Thermal energy storage simulation

1 inlet -> 1 outlet; charges or discharges a sensible-heat / PCM store (reports state of charge and time to full/empty)

Governing equations

The exact equations the solver works for a thermal energy storage — the same math shown in the app's "Theory" panel, not a black box.

$T_{out}$

fluid outlet temperature [K]

$T_{top}$

hottest (top) layer temperature [K]

$T_{bottom}$

coldest (bottom) layer temperature [K]

$\Delta T_{app}$

approach temperature at the contact end [K]

$\dot Q$

heat into the store, negative when discharging [W]

$\dot Q_{loss}$

standing loss to ambient [W]

$\dot Q_{net}$

net charge rate [W]

$UA$

loss conductance of the vessel [W/K]

$\bar T$

mass-mean store temperature [K]

$T_{amb}$

ambient temperature [K]

$\dot n$

fluid molar flow [mol/s]

$h_{in}$

inlet molar enthalpy [J/mol]

$h_{out}$

outlet molar enthalpy [J/mol]

$E$

stored energy above the window floor [J]

$E_{cap}$

storage capacity over the operating window [J]

$m_i$

mass of layer i [kg]

$m$

total medium mass [kg]

$c_p$

medium specific heat [J/kg/K]

$T_i$

layer i temperature [K]

$T_{min}$

operating-window floor [K]

$T_{max}$

operating-window ceiling [K]

$L$

PCM latent heat [J/kg]

$f_{melt}$

PCM melt fraction [-]

$SOC$

state of charge [-]

$t_{full}$

time to full at the net rate [s]

$t_{empty}$

time to empty at the net rate [s]

Parameters

a heat store the process fluid charges or draws on. 'mass' [kg] of medium; 'medium' (water | solar_salt | thermal_oil | rock | concrete) or 'cp' [J/kg/K]; the store's state as 'temperature' [K] (well-mixed) or 'layer_temperatures' [K, hottest first] for a stratified store, or a PCM via 'melting_temperature' [K] + 'latent_heat' [J/kg] (+ 'melt_fraction' 0-1); 'mode' auto | charge | discharge (auto picks from the inlet T); 'approach' [K]; 't_min'/'t_max' [K] the operating window that defines capacity and state of charge; 'ua_loss' [W/K] + 'ambient_temperature' [K] for the standing loss; 'pressure_drop' [Pa]. Charging exhausts at the COLDEST layer, discharging draws from the HOTTEST, so a stratified store delivers hotter than a mixed one holding the same energy. Steady-state: the store's temperatures do not move within a solve -- the op reports time_to_full_hours / time_to_empty_hours at the current net rate. In the Dynamics run mode and in the live DCS engine the store's layers MOVE (DYN-TES / LIVE-TES): it charges and discharges through the flowsheet's own transient, a temperature loop downstream closes through it, and the standalone transient is the 'Thermal energy storage' analysis tool

Example flowsheets that use it