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emorway-usgs committed May 17, 2024
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The Groundwater Energy (GWE) Model for \mf simulates three-dimensional transport of thermal energy in flowing groundwater based on a generalized control-volume finite-difference approach. The GWE Model is designed to work with the Groundwater Flow (GWF) Model \citep{modflow6gwf} for \mf, which simulates transient, three-dimensional groundwater flow. The version of the GWE model documented here must use the same spatial discretization used by the GWF Model; however, that spatial discretization can be represented by regular MODFLOW grids consisting of layers, rows, and columns, or by more general unstructured grids. The GWE Model simulates (1) advective transport, (2) the combined hydrodynamic dispersion processes of velocity-dependent mechanical dispersion and thermal conduction in groundwater, (3) thermal conduction in the solid aquifer material, (4) storage of thermal energy in the groundwater and solid aquifer material, (5) thermal equilibration between the groundwater and solid aquifer material, (5) zero-order decay or production of thermal energy in the groundwater and the solid, (6) mixing from groundwater sources and sinks, and (7) direct addition or removal of thermal energy. The GWE Model can also represent advective energy transport through advanced package features, such as streams, lakes, multi-aquifer wells, and the unsaturated zone. If the GWE Model application uses the Water Mover (MVR) Package to connect flow packages, then energy transport between these packages can also be represented. The transport processes described here have been implemented in a fully implicit manner and are solved in a system of equations using iterative numerical methods. The present version of the GWE Model for \mf does not have an option to calculate steady-state transport solutions; if a steady-state solution is required, then transient evolution of the temperature must be represented using multiple time steps until no further significant changes in temperature are detected.
The Groundwater Energy (GWE) Model for \mf simulates three-dimensional transport of thermal energy in flowing groundwater based on a generalized control-volume finite-difference approach. The GWE Model is designed to work with the Groundwater Flow (GWF) Model \citep{modflow6gwf} for \mf, which simulates transient, three-dimensional groundwater flow. The version of the GWE model documented here must use the same spatial discretization used by the GWF Model; however, that spatial discretization can be represented by regular MODFLOW grids consisting of layers, rows, and columns, or by more general unstructured grids. The GWE Model simulates (1) advective transport, (2) the combined hydrodynamic dispersion processes of velocity-dependent mechanical dispersion and thermal conduction in groundwater, (3) thermal conduction in the solid aquifer material, (4) storage of thermal energy in the groundwater and solid aquifer material, (5) thermal equilibration between the groundwater and solid aquifer material, (5) zero-order decay or production of thermal energy in the groundwater and the solid, (6) mixing from groundwater sources and sinks, and (7) direct addition or removal of thermal energy. The GWE Model can also represent advective energy transport through advanced package features, such as streams, lakes, multi-aquifer wells, and the unsaturated zone. If the GWF Model that provides the flow field for a GWE Model uses the Water Mover (MVR) Package to connect flow packages, then energy transport between these packages can also be represented by activating the Mover Energy Transport (MVE) Package. The transport processes described here have been implemented in a fully implicit manner and are solved in a system of equations using iterative numerical methods. The present version of the GWE Model for \mf does not have an option to calculate steady-state transport solutions; if a steady-state solution is required, then transient evolution of the temperature must be represented using multiple time steps until no further significant changes in temperature are detected. Finally, temperatures calculated by a GWE Model may be used in the Buoyancy (BUY) and Viscosity (VSC) Packages. Instructions provided in the \mf Description of Input and Output document explain how pass GWE-calculated temperatures to BUY and VSC.

Transport of thermal energy is sometimes simulated using a solute-transport model. In this approach, which takes advantage of the close analogy between the governing equations for thermal-energy transport and solute transport, the solute-transport model is run with values of input parameters that have been scaled to render the governing equation representative of thermal-energy transport \citep{thorne2006, hechtmendez, mazheng2010}. The GWT Model for \mf can be used in this way. However, the new GWE Model offers the following advantages: model input and output in terms of parameters and in units that relate directly to thermal-energy transport; variation of bulk thermal conductivity with changing saturation; and simulation of thermal conduction through the solid matrix, even in dry cells.

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