| Title | Beyond Gringarten: A closed-form solution to predict the temperature evolution of geothermal doublets (in porous, low-enthalpy settings) |
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| Authors | C. Wallmeier, P. J. Vardon, A. Daniilidis |
| Year | 2026 |
| Conference | World Geothermal Congress |
| Keywords | |
| Abstract | Direct-use geothermal energy can play a significant part in the heating transition. Once a system of wells is built, it can run for decades, providing sustainable heat at low operating costs. Because initial investment costs are high, it is important to have an estimate of how long a geothermal system will be able to operate. This is mainly determined by the temperature of the produced water, which slowly begins to decline at thermal breakthrough when colder, re-injected water arrives at the production well. Numerical models can provide insight into cooling behavior, but require detailed subsurface information, and significant time and expertise to set up and run. For typical doublet setups, an analytical expression for the time of thermal breakthrough has been known since 1975 (Gringarten & Sauty). However, equating thermal breakthrough with usable lifetime is pessimistic, as it only marks the beginning of cooling, after which doublets may still provide usable temperatures for many years. We present a closed-form model that allows to predict production temperature as a function of time. It is aimed at DUGS doublets in conduction-dominated, porous sedimentary aquifers. The model consists of a single equation. As input it takes seven parameters that are most relevant to doublet cooling and can be estimated reasonably well in locations with limited subsurface data. They are reservoir depth, thickness and porosity, thermal gradient, and well spacing, production rate and injection temperature. Comparison with numerical simulations shows excellent agreement in predicted temperature and predicted doublet lifetime. |