Thermal Energy Storage (Physical)

from watertap_contrib.reflo.solar_models import ThermalEnergyStorage

Note

This model was designed for use in a model utilizing the multiperiod framework. Steady-state applications are not recommended.

This Thermal Energy Storage (TES) model assumes the tank is at a uniform temperature (similar to a continuous stirred tank). It also assumes that both the heat transfer fluid and the storage fluid are the same. Water is used as the default heat transfer and storage fluid.

Degrees of Freedom/Variables

The TES model has 4 state variables at the inlet. Typically the variables listed below define the heat exchanger and process ports inlet and outlet.

Variables	Variable name	Symbol	Valid range	Units
Inlet mass flow rate liquid water	flow_mass_phase_comp['Liq','H2O']	\(m_{l}\)		\(\text{kg/s}\)
Inlet mass flow rate vapor water	flow_mass_phase_comp['Vap','H2O']	\(m_{v}\)		\(\text{kg/s}\)
Temperature	temperature	\(T_{f}\)	298.15 - 372.15	\(\text{K}\)
Pressure	pressure	\(P\)		\(\text{Pa}\)

The following variables should also be fixed for the model to be fully-defined. An initial temperature is assigned to the outlet stream at the heat exhanger and process loop.

Variables	Variable Name	Symbol	Valid Range	Units
Initial temperature	tes_initial_temperature	\(T_{0}\)	298.15 - 372.15	\(\text{K}\)
Time step	dt	\(dt\)		\(\text{hr}\)
Hours of storage	hours_storage	\(t_{storage}\)	0-24	\(\text{hr}\)
Design thermal output rate	heat_load	\(P_{th}\)		\(\text{MW}\)
Thermal energy storage capacity for hours of storage at design thermal output rate	thermal_energy_capacity	\(q_{TES}\)		\(\text{MWh}\)

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’]

Parameters

The following parameters are used as default values and are mutable.

Description	Parameter Name	Symbol	Default Value	Units
Heat transfer fluid density	heat_transfer_fluid_density	\(\rho_{htf}\)	1000	\(\text{kg/m}^{3}\)
Heat transfer fluid specific heat capacity	heat_transfer_fluid_csp	\(C_{sp,htf}\)	4184	\(\text{J/kg/K}\)
Pump power	pump_power	\(P_{pump}\)	1	\(\text{W}\)
Pump efficiency	pump_eff	\(\eta_{pump}\)	0.8	\(\text{dimensionless}\)
Design temperature	temperature_design	\(T_{design}\)	372.15	\(\text{K}\)
Cold temperature	temperature_cold	\(T_{cold}\)	293.15	\(\text{K}\)

Equations

Description	Equation
TES volume	\(V_{TES} = q_{TES} / (C_{sp,htf}*\rho_{htf}*(T_{design}-T_{cold}))\)
Thermal energy capacity	\(q_{TES} = t_{storage} * P_{th}\)
Pumping power demand	\(P_e = P_{pump}/\eta_{pump}\)
Tank temperature	\(T_{tank} = T_{0} + (Q_{in} - Q_{out})*dt/(V_{TES}*C_{sp,htf}*\rho_{htf})\)

Costing

The following parameters are constructed on the costing block for TES costing:

Cost Component	Variable	Symbol	Value	Units	Description
Cost per volume storage	cost_per_volume_storage	\(c_{tes}\)	2000	\(\text{USD}\text{/m}^3\)	Cost per volume for thermal storage
Contingency factor	contingency_frac_direct_cost	\(X_{c}\)	0	\(\text{dimensionless}\)	Fraction of direct costs for contingency
Indirect cost factor	indirect_frac_direct_cost	\(X_{i}\)	0.13	\(\text{dimensionless}\)	Fraction of direct costs for indirect costs
Fixed operating cost per system capacity	fixed_operating_by_capacity	\(c_{fix,op}\)	66	\(\text{USD/kW/year}\)	Fixed operating cost of flat plate plant per kW capacity

These are used the calculate the following capital and operating costs:

Cost Component	Symbol	Equation
Thermal storage cost	\(C_{tes}\)	\(c_{tes} \times V_{TES}\)
Fixed operating cost	\(C_{fix,op}\)	\(c_{fix,op} \times P_{th}\)

The direct costs include the cost of the storage, and contingency.

\[C_{direct} = C_{tes} (1 + X_{c})\]

Indirect costs are calculated as a fraction of the direct costs:

\[C_{indirect} = C_{direct} X_{i}\]

The total capital cost of the FPC system is the sum of direct and indirect costs and sales tax:

\[C_{capital} = (C_{indirect} + C_{direct}) (1 + X_{t})\]

Note that by default, REFLO assumes no sales tax (i.e., \(X_{t} = 0\)).

The total operating cost is the fixed operating cost:

\[C_{operating} = C_{fix,op}\]