Multi-Effect Distillation with Thermal Vapor Compression

from watertap_contrib.reflo.unit_models import MEDTVCSurrogate

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 ¹

Model Structure

The MED-TVC model uses the WaterTAP seawater property package for the liquid phase and the WaterTAP pure water property package for the vapor phase. The model consists of 5 StateBlocks (with 5 Ports in parenthesis below).

• Feed flow (feed)

• Distillate (dist)

• Brine flow (brine)

• Heating steam (steam)

• Motive steam (motive)

The number of effects, as a key design parameter of the MED-TVC model, should be provided via num_effects configuration argument, and can be any integer between 8 and 16. In this model, numbers of effects of 8, 10, 12, 14, 16 are verified with the operational data, while the others are interpolated.

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	\(\text{°C}\)
Motive steam pressure entering the thermocompressor	motive_steam_props.pressure	\(P_{m}\)	4 - 45	\(\text{bar}\)
Recovery ratio	recovery_vol_phase['Liq']	\(RR\)	0.3 - 0.4	\(\text{dimensionless}\)
Feed volume flow rate	feed_props.flow_vol_phase['Liq']	\(q_{f}\)	>0	\(\text{m}^3\text{/s}\)

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

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

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	\(\Delta T_{cool}\)	delta_T_cooling_reject	-3	\(\text{K}\)
System thermal loss faction	\(f_{th,loss}\)	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	\(\text{GOR}\)	gain_output_ratio	None	\(\text{dimensionless}\)
Specific total area	\(sA\)	specific_area_per_m3_day	None	\(\text{m}^2\text{/m}^3\text{/day}\)
Specific total area	\(sA_m\)	specific_area_per_kg_s	None	\(\text{m}^2\text{kg}\text{/s}\)
Heating steam mass flow rate entering the first effect	\(m_s\)	heating_steam_props[0].flow_mass_phase_comp['Vap', 'H2O']	None	\(\text{kg/s}\)
Motive steam mass flow rate entering the thermocompressor	\(m_m\)	motive_steam_props[0].flow_mass_phase_comp['Vap', 'H2O']	None	\(\text{kg/s}\)

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

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

Equations

Description	Equation
Temperature in the last effect	\(T_{last} = \Delta T_{last} + T_{f}\)
Temperature of outlet cooling water	\(T_{cool,out} = \Delta T_{cool,in} + T_{f}\)
Distillate volumetric flow rate (production rate)	\(q_{dist} = q_{f} T_{f}\)
Steam mass flow rate	\(m_{steam} = \cfrac{m_{dist}}{\text{GOR}}\)
Specific thermal energy consumption	\(\text{STEC} = \cfrac{(H_{motive,vap} - H_{heating,liq}) \rho_{dist}}{\text{GOR}}\)
Thermal power requirement	\(P_{th,req} = \text{STEC} \times q_{dist}\)
Energy balance	\(q_{sw,tot}(H_{cool} - H_{feed}) = (1 - f_{th,loss}) P_{th,req} - m_{brine} H_{brine} - m_{dist} H_{dist} + m_{feed} H_{cool}\)

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

Costing

The following parameters are constructed on the MED-TVC costing block:

Cost Component	Variable	Symbol	Value	Units	Description
Fraction of cost for evaporator	cost_fraction_evaporator	\(f_{evap}\)	0.4	\(\text{dimensionless}\)	Cost fraction of the evaporator
Fraction of cost for maintenance	cost_fraction_maintenance	\(f_{maint}\)	0.02	\(\text{year}^{-1}\)	Fraction of capital cost for maintenance
Fraction of cost for insurance	cost_fraction_insurance	\(f_{ins}\)	0.005	\(\text{year}^{-1}\)	Fraction of capital cost for insurance
Chemicals	cost_chemicals_per_vol_dist	\(c_{chem}\)	0.04	\(\text{USD/m}^3\)	Cost of chemicals per volume of distillate
Labor	cost_labor_per_vol_dist	\(c_{labor}\)	0.033	\(\text{USD/m}^3\)	Cost of labor per volume of distillate
Miscellaneous	cost_misc_per_vol_dist	\(c_{misc}\)	0.033	\(\text{USD/m}^3\)	Miscellaneous cost per volume of distillate
Brine disposal	cost_disposal_per_vol_brine	\(c_{disposal}\)	0.02	\(\text{USD/m}^3\)	Cost of brine disposal per volume of brine
Electricity consumption	specific_energy_consumption_electric	\(\text{SEC}\)	1.5	\(\text{kWh/m}^3\)	Cost of electricity consumption per volume of distillate
MED equation A parameter	med_sys_A_coeff	\(A\)	6291	\(\text{USD2018/m}^3\)	Cost of MED system A parameter
MED equation B parameter	med_sys_B_coeff	\(b_{MED}\)	-0.135	\(\text{dimensionless}\)	Cost of MED system exponent
Heat exchanger reference area	heat_exchanger_ref_area	\(A_{ref}\)	302.01	\(\text{m}^2\text{/kg/s}\)	Cost of heat exchanger reference area
Heat exchanger exponent	heat_exchanger_exp	\(b_{hx}\)	0.8	\(\text{dimensionless}\)	Heat exchanger cost equation exponent

These parameters are used to calculate the capital and operating costs of the MED-TVC system.

Cost Component	Symbol	Equation
MED specific cost	\(C_{MED}\)	\(A q_{dist}^{b_{MED}}\)
Membrane system cost	\(C_{mem}\)	\(q_{dist} \left( C_{MED} (1 - f_{evap}) \right)\)
Evaporator cost	\(C_{evap}\)	\(q_{dist} \left( C_{MED} f_{evap} \left( \cfrac{sA_m}{A_{ref}} \right)^{b_{hx}} \right)\)

The capital costs for the MED-TVC system is the sum of the membrane system and evaporator costs:

\[C_{capital} = C_{mem} + C_{evap}\]

The operating costs include maintenance, insurance, chemicals, labor, miscellaneous, brine disposal, and electricity consumption:

\[C_{operating} = C_{capital} \left(f_{maint} + f_{ins}\right) + q_{dist} \left( c_{chem} + c_{labor} + c_{misc} + c_{disposal} \right)\]

The electric power consumption is calculated as:

\[P_{electric} = \text{SEC} \times q_{dist}\]

And the thermal power consumption is calculated as:

\[P_{thermal} = \text{STEC} \times q_{dist}\]

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.