Thermal Energy Storage (TES)
This thermal energy storage (TES) model assumes the tank is at a uniform temperature (similar to a continuous stirred tank) and supports steady-state only. It also assumes that both the heat transfer fluid and the storage fluid are the same and are water as default.
Model Structure
This TES model consists of 4 StateBlocks (as 4 Ports in parenthesis below). Two ports connect to the the external heat exchanger which adds heat to the TES and two ports connect to the process side and provide heat to the treatment process.
Heat exchanger inlet (tes_hx_inlet)
Heat exchanger outlet (tes_hx_outlet)
Process inlet (tes_process_inlet)
Process outlet (tes_process_outlet)
Sets
Description |
Symbol |
Indices |
|---|---|---|
Time |
\(t\) |
[0] |
Phases |
\(p\) |
[‘Liq’, ‘Vap’] |
Components |
\(j\) |
[‘H2O’] |
Degrees of Freedom/Variables
The TES model has 4 degrees of freedom that should be fixed for the unit to be fully specified in addition to the state variables at the inlet and outlet. Typically the variables listed below define the heat exchanger and process ports inlet and outlet.
Variables |
Variable name |
Symbol |
Valid range |
Unit |
|---|---|---|---|---|
Temperature |
|
\(T_{f}\) |
298.15 - 372.15 |
\(\text{K}\) |
Pressure |
|
\(P\) |
\(Pa\) |
|
Mass flow rate of vapor phase |
|
\(m_{v}\) |
\(kg/s\) |
|
Mass flow rate of liquid phase |
|
\(m_{l}\) |
\(kg/s\) |
The following variables should also be fixed. An initial temperature is assigned to the outlet stream at the heat exhanger and process loop.
Variables |
Variable name |
Symbol |
Valid range |
Unit |
|---|---|---|---|---|
Initial temperature |
|
\(T_{0}\) |
298.15 - 372.15 |
\(\text{K}\) |
Time step |
|
\(dt\) |
\(h\) |
|
Hours of storage |
|
\(h_{storage}\) |
0-24 |
\(h\) |
Heat load |
|
\(heat_{load}\) |
\(MW\) |
Parameters
The following parameters are used as default values and are mutable.
Description |
Parameter Name |
Symbol |
Value |
Units |
|---|---|---|---|---|
Heat transfer fluid density |
|
\(\rho_{htf}\) |
1000 |
\(kg/m^{3}\) |
Heat transfer fluid specific heat capacity |
|
\(C_{sp,htf}\) |
4184 |
\(J/kg/K\) |
Pump power |
|
\(P_{pump}\) |
1 |
\(W\) |
Pump efficiency |
|
\(\eta_{pump}\) |
1 |
\(\text{dimensionless}\) |
Design temperature |
|
\(T_{design}\) |
372.15 |
\(\text{K}\) |
Cold temperature |
|
\(T_{cold}\) |
293.15 |
\(\text{K}\) |
Equations
Description |
Equation |
|---|---|
TES volume |
\(V_{TES} = \text{Thermal Energy Capacity} / (C_{sp,htf}*\rho_{htf}*(T_{design}-T_{cold}))\) |
Thermal energy capacity |
\(\text{Thermal Energy Capacity} = h_{storage} * heat_{load}\) |
Electricity |
\(electricity = P_{pump}/\eta_{pump}\) |
Tank temperature |
\(T_{tank} = T_{0} + (Q_{in} - Q_{out})*dt/(V_{TES}*C_{sp,htf}*\rho_{htf})\) |
Costing
The TES capital cost includes direct costs, indirect costs and sales tax. The direct costs include cost storage and a contingency factor. The indirect costs are a fraction of the direct cost. A fixed operating cost is calculated as a linear function of heat load of TES.
Description |
Variable Name |
Equation |
|---|---|---|
Direct capital costs |
|
\(Capital Cost_{direct} = (V_{TES} * \text{Cost per }m^{3}\text{ storage})*(1 + \text{Contingency fraction})\) |
Indirect capital costs |
|
\(Capital Cost_{indirect} = Capital Cost_{direct}*\text{Indirect capital cost fraction}\) |