Add more detailed pressure exchanger

docs/technical_reference/unit_models/pressure_exchanger.rst

@@ -5,8 +5,7 @@ This pressure exchanger unit model:
     * 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
+    * supports leakage and mixing effect
 
 .. index::
    pair: watertap.unit_models.pressure_exchanger;pressure_exchanger
@@ -32,9 +31,16 @@ Where the system is also subject to following constraints:
 
     Figure 1. Schematic representation of an energy recovery system using a pressure exchanger.
 
+When setting the ``has_mixing`` configuration option to ``True``, there is 1 additional variable ``mixing_vol`` that must be fixed.
+
+When setting the ``has_leakage`` configuration option to ``True``, there is 1 additional variable ``leakage_vol`` that must be fixed.
+
+When setting the ``pressure_exchange_calculation`` configuration option to ``PressureExchangeType.high_pressure_difference``,
+there are 2 additional variables ``high_pressure_difference`` and ``low_pressure_difference`` that must be fixed. Instead, ``efficiency_pressure_exchanger`` is unfixed.
+
 Model Structure
 ------------------
-The pressure exchanger model consists of 2 `ControlVolume0DBlocks`: one for the low-pressure side and high-pressure side.
+The pressure exchanger model consists of 2 `ControlVolume0DBlocks`: one for the feed side and brine side.
 
 Sets
 ----
@@ -56,8 +62,14 @@ The pressure exchanger unit model includes the following variables:
    :header: "Description", "Symbol", "Variable Name", "Index", "Units", "Pyomo Type" 
 
    "Efficiency", ":math:`\eta`", "efficiency_pressure_exchanger", "[t]", ":math:`\text{dimensionless}`", "Var"
+   "Volumetric leakage fraction", ":math:`\delta`", "leakage_vol", "[t]", ":math:`\text{dimensionless}`", "Var"
+   "Volumetric mixing fraction", ":math:`\chi`", "mixing_vol", "[t]", ":math:`\text{dimensionless}`", "Var"
+   "High pressure difference*", ":math:`HPD`", "high_pressure_difference", "[t]", ":math:`\text{Pa}`", "Var"
+   "Low pressure difference*", ":math:`LPD`", "low_pressure_difference", "[t]", ":math:`\text{Pa}`", "Var"
+
+\*High pressure difference and low pressure difference are non-negative values
 
-Each control volume (i.e. `low_presssure_side`, and `high_pressure_side`) has the following variables of interest:
+Each control volume (i.e. `feed_side`, and `brine_side`) has the following variables of interest:
 
 .. csv-table::
    :header: "Description", "Symbol", "Variable Name", "Index", "Units", "Pyomo Type" 
@@ -72,7 +84,9 @@ Each property block on both control volumes (i.e. `properties_in` and `propertie
 .. csv-table::
    :header: "Description", "Symbol", "Variable Name", "Index", "Units", "Pyomo Type" 
 
+   "Mass flowrate", ":math:`M`", "flow_mass_phase_comp", "[p, j]", "\*", "Var"
    "Volumetric flowrate", ":math:`Q`", "flow_vol", "None", "\*", "Var"
+   "Concentration", ":math:`C`", "conc_mass_phase_comp", "[p, j]", "\*", "Var"
    "Temperature", ":math:`T`", "temperature", "[t]", "\*", "Var"
    "Pressure", ":math:`P`", "pressure", "[t]", "\*", "Var"
 
@@ -81,17 +95,55 @@ Each property block on both control volumes (i.e. `properties_in` and `propertie
 
 Equations
 -----------
+if ``has_leakage`` and ``has_mixing`` are set to default (``False``):
 
 .. csv-table::
    :header: "Description", "Equation"
 
    "Mass balance for each side", ":math:`M_{out, j} = M_{in, j}`"
    "Momentum balance for each side", ":math:`P_{out} = P_{in} + ΔP`"
    "Isothermal assumption for each side", ":math:`T_{out} = T_{in}`"
-   "Equal volumetric flowrate*", ":math:`Q_{LPS} = Q_{HPS}`"
-   "Pressure transfer*", ":math:`ΔP_{LPS} = - \eta ΔP_{HPS}`"
+   "Equal volumetric flowrate*", ":math:`Q_{out, F} = Q_{in, F}`"
+   "Equal pressure*", ":math:`P_{out, B} = P_{in, F}`"
+   "Pressure transfer*", ":math:`ΔP_{F} = - \eta ΔP_{B}`"
+
+\* F stands for feed side, B stands for brine side
+
+if ``has_leakage`` is set to ``True``, then the equal volumetric flowrate equation is replaced by:
+
+.. csv-table::
+   :header: "Description", "Equation"
+
+   "Equal volumetric flowrate", ":math:`Q_{out, F} = (1 - \delta) Q_{in, B}`"
+
+if ``has_mixing`` is set to ``True``, the mass balance equations for each side become:
+
+.. csv-table::
+   :header: "Description", "Equation"
+
+   "Mass balance for each side*", ":math:`M_{out, j} = M_{in, j} + MTT_{j}`"
+
+\* MTT is mass transfer term into the control volume
+
+and there are 3 additional constraints:
+
+.. csv-table::
+   :header: "Description", "Equation"
+
+   "Mixing effect of solute*", ":math:`C_{out, F} = C_{in, F} (1-\chi) + C_{in, B} \chi`"
+   "Linking mass transfer terms", ":math:`MTT_{j, F} = -MTT_{j, B}`"
+   "Equal feed side volumetric flowrate", ":math:`Q_{out, F} = Q_{in, F}`"
+
+\* C represents solute concentration
+
+if ``pressure_change_calculation`` is set to ``PressureExchangeType.high_pressure_difference``,
+then there is 1 additional constraint and the equal pressure equation is replaced:
+
+.. csv-table::
+   :header: "Description", "Equation"
 
-\* LPS stands for low pressure side, HPS stands for high pressure side
+   "Pressure drop across B,in and F, out", ":math:`P_{out, F} + HPD = P_{in, B}`"
+   "Pressure drop across B, out and F, in", ":math:`P_{out, B} = P_{in, F} + LPD`"
 
 Class Documentation
 -------------------

watertap/costing/unit_models/pressure_exchanger.py

@@ -37,7 +37,7 @@ def cost_pressure_exchanger(blk):
         blk,
         blk.costing_package.pressure_exchanger.cost,
         pyo.units.convert(
-            blk.unit_model.low_pressure_side.properties_in[0].flow_vol,
+            blk.unit_model.feed_side.properties_in[0].flow_vol,
             (pyo.units.meter**3 / pyo.units.hours),
         ),
     )

watertap/examples/flowsheets/RO_with_energy_recovery/RO_with_energy_recovery.py

@@ -152,14 +152,10 @@ def build(erd_type=ERDtype.pressure_exchanger):
         m.fs.s03 = Arc(source=m.fs.P1.outlet, destination=m.fs.M1.P1)
         m.fs.s04 = Arc(source=m.fs.M1.outlet, destination=m.fs.RO.inlet)
         m.fs.s05 = Arc(source=m.fs.RO.permeate, destination=m.fs.product.inlet)
-        m.fs.s06 = Arc(
-            source=m.fs.RO.retentate, destination=m.fs.PXR.high_pressure_inlet
-        )
-        m.fs.s07 = Arc(
-            source=m.fs.PXR.high_pressure_outlet, destination=m.fs.disposal.inlet
-        )
-        m.fs.s08 = Arc(source=m.fs.S1.PXR, destination=m.fs.PXR.low_pressure_inlet)
-        m.fs.s09 = Arc(source=m.fs.PXR.low_pressure_outlet, destination=m.fs.P2.inlet)
+        m.fs.s06 = Arc(source=m.fs.RO.retentate, destination=m.fs.PXR.brine_inlet)
+        m.fs.s07 = Arc(source=m.fs.PXR.brine_outlet, destination=m.fs.disposal.inlet)
+        m.fs.s08 = Arc(source=m.fs.S1.PXR, destination=m.fs.PXR.feed_inlet)
+        m.fs.s09 = Arc(source=m.fs.PXR.feed_outlet, destination=m.fs.P2.inlet)
         m.fs.s10 = Arc(source=m.fs.P2.outlet, destination=m.fs.M1.P2)
     elif erd_type == ERDtype.pump_as_turbine:
         m.fs.s01 = Arc(source=m.fs.feed.outlet, destination=m.fs.P1.inlet)
@@ -184,8 +180,8 @@ def build(erd_type=ERDtype.pressure_exchanger):
 
     if erd_type == ERDtype.pressure_exchanger:
         iscale.set_scaling_factor(m.fs.P2.control_volume.work, 1e-3)
-        iscale.set_scaling_factor(m.fs.PXR.low_pressure_side.work, 1e-3)
-        iscale.set_scaling_factor(m.fs.PXR.high_pressure_side.work, 1e-3)
+        iscale.set_scaling_factor(m.fs.PXR.feed_side.work, 1e-3)
+        iscale.set_scaling_factor(m.fs.PXR.brine_side.work, 1e-3)
         # touch properties used in specifying and initializing the model
         m.fs.S1.mixed_state[0].mass_frac_phase_comp
         m.fs.S1.PXR_state[0].flow_vol_phase["Liq"]
@@ -407,7 +403,7 @@ def initialize_pressure_exchanger(m, optarg):
     # ---initialize splitter and pressure exchanger---
     # pressure exchanger high pressure inlet
     propagate_state(m.fs.s06)  # propagate to PXR high pressure inlet from RO retentate
-    m.fs.PXR.high_pressure_side.properties_in.initialize(optarg=optarg)
+    m.fs.PXR.brine_side.properties_in.initialize(optarg=optarg)
 
     # splitter inlet
     propagate_state(m.fs.s01)  # propagate to splitter inlet from feed
@@ -421,7 +417,7 @@ def initialize_pressure_exchanger(m, optarg):
                 "flow_vol_phase",
                 "Liq",
             ): value(  # same volumetric flow rate as PXR high pressure inlet
-                m.fs.PXR.high_pressure_side.properties_in[0].flow_vol_phase["Liq"]
+                m.fs.PXR.brine_side.properties_in[0].flow_vol_phase["Liq"]
             ),
             ("mass_frac_phase_comp", ("Liq", "NaCl")): value(
                 m.fs.S1.mixed_state[0].mass_frac_phase_comp["Liq", "NaCl"]
@@ -627,12 +623,12 @@ def print_state(s, b):
         print_state("Split 1   ", m.fs.S1.P1)
         print_state("P1 out    ", m.fs.P1.outlet)
         print_state("Split 2   ", m.fs.S1.PXR)
-        print_state("PXR LP out", m.fs.PXR.low_pressure_outlet)
+        print_state("PXR feed out", m.fs.PXR.feed_outlet)
         print_state("P2 out    ", m.fs.P2.outlet)
         print_state("Mix out   ", m.fs.M1.outlet)
         print_state("RO perm   ", m.fs.RO.permeate)
         print_state("RO reten  ", m.fs.RO.retentate)
-        print_state("PXR HP out", m.fs.PXR.high_pressure_outlet)
+        print_state("PXR brine out", m.fs.PXR.brine_outlet)
 
 
 if __name__ == "__main__":

watertap/examples/flowsheets/RO_with_energy_recovery/default_configuration.yaml

@@ -61,32 +61,32 @@ fs.P2.costing.capital_cost: 610.4424522403153
 fs.P2.ratioP[0.0]: 1.0725115194945298
 fs.P2.work_fluid[0.0]: 255.95071372759554
 fs.PXR.costing.capital_cost: 973.1020678190223
-fs.PXR.high_pressure_side.deltaP[0.0]: -7247342.029398318
-fs.PXR.high_pressure_side.properties_in[0.0].dens_mass_phase[Liq]: 1045.9125190112295
-fs.PXR.high_pressure_side.properties_in[0.0].flow_mass_phase_comp[Liq,H2O]: 0.49285444999999994
-fs.PXR.high_pressure_side.properties_in[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.035587728093265734
-fs.PXR.high_pressure_side.properties_in[0.0].flow_vol_phase[Liq]: 0.0005052451027097726
-fs.PXR.high_pressure_side.properties_in[0.0].mass_frac_phase_comp[Liq,H2O]: 0.9326553981332943
-fs.PXR.high_pressure_side.properties_in[0.0].mass_frac_phase_comp[Liq,NaCl]: 0.06734460186670563
-fs.PXR.high_pressure_side.properties_in[0.0].pressure: 7348667.029398319
-fs.PXR.high_pressure_side.properties_in[0.0].temperature: 298.1500072638073
-fs.PXR.high_pressure_side.properties_out[0.0].flow_mass_phase_comp[Liq,H2O]: 0.49285444999999994
-fs.PXR.high_pressure_side.properties_out[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.035587728093265734
-fs.PXR.high_pressure_side.properties_out[0.0].pressure: 101325.0
-fs.PXR.high_pressure_side.properties_out[0.0].temperature: 298.1500072638073
-fs.PXR.low_pressure_side.deltaP[0.0]: 6884974.927928402
-fs.PXR.low_pressure_side.properties_in[0.0].dens_mass_phase[Liq]: 1021.46
-fs.PXR.low_pressure_side.properties_in[0.0].flow_mass_phase_comp[Liq,H2O]: 0.498024594422437
-fs.PXR.low_pressure_side.properties_in[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.018063068191487355
-fs.PXR.low_pressure_side.properties_in[0.0].flow_vol_phase[Liq]: 0.0005052451027097726
-fs.PXR.low_pressure_side.properties_in[0.0].mass_frac_phase_comp[Liq,H2O]: 0.965
-fs.PXR.low_pressure_side.properties_in[0.0].mass_frac_phase_comp[Liq,NaCl]: 0.03500000000000001
-fs.PXR.low_pressure_side.properties_in[0.0].pressure: 101325.0
-fs.PXR.low_pressure_side.properties_in[0.0].temperature: 298.15
-fs.PXR.low_pressure_side.properties_out[0.0].flow_mass_phase_comp[Liq,H2O]: 0.498024594422437
-fs.PXR.low_pressure_side.properties_out[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.018063068191487355
-fs.PXR.low_pressure_side.properties_out[0.0].pressure: 6986299.927928403
-fs.PXR.low_pressure_side.properties_out[0.0].temperature: 298.15
+fs.PXR.brine_side.deltaP[0.0]: -7247342.029398318
+fs.PXR.brine_side.properties_in[0.0].dens_mass_phase[Liq]: 1045.9125190112295
+fs.PXR.brine_side.properties_in[0.0].flow_mass_phase_comp[Liq,H2O]: 0.49285444999999994
+fs.PXR.brine_side.properties_in[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.035587728093265734
+fs.PXR.brine_side.properties_in[0.0].flow_vol_phase[Liq]: 0.0005052451027097726
+fs.PXR.brine_side.properties_in[0.0].mass_frac_phase_comp[Liq,H2O]: 0.9326553981332943
+fs.PXR.brine_side.properties_in[0.0].mass_frac_phase_comp[Liq,NaCl]: 0.06734460186670563
+fs.PXR.brine_side.properties_in[0.0].pressure: 7348667.029398319
+fs.PXR.brine_side.properties_in[0.0].temperature: 298.1500072638073
+fs.PXR.brine_side.properties_out[0.0].flow_mass_phase_comp[Liq,H2O]: 0.49285444999999994
+fs.PXR.brine_side.properties_out[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.035587728093265734
+fs.PXR.brine_side.properties_out[0.0].pressure: 101325.0
+fs.PXR.brine_side.properties_out[0.0].temperature: 298.1500072638073
+fs.PXR.feed_side.deltaP[0.0]: 6884974.927928402
+fs.PXR.feed_side.properties_in[0.0].dens_mass_phase[Liq]: 1021.46
+fs.PXR.feed_side.properties_in[0.0].flow_mass_phase_comp[Liq,H2O]: 0.498024594422437
+fs.PXR.feed_side.properties_in[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.018063068191487355
+fs.PXR.feed_side.properties_in[0.0].flow_vol_phase[Liq]: 0.0005052451027097726
+fs.PXR.feed_side.properties_in[0.0].mass_frac_phase_comp[Liq,H2O]: 0.965
+fs.PXR.feed_side.properties_in[0.0].mass_frac_phase_comp[Liq,NaCl]: 0.03500000000000001
+fs.PXR.feed_side.properties_in[0.0].pressure: 101325.0
+fs.PXR.feed_side.properties_in[0.0].temperature: 298.15
+fs.PXR.feed_side.properties_out[0.0].flow_mass_phase_comp[Liq,H2O]: 0.498024594422437
+fs.PXR.feed_side.properties_out[0.0].flow_mass_phase_comp[Liq,NaCl]: 0.018063068191487355
+fs.PXR.feed_side.properties_out[0.0].pressure: 6986299.927928403
+fs.PXR.feed_side.properties_out[0.0].temperature: 298.15
 fs.RO.feed_side.K[0.0,0.0,NaCl]: 3.4512803512388215e-05
 fs.RO.feed_side.K[0.0,1.0,NaCl]: 2.7060824531310153e-05
 fs.RO.feed_side.N_Re[0.0,0.0]: 339.4894225951861

watertap/examples/flowsheets/RO_with_energy_recovery/tests/test_RO_with_energy_recovery_simulation.py

@@ -123,10 +123,10 @@ def test_build(self, system_frame):
             fs.s03: (fs.P1.outlet, fs.M1.P1),
             fs.s04: (fs.M1.outlet, fs.RO.inlet),
             fs.s05: (fs.RO.permeate, fs.product.inlet),
-            fs.s06: (fs.RO.retentate, fs.PXR.high_pressure_inlet),
-            fs.s07: (fs.PXR.high_pressure_outlet, fs.disposal.inlet),
-            fs.s08: (fs.S1.PXR, fs.PXR.low_pressure_inlet),
-            fs.s09: (fs.PXR.low_pressure_outlet, fs.P2.inlet),
+            fs.s06: (fs.RO.retentate, fs.PXR.brine_inlet),
+            fs.s07: (fs.PXR.brine_outlet, fs.disposal.inlet),
+            fs.s08: (fs.S1.PXR, fs.PXR.feed_inlet),
+            fs.s09: (fs.PXR.feed_outlet, fs.P2.inlet),
             fs.s10: (fs.P2.outlet, fs.M1.P2),
         }
         for arc, port_tpl in arc_dict.items():
@@ -197,32 +197,30 @@ def test_initialize_system(self, system_frame):
         # check results across pressure exchanger, proxy for both upstream and downstream of RO
         # high pressure inlet
         assert value(
-            m.fs.PXR.high_pressure_inlet.flow_mass_phase_comp[0, "Liq", "H2O"]
+            m.fs.PXR.brine_inlet.flow_mass_phase_comp[0, "Liq", "H2O"]
         ) == pytest.approx(0.4928, rel=1e-3)
         assert value(
-            m.fs.PXR.high_pressure_inlet.flow_mass_phase_comp[0, "Liq", "NaCl"]
+            m.fs.PXR.brine_inlet.flow_mass_phase_comp[0, "Liq", "NaCl"]
         ) == pytest.approx(3.561e-2, rel=1e-3)
-        assert value(m.fs.PXR.high_pressure_inlet.temperature[0]) == pytest.approx(
+        assert value(m.fs.PXR.brine_inlet.temperature[0]) == pytest.approx(
             298.15, rel=1e-3
         )
-        assert value(m.fs.PXR.high_pressure_inlet.pressure[0]) == pytest.approx(
+        assert value(m.fs.PXR.brine_inlet.pressure[0]) == pytest.approx(
             7.242e6, rel=1e-3
         )
         # low pressure inlet
         assert value(
-            m.fs.PXR.low_pressure_inlet.flow_mass_phase_comp[0, "Liq", "H2O"]
+            m.fs.PXR.feed_inlet.flow_mass_phase_comp[0, "Liq", "H2O"]
         ) == pytest.approx(0.4980, rel=1e-3)
         assert value(
-            m.fs.PXR.low_pressure_inlet.flow_mass_phase_comp[0, "Liq", "NaCl"]
+            m.fs.PXR.feed_inlet.flow_mass_phase_comp[0, "Liq", "NaCl"]
         ) == pytest.approx(1.806e-2, rel=1e-3)
-        assert value(m.fs.PXR.low_pressure_inlet.temperature[0]) == pytest.approx(
+        assert value(m.fs.PXR.feed_inlet.temperature[0]) == pytest.approx(
             298.15, rel=1e-3
         )
-        assert value(m.fs.PXR.low_pressure_inlet.pressure[0]) == pytest.approx(
-            101325, rel=1e-3
-        )
+        assert value(m.fs.PXR.feed_inlet.pressure[0]) == pytest.approx(101325, rel=1e-3)
         # low pressure outlet
-        assert value(m.fs.PXR.low_pressure_outlet.pressure[0]) == pytest.approx(
+        assert value(m.fs.PXR.feed_outlet.pressure[0]) == pytest.approx(
             6.885e6, rel=1e-3
         )
 
@@ -310,12 +308,12 @@ def test_display_state(self, system_frame, capsys):
 Split 1   : 0.505 kg/s, 35000 ppm, 1.0 bar
 P1 out    : 0.505 kg/s, 35000 ppm, 74.9 bar
 Split 2   : 0.516 kg/s, 35000 ppm, 1.0 bar
-PXR LP out: 0.516 kg/s, 35000 ppm, 68.9 bar
+PXR feed out: 0.516 kg/s, 35000 ppm, 68.9 bar
 P2 out    : 0.516 kg/s, 35000 ppm, 74.9 bar
 Mix out   : 1.021 kg/s, 35000 ppm, 74.9 bar
 RO perm   : 0.493 kg/s, 240 ppm, 1.0 bar
 RO reten  : 0.528 kg/s, 67424 ppm, 72.4 bar
-PXR HP out: 0.528 kg/s, 67424 ppm, 1.0 bar
+PXR brine out: 0.528 kg/s, 67424 ppm, 1.0 bar
 """
         )
 

watertap/examples/flowsheets/case_studies/seawater_RO_desalination/seawater_RO_desalination.py

@@ -288,16 +288,12 @@ def eq_flow_mass_comp(blk, j):  # pylint: disable=function-redefined
         desal.s01 = Arc(source=desal.S1.P1, destination=desal.P1.inlet)
         desal.s02 = Arc(source=desal.P1.outlet, destination=desal.M1.P1)
         desal.s03 = Arc(source=desal.M1.outlet, destination=desal.RO.inlet)
-        desal.s04 = Arc(
-            source=desal.RO.retentate, destination=desal.PXR.high_pressure_inlet
-        )
-        desal.s05 = Arc(source=desal.S1.PXR, destination=desal.PXR.low_pressure_inlet)
-        desal.s06 = Arc(
-            source=desal.PXR.low_pressure_outlet, destination=desal.P2.inlet
-        )
+        desal.s04 = Arc(source=desal.RO.retentate, destination=desal.PXR.brine_inlet)
+        desal.s05 = Arc(source=desal.S1.PXR, destination=desal.PXR.feed_inlet)
+        desal.s06 = Arc(source=desal.PXR.feed_outlet, destination=desal.P2.inlet)
         desal.s07 = Arc(source=desal.P2.outlet, destination=desal.M1.P2)
         m.fs.s_disposal = Arc(
-            source=desal.PXR.high_pressure_outlet, destination=m.fs.disposal.inlet
+            source=desal.PXR.brine_outlet, destination=m.fs.disposal.inlet
         )
     elif erd_type == "pump_as_turbine":
         m.fs.s_tb_desal = Arc(
@@ -343,8 +339,8 @@ def eq_flow_mass_comp(blk, j):  # pylint: disable=function-redefined
     iscale.set_scaling_factor(desal.RO.area, 1e-4)
     if erd_type == "pressure_exchanger":
         iscale.set_scaling_factor(desal.P2.control_volume.work, 1e-5)
-        iscale.set_scaling_factor(desal.PXR.low_pressure_side.work, 1e-5)
-        iscale.set_scaling_factor(desal.PXR.high_pressure_side.work, 1e-5)
+        iscale.set_scaling_factor(desal.PXR.feed_side.work, 1e-5)
+        iscale.set_scaling_factor(desal.PXR.brine_side.work, 1e-5)
     elif erd_type == "pump_as_turbine":
         iscale.set_scaling_factor(desal.ERD.control_volume.work, 1e-5)
     # calculate and propagate scaling factors