Single Inlet - Double Outlet Helper Methods

The build_sido method is intended to be used to rapidly construct a standard set of material balance equations for zero-order type models with a single inlet and two outlets.

Usage

from idaes.core import declare_process_block_class
from watertap.core import build_sido, ZeroOrderBaseData

@declare_process_block_class("NanofiltrationZO")
class NanofiltrationZOData(ZeroOrderBaseData):

    CONFIG = ZeroOrderBaseData.CONFIG()

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

        self._tech_type = "nanofiltration"

        build_sido(self)

Model Structure

The build_sido method constructs a simple representation of unit operation with a single inlet (named inlet) and two outlets (named treated and byproduct). A StateBlock is constructed for the inlet and each outlet with a Port associated with each of these.

Variables

The build_sido method creates the following variables in addition to those created by the StateBlocks.

Variable

Name

Indices

Notes

\(r_{t}\)

recovery_frac_mass_H2O

time

Fraction of mass flow of water in inlet that goes to treated stream.

\(f_{t,j}\)

removal_frac_mass_comp

time, component

Fraction of mass flow of each component that goes to byproduct stream.

Constraints

The build_sido method writes the following constraints which relate the inlet state to those in the treated and byproduct streams. First, a mass recovery equation for water is written to relate the flowrate at the treated outlet to that at the inlet:

water_recovery_equation(t):

\[r_t \times M_{inlet,t,H2O} = M_{treated,t,H2O}\]

where \(M_{t,H2O}\) is mass flowrate of water at time \(t\).

Next, a mass balance for water is written to relate the flowrate in the byproduct stream to that in the inlet and treated streams.

flow_balance(t):

\[M_{inlet,t,H2O} = M_{treated,t,H2O} + M_{byproduct,t,H2O}\]

Removal constraints are then written for each solute to relate the solute concentration in the byproduct stream to that in the inlet stream.

solute_removal_equation(t, j):

\[f_{t, j} \times M_{inlet,t,j} = M_{byproduct,t,j}\]

A mass balance constraint is then written for each solute.

solute_treated_equation(t, j):

\[M_{inlet,t,j} = M_{treated,t,j} + M_{byproduct,t,j}\]

Module Documentation