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A.A. Marelis
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Accurate and efficient predictions on the behavior of fluid flow and heat transport are required in the development of low-enthalpy geothermal reservoirs in fractured formations. Key challenges include the demand for high-resolution computational grids, the non-linear behavior of the system due to strong mass-heat coupling and the presence of fractures with large heterogeneity contrasts. In this work, a comparison is made between natural and molar variable formulation used to describe the coupled fluid-heat transport under non-isothermal conditions in low-enthalpy fractured porous media. The solutions and performance of the newly implemented molar formulation are compared to those of the existing natural variable formulation in the DARSim2 reservoir simulation framework. A fully implicit scheme (FIM) is applied to solve the coupled discrete system including mass and energy balance equations. Application of the Algebraic Dynamic Multilevel (ADM) method with projection-based Embedded Discrete Fracture Model (pEDFM) provides a scalable and efficient simulation framework for field-scale fractured reservoirs. The ADM method maps the fine-scale system onto a dynamically defined multilevel grid resolution system (Cusini et al., 2016, HosseiniMehr et al., 2020) based on the solution gradient and a series of restriction and prolongation operators, which ensure accurate capturing of fine-scale heterogeneities. Fractures are defined explicitly as either (highly) conductive passageways or flow barriers using the pEDFM formulation (Tene et al., 2017). Simulation results using the molar formulation are compared with an analytical solution as verification of the implementation. Results of various (un-)fractured test cases with homogeneous and heterogeneous permeability fields show that there is no clear difference between the solutions and performance of the different primary variable formulations, and the performance itself is largely dependent on the level of complexity embedded in the numerical model independent of the simulation strategy applied.
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Accurate and efficient predictions on the behavior of fluid flow and heat transport are required in the development of low-enthalpy geothermal reservoirs in fractured formations. Key challenges include the demand for high-resolution computational grids, the non-linear behavior of the system due to strong mass-heat coupling and the presence of fractures with large heterogeneity contrasts. In this work, a comparison is made between natural and molar variable formulation used to describe the coupled fluid-heat transport under non-isothermal conditions in low-enthalpy fractured porous media. The solutions and performance of the newly implemented molar formulation are compared to those of the existing natural variable formulation in the DARSim2 reservoir simulation framework. A fully implicit scheme (FIM) is applied to solve the coupled discrete system including mass and energy balance equations. Application of the Algebraic Dynamic Multilevel (ADM) method with projection-based Embedded Discrete Fracture Model (pEDFM) provides a scalable and efficient simulation framework for field-scale fractured reservoirs. The ADM method maps the fine-scale system onto a dynamically defined multilevel grid resolution system (Cusini et al., 2016, HosseiniMehr et al., 2020) based on the solution gradient and a series of restriction and prolongation operators, which ensure accurate capturing of fine-scale heterogeneities. Fractures are defined explicitly as either (highly) conductive passageways or flow barriers using the pEDFM formulation (Tene et al., 2017). Simulation results using the molar formulation are compared with an analytical solution as verification of the implementation. Results of various (un-)fractured test cases with homogeneous and heterogeneous permeability fields show that there is no clear difference between the solutions and performance of the different primary variable formulations, and the performance itself is largely dependent on the level of complexity embedded in the numerical model independent of the simulation strategy applied.
Energy capacity of a geothermal reservoir
The effect of conductive heat transfer recharge on reservoir lifetime at low temperature conduction regimes
The effect of conductive heat transfer recharge originating from the surrounding conduction dominated geothermal system on the geothermal reservoir lifetime has been reviewed during its development, by studying the effect of multiple reservoir and production parameters. A two dimensional (2D) finite volume implicit coupling strategy, using a direct solver method, is applied on a non-isothermal lumped-parameter model to simulate reservoir development over a period of 35 years. Two test cases are investigated, modelled after the low temperature geothermal fields of Middenmeer in The Netherlands and Soultz-sous-Forêts in France. Resulting produced thermal water temperature and thermal energy flow rate profiles are simulated with and without consideration of the geothermal system. A resolution of 200×200 equidistant structured cells is applied to cover an integrated (reservoir and surrounding) domain that extends 2 km vertically and 10 km horizontally. The reservoir domain extends 200 m vertically and 1 km horizontally, covered by a computational grid resolution of 20×20. Sensitivity analysis show that this is the best resolution that can be applied without losing simulator stability and accuracy.
Results show that the conductive heat transfer recharge originating from the surrounding geothermal system has a significant effect on reservoir lifetime by reducing temperatures after thermal drawdown up to 26.5% in the first test case and up to %22.6 in the second test case. In addition, it lead to an increase in the average annual thermal energy production, up to %12.5 and %14.3 respectively. The consideration of the conductive recharge from the surrounding domain shows a significantly increased lifetime estimate for low temperature geothermal reservoirs. Furthermore, permeability, rock thermal conductivity and (re-)injection temperature are the reservoir and production parameters that can greatly influence the reservoir lifetime.
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Results show that the conductive heat transfer recharge originating from the surrounding geothermal system has a significant effect on reservoir lifetime by reducing temperatures after thermal drawdown up to 26.5% in the first test case and up to %22.6 in the second test case. In addition, it lead to an increase in the average annual thermal energy production, up to %12.5 and %14.3 respectively. The consideration of the conductive recharge from the surrounding domain shows a significantly increased lifetime estimate for low temperature geothermal reservoirs. Furthermore, permeability, rock thermal conductivity and (re-)injection temperature are the reservoir and production parameters that can greatly influence the reservoir lifetime.
...
The effect of conductive heat transfer recharge originating from the surrounding conduction dominated geothermal system on the geothermal reservoir lifetime has been reviewed during its development, by studying the effect of multiple reservoir and production parameters. A two dimensional (2D) finite volume implicit coupling strategy, using a direct solver method, is applied on a non-isothermal lumped-parameter model to simulate reservoir development over a period of 35 years. Two test cases are investigated, modelled after the low temperature geothermal fields of Middenmeer in The Netherlands and Soultz-sous-Forêts in France. Resulting produced thermal water temperature and thermal energy flow rate profiles are simulated with and without consideration of the geothermal system. A resolution of 200×200 equidistant structured cells is applied to cover an integrated (reservoir and surrounding) domain that extends 2 km vertically and 10 km horizontally. The reservoir domain extends 200 m vertically and 1 km horizontally, covered by a computational grid resolution of 20×20. Sensitivity analysis show that this is the best resolution that can be applied without losing simulator stability and accuracy.
Results show that the conductive heat transfer recharge originating from the surrounding geothermal system has a significant effect on reservoir lifetime by reducing temperatures after thermal drawdown up to 26.5% in the first test case and up to %22.6 in the second test case. In addition, it lead to an increase in the average annual thermal energy production, up to %12.5 and %14.3 respectively. The consideration of the conductive recharge from the surrounding domain shows a significantly increased lifetime estimate for low temperature geothermal reservoirs. Furthermore, permeability, rock thermal conductivity and (re-)injection temperature are the reservoir and production parameters that can greatly influence the reservoir lifetime.
Results show that the conductive heat transfer recharge originating from the surrounding geothermal system has a significant effect on reservoir lifetime by reducing temperatures after thermal drawdown up to 26.5% in the first test case and up to %22.6 in the second test case. In addition, it lead to an increase in the average annual thermal energy production, up to %12.5 and %14.3 respectively. The consideration of the conductive recharge from the surrounding domain shows a significantly increased lifetime estimate for low temperature geothermal reservoirs. Furthermore, permeability, rock thermal conductivity and (re-)injection temperature are the reservoir and production parameters that can greatly influence the reservoir lifetime.