Crystallizer Effect

from watertap_contrib.reflo.unit_models import CrystallizerEffect

The crystallizer-effect unit model calculates the energy required by a single effect to heat an incoming brine stream and vaporize a pure water vapor stream, leaving behind solids present in the This model inherits much of its structure and equations from the WaterTAP crystallizer model and adds in heat balance equations relevant to a heating steam and heat exchanger. Additionally, the water vapor stream is considered to be recovered as a pure water. This unit model supports steady-state only.

Note

Though this model can be used a standalone crystallizer, it is primarily intended to be used in the multi-effect crystallizer model.

Model Structure

The crystallizer effect model uses the WaterTAP crystallizer NaCl property package. It consists of the 4 StateBlocks (as 4 Ports in parenthesis below) already defined in the WaterTAP crystallizer model:

Properties in (inlet)
Properties out (outlet)
Solid Precipitate (solids)
Water Vapor (vapor)

In addition, this model includes the following additional StateBlocks (as Ports in parenthesis below):

Condensed Water Vapor (pure_vapor)
Heating Steam (steam)

Degrees of Freedom

Similar to the crystallizer model in WaterTAP, the crystallizer-effect model requires the feed state variables (i.e. temperature, pressure, component flowrates) be specified. Additionally, the following variables are fixed for the unit to be fully specified:

Variables	Variable Name	Units
Crystallization yield	`crystallization_yield['NaCl']`	\(\text{dimensionless}\)
Crystal growth rate	`crystal_growth_rate`	\(\text{m} / \text{s}\)
Desired median length of solid crystals	`crystal_median_length`	\(\text{m}\)
Parameter for Sounders-Brown relation	`souders_brown_constant`	\(\text{W} / \text{m}^2 / \text{K}\)
Overall heat transfer coefficient	`overall_heat_transfer_coefficient`	\(\text{W} / \text{m}^2 / \text{K}\)
Operating pressure	`operating_pressure`	\(\text{Pa}\)

Sets

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

Variables

Description	Variable Name	Symbol	Units
Steam pressure (gauge) for crystallizer heating	`steam_pressure`	\(p_{steam}\)	\(\text{bar}\)
Crystallizer pump efficiency	`efficiency_pump`	\(\eta_{pump}\)	\(\text{dimensionless}\)
Temperature difference at the inlet side	`delta_temperature_in`	\(\Delta T_{in}\)	\(\text{K}\)
Temperature difference at the outlet side	`delta_temperature_out`	\(\Delta T_{out}\)	\(\text{K}\)
Heat exchanger area	`heat_exchanger_area`	\(A_{hx}\)	\(\text{m}^2\)

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

Description	Variable Name	Symbol	Units
Energy that could be supplied from vapor	`energy_flow_superheated_vapor`	\(J_{vap}\)	\(\text{W}\)
Crystallizer thermal energy requirement	`work_mechanical[0]`	\(P_{th}\)	\(\text{kW}\)

The unit also makes use of the latent heat of vaporization and enthalpy state variables from the property package:

Description	Symbol
Latent heat of vaporization	\(L_{i}\)
Enthalpy of state i	\(H_{i}\)

Equations

Description	Equation
Pure water production rate	\(m_{liq,H2O} = m_{vap,H2O}\)
Thermal energy in the vapor	\(J_{vap} = m_{vap,H2O} \times L_{pure water} + H_{vap} - H_{liq}\)
Change in temperature at inlet	\(\Delta T_{in} = T_{steam} - T_{operating}\)
Change in temperature at outlet	\(\Delta T_{out} = T_{steam} - T_{in}\)
Heating steam flow rate	\(W _{mechanical} = L_{vap,steam} \times m_{steam}\)

Costing Equations

The crystallizer-effect model is costed using the equations from the multi-effect crystallizer model but only for a single effect.