Custom Compressor Unit Model

Custom Compressor Unit Model#

Author: Andrew Lee
Maintainer: Andrew Lee
Updated: 2023-06-01

To demonstrate creation of a new unit model, we will create a constant-heat-capacity ideal-gas isentropic compressor. This will be a simple textbook model. We will utilize the mass and energy balances provided by IDAES control volumes, but we will write our own isentropic constraint based off of equations 7.18 and 7.23 from “Introduction to Chemical Engineering Thermodynamics” by J.M. Smith, H.C. Van Ness, and M.M. Abbott.

The outlet temperature of an ideal gas undergoing isentropic compression is given by $$ t_{out} = t_{in} + \frac{1}{\eta} \left(t_{in} \left(\frac{p_{out}}{p_{in}}\right)^{\frac{\gamma - 1}{\gamma}} - t_{in}\right) $$ where $p$ is pressure, $t$ is temperature, and $\gamma$ is the ratio of constant pressure heat capacity to constant volume heat capacity.

We will begin with relevant imports. We will need

Pyomo for writing our energy balance constraints
ConfigBlocks for specifying options for our compressor
ControlVolume0DBlocks for creating the appropriate state blocks for the inlet and outlet and for defining mas balances
IdealParameterBlock which provides a simple ideal-gas property package.
A few other helpful functions and enums from IDAES

import pyomo.environ as pe
from pyomo.common.config import ConfigBlock, ConfigValue, In
from idaes.core import (
    ControlVolume0DBlock,
    declare_process_block_class,
    EnergyBalanceType,
    MomentumBalanceType,
    MaterialBalanceType,
    UnitModelBlockData,
    useDefault,
    FlowsheetBlock,
)
from idaes.core.util.config import is_physical_parameter_block
from idaes_examples.mod.methanol.methanol_param_VLE import PhysicalParameterBlock
from idaes.core.util.misc import add_object_reference

Now, we can write a function to create a control volume for our compressor. The control volume will define the inlet and outlet streams along with the appropriate state variables (specified by the property package). We will also use the control volume to create mass and energy balance constraints.

Our function will take the compressor unit model object, the name of the control volume, and configuration options as arguments. Our compressor will only support steady-state models, so we will first ensure that dynamic and has_holdup are both False.

Next, we will create a 0D control volume. We are using a 0D control volume because our model does not depend on space. We then

Attach the control volume to the compressor
Create the appropriate state blocks with the control volume (for the inlet and outlet streams)
Use the control volume to add mass balance constraints
Use the control volume to add energy balance constraints

def make_control_volume(unit, name, config):
    if config.dynamic is not False:
        raise ValueError("IdealGasIsentropcCompressor does not support dynamics")
    if config.has_holdup is not False:
        raise ValueError("IdealGasIsentropcCompressor does not support holdup")

    control_volume = ControlVolume0DBlock(
        property_package=config.property_package,
        property_package_args=config.property_package_args,
    )

    setattr(unit, name, control_volume)

    control_volume.add_state_blocks(has_phase_equilibrium=config.has_phase_equilibrium)
    control_volume.add_material_balances(
        balance_type=config.material_balance_type,
        has_phase_equilibrium=config.has_phase_equilibrium,
    )
    control_volume.add_total_enthalpy_balances(
        has_heat_of_reaction=False, has_heat_transfer=False, has_work_transfer=True
    )

Next, we will write a function to add constraints to specify that the compressor is isentropic.

Create a pressure_ratio variable to represent $p_{out}/p_{in}$. The lower bound is $1$, because we only want to allow compression (and not expansion).
Create a ConstraintList to hold the constraints.
Add the ConstraintList to the compressor
Create the local variables inlet and outlet to reference the inlet and outlet state blocks.
Add a constraint relating the inlet pressure, outlet pressure, and pressure ratio variables: \begin{align} p_{in} p_{ratio} = p_{out} \end{align}
Add a constraint relating the inlet and outlet temperatures: \begin{align} & t_{out} = t_{in} + \frac{1}{\eta} \left(t_{in} p_{ratio}^{\frac{\gamma - 1}{\gamma}} - t_{in}\right) \end{align}

def add_isentropic(unit, name, config):
    unit.pressure_ratio = pe.Var(initialize=1.0, bounds=(1, None))
    cons = pe.ConstraintList()
    setattr(unit, name, cons)
    inlet = unit.control_volume.properties_in[0.0]
    outlet = unit.control_volume.properties_out[0.0]
    gamma = inlet.params.gamma
    cons.add(inlet.pressure * unit.pressure_ratio == outlet.pressure)
    cons.add(
        outlet.temperature
        == (
            inlet.temperature
            + 1
            / config.compressor_efficiency
            * (
                inlet.temperature * unit.pressure_ratio ** ((gamma - 1) / gamma)
                - inlet.temperature
            )
        )
    )

We also need a function to specify configuration options for the compressor.

def make_compressor_config_block(config):
    config.declare(
        "material_balance_type",
        ConfigValue(
            default=MaterialBalanceType.componentPhase, domain=In(MaterialBalanceType)
        ),
    )
    config.declare(
        "energy_balance_type",
        ConfigValue(
            default=EnergyBalanceType.enthalpyTotal,
            domain=In([EnergyBalanceType.enthalpyTotal]),
        ),
    )
    config.declare(
        "momentum_balance_type",
        ConfigValue(
            default=MomentumBalanceType.none, domain=In([MomentumBalanceType.none])
        ),
    )
    config.declare(
        "has_phase_equilibrium", ConfigValue(default=False, domain=In([False]))
    )
    config.declare(
        "has_pressure_change", ConfigValue(default=False, domain=In([False]))
    )
    config.declare(
        "property_package",
        ConfigValue(default=useDefault, domain=is_physical_parameter_block),
    )
    config.declare("property_package_args", ConfigBlock(implicit=True))
    config.declare("compressor_efficiency", ConfigValue(default=0.75, domain=float))

Finally, we can define the ideal-gas isentropic compressor. To do so, we create a class called IdealGasIsentropicCompressorData and use the declare_process_block_class decorator. For now, just consider the decorator to be boiler-plate. We then need to define the config block and write the build method. The build method should always call super. Next, we simply call the functions we wrote to build the control volume, energy balance, and electricity requirement performance equation. Finally, we need to call self.add_inlet_port() and self.add_outlet_port(). These methods need to be called in order to create the ports which are used for connecting the unit to other units.

@declare_process_block_class("IdealGasIsentropicCompressor")
class IdealGasIsentropicCompressorData(UnitModelBlockData):
    CONFIG = UnitModelBlockData.CONFIG()
    make_compressor_config_block(CONFIG)

    def build(self):
        super(IdealGasIsentropicCompressorData, self).build()

        make_control_volume(self, "control_volume", self.config)
        add_isentropic(self, "isentropic", self.config)

        self.add_inlet_port()
        self.add_outlet_port()

        add_object_reference(self, "work", self.control_volume.work[0.0])

The compressor model is complete and can now be used like other IDAES unit models. Note that the input temperature is in hectoKelvin, the input pressure is in MPa and energy units are in MJ. This is to simplify user input and is accounted for in the property package files; the standard unit definitions may be found in the metadata section at the end of the main parameter property package.

m = pe.ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)
m.fs.properties = props = PhysicalParameterBlock(
    Cp=0.038056, valid_phase="Vap"
)  # MJ/kmol-K

m.fs.compressor = IdealGasIsentropicCompressor(
    property_package=props, has_phase_equilibrium=False
)
m.fs.compressor.inlet.flow_mol.fix(1)  # kmol
m.fs.compressor.inlet.mole_frac_comp[0, "CH3OH"].fix(0.25)
m.fs.compressor.inlet.mole_frac_comp[0, "CH4"].fix(0.25)
m.fs.compressor.inlet.mole_frac_comp[0, "H2"].fix(0.25)
m.fs.compressor.inlet.mole_frac_comp[0, "CO"].fix(0.25)
m.fs.compressor.inlet.pressure.fix(0.14)  # MPa
m.fs.compressor.inlet.temperature.fix(2.9315)  # hK [100K]
m.fs.compressor.outlet.pressure.fix(0.56)  # MPa

opt = pe.SolverFactory("ipopt")
opt.options["linear_solver"] = "ma27"
res = opt.solve(m, tee=True)
print(res.solver.termination_condition)
m.fs.compressor.outlet.display()
print("work: ", round(m.fs.compressor.work.value, 2), " MJ")  # MJ

WARNING: Could not locate the 'ipopt' executable, which is required for solver
ipopt

---------------------------------------------------------------------------
ApplicationError                          Traceback (most recent call last)
Cell In[7], line 21
     19 opt = pe.SolverFactory("ipopt")
     20 opt.options["linear_solver"] = "ma27"
---> 21 res = opt.solve(m, tee=True)
     22 print(res.solver.termination_condition)
     23 m.fs.compressor.outlet.display()

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/opt/base/solvers.py:534, in OptSolver.solve(self, *args, **kwds)
    531 def solve(self, *args, **kwds):
    532     """Solve the problem"""
--> 534     self.available(exception_flag=True)
    535     #
    536     # If the inputs are models, then validate that they have been
    537     # constructed! Collect suffix names to try and import from solution.
    538     #
    539     from pyomo.core.base.block import BlockData

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/opt/solver/shellcmd.py:140, in SystemCallSolver.available(self, exception_flag)
    138     if exception_flag:
    139         msg = "No executable found for solver '%s'"
--> 140         raise ApplicationError(msg % self.name)
    141     return False
    142 return True

ApplicationError: No executable found for solver 'ipopt'