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Mechanical Vapor Compression (MVC)

Modeling a mechanical vapor compression (MVC) system is performed through flowsheet connectivity of individual model block components. The model is simulated under the following criteria:

  • property package(s) must support liquid and vapor phases
  • all model components are 0D
  • all model components support steady-state only
  • the operating conditions of the evaporator are fixed
  • compressor performance is governed by isentropic efficiency
  • assumed complete condensation in the condenser
.. index::
   pair: watertap.unit_models.mvc;mvc


.. currentmodule:: watertap.unit_models.mvc

Introduction

The MVC model is simulated as a modular combination of evaporator, compressor, and complete condenser unit models. These three models may be connected in a flowsheet for the fundamental MVC desalination process. For additional integration, pump and heat exchange unit operations may be added for pre- and post-processing of feed, brine, and distillate streams. Due to this connectivity, specialized initialization routines and modified unit models have been developed for this system and are located in a dedicated MVC directory.

Degrees of Freedom

Degrees of freedom for the MVC system are separated into the independent unit models. In this documentation, the description of the MVC system will only include the evaporator, compressor, and complete condenser unit models. The total system has 6 degrees of freedom in addition to the inlet feed state variables. Beginning from the feed, the evaporator has 3 degrees of freedom:

  • 1 outlet condition (brine or vapor temperature or pressure)
  • overall heat transfer coefficient
  • area for heat exchange

The compressor which the vapor enters has 3 degrees of freedom:

  • pressure ratio
  • work (control volume variable)
  • isentropic efficiency

By utilizing the evaporator in the MVC directory a custom connect_to_condenser routine equates the heat exchange between the evaporator and condenser unit models. Assuming the vapor will completely condense, there are no degrees of freedom in the condenser. When combined in a flowsheet, water recovery may also be calculated. This may be used in place of the specification of the evaporator outlet condition.

Model Structure

Construction of the ports, state blocks, and use of control volumes are defined in the variables section and separated by unit. Property packages must be declared for the liquid and vapor phases of evaporator and condenser models. This may be a two-phase property package or two different property packages respective to each phase.

Sets

Description Symbol Indices
Time t [0]
Phases p ['Liq']
Components j ['H2O', other]

Variables

Evaporator Variables

The evaporator contains 3 state blocks corresponding to the feed inlet, brine outlet, and vapor outlet (inlet_feed, outlet_brine, and outlet_vapor, respectively).

Description Symbol Variable Name Index Units
Overall heat transfer coefficient U U None W/\left(m^2K\right)
Heat transfer area A area None m^2
Approach temperature in \Delta T_{in} delta_temperature_in None K
Approach temperature out \Delta T_{out} delta_temperature_in None K
Log-mean temperature difference LMTD lmtd None K
Evaporator heat requirement Q_{evap} heat_transfer None W

Compressor Variables

The condenser consists of 1 ControlVolume0DBlock. Pressure differential and work variables are constructed on the control volume.

Description Symbol Variable Name Index Units
Pressure ratio PR pressure_ratio None W/\left(m^2K\right)
Isentropic efficiency \eta efficiency None \text{dimensionless}

Condenser Variables

The condenser consists of 1 ControlVolume0DBlock. No additional variables are constructed outside of those on the control volume.

Equations

Evaporator Equations

Description Equation
Mass balance \dot{m}_{feed} = \dot{m}_{vapor}^{vap}+\dot{m}_{brine}^{liq}
Energy balance H_{vapor}^{vap}+H_{brine}^{vap}-H_{feed} = Q_{evap}
Vapor temperature T_{vapor} = T_{brine}
Log-mean temperature difference (Chen, 1987) LMTD = \left(\frac{1}{2}\left(\Delta T_{in}+\Delta T_{out}\right)\Delta T_{in}\Delta T_{out}\right)^\frac{1}{3}
Evaporator heat requirement Q_{evap} = UA(LMTD)
Approach temperature in* \Delta T_{in} = T_{condenser,in}-T_{brine}
Approach temperature out* \Delta T_{out} = T_{condenser,out}-T_{brine}
Heat transfer balance* Q_{evap} = -Q_{cond}

*Equations are coupled with the condenser through the connect_to_condenser method.

Compressor Equations

Description Equation
Pressure ratio P_{out} = (PR)P_{in}
Isentropic temperature T_{out}=T_{in}(PR)^{1-\frac{1}{\gamma}}
Efficiency \eta\left(H_{out}-H_{in}\right) = H_{isentropic,out}-H_{in}

Condenser Equations

The condenser performance is related through the equations denoted by the footnote in the evaporator section.

Description Equation
Complete condensation condition P_{out} >= P_{sat,out}\left(T_{out}\right)

Code Documentation

References

Chen, J. J. J. (1987). Comments on improvements on a replacement for the logarithmic mean. Chemical Engineering Science, 42(10), 2488–2489. https://doi.org/10.1016/0009-2509(87)80128-8