Modelling the influence of uncertain reservoir parameters on the occurence of natural convection in geothermal reservoirs
Aachen (2019, 2020) [Dissertation / PhD Thesis]
Observing a global trend to switch energy sources from fossil to renewable where possible and feasible, geothermal energy as a base load technology fills a niche complementary to solar and wind energy. Identifying and quantifying the resource potential of a reservoir system for geothermal energy production is important. The heat transport process of natural convection (also called free convection) can be considered significantly important in (sedimentary) geothermal reservoir systems. In natural convective systems, less dense hot water rises to shallower depths. Localising these upflow zones is therefore of crucial interest for geothermal energy production. Thus, free convection increases the resource potential of a reservoir system, but also the uncertainty of predicted temperatures at depth. Several parameters, such as permeability, significantly affect the formation of free convection cells. But since these parameters vary spatially in the subsurface, their influence and their uncertain heterogeneity on a convection pattern needs to be assessed in order to provide sophisticated predictions concerning the convection system. The content presented in this work is the result of different collaborative studies with other researchers, mostly also presented in peer-reviewed scientific journal papers. In this work, I adress this problem by presenting methods for studying and quantifying the influence of heterogeneous parameter distributions on natural convection patterns. For instance, I study the impact of spatially heterogeneous permeability on the formation and shape of hydrothermal porous convective flow in the Yarragadee Aquifer in the central Perth Basin, by modelling three simulation scenarios, each with differing permeability distributions. In all scenarios, the southern part of the model is characterised by convection rolls, while the north of assessed Perth Basin model is dominated by a stable region of decreased temperatures at depth due to hydraulic interaction with shallower aquifers. This suggests that reservoir sturcture is a first-order controlling factor for the formation of the free (natural) convective system. The convective system adjusts to the spatially heterogeneous permeability distribution, yielding locally different convection patterns. I not only adress the influence of spatially uncertain permeability on a convective system but also assess the influence of its spatial continuity. To this end, I set up multiple Monte Carlo ensembles of a 2D Model of the central Perth Basin. I study the effect of varying spatial continuity of porosity and permeability by assessing the entropy production number of the whole system. This number is based on the concept of lateral heat flow caused by the convective system and a resulting increase in entropy. An initial decrease of the average entropy production number with increasing lateral correlation length (i.e. continuity) shows that less ensemble members show convection. If the ensemble members which do not show convection are neglected, we do not see a change in the convection system for lateral correlation lengths larger than 2000 m. Often, models simulating a convection system do not reach a true steady state. Whether there is no steady state, or the system just oscillates, can be assessed by the concept of attractors. Using this concept, I analyse models of the Perth Basin concerning their transient behaviour in a phase space. This phase space is set up by the enthalpy of the system and its change in time. The resulting attractors show that our simulations of the Perth Basin reach a dynamic steady state, as the results orbit around a point in their phase space. They can be used as a diagnostic convergence criterium for oscillating simulations. Once the natural state of a reservoir system is assessed in form of a well calibrated model comprising methods such as attractors or entropy production, a subsequent step in an exploration workflow is the simulation of potential production wells. In presence of convective currents, placement of geothermal wells should consider the lateral differences in temperature which are introduced by convection. I adress this problem by using a tool for finding the best location and layouts for geothermal doublets of given specifications based on numerical modeling of hydrothermal flow. This approach also honors different constraints at the surface, like settlements, or natural reserves. I demonstrate the method by assessing the geothermal potential of a carbonate reservoir at Guardia Lombardi in Campania, Italy. The anticlinal structure of the reservoir body enables free convection with upflow focused along the limbs of the anticline. Temperatures at the top of the folded reservoir range from 85 °C to 265 °C. Using calibrated simulation results of the regional reservoir model, I apply surface constraints for excluding locations for drilling geothermal wells. The developed algorithm proposes multiple potential positions for doublet installations. As an example, I simulate the continuous operation of one of these proposed installations for an operation time of 35 years with different offsets between injection and production borehole. At a minimum distance of about 700 m, no significant decrease in production temperatures occurs during this time. The presented methods and their application to real-world reservoirs helps characterising convection patterns in geothermal reservoir systems. This can be useful for decision makers for estimating uncertainty and corresponding risks in the exploitation of geothermal reservoirs in the presence of natural convection in the reservoir.
Niederau, Jan Frederik