Analytical solutions for aquifer thermal energy storage

Abstract

The concept of aquifer thermal energy storage involves injection of water at elevated temperature, and possibly nonambient salinity, into a host aquifer. We consider axisymmetric injection, wherein both the composition and temperature of the injected fluid differ from the fluid in the target aquifer. In this setting, we derive the governing equations within a vertically integrated framework, and show their self‐similar structure. We subsequently derive explicit approximate solutions to the self‐similar equations for parameter ranges of relevance to thermal energy storage (small density and viscosity differences). The analysis is supported by numerical validation, covering the relevant parameter regime. The resulting comparisons demonstrate the mathematical qualities of the analytical approximations. A study based on field data from analogue sites justifies the assertions regarding the magnitude of the dimensionless parameters used in the analysis.

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

“…Thermal perturbations to underground formations can be caused by injecting fluids of different temperature into the deep subsurface or by natural recharge of surface water with sinusoidally time-varying temperature into the shallow subsurface. Relevant applications involving fluid injection may be directly related to energy storage and production, such as for thermal oil recovery (Kuhn & Koch, 1953;Walter, 1957), aquifer thermal energy storage (Andersson et al, 2013;Meyer & Todd, 1973;Nordbotten, 2017;Tsang et al, 1982), and geothermal energy production (Bodvarsson & Eggers, 1972;Harlow & Pracht, 1972), or they may not be energy related, such as for waste-water disposal, water flooding for secondary oil recovery, and geological CO 2 storage. Relevant applications in the latter include estimating the rate of groundwater recharge using field temperature measurements (Bredehoeft & Papadopulos, 1965;Constantz et al, 2002;Hatch et al, 2006;Silliman et al, 1995;Stallman, 1965;Suzuki, 1960).…”

Analytical Model for Heat Transfer Accounting for Both Conduction and Dispersion in Aquifers With a Robin‐Type Boundary Condition at the Injection Well

“…Ganguly and Kumar (2014) improved Bodvarsson and Tsang's (1982) model by incorporating the effect of thermal conduction due to the cold water injection in the Cartesian coordinates system. Nordbotten (2017) derived an analytical solution and approximate solutions incorporating the density and viscosity differences in an ATES system for describing the thermal front distribution in a confined aquifer without the effect of heat fluxes across its confining rocks. It is worth noting that all of those studies set the inner boundary condition as a Dirichlet type for the injection source, implying that there is an extremely large heat source (Yeh & Yeh, 2007).…”

Thermal Dispersion in a Fracture‐Matrix System With Application to Geothermal Energy Extraction

“…It utilizes produced hot fluids from sedimentary basins (>100°C) to generate electricity (Parisio & Yoshioka, 2020;Porro et al, 2012). Recently, geothermal resource development has gained momentum worldwide, and its contribution to the global energy portfolio is expected to increase (Nordbotten, 2017). This implies that geothermal energy may play an essential role during the energy transition.Fractured geothermal reservoirs are spread worldwide, constituting a significant share of geothermal energy globally (Goldscheider et al, 2010;Ishibashi et al, 2016;Wei et al, 2021).…”