Multi-effect Distillation with Thermal Vapor Compression (MED-TVC)

This Multi-effect Distillation with Thermal Vapor Compression (MED-TVC) unit model

• supports steady-state only

• is a surrogate model

• is verified against the operation data in Plataforma Solar de Almeria (PSA) [1]

Degrees of Freedom

The MED-TVC model has 5 degrees of freedom that should be fixed for the unit to be fully specified.

Typically, the following variables are fixed, including the state variables at the inlet. The valid range of each variable is listed based on the tested range of the surrogate equations.

Variables	Variable name	Symbol	Valid range	Unit
Feed salinity	feed_props.conc_mass_phase_comp[‘Liq’, ‘TDS’]	\(X_{f}\)	30 - 60	\(\text{g/}\text{L}\)
Feed temperature	feed_props.temperature	\(T_{f}\)	25 - 35	\(^o\text{C}\)
Motive steam pressure entering the thermocompressor	motive_steam_props.pressure	\(P_{m}\)	4 - 45	\(bar\)
Recovery ratio	recovery_vol_phase[‘Liq’]	\(RR\)	0.3 - 0.4	\(\text{dimensionless}\)
Feed volume flow rate	feed_props.flow_vol_phase[‘Liq’]	\(v_{f}\)		\(\text{m}^3 / \text{s}\)

All five variables above are independent input variables to the surrogate equations. Typicall the feed volume flow rate can be determined given a desired system capacity:

\(v_{f}\) = \(\frac{Capacity}{RR}\)

Model Structure

This MED-TVC model consists of 5 StateBlocks (as 5 Ports in parenthesis below).

• Feed flow (feed)

• Distillate (distillate)

• Brine flow (brine)

• Heating steam (steam)

• Motive steam (motive)

The number of effects, as a key design parameter of the LT-MED model, should be provided in the spefic configuration key-value pair below.

num_effects: an integer between 8 to 16.

In this model, numbers of effects of 8, 10, 12, 14, 16 are verified with the operational data, and the other numbers in between are interpolated by those validated numbers.

Sets

Description	Symbol	Indices
Time	\(t\)	[0]
Phases	\(p\)	[‘Liq’, ‘Vap’]
Components	\(j\)	[‘H2O’, ‘TDS’]

Variables

The system configuration variables should be fixed at the default values, with which the surrogate model was developed:

Description	Symbol	Variable Name	Value	Units
Temperature difference between the last and first effect	\(\Delta T_{last}\)	delta_T_last_effect	10	\(\text{K}\)
Temperature decrease in cooling reject water	\(\Delta T_{cooling}\)	delta_T_cooling_reject	-3	\(\text{K}\)
System thermal loss faction	\(f_{Q_{loss}}\)	thermal_loss	0.054	\(\text{dimensionless}\)

The following performance variables are derived from the surrogate equations:

Description	Symbol	Variable Name	Index	Units
Gain output ratio	\(GOR\)	gain_output_ratio	None	\(\text{dimensionless}\)
Specific total area	\(sA\)	specific_area_per_m3_day	None	\(\text{m}^2\text{ per m}^3\text{/day}\)
Heating steam mass flow rate entering the first effect	\(q_s\)	None	\(kg/s\)
Motive steam mass flow rate entering the thermocompressor	\(q_m\)	None	\(kg/s\)

The following variables are calculated by fixing the default degree of freedoms above.

Description	Symbol	Variable Name	Units
Thermal power requirement	\(P_{req}\)	thermal_power_requirement	\(\text{kW}\)
Specific thermal energy consumption	\(STEC\)	specific_energy_consumption_thermal	\(\text{kWh} / \text{m}^3\)
Total seawater mass flow rate (feed + cooling)	\(m_{seawater_{total}}\)	feed_cool_mass_flow	\(\text{kg} / \text{s}\)
Total seawater volumetric flow rate (feed + cooling)	\(v_{seawater_{total}}\)	feed_cool_vol_flow	\(\text{m}^3 / \text{h}\)

Equations

Description	Equation
Temperature in the last effect	\(T_{last} = \Delta T_{last} + T_{feed}\)
Temperature of outlet cooling water	\(T_{cooling,out} = \Delta T_{cooling,in} + T_{f}\)
Distillate volumetric flow rate (production rate)	\(v_{distillate} = v_{feed} T_{f}\)
Steam mass flow rate	\(m_{steam} = m_{distillate} / GOR\)
Specific thermal energy consumption	\(STEC = \frac{(H_{motive,vap} - H_{heating,liq}) \rho_{distillate}}{GOR}\)
Thermal power requirement	\(P_{req} = STEC \times v_{distillate}\)
Energy balance	\(v_{seawater_{total}} \times (H_{cooling} - H_{feed}) = (1 - f_{Q_{loss}})\times P_{req} - m_{brine} H_{brine} - m_{distillate} H_{distillate} + m_{feed} H_{cooling}\)

Surrogate equations and the corresponding coefficients for different number of effects can be found in the unit model class.

References

[1] Ortega-Delgado, B., Palenzuela, P., & Alarcón-Padilla, D. C. (2016). Parametric study of a multi-effect distillation plant with thermal vapor compression for its integration into a Rankine cycle power block. Desalination, 394, 18-29.