Low Temperature Multi-Effect Distillation

from watertap_contrib.reflo.unit_models import LTMEDSurrogate

This Low Temperature Multi-Effect Distillation (LT-MED) unit model:

supports steady-state only

is a surrogate model

is verified against the operation data from pilot-scale systems in Plataforma Solar de Almeria (PSA)

Degrees of Freedom

The LT-MED 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`	\(T_{f}\)	15 - 35	\(^o\text{C}\)
Heating steam temperature	`steam_props.temperature`	\(T_{s}\)	60 - 85	\(^o\text{C}\)
Recovery ratio	`recovery_vol_phase['Liq']`	\(RR\)	0.3 - 0.5	\(\text{dimensionless}\)
Feed volume flow rate	`feed_props.flow_vol_phase['Liq']`	\(q_{f}\)	>0	\(\text{m}^3 / \text{s}\)

The first four variables are independent input variables to the surrogate equations. Typically the feed volume flow rate can be determined given a desired system capacity:

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

Model Structure

This LT-MED model consists of 4 StateBlocks (as 4 Ports in parenthesis below).

Feed flow (feed)
Distillate (distillate)
Brine flow (brine)
Heating steam (steam)

The number of effects, as a key design parameter of the LT-MED model, should be provided via num_effects configuration argument, and can be any integer between 3 and 14. In this model, numbers of effects of 3, 6, 9, 12, 14 are verified with the operational data, while the others are interpolated.

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	\(\text{m}^2\text{ per m}^3\text{/day}\)

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	\(T_{cooling,out} = \Delta T_{cooling,in} + T_{feed}\)
Distillate volumetric flow rate (production rate)	\(v_{distillate} = v_{feed} T_{feed}\)
Steam mass flow rate	\(m_{steam} = m_{distillate} / GOR\)
Specific thermal energy consumption	\(STEC = \frac{\Delta H_{vap} \times \rho_{distillate}}{GOR}\)
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] Palenzuela, P., Hassan, A. S., Zaragoza, G., & Alarcón-Padilla, D. C. (2014). Steady state model for multi-effect distillation case study: Plataforma Solar de Almería MED pilot plant. Desalination, 337, 31-42.

[2] Ortega-Delgado, B., Garcia-Rodriguez, L., & Alarcón-Padilla, D. C. (2017). Opportunities of improvement of the MED seawater desalination process by pretreatments allowing high-temperature operation. Desalin Water Treat, 97, 94-108.