docs(supptechinfo): minor edits to GWE chapter (chap. 10) (#1819)

doc/SuppTechInfo/groundwater-energy-model.tex

@@ -1,5 +1,5 @@
 
-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.
 
@@ -19,7 +19,7 @@ \subsection{Mathematical Model} \label{sec:mathmodel}
 \end{aligned}
 \end{equation}
 
-\noindent The two terms on the left-hand side of equation \ref{eqn:pdegwe} represent the rates of change in thermal energy storage in the water and the solid matrix, respectively. The six terms on the right-hand side of equation \ref{eqn:pdegwe} represent the rates at which thermal energy is advected, dispersed and/or conducted, added or removed by groundwater inflows or outflows, added or removed directly to or from the water, produced/decayed in the water, and produced/decayed in the solid matrix, respectively. The parameters and variables in equation \ref{eqn:pdegwe} are defined as follows: $S_w$ is the water saturation (dimensionless) defined as the volume of water per volume of voids; $\theta$ is the effective porosity, defined as volume of voids participating in transport per unit volume of aquifer; $\rho_w$ and $\rho_s$ are the densities ($M/L^3$) of the water and solid-matrix material, respectively; $C_{pw}$ and $C_{ps}$ are the specific heats ($E/(M \, deg)$) of the water and solid-matrix material, respectively; $T$ is temperature ($deg$); $t$ is time ($T$); $\matr{q}$ is the vector of specific discharge ($L/T$); $\matr{D}_T$ is the second-order tensor of hydrodynamic dispersion coeffiients for thermal energy transport ($L^2/T$); $q'_s$ is the volumetric flow rate per unit volume of aquifer (defined as positive for flow into the aquifer) for fluid sources and sinks ($1/T$), $T_s$ is the temperature of the source or sink fluid ($deg$), $E_s$ is rate of energy loading per unit volume of aquifer ($M/L^3T$), $E_a$ is rate of energy exchange with advanced stress packages ($M/L^3T$), $\gamma_{1w}$ is the zero-order energy decay rate coefficient in the water ($E/L^3T$), and $\gamma_{1s}$ is the zero-order energy decay rate coefficient in the solid ($E/MT$). Note that $\gamma_{1w}$ is defined on a per-volume-of-water basis, whereas $\gamma_{1s}$ is defined on a per-mass-of-solid basis. Note that $\rho_w$, $\rho_s$, $C_{pw}$, and $C_{ps}$ are assumed to remain constant with time, although the solid properties can vary spatially from cell to cell.
+\noindent The two terms on the left-hand side of equation \ref{eqn:pdegwe} represent the rates of change in thermal energy storage in the water and the solid matrix, respectively. The six terms on the right-hand side of equation \ref{eqn:pdegwe} represent the rates at which thermal energy is advected, dispersed and/or conducted, added or removed by groundwater inflows or outflows, added or removed directly to or from the water, produced/decayed in the water, and produced/decayed in the solid matrix, respectively. The parameters and variables in equation \ref{eqn:pdegwe} are defined as follows: $S_w$ is the water saturation (dimensionless) defined as the volume of water per volume of voids; $\theta$ is the effective porosity, defined as volume of voids participating in transport per unit volume of aquifer; $\rho_w$ and $\rho_s$ are the densities ($M/L^3$) of the water and solid-matrix material, respectively; $C_{pw}$ and $C_{ps}$ are the specific heat capacities ($E/(M \, deg)$) of the water and solid-matrix material, respectively; $T$ is temperature ($deg$); $t$ is time ($T$); $\matr{q}$ is the vector of specific discharge ($L/T$); $\matr{D}_T$ is the second-order tensor of hydrodynamic dispersion coefficients for thermal energy transport ($L^2/T$); $q'_s$ is the volumetric flow rate per unit volume of aquifer (defined as positive for flow into the aquifer) for fluid sources and sinks ($1/T$), $T_s$ is the temperature of the source or sink fluid ($deg$), $E_s$ is rate of energy loading per unit volume of aquifer ($M/L^3T$), $E_a$ is rate of energy exchange with advanced stress packages ($M/L^3T$), $\gamma_{1w}$ is the zero-order energy decay rate coefficient in the water ($E/L^3T$), and $\gamma_{1s}$ is the zero-order energy decay rate coefficient in the solid ($E/MT$). Note that $\gamma_{1w}$ is defined on a per-volume-of-water basis, whereas $\gamma_{1s}$ is defined on a per-mass-of-solid basis. Note that $\rho_w$, $\rho_s$, $C_{pw}$, and $C_{ps}$ are assumed to remain constant with time, although the solid properties can vary spatially from cell to cell.
 
 Equation \ref{eqn:pdegwe} is closely analogous to the equation solved by the Groundwater Transport (GWT) Model for solute transport \citep{modflow6gwt}, with the following differences:
 
@@ -112,7 +112,7 @@ \subsubsection{Conduction and Dispersion (CND) Package}
 
 \subsubsection{Advanced Stress Packages}
 
-The version of the GWE Model described here offers four advanced stress packages, each of which is analogous and functions similarly to an advanced package in the GWT Model: Lake Energy Transport (LKE), Multi-Aquifer Well Energy Transport (MWE), Streamflow Energy Transport (SFE), and Unsaturated Zone Energy Transport (UZE). The GWE advanced stress packages will not be described in detail here except to note differences from the corresponding GWT packages. The primary difference, of course, is that GWE advanced stress packages deal with transport of thermal energy, not solute mass.
+The version of the GWE Model described here offers four advanced stress packages, each of which is analogous and functions similarly to an advanced package in the GWT Model: Lake Energy Transport (LKE), Multi-Aquifer Well Energy Transport (MWE), Streamflow Energy Transport (SFE), and Unsaturated Zone Energy Transport (UZE). The GWE advanced stress packages will not be described in detail here except to note differences from the corresponding GWT packages. The primary difference, of course, is that GWE advanced stress packages explicitly simulate thermal energy transport within their respective features, not solute mass. Optionally, the SSM package may be used to represent the effects of thermal energy exchange between an advanced transport package and the subsurface for cases where the temperature of the feature is known.
 
 The LKE, SFE, and MWE Packages offer a mechanism for energy to conduct between the lake or stream reach and the aquifer through a thermally conductive layer that can represent, for example,  a lake or stream bed or a well casing. The LKT, SFT, and MWT packages do not offer analogous diffusion of solute through the a conductive layer. The LKE and SFE packages also account for removal of thermal energy from surface water by evaporation.