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SGW 2023

48th Stanford Geothermal Workshop is scheduled for February 6-8, 2023

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Thermal Forecasting Ability of Temperature-Sensitive Tracers (2011-2016)

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Investigator(s): Morgan Ames

In order to assess whether particle tracers can provide more useful information about future thermal behavior of reservoirs than existing solute tracers, models were developed for both solute tracers and particle tracers. Three existing solute tracer types were modeled: conservative solute tracers (CSTs), reactive solute tracers with temperature dependent reaction kinetics (RSTs), and sorbing solute tracers that sorb reversibly to fracture walls (SSTs). Additionally three particle tracers which have not yet been developed in practice were modeled: dye releasing tracers (DRTs) that release a solute dye at a specified temperature threshold is reached, threshold nanoreactor tracers (TNRTs) with an encapsulated reaction that does not begin until a specified temperature threshold is reached, and temperature-time tracers (TTTs) capable of recording detailed temperature-time histories of each particle. In this study, TTTs represent the most informative tracer with respect to thermal breakthrough. These models were used in the context of an inverse problem in which synthetic tracer data was calculated for several “true” discrete fracture networks. Computational optimization was used to match the location, length, and orientation of a variable number of fractures. Finally, the thermal behavior of the fracture networks with the best fit to the data was compared to that of the true fracture networks, and the forecast accuracy was compared for all tracer types.

In this work, discrete fracture network models were developed to gain insight regarding the usefulness of the data provided by various tracer types with respect to thermal breakthrough forecasting in geothermal reservoirs. Three existing solute tracer types were modeled: conservative solute tracers (CSTs), reactive solute tracers with temperature dependent reaction kinetics (RSTs), and sorbing solute tracers that sorb reversibly to fracture walls (SSTs). Additionally three hypothetical particle tracers which have not been developed in practice were modeled: dye-releasing tracers (DRTs) that release a solute dye at a specified temperature threshold is reached, threshold nanoreactor tracers (TNRTs) with an encapsulated reaction that does not begin until a specified temperature threshold is reached, and temperature-time tracers (TTTs) capable of recording detailed temperature-time histories of each particle. An analytical model for temperature in a discrete fracture network developed by Fox (2016) was used to calculate temperature distributions used in tracer models. The tracer models were used to generate synthetic tracer data for three “true” fracture networks based on the Tamiaru fractured granite outcrop in Spain. These three fracture networks were named network 7, network 9, and network 15 and consist of of 7, 9, and 15 fractures, respectively. Both the complexity of the flow topology and the total network surface area increases with the number of fractures in these networks. These data were then fit using the PSO-MADS optimization algorithm developed by Isebor (2013) to search the space of possible fracture networks. Decision variables used in optimization were fracture location, length, and orientation and a binary “existence” variable for each fracture that turned fractures on and off in order to achieve a variable number of fractures. This resulted in a mixed-integer nonlinear programming (MINLP) problem for which PSO-MADS is well-suited. Next, the thermal model developed by Fox (2016) was utilized to calculate thermal breakthrough behavior of optimal fracture networks, and the forecast accuracy was compared for each tracer type using two forecast error metrics: TBAD (the percent area between the forecasted thermal breakthrough curve and the true thermal breakthrough curve) and 〖PTD〗_(x℃) (the percent error in the forecast of the time of a x℃ temperature drop (temperature drops of 10℃, 20℃, and 25℃ were used). Finally, relationships between forecast error metrics, objective function value, and total swept surface area in the fracture network were examined.

References: 

Fox, Don Bruce. “Thermal Hydraulic Modeling of Discretely Fractured Geothermal Reservoirs.” Cornell University, 2016.