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Pressure Exchanger

This pressure exchanger unit model:
  • is 0-dimensional
  • is isothermal
  • supports a single liquid phase only
  • supports steady-state only
  • assumes no mixing or leakage between the low and high pressure side
  • assumes equal flowrates on both sides

pair: watertap.unit_models.pressure_exchanger;pressure_exchanger

watertap.unit_models.pressure_exchanger

Degrees of Freedom

Generally, pressure exchangers are not used in isolation and are part of an energy recovery system that includes a mixer, splitter, and a booster pump, as shown in Figure 1. This energy recovery system only adds one degree of freedom to the overall model.

Typically, the following variables are fixed to fully specify the energy recovery system:
  • the pressure exchanger efficiency (efficiency_pressure_exchanger located on the pressure exchanger unit model)
  • the booster pump efficiency (efficiency_pump located on the pump unit model)
Where the system is also subject to following constraints:
  • volumetric flowrate is equal on both sides of the pressure exchanger (constraint is included in pressure exchanger unit model)
  • booster pump matches the high pressure pump outlet pressure (constraint must be added by the user or at the mixer with the equality momentum mixing type option)

Figure 1. Schematic representation of an energy recovery system using a pressure exchanger.

Figure 1. Schematic representation of an energy recovery system using a pressure exchanger.

Model Structure

The pressure exchanger model consists of 2 `ControlVolume0DBlocks`: one for the low-pressure side and high-pressure side.

Sets

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

*Solute depends on the imported property package; example shown here is for the NaCl property model.

Variables

The pressure exchanger unit model includes the following variables:

Description Symbol Variable Name Index Units Pyomo Type
Efficiency η efficiency_pressure_exchanger [t] dimensionless Var

Each control volume (i.e. low_presssure_side, and high_pressure_side) has the following variables of interest:

Description Symbol Variable Name Index Units Pyomo Type
Pressure change ΔP deltaP [t] * Var
Work W work [t] * Expression

*Units depends on the imported property package

Each property block on both control volumes (i.e. properties_in and properties_out) has the following variables of interest:

Description Symbol Variable Name Index Units Pyomo Type
Volumetric flowrate Q flow_vol None * Var
Temperature T temperature [t] * Var
Pressure P pressure [t] * Var

*Units depends on the imported property package

Equations

Description Equation
Mass balance for each side Mout, j = Min, j
Momentum balance for each side Pout = Pin + ΔP
Isothermal assumption for each side Tout = Tin
Equal volumetric flowrate* QLPS = QHPS
Pressure transfer* ΔPLPS =  − ηΔPHPS

* LPS stands for low pressure side, HPS stands for high pressure side

Class Documentation

  • watertap.unit_models.pressure_exchanger