common to study OED for problems arising from geothermal energy. However, OED is used to a greater extent in other areas of the geosciences. The overall goal is to analyze simulation models in decision making for groundwater management. We solve an OED problem for a geothermal reservoir in regions of western Australia and in the Tuscany region, Italy. The engineering problem consists of determining the location of a borehole such that the uncertainty of estimating the hydraulic permeability from temperature measurements is minimized. The solution procedure, however, is not restricted to this particular OED problem; it is also applicable to a wide range of different OED problems arising from engineering applications. During the usage of OED methodology on the geothermal models, we get a new challenge - computation time and numerical cost of the models. The complexity of the problem requires extensive computational efforts and parallelized execution of the computer codes. Parallelization, however, is needed, since a large range of parameters in question have to be analyzed for the multiple OED problems.We solve this problem independently. For the given problem, the time to evaluate the parallelized forward model using SHEMAT-Suite is about 1 min on a single shared-memory cluster node with eight cores. The time to perform a single execution of the automatic differentiation code to evaluate the forward model with its first-order derivatives takes also about 1 min, parallelized on that same node. To obtain the results for the ten different permeability values, the resulting parallel runtime would be in the order of 30 days on a single shared memory node. However, using a different shared-memory node of the compute cluster for each value of permeability, the overall parallel run time is reduced to just 3 days with the help of EFCOSS.