Simulation of Geothermal Flow in Deep Sedimentary Basins in Alberta, OFR 2009-11

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With geothermal gradients of up to 50°C/km, Alberta has the potential to use geothermal energy economically. Mathematical models are excellent tools to predict the flow of geothermal energy and to forecast the productivity of a geothermal reservoir. This report investigates the flow of geothermal energy under the influence of water density variations due to temperature changes. As temperature increases, water density decreases, leading to upwelling of hot water. The associated interaction between heat flux and water flow is simulated numerically using an extended version of the HydroGeoSphere model that has been further developed. Alberta Geological Survey developed a groundwater model that numerically simulates the coupled flow of formation fluids and geothermal energy. The model accounts for variations of fluid density and viscosity and for buoyancy-induced groundwater flow. A wide temperature range of 0°C to 300°C is covered. The model has been verified against existing numerical and analytical test cases of free convective geothermal groundwater flow. Future work will also incorporate the effect of water salinity on buoyancy-induced fluid flow.
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  ERCB/AGS Open File Report 2009-11 Simulation of Geothermal Flow in DeepSedimentary Basins in Alberta  ERCB/AGS Open File Report 2009-11 Simulation of GeothermalFlow in Deep SedimentaryBasins in Alberta T. Graf  Energy Resources Conservation Board Alberta Geological SurveyJuly 2009  ©Her Majesty the Queen in Right of Alberta, 2009ISBN 978-0-7785-6980-0The Energy Resources Conservation Board/Alberta Geological Survey (ERCB/AGS) and its employeesand contractors make no warranty, guarantee or representation, express or implied, or assume any legalliability regarding the correctness, accuracy, completeness or reliability of this publication. Any softwaresupplied with this publication is subject to its licence conditions. Any references to proprietary softwarein the documentation, and/or any use of proprietary data formats in this release, do not constituteendorsement by ERCB/AGS of any manufacturer's product.When using information from this publication in other publications or presentations, due acknowledgmentshould be given to the ERCB/AGS. The following reference format is recommended:Graf, T. (2009): Simulation of geothermal flow in deep sedimentary basins in Alberta; Energy ResourcesConservation Board, ERCB/AGS Open File Report 2009-11, 17 p. Published July 2009 by: Energy Resources Conservation BoardAlberta Geological Survey4th Floor, Twin Atria Building4999 – 98th AvenueEdmonton, AlbertaT6B 2X3CanadaTel: 780-422-1927Fax: 780-422-1918E-mail:AGS-Info@ercb.ca Website:www.ags.gov.ab.ca  ERCB/AGS Open File Report 2009-11 (July 2009)   ã   iii  Contents Acknowledgments.........................................................................................................................................v   Abstract........................................................................................................................................................vi   1   Introduction............................................................................................................................................1   2   Mathematical Model...............................................................................................................................3   2.1   Model Selection.............................................................................................................................3   2.2   Governing Equations.....................................................................................................................3   2.2.1   Fluid Flow.........................................................................................................................3   2.2.2   Heat Transfer.....................................................................................................................5   2.2.3   Constitutive Equations.......................................................................................................6   2.2.4   Coupled System.................................................................................................................6   2.3   Model Development......................................................................................................................8   2.4   Model Verification........................................................................................................................9   2.4.1   Elder (1967) Problem........................................................................................................9   2.4.2   Caltagirone (1982) Analytical Solution...........................................................................10   3   Geothermal Test Case..........................................................................................................................12   4   Model Applicability and Outlook.........................................................................................................14   5   References............................................................................................................................................15   Tables Table 1. Parameters for the Elder (1967) thermal-convection problem (Oldenburg et al., 1995)..............10   Figures Figure 1. Block model of geological formations that represent a geothermal reservoir...............................1   Figure 2. Cross-sectional view (AA’) across the Western Canada Sedimentary Basin in Alberta...............2   Figure 3. Horizontal distribution of the integral geothermal gradient (between bottom and top of thesedimentary column) in the Western Canada Sedimentary Basin.................................................4   Figure 4. Variation of water density and viscosity with temperature...........................................................7   Figure 5. Picard iteration to solve for variable-density variable-viscosity geothermal flow........................8   Figure 6. Configuration of the Elder problem...............................................................................................9   Figure 7. Verification of the HydroGeoSphere model with the Elder problem of free thermal convection......................................................................................................................................................10   Figure 8. Conceptual 2-D model for the model verification with the Caltagirone analytical solution.......12   Figure 9. Verification of the HydroGeoSphere model with the Caltagirone analytical solution................13   ERCB/AGS Open File Report 2009-11 (July 2009)   ã   iv
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