diff --git a/LICENSE b/LICENSE index d8f2a15..71a9fa0 100644 --- a/LICENSE +++ b/LICENSE @@ -1,6 +1,6 @@ BSD 3-Clause License -Copyright (c) 2020, Ignacio Grossmann Research Group +Copyright (c) 2024, SECQUOIA Research Group All rights reserved. Redistribution and use in source and binary forms, with or without diff --git a/gdplib/ ex1_linan_2023/ ex1_linan_2023.py b/gdplib/ ex1_linan_2023/ ex1_linan_2023.py new file mode 100644 index 0000000..b48a31b --- /dev/null +++ b/gdplib/ ex1_linan_2023/ ex1_linan_2023.py @@ -0,0 +1,263 @@ +""" +ex1_linan_2023.py: Toy problem from Liñán and Ricardez-Sandoval (2023) [1] + +TThe ex1_linan.py file is a simple optimization problem that involves two Boolean variables, two continuous variables, and a nonlinear objective function. +The problem is formulated as a Generalized Disjunctive Programming (GDP) model. +The Boolean variables are associated with disjuncts that define the feasible regions of the continuous variables. +The problem includes logical constraints that ensure that only one Boolean variable is true at a time. +Additionally, there are two disjunctions, one for each Boolean variable, where only one disjunct in each disjunction must be true. +A specific logical constraint also enforces that Y1[3] must be false, making this particular disjunct infeasible. +The objective function is -0.9995999999999999 when the continuous variables are alpha = 0 (Y1[2]=True) and beta=-0.7 (Y2[3]=True). + +References +---------- +[1] Liñán, D. A., & Ricardez-Sandoval, L. A. (2023). A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions. AIChE Journal, 69(5), e18008. https://doi.org/10.1002/aic.18008 +[2] Gomez, S., & Levy, A. V. (1982). The tunnelling method for solving the constrained global optimization problem with several non-connected feasible regions. In Numerical Analysis: Proceedings of the Third IIMAS Workshop Held at Cocoyoc, Mexico, January 1981 (pp. 34-47). Springer Berlin Heidelberg. https://doi.org/10.1007/BFb0092958 +""" + +import pyomo.environ as pyo +from pyomo.gdp import Disjunct, Disjunction + + +def build_model(): + """ + Build the toy problem model + + Returns + ------- + Pyomo.ConcreteModel + Toy problem model + """ + + # Build Model + m = pyo.ConcreteModel() + + # Sets + m.set1 = pyo.RangeSet(1, 5, doc="set of first group of Boolean variables") + m.set2 = pyo.RangeSet(1, 5, doc="set of second group of Boolean variables") + + m.sub1 = pyo.Set(initialize=[3], within=m.set1) + + # Variables + m.Y1 = pyo.BooleanVar(m.set1, doc="Boolean variable associated to set 1") + m.Y2 = pyo.BooleanVar(m.set2, doc="Boolean variable associated to set 2") + + m.alpha = pyo.Var( + within=pyo.Reals, bounds=(-0.1, 0.4), doc="continuous variable alpha" + ) + m.beta = pyo.Var( + within=pyo.Reals, bounds=(-0.9, -0.5), doc="continuous variable beta" + ) + + # Objective Function + def obj_fun(m): + """ + Objective function + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.Objective + Build the objective function of the toy problem + """ + return ( + 4 * (pow(m.alpha, 2)) + - 2.1 * (pow(m.alpha, 4)) + + (1 / 3) * (pow(m.alpha, 6)) + + m.alpha * m.beta + - 4 * (pow(m.beta, 2)) + + 4 * (pow(m.beta, 4)) + ) + + m.obj = pyo.Objective(rule=obj_fun, sense=pyo.minimize, doc="Objective function") + + # First Disjunction + def build_disjuncts1(m, set1): # Disjuncts for first Boolean variable + """ + Build disjuncts for the first Boolean variable + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + set1 : RangeSet + Set of first group of Boolean variables + """ + + def constraint1(m): + """_summary_ + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.Constraint + Constraint that defines the value of alpha for each disjunct + """ + return m.model().alpha == -0.1 + 0.1 * ( + set1 - 1 + ) # .model() is required when writing constraints inside disjuncts + + m.constraint1 = pyo.Constraint(rule=constraint1) + + m.Y1_disjunct = Disjunct( + m.set1, rule=build_disjuncts1, doc="each disjunct is defined over set 1" + ) + + def Disjunction1(m): # Disjunction for first Boolean variable + """ + Disjunction for first Boolean variable + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.Disjunction + Build the disjunction for the first Boolean variable set + """ + return [m.Y1_disjunct[j] for j in m.set1] + + m.Disjunction1 = Disjunction(rule=Disjunction1, xor=False) + + # Associate boolean variables to disjuncts + for n1 in m.set1: + m.Y1[n1].associate_binary_var(m.Y1_disjunct[n1].indicator_var) + + # Second disjunction + def build_disjuncts2(m, set2): # Disjuncts for second Boolean variable + """ + Build disjuncts for the second Boolean variable + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + set2 : RangeSet + Set of second group of Boolean variables + """ + + def constraint2(m): + """_summary_ + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.Constraint + Constraint that defines the value of beta for each disjunct + """ + return m.model().beta == -0.9 + 0.1 * ( + set2 - 1 + ) # .model() is required when writing constraints inside disjuncts + + m.constraint2 = pyo.Constraint(rule=constraint2) + + m.Y2_disjunct = Disjunct( + m.set2, rule=build_disjuncts2, doc="each disjunct is defined over set 2" + ) + + def Disjunction2(m): # Disjunction for first Boolean variable + """ + Disjunction for second Boolean variable + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.Disjunction + Build the disjunction for the second Boolean variable set + """ + return [m.Y2_disjunct[j] for j in m.set2] + + m.Disjunction2 = Disjunction(rule=Disjunction2, xor=False) + + # Associate boolean variables to disjuncts + for n2 in m.set2: + m.Y2[n2].associate_binary_var(m.Y2_disjunct[n2].indicator_var) + + # Logical constraints + + # Constraint that allow to apply the reformulation over Y1 + def select_one_Y1(m): + """ + Logical constraint that allows to apply the reformulation over Y1 + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.LogicalConstraint + Logical constraint that make Y1 to be true for only one element + """ + return pyo.exactly(1, m.Y1) + + m.oneY1 = pyo.LogicalConstraint(rule=select_one_Y1) + + # Constraint that allow to apply the reformulation over Y2 + def select_one_Y2(m): + """ + Logical constraint that allows to apply the reformulation over Y2 + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.LogicalConstraint + Logical constraint that make Y2 to be true for only one element + """ + return pyo.exactly(1, m.Y2) + + m.oneY2 = pyo.LogicalConstraint(rule=select_one_Y2) + + # Constraint that define an infeasible region with respect to Boolean variables + + def infeasR_rule(m): + """ + Logical constraint that defines an infeasible region with respect to Boolean variables + + Parameters + ---------- + m : Pyomo.ConcreteModel + Toy problem model + + Returns + ------- + Pyomo.LogicalConstraint + Logical constraint that defines an infeasible region on Y1[3] + """ + return pyo.land([pyo.lnot(m.Y1[j]) for j in m.sub1]) + + m.infeasR = pyo.LogicalConstraint(rule=infeasR_rule) + + return m + + +if __name__ == "__main__": + m = build_model() + pyo.TransformationFactory("gdp.bigm").apply_to(m) + solver = pyo.SolverFactory("gams") + solver.solve(m, solver="baron", tee=True) + print("Solution: alpha=", pyo.value(m.alpha), " beta=", pyo.value(m.beta)) + print("Objective function value: ", pyo.value(m.obj)) diff --git a/gdplib/ ex1_linan_2023/README.md b/gdplib/ ex1_linan_2023/README.md new file mode 100644 index 0000000..1802e16 --- /dev/null +++ b/gdplib/ ex1_linan_2023/README.md @@ -0,0 +1,14 @@ +## Example 1 Problem of Liñán (2023) + +The Example 1 Problem of Liñán (2023) is a simple optimization problem that involves two Boolean variables, two continuous variables, and a nonlinear objective function. The problem is formulated as a Generalized Disjunctive Programming (GDP) model. + +The Boolean variables are associated with disjuncts that define the feasible regions of the continuous variables. The problem also includes logical constraints that ensure that only one Boolean variable is true at a time. Additionally, there are two disjunctions, one for each Boolean variable, where only one disjunct in each disjunction must be true. A specific logical constraint also enforces that `Y1[3]` must be false, making this particular disjunct infeasible. + +The objective function is -0.9995999999999999 when the continuous variables are alpha = 0 (`Y1[2]=True`) and beta=-0.7 (`Y2[3]=True`). + +The objective function originates from Problem No. 6 of Gomez's paper, and Liñán introduced logical propositions, logical disjunctions, and the following equations as constraints. + +### References + +[1] Liñán, D. A., & Ricardez-Sandoval, L. A. (2023). A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions. AIChE Journal, 69(5), e18008. https://doi.org/10.1002/aic.18008 +[2] Gomez, S., & Levy, A. V. (1982). The tunnelling method for solving the constrained global optimization problem with several non-connected feasible regions. In Numerical Analysis: Proceedings of the Third IIMAS Workshop Held at Cocoyoc, Mexico, January 1981 (pp. 34-47). Springer Berlin Heidelberg. https://doi.org/10.1007/BFb0092958 diff --git a/gdplib/kaibel/kaibel_init.py b/gdplib/kaibel/kaibel_init.py index ce28540..5a510be 100644 --- a/gdplib/kaibel/kaibel_init.py +++ b/gdplib/kaibel/kaibel_init.py @@ -1,287 +1,399 @@ -""" - Calculation of the theoretical minimum number of trays and initial - temperature values. - (written by E. Soraya Rawlings, esoraya@rwlngs.net) - - The separation of four components require a sequence of at least three distillation - columns. Here, we calculate the minimum number of theoretical trays for the three - columns. The sequence is shown in Figure 2. - - COLUMN 1 COLUMN 2 COLUMN 3 - ----- ---- ----- - | | | | | | - ----- | A ----- | ----- | - | |<---> B -- | |<----> A -- | |<---> A - | | C | | | B | | | - A | | | | | | | | - B | | | | | | | | - C --->| | -->| | -->| | - D | | | | | | - | | | | | | - | |<- | |<- | |<- - ----- | ----- | ----- | - | | | | | | - -------> D -------> C -------> B - Figure 2. Sequence of columns for the separation of a quaternary mixture -""" - -from __future__ import division - -from pyomo.environ import ( - exp, - log10, - minimize, - NonNegativeReals, - Objective, - RangeSet, - SolverFactory, - value, - Var, -) - -from gdplib.kaibel.kaibel_prop import get_model_with_properties - - -def initialize_kaibel(): - m = get_model_with_properties() - - ## Operating conditions - m.Preb = 1.2 # Reboiler pressure in bar - m.Pcon = 1.05 # Condenser pressure in bar - m.Pf = 1.02 - - Pnmin = {} # Pressure in bars - Pnmin[1] = m.Preb # Reboiler pressure in bars - Pnmin[3] = m.Pcon # Distillate pressure in bars - Pnmin[2] = m.Pf # Side feed pressure in bars - - xi_nmin = {} # Initial liquid composition: first number = column and - # second number = 1 reboiler, 2 side feed, and - # 3 for condenser - - ## Column 1 - c_c1 = 4 # Components in Column 1 - lc_c1 = 3 # Light component in Column 1 - hc_c1 = 4 # Heavy component in Column 1 - inter1_c1 = 1 # Intermediate component in Column 1 - inter2_c1 = 2 # Intermediate component in Column 1 - - xi_nmin[1, 1, hc_c1] = 0.999 - xi_nmin[1, 1, lc_c1] = (1 - xi_nmin[1, 1, hc_c1]) / (c_c1 - 1) - xi_nmin[1, 1, inter1_c1] = (1 - xi_nmin[1, 1, hc_c1]) / (c_c1 - 1) - xi_nmin[1, 1, inter2_c1] = (1 - xi_nmin[1, 1, hc_c1]) / (c_c1 - 1) - xi_nmin[1, 3, lc_c1] = 0.33 - xi_nmin[1, 3, inter1_c1] = 0.33 - xi_nmin[1, 3, inter2_c1] = 0.33 - xi_nmin[1, 3, hc_c1] = 1 - ( - xi_nmin[1, 3, lc_c1] + xi_nmin[1, 3, inter1_c1] + xi_nmin[1, 3, inter2_c1] - ) - xi_nmin[1, 2, lc_c1] = 1 / c_c1 - xi_nmin[1, 2, inter1_c1] = 1 / c_c1 - xi_nmin[1, 2, inter2_c1] = 1 / c_c1 - xi_nmin[1, 2, hc_c1] = 1 / c_c1 - - ## Column 2 - c_c2 = 3 # Light components in Column 2 - lc_c2 = 2 # Light component in Column 2 - hc_c2 = 3 # Heavy component in Column 2 - inter_c2 = 1 # Intermediate component in Column 2 - - xi_nmin[2, 1, hc_c2] = 0.999 - xi_nmin[2, 1, lc_c2] = (1 - xi_nmin[2, 1, hc_c2]) / (c_c2 - 1) - xi_nmin[2, 1, inter_c2] = (1 - xi_nmin[2, 1, hc_c2]) / (c_c2 - 1) - xi_nmin[2, 3, lc_c2] = 0.499 - xi_nmin[2, 3, inter_c2] = 0.499 - xi_nmin[2, 3, hc_c2] = 1 - (xi_nmin[2, 3, lc_c2] + xi_nmin[2, 3, inter_c2]) - xi_nmin[2, 2, lc_c2] = 1 / c_c2 - xi_nmin[2, 2, inter_c2] = 1 / c_c2 - xi_nmin[2, 2, hc_c2] = 1 / c_c2 - - ## Column 3 - c_c3 = 2 # Components in Column 3 - lc_c3 = 1 # Light component in Column 3 - hc_c3 = 2 # Heavy component in Column 3 - - xi_nmin[3, 1, hc_c3] = 0.999 - xi_nmin[3, 1, lc_c3] = 1 - xi_nmin[3, 1, hc_c3] - xi_nmin[3, 3, lc_c3] = 0.999 - xi_nmin[3, 3, hc_c3] = 1 - xi_nmin[3, 3, lc_c3] - xi_nmin[3, 2, lc_c3] = 0.50 - xi_nmin[3, 2, hc_c3] = 0.50 - - #### - - mn = m.clone() - - mn.name = "Initialization Code" - - mn.cols = RangeSet(3, doc='Number of columns ') - mn.sec = RangeSet(3, doc='Sections in column: 1 reb, 2 side feed, 3 cond') - mn.nc1 = RangeSet(c_c1, doc='Number of components in Column 1') - mn.nc2 = RangeSet(c_c2, doc='Number of components in Column 2') - mn.nc3 = RangeSet(c_c3, doc='Number of components in Column 3') - - mn.Tnmin = Var( - mn.cols, - mn.sec, - doc='Temperature in K', - bounds=(0, 500), - domain=NonNegativeReals, - ) - mn.Tr1nmin = Var( - mn.cols, - mn.sec, - mn.nc1, - doc='Temperature term for vapor pressure', - domain=NonNegativeReals, - bounds=(0, None), - ) - mn.Tr2nmin = Var( - mn.cols, - mn.sec, - mn.nc2, - doc='Temperature term for vapor pressure', - domain=NonNegativeReals, - bounds=(0, None), - ) - mn.Tr3nmin = Var( - mn.cols, - mn.sec, - mn.nc3, - doc='Temperature term for vapor pressure', - domain=NonNegativeReals, - bounds=(0, None), - ) - - @mn.Constraint(mn.cols, mn.sec, mn.nc1, doc="Temperature term for vapor pressure") - def _column1_reduced_temperature(mn, col, sec, nc): - return mn.Tr1nmin[col, sec, nc] * mn.Tnmin[col, sec] == mn.prop[nc, 'TC'] - - @mn.Constraint(mn.cols, mn.sec, mn.nc2, doc="Temperature term for vapor pressure") - def _column2_reduced_temperature(mn, col, sec, nc): - return mn.Tr2nmin[col, sec, nc] * mn.Tnmin[col, sec] == mn.prop[nc, 'TC'] - - @mn.Constraint(mn.cols, mn.sec, mn.nc3, doc="Temperature term for vapor pressure") - def _column3_reduced_temperature(mn, col, sec, nc): - return mn.Tr3nmin[col, sec, nc] * mn.Tnmin[col, sec] == mn.prop[nc, 'TC'] - - @mn.Constraint(mn.cols, mn.sec, doc="Boiling point temperature") - def _equilibrium_equation(mn, col, sec): - if col == 1: - a = mn.Tr1nmin - b = mn.nc1 - elif col == 2: - a = mn.Tr2nmin - b = mn.nc2 - elif col == 3: - a = mn.Tr3nmin - b = mn.nc3 - return ( - sum( - xi_nmin[col, sec, nc] - * mn.prop[nc, 'PC'] - * exp( - a[col, sec, nc] - * ( - mn.prop[nc, 'vpA'] - * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) - + mn.prop[nc, 'vpB'] - * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) ** 1.5 - + mn.prop[nc, 'vpC'] - * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) ** 3 - + mn.prop[nc, 'vpD'] - * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) ** 6 - ) - ) - / Pnmin[sec] - for nc in b - ) - == 1 - ) - - mn.OBJ = Objective(expr=1, sense=minimize) - - #### - - SolverFactory('ipopt').solve(mn) - - yc = {} # Vapor composition - kl = {} # Light key component - kh = {} # Heavy key component - alpha = {} # Relative volatility of kl - ter = {} # Term to calculate the minimum number of trays - Nmin = {} # Minimum number of stages - Nminopt = {} # Total optimal minimum number of trays - Nfeed = {} # Side feed optimal location using Kirkbride's method: - # 1 = number of trays in rectifying section and - # 2 = number of trays in stripping section - side_feed = {} # Side feed location - av_alpha = {} # Average relative volatilities - xi_lhc = {} # Liquid composition in columns - rel = mn.Bdes / mn.Ddes # Ratio between products flowrates - ln = {} # Light component for the different columns - hn = {} # Heavy component for the different columns - ln[1] = lc_c1 - ln[2] = lc_c2 - ln[3] = lc_c3 - hn[1] = hc_c1 - hn[2] = hc_c2 - hn[3] = hc_c3 - - for col in mn.cols: - if col == 1: - b = mn.nc1 - elif col == 2: - b = mn.nc2 - else: - b = mn.nc3 - for sec in mn.sec: - for nc in b: - yc[col, sec, nc] = ( - xi_nmin[col, sec, nc] - * mn.prop[nc, 'PC'] - * exp( - mn.prop[nc, 'TC'] - / value(mn.Tnmin[col, sec]) - * ( - mn.prop[nc, 'vpA'] - * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) - + mn.prop[nc, 'vpB'] - * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) ** 1.5 - + mn.prop[nc, 'vpC'] - * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) ** 3 - + mn.prop[nc, 'vpD'] - * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) ** 6 - ) - ) - / Pnmin[sec] - ) - - for col in mn.cols: - xi_lhc[col, 4] = xi_nmin[col, 1, ln[col]] / xi_nmin[col, 3, hn[col]] - for sec in mn.sec: - kl[col, sec] = yc[col, sec, ln[col]] / xi_nmin[col, sec, ln[col]] - kh[col, sec] = yc[col, sec, hn[col]] / xi_nmin[col, sec, hn[col]] - xi_lhc[col, sec] = xi_nmin[col, sec, hn[col]] / xi_nmin[col, sec, ln[col]] - alpha[col, sec] = kl[col, sec] / kh[col, sec] - - for col in mn.cols: - av_alpha[col] = (alpha[col, 1] * alpha[col, 2] * alpha[col, 3]) ** (1 / 3) - Nmin[col] = log10((1 / xi_lhc[col, 3]) * xi_lhc[col, 1]) / log10(av_alpha[col]) - ter[col] = (rel * xi_lhc[col, 2] * (xi_lhc[col, 4] ** 2)) ** 0.206 - Nfeed[1, col] = ter[col] * Nmin[col] / (1 + ter[col]) - Nfeed[2, col] = Nfeed[1, col] / ter[col] - side_feed[col] = Nfeed[2, col] - - m.Nmintot = sum(Nmin[col] for col in mn.cols) - m.Knmin = int(m.Nmintot) + 1 - - m.TB0 = value(mn.Tnmin[1, 1]) - m.Tf0 = value(mn.Tnmin[1, 2]) - m.TD0 = value(mn.Tnmin[2, 3]) - - return m - - -if __name__ == "__main__": - initialize_kaibel() +""" + Calculation of the theoretical minimum number of trays and initial + temperature values. + (written by E. Soraya Rawlings, esoraya@rwlngs.net) + + The separation of four components require a sequence of at least three distillation + columns. Here, we calculate the minimum number of theoretical trays for the three + columns. The sequence is shown in Figure 2. + + COLUMN 1 COLUMN 2 COLUMN 3 + ----- ---- ----- + | | | | | | + ----- | A ----- | ----- | + | |<---> B -- | |<----> A -- | |<---> A + | | C | | | B | | | + A | | | | | | | | + B | | | | | | | | + C --->| | -->| | -->| | + D | | | | | | + | | | | | | + | |<- | |<- | |<- + ----- | ----- | ----- | + | | | | | | + -------> D -------> C -------> B + Figure 2. Sequence of columns for the separation of a quaternary mixture +""" + +from __future__ import division + +from pyomo.environ import ( + exp, + log10, + minimize, + NonNegativeReals, + Objective, + RangeSet, + SolverFactory, + value, + Var, +) + +from gdplib.kaibel.kaibel_prop import get_model_with_properties + +# from .kaibel_prop import get_model_with_properties + + +def initialize_kaibel(): + """Initialize the Kaibel optimization model. + + This function initializes the Kaibel optimization model by setting up the operating conditions, + initial liquid compositions, and creating the necessary variables and constraints. + + Returns + ------- + None + """ + + ## Get the model with properties from kaibel_prop.py + m = get_model_with_properties() + + ## Operating conditions + m.Preb = 1.2 # Reboiler pressure in bar + m.Pcon = 1.05 # Condenser pressure in bar + m.Pf = 1.02 + + Pnmin = {} # Pressure in bars + Pnmin[1] = m.Preb # Reboiler pressure in bars + Pnmin[3] = m.Pcon # Distillate pressure in bars + Pnmin[2] = m.Pf # Side feed pressure in bars + + xi_nmin = {} # Initial liquid composition: first number = column and + # second number = 1 reboiler, 2 side feed, and + # 3 for condenser + + ## Column 1 + c_c1 = 4 # Components in Column 1 + lc_c1 = 3 # Light component in Column 1 + hc_c1 = 4 # Heavy component in Column 1 + inter1_c1 = 1 # Intermediate component in Column 1 + inter2_c1 = 2 # Intermediate component in Column 1 + + xi_nmin[1, 1, hc_c1] = 0.999 + xi_nmin[1, 1, lc_c1] = (1 - xi_nmin[1, 1, hc_c1]) / (c_c1 - 1) + xi_nmin[1, 1, inter1_c1] = (1 - xi_nmin[1, 1, hc_c1]) / (c_c1 - 1) + xi_nmin[1, 1, inter2_c1] = (1 - xi_nmin[1, 1, hc_c1]) / (c_c1 - 1) + xi_nmin[1, 3, lc_c1] = 0.33 + xi_nmin[1, 3, inter1_c1] = 0.33 + xi_nmin[1, 3, inter2_c1] = 0.33 + xi_nmin[1, 3, hc_c1] = 1 - ( + xi_nmin[1, 3, lc_c1] + xi_nmin[1, 3, inter1_c1] + xi_nmin[1, 3, inter2_c1] + ) + xi_nmin[1, 2, lc_c1] = 1 / c_c1 + xi_nmin[1, 2, inter1_c1] = 1 / c_c1 + xi_nmin[1, 2, inter2_c1] = 1 / c_c1 + xi_nmin[1, 2, hc_c1] = 1 / c_c1 + + ## Column 2 + c_c2 = 3 # Light components in Column 2 + lc_c2 = 2 # Light component in Column 2 + hc_c2 = 3 # Heavy component in Column 2 + inter_c2 = 1 # Intermediate component in Column 2 + + xi_nmin[2, 1, hc_c2] = 0.999 + xi_nmin[2, 1, lc_c2] = (1 - xi_nmin[2, 1, hc_c2]) / (c_c2 - 1) + xi_nmin[2, 1, inter_c2] = (1 - xi_nmin[2, 1, hc_c2]) / (c_c2 - 1) + xi_nmin[2, 3, lc_c2] = 0.499 + xi_nmin[2, 3, inter_c2] = 0.499 + xi_nmin[2, 3, hc_c2] = 1 - (xi_nmin[2, 3, lc_c2] + xi_nmin[2, 3, inter_c2]) + xi_nmin[2, 2, lc_c2] = 1 / c_c2 + xi_nmin[2, 2, inter_c2] = 1 / c_c2 + xi_nmin[2, 2, hc_c2] = 1 / c_c2 + + ## Column 3 + c_c3 = 2 # Components in Column 3 + lc_c3 = 1 # Light component in Column 3 + hc_c3 = 2 # Heavy component in Column 3 + + xi_nmin[3, 1, hc_c3] = 0.999 + xi_nmin[3, 1, lc_c3] = 1 - xi_nmin[3, 1, hc_c3] + xi_nmin[3, 3, lc_c3] = 0.999 + xi_nmin[3, 3, hc_c3] = 1 - xi_nmin[3, 3, lc_c3] + xi_nmin[3, 2, lc_c3] = 0.50 + xi_nmin[3, 2, hc_c3] = 0.50 + + #### + + mn = m.clone() # Clone the model to add the initialization code + + mn.name = "Initialization Code" + + mn.cols = RangeSet(3, doc='Number of columns ') + mn.sec = RangeSet(3, doc='Sections in column: 1 reb, 2 side feed, 3 cond') + mn.nc1 = RangeSet(c_c1, doc='Number of components in Column 1') + mn.nc2 = RangeSet(c_c2, doc='Number of components in Column 2') + mn.nc3 = RangeSet(c_c3, doc='Number of components in Column 3') + + mn.Tnmin = Var( + mn.cols, + mn.sec, + doc='Temperature in K', + bounds=(0, 500), + domain=NonNegativeReals, + ) + mn.Tr1nmin = Var( + mn.cols, + mn.sec, + mn.nc1, + doc='Temperature term for vapor pressure', + domain=NonNegativeReals, + bounds=(0, None), + ) + mn.Tr2nmin = Var( + mn.cols, + mn.sec, + mn.nc2, + doc='Temperature term for vapor pressure', + domain=NonNegativeReals, + bounds=(0, None), + ) + mn.Tr3nmin = Var( + mn.cols, + mn.sec, + mn.nc3, + doc='Temperature term for vapor pressure', + domain=NonNegativeReals, + bounds=(0, None), + ) + + @mn.Constraint(mn.cols, mn.sec, mn.nc1, doc="Temperature term for vapor pressure") + def _column1_reduced_temperature(mn, col, sec, nc): + """Calculate the reduced temperature for column 1. + + This function calculates the reduced temperature for column 1 based on the given parameters using the Peng-Robinson equation of state. + + Parameters + ---------- + mn : Pyomo ConcreteModel + The optimization model + col : int + The column index + sec : int + The section index + nc : int + The component index in column 1 + + Returns + ------- + Constraint + The constraint statement to calculate the reduced temperature. + """ + return mn.Tr1nmin[col, sec, nc] * mn.Tnmin[col, sec] == mn.prop[nc, 'TC'] + + @mn.Constraint(mn.cols, mn.sec, mn.nc2, doc="Temperature term for vapor pressure") + def _column2_reduced_temperature(mn, col, sec, nc): + """Calculate the reduced temperature for column 2. + + This function calculates the reduced temperature for column 2 based on the given parameters using the Peng-Robinson equation of state. + + Parameters + ---------- + mn : Pyomo ConcreteModel + The optimization model + col : int + The column index + sec : int + The section index + nc : int + The component index in column 2 + + Returns + ------- + Constraint + The constraint equation to calculate the reduced temperature + """ + return mn.Tr2nmin[col, sec, nc] * mn.Tnmin[col, sec] == mn.prop[nc, 'TC'] + + @mn.Constraint(mn.cols, mn.sec, mn.nc3, doc="Temperature term for vapor pressure") + def _column3_reduced_temperature(mn, col, sec, nc): + """Calculate the reduced temperature for column 3. + + This function calculates the reduced temperature for column 3 based on the given parameters. + + Parameters + ---------- + mn : Pyomo ConcreteModel + The optimization model + col : int + The column index + sec : int + The section index + nc : int + The component index in column 3 + + Returns + ------- + Constraint + The constraint equation to calculate the reduced temperature in column 3 + """ + return mn.Tr3nmin[col, sec, nc] * mn.Tnmin[col, sec] == mn.prop[nc, 'TC'] + + @mn.Constraint(mn.cols, mn.sec, doc="Boiling point temperature") + def _equilibrium_equation(mn, col, sec): + """Equilibrium equations for a given column and section. + + Parameters + ---------- + mn : Pyomo ConcreteModel + The optimization model object with properties + col : int + The column index + sec : int + The section index + + Returns + ------- + Constraint + The constraint equation to calculate the boiling point temperature using the Peng-Robinson equation of state + """ + if col == 1: + a = mn.Tr1nmin + b = mn.nc1 + elif col == 2: + a = mn.Tr2nmin + b = mn.nc2 + elif col == 3: + a = mn.Tr3nmin + b = mn.nc3 + return ( + sum( + xi_nmin[col, sec, nc] + * mn.prop[nc, 'PC'] + * exp( + a[col, sec, nc] + * ( + mn.prop[nc, 'vpA'] + * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) + + mn.prop[nc, 'vpB'] + * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) ** 1.5 + + mn.prop[nc, 'vpC'] + * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) ** 3 + + mn.prop[nc, 'vpD'] + * (1 - mn.Tnmin[col, sec] / mn.prop[nc, 'TC']) ** 6 + ) + ) + / Pnmin[sec] + for nc in b + ) + == 1 + ) + + mn.OBJ = Objective(expr=1, sense=minimize) + + #### + + SolverFactory('ipopt').solve(mn) + + yc = {} # Vapor composition + kl = {} # Light key component + kh = {} # Heavy key component + alpha = {} # Relative volatility of kl + ter = {} # Term to calculate the minimum number of trays + Nmin = {} # Minimum number of stages + Nminopt = {} # Total optimal minimum number of trays + Nfeed = {} # Side feed optimal location using Kirkbride's method: + # 1 = number of trays in rectifying section and + # 2 = number of trays in stripping section + side_feed = {} # Side feed location + av_alpha = {} # Average relative volatilities + xi_lhc = {} # Liquid composition in columns + rel = mn.Bdes / mn.Ddes # Ratio between products flowrates + ln = {} # Light component for the different columns + hn = {} # Heavy component for the different columns + ln[1] = lc_c1 + ln[2] = lc_c2 + ln[3] = lc_c3 + hn[1] = hc_c1 + hn[2] = hc_c2 + hn[3] = hc_c3 + + for col in mn.cols: + if col == 1: + b = mn.nc1 + elif col == 2: + b = mn.nc2 + else: + b = mn.nc3 + # For each component in the column and section calculate the vapor composition with the Peng-Robinson equation of state + for sec in mn.sec: + for nc in b: + yc[col, sec, nc] = ( + xi_nmin[col, sec, nc] + * mn.prop[nc, 'PC'] + * exp( + mn.prop[nc, 'TC'] + / value(mn.Tnmin[col, sec]) + * ( + mn.prop[nc, 'vpA'] + * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) + + mn.prop[nc, 'vpB'] + * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) ** 1.5 + + mn.prop[nc, 'vpC'] + * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) ** 3 + + mn.prop[nc, 'vpD'] + * (1 - value(mn.Tnmin[col, sec]) / mn.prop[nc, 'TC']) ** 6 + ) + ) + ) / Pnmin[ + sec + ] # Vapor composition in the different sections for the different components in the columns + + for col in mn.cols: + # Calculate the relative volatility of the light and heavy components in the different sections for the different columns + xi_lhc[col, 4] = ( + xi_nmin[col, 1, ln[col]] / xi_nmin[col, 3, hn[col]] + ) # Liquid composition in the different sections with the initial liquid composition of the components in the different sections and columns and ln and hn which are the light and heavy components in the different columns + for sec in mn.sec: + kl[col, sec] = ( + yc[col, sec, ln[col]] / xi_nmin[col, sec, ln[col]] + ) # Light component in the different sections + kh[col, sec] = ( + yc[col, sec, hn[col]] / xi_nmin[col, sec, hn[col]] + ) # Heavy component in the different sections + xi_lhc[col, sec] = ( + xi_nmin[col, sec, hn[col]] / xi_nmin[col, sec, ln[col]] + ) # Liquid composition in the different sections + alpha[col, sec] = ( + kl[col, sec] / kh[col, sec] + ) # Relative volatility in the different sections + + for col in mn.cols: + # Calculate the average relative volatilities and the minimum number of trays with Fenske's and Kirkbride's method + av_alpha[col] = (alpha[col, 1] * alpha[col, 2] * alpha[col, 3]) ** ( + 1 / 3 + ) # Average relative volatilities calculated with the relative volatilities of the components in the three sections + Nmin[col] = log10((1 / xi_lhc[col, 3]) * xi_lhc[col, 1]) / log10( + av_alpha[col] + ) # Minimum number of trays calculated with Fenske's method + ter[col] = ( + rel * xi_lhc[col, 2] * (xi_lhc[col, 4] ** 2) + ) ** 0.206 # Term to calculate the minimum number of trays with Kirkbride's method + # Side feed optimal location using Kirkbride's method + Nfeed[1, col] = ( + ter[col] * Nmin[col] / (1 + ter[col]) + ) # Number of trays in rectifying section + Nfeed[2, col] = Nfeed[1, col] / ter[col] # Number of trays in stripping section + side_feed[col] = Nfeed[2, col] # Side feed location + + m.Nmintot = sum(Nmin[col] for col in mn.cols) # Total minimum number of trays + m.Knmin = int(m.Nmintot) + 1 # Total optimal minimum number of trays + + m.TB0 = value(mn.Tnmin[1, 1]) # Reboiler temperature in K in column 1 + m.Tf0 = value(mn.Tnmin[1, 2]) # Side feed temperature in K in column 1 + m.TD0 = value(mn.Tnmin[2, 3]) # Distillate temperature in K in column 2 + + return m + + +if __name__ == "__main__": + initialize_kaibel() diff --git a/gdplib/kaibel/kaibel_prop.py b/gdplib/kaibel/kaibel_prop.py index 9243a9d..3cae0f1 100644 --- a/gdplib/kaibel/kaibel_prop.py +++ b/gdplib/kaibel/kaibel_prop.py @@ -1,49 +1,56 @@ """ Properties of the system """ -from __future__ import division - from pyomo.environ import ConcreteModel def get_model_with_properties(): - """Attach properties to the model.""" + """ + Attach properties to the model and return the updated model. + The properties are the physical properties of the components in the system and constants for the calculation of liquid heat capacity. + It also includes the known initial values and scaling factors for the system, such as the number of trays, components, and flowrates. + Specifications for the product and the column are also included. + Case Study: methanol (1), ethanol (2), propanol (3), and butanol (4) + + Returns: + Pyomo ConcreteModel: The Pyomo model object with attached properties. + """ - m = ConcreteModel() + m = ConcreteModel("Properties of the system") # ------------------------------------------------------------------ # Data # ------------------------------------------------------------------ - m.np = 25 # Number of possible tays - m.c = 4 # Number of components - m.lc = 1 # Light component - m.hc = 4 # Heavy component + m.np = 25 # Number of possible trays. Upper bound for each section. + m.c = 4 # Number of components. Methanol (1), ethanol (2), propanol (3), and butanol (4) + m.lc = 1 # Light component, methanol + m.hc = 4 # Heavy component, butanol #### Constant parameters - m.Rgas = 8.314 # Ideal gas constant in J/mol K - m.Tref = 298.15 # Reference temperature in K + m.Rgas = 8.314 # Ideal gas constant [J/mol/K] + m.Tref = 298.15 # Reference temperature [K] #### Product specifications m.xspec_lc = 0.99 # Final liquid composition for methanol (1) m.xspec_hc = 0.99 # Fnal liquid composition for butanol (4) m.xspec_inter2 = 0.99 # Final liquid composition for ethanol (2) m.xspec_inter3 = 0.99 # Final liquid composition for propanol (3) - m.Ddes = 50 # Final flowrate in distillate in mol/s - m.Bdes = 50 # Final flowrate in bottoms in mol/s - m.Sdes = 50 # Final flowrate in side product streams in mol/s + m.Ddes = 50 # Final flowrate in distillate [mol/s] + m.Bdes = 50 # Final flowrate in bottoms [mol/s] + m.Sdes = 50 # Final flowrate in side product streams [mol/s] # #### Known initial values - m.Fi = m.Ddes + m.Bdes + 2 * m.Sdes # Side feed flowrate in mol/s - m.Vi = 400 # Initial value for vapor flowrate in mol/s - m.Li = 400 # Initial value for liquid flowrate in mol/s + m.Fi = m.Ddes + m.Bdes + 2 * m.Sdes # Side feed flowrate [mol/s] + m.Vi = 400 # Initial value for vapor flowrate [mol/s] + m.Li = 400 # Initial value for liquid flowrate [mol/s] - m.Tf = 358 # Side feed temperature in K + m.Tf = 358 # Side feed temperature [K] - m.Preb = 1.2 # Reboiler pressure in bar - m.Pbot = 1.12 # Bottom-most tray pressure in bar - m.Ptop = 1.08 # Top-most tray pressure in bar - m.Pcon = 1.05 # Condenser pressure in bar - m.Pf = 1.02 + m.Preb = 1.2 # Reboiler pressure [bar] + m.Pbot = 1.12 # Bottom-most tray pressure [bar] + m.Ptop = 1.08 # Top-most tray pressure [bar] + m.Pcon = 1.05 # Condenser pressure [bar] + m.Pf = 1.02 # Column pressure [bar] m.rr0 = 0.893 # Internal reflux ratio initial value m.bu0 = 0.871 # Internal reflux ratio initial value @@ -66,15 +73,15 @@ def get_model_with_properties(): # Physical Properties # # Notation: - # MW ........................ molecular weight in g/gmol - # TB ........................ boiling point temperature in K - # TC ........................ critical temperature in K - # PC ........................ critical pressure in bar + # MW ........................ molecular weight [g/mol] + # TB ........................ boiling point temperature [K] + # TC ........................ critical temperature [K] + # PC ........................ critical pressure [bar] # w ........................ acentric factor - # lden ...................... liquid density g/m3, - # dHvap ..................... heat of vaporization in J/mol. + # lden ...................... liquid density [g/m3], + # dHvap ..................... heat of vaporization [J/mol]. # vpA, vpB, vpC, and vpD .... vapor pressure constants - # cpA, cpB, cpC, and cpD .... heat capacity constants J/mol: + # cpA, cpB, cpC, and cpD .... heat capacity constants [J/mol]: # 1 for liq and 2 for vapor phase # # Reference A: R.C. Reid, J.M. Prausnitz and B.E. Poling, diff --git a/gdplib/kaibel/kaibel_side_flash.py b/gdplib/kaibel/kaibel_side_flash.py index ca2960c..dfe38f4 100644 --- a/gdplib/kaibel/kaibel_side_flash.py +++ b/gdplib/kaibel/kaibel_side_flash.py @@ -1,7 +1,5 @@ """ Side feed flash """ -from __future__ import division - from pyomo.environ import ( ConcreteModel, Constraint, @@ -18,11 +16,30 @@ def calc_side_feed_flash(m): - msf = ConcreteModel('SIDE FEED FLASH') + """Calculate the side feed flash. + + This function solves a flash calculation for a side feed in a distillation process. + It calculates the vapor-liquid equilibrium, vapor pressure, and liquid and vapor compositions + for the given side feed. + + Parameters + ---------- + m : Pyomo ConcreteModel + The Pyomo model object containing the necessary parameters and variables. + + Returns + ------- + Pyomo ConcreteModel + The updated Pyomo model with the calculated values, which include the vapor-liquid equilibrium, vapor pressure, and liquid and vapor compositions for the side feed. + + """ + msf = ConcreteModel('SIDE FEED FLASH') # Main side feed flash model msf.nc = RangeSet(1, m.c, doc='Number of components') - m.xfi = {} + m.xfi = ( + {} + ) # Liquid composition in the side feed of the main model for each component. for nc in msf.nc: m.xfi[nc] = 1 / m.c @@ -61,6 +78,18 @@ def calc_side_feed_flash(m): @msf.Constraint(doc="Vapor fraction") def _algq(msf): + """This function calculates the vapor fraction (q) in the side feed using the Peng-Robinson equation of state. + + Parameters + ---------- + msf : Pyomo ConcreteModel + The main side feed flash model. + + Returns + ------- + q : float + The vapor fraction in the side feed. + """ return ( sum( m.xfi[nc] * (1 - msf.Keqf[nc]) / (1 + msf.q * (msf.Keqf[nc] - 1)) @@ -71,18 +100,82 @@ def _algq(msf): @msf.Constraint(msf.nc, doc="Side feed liquid composition") def _algx(msf, nc): + """Side feed liquid composition + + This function calculates the liquid composition (xf) for a given component (nc) in the side feed. + + Parameters + ---------- + msf : Pyomo ConcreteModel + The main side feed flash model. + nc : int + The component index. + + Returns + ------- + xf : float + The liquid composition for the given component with Keqf, q, and xfi, which are the equilibrium constant, vapor fraction, and liquid composition in the side feed, respectively. + """ return msf.xf[nc] * (1 + msf.q * (msf.Keqf[nc] - 1)) == m.xfi[nc] @msf.Constraint(msf.nc, doc="Side feed vapor composition") def _algy(msf, nc): + """Side feed vapor composition + + This function calculates the vapor composition (ysf) for a given component (nc) in the side. + + Parameters + ---------- + msf : Pyomo ConcreteModel + The main side feed flash model. + nc : int + The component index. + + Returns + ------- + yf : float + The vapor composition for the given component given the liquid composition (xf) and the equilibrium constant (Keqf). + """ return msf.yf[nc] == msf.xf[nc] * msf.Keqf[nc] + # TODO: Is it computed using the Peng-Robinson equation of state? + @msf.Constraint(msf.nc, doc="Vapor-liquid equilibrium constant") def _algKeq(msf, nc): + """Calculate the vapor-liquid equilibrium constant for a given component using the Peng-Robinson equation of state. + + Parameters + ---------- + msf : Pyomo ConcreteModel + The MultiStageFlash model. + nc : int + The component index. + + Returns + ------- + Keqf : float + The equilibrium constant for the component taking into account the vapor pressure (Pvf) and the liquid pressure (Pf). + """ return msf.Keqf[nc] * m.Pf == msf.Pvf[nc] @msf.Constraint(msf.nc, doc="Side feed vapor pressure") def _algPvf(msf, nc): + """Calculate the vapor fraction for a given component. + + This function calculates the vapor fraction (Pvf) for a given component (nc) using the Peng-Robinson equation of state. + + Parameters + ---------- + msf : Pyomo ConcreteModel + The main side flash object. + nc : int + The component index. + + Returns + ------- + Pvf : float + The vapor fraction for the given component considering the temperature (Tf) and the properties of the component set in the main model. + """ return msf.Pvf[nc] == m.prop[nc, 'PC'] * exp( m.prop[nc, 'TC'] / msf.Tf @@ -94,15 +187,18 @@ def _algPvf(msf, nc): ) ) + # TODO: Is it computed using the Peng-Robinson equation of state? + msf.OBJ = Objective(expr=1, sense=minimize) #### SolverFactory('ipopt').solve(msf, tee=False) - m.yfi = {} + # Update the main model with the calculated values + m.yfi = {} # Vapor composition for nc in msf.nc: m.yfi[nc] = value(msf.yf[nc]) - m.q_init = value(msf.q) + m.q_init = value(msf.q) # Vapor fraction return m diff --git a/gdplib/kaibel/kaibel_solve_gdp.py b/gdplib/kaibel/kaibel_solve_gdp.py index 354bd50..7aca6f6 100644 --- a/gdplib/kaibel/kaibel_solve_gdp.py +++ b/gdplib/kaibel/kaibel_solve_gdp.py @@ -1,1349 +1,2662 @@ -""" Kaibel Column model: GDP formulation """ - -from __future__ import division - -from math import copysign - -from pyomo.environ import ( - Constraint, - exp, - minimize, - NonNegativeReals, - Objective, - RangeSet, - Set, - Var, -) -from pyomo.gdp import Disjunct - -from gdplib.kaibel.kaibel_init import initialize_kaibel - -from gdplib.kaibel.kaibel_side_flash import calc_side_feed_flash - - -def build_model(): - - m = initialize_kaibel() - - # Side feed init - m = calc_side_feed_flash(m) - - m.name = "GDP Kaibel Column" - - #### Calculated initial values - m.Treb = m.TB0 + 5 # Reboiler temperature in K - m.Tbot = m.TB0 # Bottom-most tray temperature in K - m.Ttop = m.TD0 # Top-most tray temperature in K - m.Tcon = m.TD0 - 5 # Condenser temperature in K - - m.dv0 = {} # Initial vapor distributor value - m.dl0 = {} # Initial liquid distributor value - m.dv0[2] = 0.516 - m.dv0[3] = 1 - m.dv0[2] - m.dl0[2] = 0.36 - m.dl0[3] = 1 - m.dl0[2] - - #### Calculated upper and lower bounds - m.min_tray = m.Knmin * 0.8 # Lower bound on number of trays - m.Tlo = m.Tcon - 20 # Temperature lower bound - m.Tup = m.Treb + 20 # Temperature upper bound - - m.flow_max = 1e3 # Flowrates upper bound - m.Qmax = 60 # Heat loads upper bound - - #### Column tray details - m.num_trays = m.np # Trays per section - m.min_num_trays = 10 # Minimum number of trays per section - m.num_total = m.np * 3 # Total number of trays - m.feed_tray = 12 # Side feed tray - m.sideout1_tray = 8 # Side outlet 1 tray - m.sideout2_tray = 17 # Side outlet 2 tray - m.reb_tray = 1 # Reboiler tray - m.con_tray = m.num_trays # Condenser tray - - # ------------------------------------------------------------------ - - # Beginning of model - - # ------------------------------------------------------------------ - - ## Sets - m.section = RangeSet( - 4, doc="Column sections:1=top, 2=feed side, 3=prod side, 4=bot" - ) - m.section_main = Set(initialize=[1, 4]) - - m.tray = RangeSet(m.np, doc="Potential trays in each section") - m.tray_total = RangeSet(m.num_total, doc="Total trays in the column") - m.tray_below_feed = RangeSet(m.feed_tray, doc="Trays below feed") - m.tray_below_so1 = RangeSet(m.sideout1_tray, doc="Trays below side outlet 1") - m.tray_below_so2 = RangeSet(m.sideout2_tray, doc="Trays below side outlet 1") - - m.comp = RangeSet(4, doc="Components") - m.dw = RangeSet(2, 3, doc="Dividing wall sections") - m.cplv = RangeSet(2, doc="Heat capacity: 1=liquid, 2=vapor") - m.so = RangeSet(2, doc="Side product outlets") - m.bounds = RangeSet(2, doc="Number of boundary condition values") - - m.candidate_trays_main = Set( - initialize=m.tray - [m.con_tray, m.reb_tray], - doc="Candidate trays for top and \ - bottom sections 1 and 4", - ) - m.candidate_trays_feed = Set( - initialize=m.tray - [m.con_tray, m.feed_tray, m.reb_tray], - doc="Candidate trays for feed section 2", - ) - m.candidate_trays_product = Set( - initialize=m.tray - [m.con_tray, m.sideout1_tray, m.sideout2_tray, m.reb_tray], - doc="Candidate trays for product section 3", - ) - - ## Calculation of initial values - m.dHvap = {} # Heat of vaporization - - m.P0 = {} # Initial pressure - m.T0 = {} # Initial temperature - m.L0 = {} # Initial individual liquid flowrate in mol/s - m.V0 = {} # Initial individual vapor flowrate - m.Vtotal0 = {} # Initial total vapor flowrate in mol/s - m.Ltotal0 = {} # Initial liquid flowrate in mol/s - m.x0 = {} # Initial liquid composition - m.y0 = {} # Initial vapor composition - m.actv0 = {} # Initial activity coefficients - m.cpdT0 = {} # Initial heat capacity for liquid and vapor phases - m.hl0 = {} # Initial liquid enthalpy in J/mol - m.hv0 = {} # Initial vapor enthalpy in J/mol - m.Pi = m.Preb # Initial given pressure value - m.Ti = {} # Initial known temperature values - - for sec in m.section: - for n_tray in m.tray: - m.P0[sec, n_tray] = m.Pi - - for sec in m.section: - for n_tray in m.tray: - for comp in m.comp: - m.L0[sec, n_tray, comp] = m.Li - m.V0[sec, n_tray, comp] = m.Vi - - for sec in m.section: - for n_tray in m.tray: - m.Ltotal0[sec, n_tray] = sum(m.L0[sec, n_tray, comp] for comp in m.comp) - m.Vtotal0[sec, n_tray] = sum(m.V0[sec, n_tray, comp] for comp in m.comp) - - for n_tray in m.tray_total: - if n_tray == m.reb_tray: - m.Ti[n_tray] = m.Treb - elif n_tray == m.num_total: - m.Ti[n_tray] = m.Tcon - else: - m.Ti[n_tray] = m.Tbot + (m.Ttop - m.Tbot) * (n_tray - 2) / (m.num_total - 3) - - for n_tray in m.tray_total: - if n_tray <= m.num_trays: - m.T0[1, n_tray] = m.Ti[n_tray] - elif n_tray >= m.num_trays and n_tray <= m.num_trays * 2: - m.T0[2, n_tray - m.num_trays] = m.Ti[n_tray] - m.T0[3, n_tray - m.num_trays] = m.Ti[n_tray] - elif n_tray >= m.num_trays * 2: - m.T0[4, n_tray - m.num_trays * 2] = m.Ti[n_tray] - - for sec in m.section: - for n_tray in m.tray: - for comp in m.comp: - m.x0[sec, n_tray, comp] = m.xfi[comp] - m.actv0[sec, n_tray, comp] = 1 - m.y0[sec, n_tray, comp] = m.xfi[comp] - - ## Enthalpy boundary values - hlb = {} # Liquid enthalpy - hvb = {} # Vapor enthalpy - cpb = {} # Heact capacity - dHvapb = {} # Heat of vaporization - Tbounds = {} # Temperature bounds - kc = {} # Light and heavy key components - Tbounds[1] = m.Tcon - Tbounds[2] = m.Treb - kc[1] = m.lc - kc[2] = m.hc - - for comp in m.comp: - dHvapb[comp] = -( - m.Rgas - * m.prop[comp, 'TC'] - * ( - m.prop[comp, 'vpA'] * (1 - m.Tref / m.prop[comp, 'TC']) - + m.prop[comp, 'vpB'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 1.5 - + m.prop[comp, 'vpC'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 3 - + m.prop[comp, 'vpD'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 6 - ) - + m.Rgas - * m.Tref - * ( - m.prop[comp, 'vpA'] - + 1.5 * m.prop[comp, 'vpB'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 0.5 - + 3 * m.prop[comp, 'vpC'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 2 - + 6 * m.prop[comp, 'vpD'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 5 - ) - ) - - for b in m.bounds: - for cp in m.cplv: - cpb[b, cp] = m.cpc[cp] * ( - (Tbounds[b] - m.Tref) * m.prop[kc[b], 'cpA', cp] - + (Tbounds[b] ** 2 - m.Tref**2) - * m.prop[kc[b], 'cpB', cp] - * m.cpc2['A', cp] - / 2 - + (Tbounds[b] ** 3 - m.Tref**3) - * m.prop[kc[b], 'cpC', cp] - * m.cpc2['B', cp] - / 3 - + (Tbounds[b] ** 4 - m.Tref**4) * m.prop[kc[b], 'cpD', cp] / 4 - ) - hlb[b] = cpb[b, 1] - hvb[b] = cpb[b, 2] + dHvapb[b] - - m.hllo = (1 - copysign(0.2, hlb[1])) * hlb[1] / m.Hscale - m.hlup = (1 + copysign(0.2, hlb[2])) * hlb[2] / m.Hscale - m.hvlo = (1 - copysign(0.2, hvb[1])) * hvb[1] / m.Hscale - m.hvup = (1 + copysign(0.2, hvb[2])) * hvb[2] / m.Hscale - - for comp in m.comp: - m.dHvap[comp] = dHvapb[comp] / m.Hscale - - for sec in m.section: - for n_tray in m.tray: - for comp in m.comp: - for cp in m.cplv: - m.cpdT0[sec, n_tray, comp, cp] = ( - m.cpc[cp] - * ( - (m.T0[sec, n_tray] - m.Tref) * m.prop[comp, 'cpA', cp] - + (m.T0[sec, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', cp] - * m.cpc2['A', cp] - / 2 - + (m.T0[sec, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', cp] - * m.cpc2['B', cp] - / 3 - + (m.T0[sec, n_tray] ** 4 - m.Tref**4) - * m.prop[comp, 'cpD', cp] - / 4 - ) - / m.Hscale - ) - - for sec in m.section: - for n_tray in m.tray: - for comp in m.comp: - m.hl0[sec, n_tray, comp] = m.cpdT0[sec, n_tray, comp, 1] - m.hv0[sec, n_tray, comp] = m.cpdT0[sec, n_tray, comp, 2] + m.dHvap[comp] - - #### Side feed - m.cpdTf = {} # Heat capacity for side feed J/mol K - m.hlf = {} # Liquid enthalpy for side feed in J/mol - m.hvf = {} # Vapor enthalpy for side feed in J/mol - m.F0 = {} # Side feed flowrate per component in mol/s - - for comp in m.comp: - for cp in m.cplv: - m.cpdTf[comp, cp] = ( - m.cpc[cp] - * ( - (m.Tf - m.Tref) * m.prop[comp, 'cpA', cp] - + (m.Tf**2 - m.Tref**2) - * m.prop[comp, 'cpB', cp] - * m.cpc2['A', cp] - / 2 - + (m.Tf**3 - m.Tref**3) - * m.prop[comp, 'cpC', cp] - * m.cpc2['B', cp] - / 3 - + (m.Tf**4 - m.Tref**4) * m.prop[comp, 'cpD', cp] / 4 - ) - / m.Hscale - ) - - for comp in m.comp: - m.F0[comp] = m.xfi[comp] * m.Fi - m.hlf[comp] = m.cpdTf[comp, 1] - m.hvf[comp] = m.cpdTf[comp, 2] + m.dHvap[comp] - - m.P = Var( - m.section, - m.tray, - doc="Pressure at each potential tray in bars", - domain=NonNegativeReals, - bounds=(m.Pcon, m.Preb), - initialize=m.P0, - ) - m.T = Var( - m.section, - m.tray, - doc="Temperature at each potential tray in K", - domain=NonNegativeReals, - bounds=(m.Tlo, m.Tup), - initialize=m.T0, - ) - - m.x = Var( - m.section, - m.tray, - m.comp, - doc="Liquid composition", - domain=NonNegativeReals, - bounds=(0, 1), - initialize=m.x0, - ) - m.y = Var( - m.section, - m.tray, - m.comp, - doc="Vapor composition", - domain=NonNegativeReals, - bounds=(0, 1), - initialize=m.y0, - ) - - m.dl = Var(m.dw, doc="Liquid distributor", bounds=(0.2, 0.8), initialize=m.dl0) - m.dv = Var( - m.dw, - doc="Vapor distributor", - bounds=(0, 1), - domain=NonNegativeReals, - initialize=m.dv0, - ) - - m.V = Var( - m.section, - m.tray, - m.comp, - doc="Vapor flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.V0, - ) - m.L = Var( - m.section, - m.tray, - m.comp, - doc="Liquid flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.L0, - ) - m.Vtotal = Var( - m.section, - m.tray, - doc="Total vapor flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Vtotal0, - ) - m.Ltotal = Var( - m.section, - m.tray, - doc="Total liquid flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Ltotal0, - ) - - m.D = Var( - m.comp, - doc="Distillate flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Ddes, - ) - m.B = Var( - m.comp, - doc="Bottoms flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Bdes, - ) - m.S = Var( - m.so, - m.comp, - doc="Product 2 and 3 flowrates in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Sdes, - ) - m.Dtotal = Var( - doc="Distillate flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Ddes, - ) - m.Btotal = Var( - doc="Bottoms flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Bdes, - ) - m.Stotal = Var( - m.so, - doc="Total product 2 and 3 side flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, m.flow_max), - initialize=m.Sdes, - ) - - m.hl = Var( - m.section, - m.tray, - m.comp, - doc='Liquid enthalpy in J/mol', - bounds=(m.hllo, m.hlup), - initialize=m.hl0, - ) - m.hv = Var( - m.section, - m.tray, - m.comp, - doc='Vapor enthalpy in J/mol', - bounds=(m.hvlo, m.hvup), - initialize=m.hv0, - ) - m.Qreb = Var( - doc="Reboiler heat duty in J/s", - domain=NonNegativeReals, - bounds=(0, m.Qmax), - initialize=1, - ) - m.Qcon = Var( - doc="Condenser heat duty in J/s", - domain=NonNegativeReals, - bounds=(0, m.Qmax), - initialize=1, - ) - - m.rr = Var( - doc="Internal reflux ratio", - domain=NonNegativeReals, - bounds=(0.7, 1), - initialize=m.rr0, - ) - m.bu = Var( - doc="Boilup rate", domain=NonNegativeReals, bounds=(0.7, 1), initialize=m.bu0 - ) - - m.F = Var( - m.comp, - doc="Side feed flowrate in mol/s", - domain=NonNegativeReals, - bounds=(0, 50), - initialize=m.F0, - ) - m.q = Var( - doc="Vapor fraction in side feed", - domain=NonNegativeReals, - bounds=(0, 1), - initialize=1, - ) - - m.actv = Var( - m.section, - m.tray, - m.comp, - doc="Liquid activity coefficient", - domain=NonNegativeReals, - bounds=(0, 10), - initialize=m.actv0, - ) - - m.errx = Var(m.section, m.tray, bounds=(-1e-3, 1e-3), initialize=0) - m.erry = Var(m.section, m.tray, bounds=(-1e-3, 1e-3), initialize=0) - m.slack = Var( - m.section, - m.tray, - m.comp, - doc="Slack variable", - bounds=(-1e-8, 1e-8), - initialize=0, - ) - - m.tray_exists = Disjunct(m.section, m.tray, rule=_build_tray_equations) - m.tray_absent = Disjunct(m.section, m.tray, rule=_build_pass_through_eqns) - - @m.Disjunction( - m.section, m.tray, doc="Disjunction between whether each tray exists or not" - ) - def tray_exists_or_not(m, sec, n_tray): - return [m.tray_exists[sec, n_tray], m.tray_absent[sec, n_tray]] - - @m.Constraint(m.section_main) - def minimum_trays_main(m, sec): - return ( - sum( - m.tray_exists[sec, n_tray].binary_indicator_var - for n_tray in m.candidate_trays_main - ) - + 1 - >= m.min_num_trays - ) - - @m.Constraint() - def minimum_trays_feed(m): - return ( - sum( - m.tray_exists[2, n_tray].binary_indicator_var - for n_tray in m.candidate_trays_feed - ) - + 1 - >= m.min_num_trays - ) - - @m.Constraint() - def minimum_trays_product(m): - return ( - sum( - m.tray_exists[3, n_tray].binary_indicator_var - for n_tray in m.candidate_trays_product - ) - + 1 - >= m.min_num_trays - ) - - ## Fixed trays - enforce_tray_exists(m, 1, 1) # reboiler - enforce_tray_exists(m, 1, m.num_trays) # vapor distributor - enforce_tray_exists(m, 2, 1) # dividing wall starting tray - enforce_tray_exists(m, 2, m.feed_tray) # feed tray - enforce_tray_exists(m, 2, m.num_trays) # dividing wall ending tray - enforce_tray_exists(m, 3, 1) # dividing wall starting tray - enforce_tray_exists(m, 3, m.sideout1_tray) # side outlet 1 for product 3 - enforce_tray_exists(m, 3, m.sideout2_tray) # side outlet 2 for product 2 - enforce_tray_exists(m, 3, m.num_trays) # dividing wall ending tray - enforce_tray_exists(m, 4, 1) # liquid distributor - enforce_tray_exists(m, 4, m.num_trays) # condenser - - #### Global constraints - @m.Constraint(m.dw, m.tray, doc="Monotonic temperature") - def monotonic_temperature(m, sec, n_tray): - return m.T[sec, n_tray] <= m.T[1, m.num_trays] - - @m.Constraint(doc="Liquid distributor") - def liquid_distributor(m): - return sum(m.dl[sec] for sec in m.dw) - 1 == 0 - - @m.Constraint(doc="Vapor distributor") - def vapor_distributor(m): - return sum(m.dv[sec] for sec in m.dw) - 1 == 0 - - @m.Constraint(doc="Reboiler composition specification") - def heavy_product(m): - return m.x[1, m.reb_tray, m.hc] >= m.xspec_hc - - @m.Constraint(doc="Condenser composition specification") - def light_product(m): - return m.x[4, m.con_tray, m.lc] >= m.xspec_lc - - @m.Constraint(doc="Side outlet 1 final liquid composition") - def intermediate1_product(m): - return m.x[3, m.sideout1_tray, 3] >= m.xspec_inter3 - - @m.Constraint(doc="Side outlet 2 final liquid composition") - def intermediate2_product(m): - return m.x[3, m.sideout2_tray, 2] >= m.xspec_inter2 - - @m.Constraint(doc="Reboiler flowrate") - def _heavy_product_flow(m): - return m.Btotal >= m.Bdes - - @m.Constraint(doc="Condenser flowrate") - def _light_product_flow(m): - return m.Dtotal >= m.Ddes - - @m.Constraint(m.so, doc="Intermediate flowrate") - def _intermediate_product_flow(m, so): - return m.Stotal[so] >= m.Sdes - - @m.Constraint(doc="Internal boilup ratio, V/L") - def _internal_boilup_ratio(m): - return m.bu * m.Ltotal[1, m.reb_tray + 1] == m.Vtotal[1, m.reb_tray] - - @m.Constraint(doc="Internal reflux ratio, L/V") - def internal_reflux_ratio(m): - return m.rr * m.Vtotal[4, m.con_tray - 1] == m.Ltotal[4, m.con_tray] - - @m.Constraint(doc="External boilup ratio relation with bottoms") - def _external_boilup_ratio(m): - return m.Btotal == (1 - m.bu) * m.Ltotal[1, m.reb_tray + 1] - - @m.Constraint(doc="External reflux ratio relation with distillate") - def _external_reflux_ratio(m): - return m.Dtotal == (1 - m.rr) * m.Vtotal[4, m.con_tray - 1] - - @m.Constraint(m.section, m.tray, doc="Total vapor flowrate") - def _total_vapor_flowrate(m, sec, n_tray): - return sum(m.V[sec, n_tray, comp] for comp in m.comp) == m.Vtotal[sec, n_tray] - - @m.Constraint(m.section, m.tray, doc="Total liquid flowrate") - def _total_liquid_flowrate(m, sec, n_tray): - return sum(m.L[sec, n_tray, comp] for comp in m.comp) == m.Ltotal[sec, n_tray] - - @m.Constraint(m.comp, doc="Bottoms and liquid relation") - def bottoms_equality(m, comp): - return m.B[comp] == m.L[1, m.reb_tray, comp] - - @m.Constraint(m.comp) - def condenser_total(m, comp): - return m.V[4, m.con_tray, comp] == 0 - - @m.Constraint() - def total_bottoms_product(m): - return sum(m.B[comp] for comp in m.comp) == m.Btotal - - @m.Constraint() - def total_distillate_product(m): - return sum(m.D[comp] for comp in m.comp) == m.Dtotal - - @m.Constraint(m.so) - def total_side_product(m, so): - return sum(m.S[so, comp] for comp in m.comp) == m.Stotal[so] - - m.obj = Objective( - expr=(m.Qcon + m.Qreb) * m.Hscale - + 1e3 - * ( - sum( - sum( - m.tray_exists[sec, n_tray].binary_indicator_var - for n_tray in m.candidate_trays_main - ) - for sec in m.section_main - ) - + sum( - m.tray_exists[2, n_tray].binary_indicator_var - for n_tray in m.candidate_trays_feed - ) - + sum( - m.tray_exists[3, n_tray].binary_indicator_var - for n_tray in m.candidate_trays_product - ) - + 1 - ), - sense=minimize, - ) - - @m.Constraint(m.section_main, m.candidate_trays_main) - def _logic_proposition_main(m, sec, n_tray): - if n_tray > m.reb_tray and (n_tray + 1) < m.num_trays: - return ( - m.tray_exists[sec, n_tray].binary_indicator_var - <= m.tray_exists[sec, n_tray + 1].binary_indicator_var - ) - else: - return Constraint.NoConstraint - - @m.Constraint(m.candidate_trays_feed) - def _logic_proposition_feed(m, n_tray): - if n_tray > m.reb_tray and (n_tray + 1) < m.feed_tray: - return ( - m.tray_exists[2, n_tray].binary_indicator_var - <= m.tray_exists[2, n_tray + 1].binary_indicator_var - ) - elif n_tray > m.feed_tray and (n_tray + 1) < m.con_tray: - return ( - m.tray_exists[2, n_tray + 1].binary_indicator_var - <= m.tray_exists[2, n_tray].binary_indicator_var - ) - else: - return Constraint.NoConstraint - - @m.Constraint(m.candidate_trays_product) - def _logic_proposition_section3(m, n_tray): - if n_tray > 1 and (n_tray + 1) < m.num_trays: - return ( - m.tray_exists[3, n_tray].binary_indicator_var - <= m.tray_exists[3, n_tray + 1].binary_indicator_var - ) - else: - return Constraint.NoConstraint - - @m.Constraint(m.tray) - def equality_feed_product_side(m, n_tray): - return ( - m.tray_exists[2, n_tray].binary_indicator_var - == m.tray_exists[3, n_tray].binary_indicator_var - ) - - @m.Constraint() - def _existent_minimum_numbertrays(m): - return sum( - sum(m.tray_exists[sec, n_tray].binary_indicator_var for n_tray in m.tray) - for sec in m.section - ) - sum( - m.tray_exists[3, n_tray].binary_indicator_var for n_tray in m.tray - ) >= int( - m.min_tray - ) - - return m - - -def enforce_tray_exists(m, sec, n_tray): - m.tray_exists[sec, n_tray].indicator_var.fix(True) - m.tray_absent[sec, n_tray].deactivate() - - -def _build_tray_equations(m, sec, n_tray): - build_function = { - 1: _build_bottom_equations, - 2: _build_feed_side_equations, - 3: _build_product_side_equations, - 4: _build_top_equations, - } - build_function[sec](m, n_tray) - - -def _build_bottom_equations(disj, n_tray): - m = disj.model() - - @disj.Constraint(m.comp, doc="Bottom section 1 mass per component balances") - def _bottom_mass_percomponent_balances(disj, comp): - return (m.L[1, n_tray + 1, comp] if n_tray < m.num_trays else 0) + ( - m.L[2, 1, comp] if n_tray == m.num_trays else 0 - ) + (m.L[3, 1, comp] if n_tray == m.num_trays else 0) - ( - m.L[1, n_tray, comp] if n_tray > m.reb_tray else 0 - ) + ( - m.V[1, n_tray - 1, comp] if n_tray > m.reb_tray else 0 - ) - ( - m.V[1, n_tray, comp] * m.dv[2] if n_tray == m.num_trays else 0 - ) - ( - m.V[1, n_tray, comp] * m.dv[3] if n_tray == m.num_trays else 0 - ) - ( - m.V[1, n_tray, comp] if n_tray < m.num_trays else 0 - ) - ( - m.B[comp] if n_tray == m.reb_tray else 0 - ) == m.slack[ - 1, n_tray, comp - ] - - @disj.Constraint(doc="Bottom section 1 energy balances") - def _bottom_energy_balances(disj): - return ( - sum( - ( - m.L[1, n_tray + 1, comp] * m.hl[1, n_tray + 1, comp] - if n_tray < m.num_trays - else 0 - ) - + (m.L[2, 1, comp] * m.hl[2, 1, comp] if n_tray == m.num_trays else 0) - + (m.L[3, 1, comp] * m.hl[3, 1, comp] if n_tray == m.num_trays else 0) - - ( - m.L[1, n_tray, comp] * m.hl[1, n_tray, comp] - if n_tray > m.reb_tray - else 0 - ) - + ( - m.V[1, n_tray - 1, comp] * m.hv[1, n_tray - 1, comp] - if n_tray > m.reb_tray - else 0 - ) - - ( - m.V[1, n_tray, comp] * m.dv[2] * m.hv[1, n_tray, comp] - if n_tray == m.num_trays - else 0 - ) - - ( - m.V[1, n_tray, comp] * m.dv[3] * m.hv[1, n_tray, comp] - if n_tray == m.num_trays - else 0 - ) - - ( - m.V[1, n_tray, comp] * m.hv[1, n_tray, comp] - if n_tray < m.num_trays - else 0 - ) - - (m.B[comp] * m.hl[1, n_tray, comp] if n_tray == m.reb_tray else 0) - for comp in m.comp - ) - * m.Qscale - + (m.Qreb if n_tray == m.reb_tray else 0) - == 0 - ) - - @disj.Constraint(m.comp, doc="Bottom section 1 liquid flowrate per component") - def _bottom_liquid_percomponent(disj, comp): - return m.L[1, n_tray, comp] == m.Ltotal[1, n_tray] * m.x[1, n_tray, comp] - - @disj.Constraint(m.comp, doc="Bottom section 1 vapor flowrate per component") - def _bottom_vapor_percomponent(disj, comp): - return m.V[1, n_tray, comp] == m.Vtotal[1, n_tray] * m.y[1, n_tray, comp] - - @disj.Constraint(doc="Bottom section 1 liquid composition equilibrium summation") - def bottom_liquid_composition_summation(disj): - return sum(m.x[1, n_tray, comp] for comp in m.comp) - 1 == m.errx[1, n_tray] - - @disj.Constraint(doc="Bottom section 1 vapor composition equilibrium summation") - def bottom_vapor_composition_summation(disj): - return sum(m.y[1, n_tray, comp] for comp in m.comp) - 1 == m.erry[1, n_tray] - - @disj.Constraint(m.comp, doc="Bottom section 1 vapor composition") - def bottom_vapor_composition(disj, comp): - return ( - m.y[1, n_tray, comp] - == m.x[1, n_tray, comp] - * ( - m.actv[1, n_tray, comp] - * ( - m.prop[comp, 'PC'] - * exp( - m.prop[comp, 'TC'] - / m.T[1, n_tray] - * ( - m.prop[comp, 'vpA'] - * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) - + m.prop[comp, 'vpB'] - * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) ** 1.5 - + m.prop[comp, 'vpC'] - * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) ** 3 - + m.prop[comp, 'vpD'] - * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) ** 6 - ) - ) - ) - ) - / m.P[1, n_tray] - ) - - @disj.Constraint(m.comp, doc="Bottom section 1 liquid enthalpy") - def bottom_liquid_enthalpy(disj, comp): - return m.hl[1, n_tray, comp] == ( - m.cpc[1] - * ( - (m.T[1, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] - + (m.T[1, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 1] - * m.cpc2['A', 1] - / 2 - + (m.T[1, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 1] - * m.cpc2['B', 1] - / 3 - + (m.T[1, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 - ) - / m.Hscale - ) - - @disj.Constraint(m.comp, doc="Bottom section 1 vapor enthalpy") - def bottom_vapor_enthalpy(disj, comp): - return m.hv[1, n_tray, comp] == ( - m.cpc[2] - * ( - (m.T[1, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] - + (m.T[1, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 2] - * m.cpc2['A', 2] - / 2 - + (m.T[1, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 2] - * m.cpc2['B', 2] - / 3 - + (m.T[1, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 - ) - / m.Hscale - + m.dHvap[comp] - ) - - @disj.Constraint(m.comp, doc="Bottom section 1 liquid activity coefficient") - def bottom_activity_coefficient(disj, comp): - return m.actv[1, n_tray, comp] == 1 - - -def _build_feed_side_equations(disj, n_tray): - m = disj.model() - - @disj.Constraint(m.comp, doc="Feed section 2 mass per component balances") - def _feedside_masspercomponent_balances(disj, comp): - return (m.L[2, n_tray + 1, comp] if n_tray < m.num_trays else 0) + ( - m.L[4, 1, comp] * m.dl[2] if n_tray == m.num_trays else 0 - ) - m.L[2, n_tray, comp] + ( - m.V[1, m.num_trays, comp] * m.dv[2] if n_tray == 1 else 0 - ) + ( - m.V[2, n_tray - 1, comp] if n_tray > 1 else 0 - ) - m.V[ - 2, n_tray, comp - ] + ( - m.F[comp] if n_tray == m.feed_tray else 0 - ) == 0 - - @disj.Constraint(doc="Feed section 2 energy balances") - def _feedside_energy_balances(disj): - return ( - sum( - ( - m.L[2, n_tray + 1, comp] * m.hl[2, n_tray + 1, comp] - if n_tray < m.num_trays - else 0 - ) - + ( - m.L[4, 1, comp] * m.dl[2] * m.hl[4, 1, comp] - if n_tray == m.num_trays - else 0 - ) - - m.L[2, n_tray, comp] * m.hl[2, n_tray, comp] - + ( - m.V[1, m.num_trays, comp] * m.dv[2] * m.hv[1, m.num_trays, comp] - if n_tray == 1 - else 0 - ) - + ( - m.V[2, n_tray - 1, comp] * m.hv[2, n_tray - 1, comp] - if n_tray > 1 - else 0 - ) - - m.V[2, n_tray, comp] * m.hv[2, n_tray, comp] - for comp in m.comp - ) - * m.Qscale - + sum( - ( - m.F[comp] * (m.hlf[comp] * (1 - m.q) + m.hvf[comp] * m.q) - if n_tray == m.feed_tray - else 0 - ) - for comp in m.comp - ) - * m.Qscale - == 0 - ) - - @disj.Constraint(m.comp, doc="Feed section 2 liquid flowrate per component") - def _feedside_liquid_percomponent(disj, comp): - return m.L[2, n_tray, comp] == m.Ltotal[2, n_tray] * m.x[2, n_tray, comp] - - @disj.Constraint(m.comp, doc="Feed section 2 vapor flowrate per component") - def _feedside_vapor_percomponent(disj, comp): - return m.V[2, n_tray, comp] == m.Vtotal[2, n_tray] * m.y[2, n_tray, comp] - - @disj.Constraint(doc="Feed section 2 liquid composition equilibrium summation") - def feedside_liquid_composition_summation(disj): - return sum(m.x[2, n_tray, comp] for comp in m.comp) - 1 == m.errx[2, n_tray] - - @disj.Constraint(doc="Feed section 2 vapor composition equilibrium summation") - def feedside_vapor_composition_summation(disj): - return sum(m.y[2, n_tray, comp] for comp in m.comp) - 1 == m.erry[2, n_tray] - - @disj.Constraint(m.comp, doc="Feed section 2 vapor composition") - def feedside_vapor_composition(disj, comp): - return ( - m.y[2, n_tray, comp] - == m.x[2, n_tray, comp] - * ( - m.actv[2, n_tray, comp] - * ( - m.prop[comp, 'PC'] - * exp( - m.prop[comp, 'TC'] - / m.T[2, n_tray] - * ( - m.prop[comp, 'vpA'] - * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) - + m.prop[comp, 'vpB'] - * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) ** 1.5 - + m.prop[comp, 'vpC'] - * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) ** 3 - + m.prop[comp, 'vpD'] - * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) ** 6 - ) - ) - ) - ) - / m.P[2, n_tray] - ) - - @disj.Constraint(m.comp, doc="Feed section 2 liquid enthalpy") - def feedside_liquid_enthalpy(disj, comp): - return m.hl[2, n_tray, comp] == ( - m.cpc[1] - * ( - (m.T[2, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] - + (m.T[2, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 1] - * m.cpc2['A', 1] - / 2 - + (m.T[2, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 1] - * m.cpc2['B', 1] - / 3 - + (m.T[2, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 - ) - / m.Hscale - ) - - @disj.Constraint(m.comp, doc="Feed section 2 vapor enthalpy") - def feedside_vapor_enthalpy(disj, comp): - return m.hv[2, n_tray, comp] == ( - m.cpc[2] - * ( - (m.T[2, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] - + (m.T[2, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 2] - * m.cpc2['A', 2] - / 2 - + (m.T[2, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 2] - * m.cpc2['B', 2] - / 3 - + (m.T[2, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 - ) - / m.Hscale - + m.dHvap[comp] - ) - - @disj.Constraint(m.comp, doc="Feed section 2 liquid activity coefficient") - def feedside_activity_coefficient(disj, comp): - return m.actv[2, n_tray, comp] == 1 - - -def _build_product_side_equations(disj, n_tray): - m = disj.model() - - @disj.Constraint(m.comp, doc="Product section 3 mass per component balances") - def _productside_masspercomponent_balances(disj, comp): - return (m.L[3, n_tray + 1, comp] if n_tray < m.num_trays else 0) + ( - m.L[4, 1, comp] * m.dl[3] if n_tray == m.num_trays else 0 - ) - m.L[3, n_tray, comp] + ( - m.V[1, m.num_trays, comp] * m.dv[3] if n_tray == 1 else 0 - ) + ( - m.V[3, n_tray - 1, comp] if n_tray > 1 else 0 - ) - m.V[ - 3, n_tray, comp - ] - ( - m.S[1, comp] if n_tray == m.sideout1_tray else 0 - ) - ( - m.S[2, comp] if n_tray == m.sideout2_tray else 0 - ) == 0 - - @disj.Constraint(doc="Product section 3 energy balances") - def _productside_energy_balances(disj): - return ( - sum( - ( - m.L[3, n_tray + 1, comp] * m.hl[3, n_tray + 1, comp] - if n_tray < m.num_trays - else 0 - ) - + ( - m.L[4, 1, comp] * m.dl[3] * m.hl[4, 1, comp] - if n_tray == m.num_trays - else 0 - ) - - m.L[3, n_tray, comp] * m.hl[3, n_tray, comp] - + ( - m.V[1, m.num_trays, comp] * m.dv[3] * m.hv[1, m.num_trays, comp] - if n_tray == 1 - else 0 - ) - + ( - m.V[3, n_tray - 1, comp] * m.hv[3, n_tray - 1, comp] - if n_tray > 1 - else 0 - ) - - m.V[3, n_tray, comp] * m.hv[3, n_tray, comp] - - ( - m.S[1, comp] * m.hl[3, n_tray, comp] - if n_tray == m.sideout1_tray - else 0 - ) - - ( - m.S[2, comp] * m.hl[3, n_tray, comp] - if n_tray == m.sideout2_tray - else 0 - ) - for comp in m.comp - ) - * m.Qscale - == 0 - ) - - @disj.Constraint(m.comp, doc="Product section 3 liquid flowrate per component") - def _productside_liquid_percomponent(disj, comp): - return m.L[3, n_tray, comp] == m.Ltotal[3, n_tray] * m.x[3, n_tray, comp] - - @disj.Constraint(m.comp, doc="Product section 3 vapor flowrate per component") - def _productside_vapor_percomponent(disj, comp): - return m.V[3, n_tray, comp] == m.Vtotal[3, n_tray] * m.y[3, n_tray, comp] - - @disj.Constraint(doc="Product section 3 liquid composition equilibrium summation") - def productside_liquid_composition_summation(disj): - return sum(m.x[3, n_tray, comp] for comp in m.comp) - 1 == m.errx[3, n_tray] - - @disj.Constraint(doc="Product section 3 vapor composition equilibrium summation") - def productside_vapor_composition_summation(disj): - return sum(m.y[3, n_tray, comp] for comp in m.comp) - 1 == m.erry[3, n_tray] - - @disj.Constraint(m.comp, doc="Product section 3 vapor composition") - def productside_vapor_composition(disj, comp): - return ( - m.y[3, n_tray, comp] - == m.x[3, n_tray, comp] - * ( - m.actv[3, n_tray, comp] - * ( - m.prop[comp, 'PC'] - * exp( - m.prop[comp, 'TC'] - / m.T[3, n_tray] - * ( - m.prop[comp, 'vpA'] - * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) - + m.prop[comp, 'vpB'] - * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) ** 1.5 - + m.prop[comp, 'vpC'] - * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) ** 3 - + m.prop[comp, 'vpD'] - * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) ** 6 - ) - ) - ) - ) - / m.P[3, n_tray] - ) - - @disj.Constraint(m.comp, doc="Product section 3 liquid enthalpy") - def productside_liquid_enthalpy(disj, comp): - return m.hl[3, n_tray, comp] == ( - m.cpc[1] - * ( - (m.T[3, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] - + (m.T[3, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 1] - * m.cpc2['A', 1] - / 2 - + (m.T[3, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 1] - * m.cpc2['B', 1] - / 3 - + (m.T[3, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 - ) - / m.Hscale - ) - - @disj.Constraint(m.comp, doc="Product section 3 vapor enthalpy") - def productside_vapor_enthalpy(disj, comp): - return m.hv[3, n_tray, comp] == ( - m.cpc[2] - * ( - (m.T[3, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] - + (m.T[3, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 2] - * m.cpc2['A', 2] - / 2 - + (m.T[3, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 2] - * m.cpc2['B', 2] - / 3 - + (m.T[3, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 - ) - / m.Hscale - + m.dHvap[comp] - ) - - @disj.Constraint(m.comp, doc="Product section 3 liquid activity coefficient") - def productside_activity_coefficient(disj, comp): - return m.actv[3, n_tray, comp] == 1 - - -def _build_top_equations(disj, n_tray): - m = disj.model() - - @disj.Constraint(m.comp, doc="Top section 4 mass per component balances") - def _top_mass_percomponent_balances(disj, comp): - return (m.L[4, n_tray + 1, comp] if n_tray < m.con_tray else 0) - ( - m.L[4, n_tray, comp] * m.dl[2] if n_tray == 1 else 0 - ) - (m.L[4, n_tray, comp] * m.dl[3] if n_tray == 1 else 0) - ( - m.L[4, n_tray, comp] if n_tray > 1 else 0 - ) + ( - m.V[2, m.num_trays, comp] if n_tray == 1 else 0 - ) + ( - m.V[3, m.num_trays, comp] if n_tray == 1 else 0 - ) + ( - m.V[4, n_tray - 1, comp] if n_tray > 1 else 0 - ) - ( - m.V[4, n_tray, comp] if n_tray < m.con_tray else 0 - ) - ( - m.D[comp] if n_tray == m.con_tray else 0 - ) == 0 - - @disj.Constraint(doc="Top scetion 4 energy balances") - def _top_energy_balances(disj): - return ( - sum( - ( - m.L[4, n_tray + 1, comp] * m.hl[4, n_tray + 1, comp] - if n_tray < m.con_tray - else 0 - ) - - ( - m.L[4, n_tray, comp] * m.dl[2] * m.hl[4, n_tray, comp] - if n_tray == 1 - else 0 - ) - - ( - m.L[4, n_tray, comp] * m.dl[3] * m.hl[4, n_tray, comp] - if n_tray == 1 - else 0 - ) - - (m.L[4, n_tray, comp] * m.hl[4, n_tray, comp] if n_tray > 1 else 0) - + ( - m.V[2, m.num_trays, comp] * m.hv[2, m.num_trays, comp] - if n_tray == 1 - else 0 - ) - + ( - m.V[3, m.num_trays, comp] * m.hv[3, m.num_trays, comp] - if n_tray == 1 - else 0 - ) - + ( - m.V[4, n_tray - 1, comp] * m.hv[4, n_tray - 1, comp] - if n_tray > 1 - else 0 - ) - - ( - m.V[4, n_tray, comp] * m.hv[4, n_tray, comp] - if n_tray < m.con_tray - else 0 - ) - - (m.D[comp] * m.hl[4, n_tray, comp] if n_tray == m.con_tray else 0) - for comp in m.comp - ) - * m.Qscale - - (m.Qcon if n_tray == m.con_tray else 0) - == 0 - ) - - @disj.Constraint(m.comp, doc="Top section 4 liquid flowrate per component") - def _top_liquid_percomponent(disj, comp): - return m.L[4, n_tray, comp] == m.Ltotal[4, n_tray] * m.x[4, n_tray, comp] - - @disj.Constraint(m.comp, doc="Top section 4 vapor flowrate per component") - def _top_vapor_percomponent(disj, comp): - return m.V[4, n_tray, comp] == m.Vtotal[4, n_tray] * m.y[4, n_tray, comp] - - @disj.Constraint(doc="Top section 4 liquid composition equilibrium summation") - def top_liquid_composition_summation(disj): - return sum(m.x[4, n_tray, comp] for comp in m.comp) - 1 == m.errx[4, n_tray] - - @disj.Constraint(doc="Top section 4 vapor composition equilibrium summation") - def top_vapor_composition_summation(disj): - return sum(m.y[4, n_tray, comp] for comp in m.comp) - 1 == m.erry[4, n_tray] - - @disj.Constraint(m.comp, doc="Top scetion 4 vapor composition") - def top_vapor_composition(disj, comp): - return ( - m.y[4, n_tray, comp] - == m.x[4, n_tray, comp] - * ( - m.actv[4, n_tray, comp] - * ( - m.prop[comp, 'PC'] - * exp( - m.prop[comp, 'TC'] - / m.T[4, n_tray] - * ( - m.prop[comp, 'vpA'] - * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) - + m.prop[comp, 'vpB'] - * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) ** 1.5 - + m.prop[comp, 'vpC'] - * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) ** 3 - + m.prop[comp, 'vpD'] - * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) ** 6 - ) - ) - ) - ) - / m.P[4, n_tray] - ) - - @disj.Constraint(m.comp, doc="Top section 4 liquid enthalpy") - def top_liquid_enthalpy(disj, comp): - return m.hl[4, n_tray, comp] == ( - m.cpc[1] - * ( - (m.T[4, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] - + (m.T[4, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 1] - * m.cpc2['A', 1] - / 2 - + (m.T[4, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 1] - * m.cpc2['B', 1] - / 3 - + (m.T[4, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 - ) - / m.Hscale - ) - - @disj.Constraint(m.comp, doc="Top section 4 vapor enthalpy") - def top_vapor_enthalpy(disj, comp): - return m.hv[4, n_tray, comp] == ( - m.cpc[2] - * ( - (m.T[4, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] - + (m.T[4, n_tray] ** 2 - m.Tref**2) - * m.prop[comp, 'cpB', 2] - * m.cpc2['A', 2] - / 2 - + (m.T[4, n_tray] ** 3 - m.Tref**3) - * m.prop[comp, 'cpC', 2] - * m.cpc2['B', 2] - / 3 - + (m.T[4, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 - ) - / m.Hscale - + m.dHvap[comp] - ) - - @disj.Constraint(m.comp, doc="Top section 4 liquid activity coefficient") - def top_activity_coefficient(disj, comp): - return m.actv[4, n_tray, comp] == 1 - - -def _build_pass_through_eqns(disj, sec, n_tray): - m = disj.model() - - if n_tray == 1 or n_tray == m.num_trays: - return - - @disj.Constraint(m.comp, doc="Pass through liquid flowrate") - def pass_through_liquid_flowrate(disj, comp): - return m.L[sec, n_tray, comp] == m.L[sec, n_tray + 1, comp] - - @disj.Constraint(m.comp, doc="Pass through vapor flowrate") - def pass_through_vapor_flowrate(disj, comp): - return m.V[sec, n_tray, comp] == m.V[sec, n_tray - 1, comp] - - @disj.Constraint(m.comp, doc="Pass through liquid composition") - def pass_through_liquid_composition(disj, comp): - return m.x[sec, n_tray, comp] == m.x[sec, n_tray + 1, comp] - - @disj.Constraint(m.comp, doc="Pass through vapor composition") - def pass_through_vapor_composition(disj, comp): - return m.y[sec, n_tray, comp] == m.y[sec, n_tray + 1, comp] - - @disj.Constraint(m.comp, doc="Pass through liquid enthalpy") - def pass_through_liquid_enthalpy(disj, comp): - return m.hl[sec, n_tray, comp] == m.hl[sec, n_tray + 1, comp] - - @disj.Constraint(m.comp, doc="Pass through vapor enthalpy") - def pass_through_vapor_enthalpy(disj, comp): - return m.hv[sec, n_tray, comp] == m.hv[sec, n_tray - 1, comp] - - @disj.Constraint(doc="Pass through temperature") - def pass_through_temperature(disj): - return m.T[sec, n_tray] == m.T[sec, n_tray - 1] - - -if __name__ == "__main__": - model = build_model() +""" Kaibel Column model: GDP formulation. + +The solution requires the specification of certain parameters, such as the number trays, feed location, etc., and an initialization procedure, which consists of the next three steps: +(i) a preliminary design of the separation considering a sequence of indirect continuous distillation columns (CDCs) to obtain the minimum number of stages with Fenske Equation in the function initialize_kaibel in kaibel_init.py +(ii) flash calculation for the feed with the function calc_side_feed_flash in kaibel_side_flash.py +(iii) calculation of variable bounds by solving the NLP problem. + +After the initialization, the GDP model is built. +""" + +from math import copysign + +from pyomo.environ import ( + Constraint, + exp, + minimize, + NonNegativeReals, + Objective, + RangeSet, + Set, + Var, +) +from pyomo.gdp import Disjunct + +from gdplib.kaibel.kaibel_init import initialize_kaibel + +from gdplib.kaibel.kaibel_side_flash import calc_side_feed_flash + +# from .kaibel_side_flash import calc_side_feed_flash + + +def build_model(): + """ + Build the GDP Kaibel Column model. + It combines the initialization of the model and the flash calculation for the side feed before the GDP formulation. + + Returns + ------- + ConcreteModel + The constructed GDP Kaibel Column model. + """ + + # Calculation of the theoretical minimum number of trays (Knmin) and initial temperature values (TB0, Tf0, TD0). + m = initialize_kaibel() + + # Side feed init. Returns side feed vapor composition yfi and vapor fraction q_init + m = calc_side_feed_flash(m) + + m.name = "GDP Kaibel Column" + + #### Calculated initial values + m.Treb = m.TB0 + 5 # Reboiler temperature [K] + m.Tbot = m.TB0 # Bottom-most tray temperature [K] + m.Ttop = m.TD0 # Top-most tray temperature [K] + m.Tcon = m.TD0 - 5 # Condenser temperature [K] + + m.dv0 = {} # Initial vapor distributor value + m.dl0 = {} # Initial liquid distributor value + m.dv0[2] = 0.516 + m.dv0[3] = 1 - m.dv0[2] + m.dl0[2] = 0.36 + m.dl0[3] = 1 - m.dl0[2] + + #### Calculated upper and lower bounds + m.min_tray = m.Knmin * 0.8 # Lower bound on number of trays + m.Tlo = m.Tcon - 20 # Temperature lower bound + m.Tup = m.Treb + 20 # Temperature upper bound + + m.flow_max = 1e3 # Flowrates upper bound [mol/s] + m.Qmax = 60 # Heat loads upper bound [J/s] + + #### Column tray details + m.num_trays = m.np # Trays per section. np = 25 + m.min_num_trays = 10 # Minimum number of trays per section + m.num_total = m.np * 3 # Total number of trays + m.feed_tray = 12 # Side feed tray + m.sideout1_tray = 8 # Side outlet 1 tray + m.sideout2_tray = 17 # Side outlet 2 tray + m.reb_tray = 1 # Reboiler tray. Dividing wall starting tray + m.con_tray = m.num_trays # Condenser tray. Dividing wall ending tray + + # ------------------------------------------------------------------ + + # Beginning of model + + # ------------------------------------------------------------------ + + ## Sets + m.section = RangeSet( + 4, doc="Column sections:1=top, 2=feed side, 3=prod side, 4=bot" + ) + m.section_main = Set(initialize=[1, 4], doc="Main sections of the column") + + m.tray = RangeSet(m.np, doc="Potential trays in each section") + m.tray_total = RangeSet(m.num_total, doc="Total trays in the column") + m.tray_below_feed = RangeSet(m.feed_tray, doc="Trays below feed") + m.tray_below_so1 = RangeSet(m.sideout1_tray, doc="Trays below side outlet 1") + m.tray_below_so2 = RangeSet(m.sideout2_tray, doc="Trays below side outlet 2") + + m.comp = RangeSet(4, doc="Components") + m.dw = RangeSet(2, 3, doc="Dividing wall sections") + m.cplv = RangeSet(2, doc="Heat capacity: 1=liquid, 2=vapor") + m.so = RangeSet(2, doc="Side product outlets") + m.bounds = RangeSet(2, doc="Number of boundary condition values") + + m.candidate_trays_main = Set( + initialize=m.tray - [m.con_tray, m.reb_tray], + doc="Candidate trays for top and \ + bottom sections 1 and 4", + ) + m.candidate_trays_feed = Set( + initialize=m.tray - [m.con_tray, m.feed_tray, m.reb_tray], + doc="Candidate trays for feed section 2", + ) + m.candidate_trays_product = Set( + initialize=m.tray - [m.con_tray, m.sideout1_tray, m.sideout2_tray, m.reb_tray], + doc="Candidate trays for product section 3", + ) + + ## Calculation of initial values + m.dHvap = {} # Heat of vaporization [J/mol] + + m.P0 = {} # Initial pressure [bar] + m.T0 = {} # Initial temperature [K] + m.L0 = {} # Initial individual liquid flowrate [mol/s] + m.V0 = {} # Initial individual vapor flowrate [mol/s] + m.Vtotal0 = {} # Initial total vapor flowrate [mol/s] + m.Ltotal0 = {} # Initial liquid flowrate [mol/s] + m.x0 = {} # Initial liquid composition + m.y0 = {} # Initial vapor composition + m.actv0 = {} # Initial activity coefficients + m.cpdT0 = {} # Initial heat capacity for liquid and vapor phases [J/mol/K] + m.hl0 = {} # Initial liquid enthalpy [J/mol] + m.hv0 = {} # Initial vapor enthalpy [J/mol] + m.Pi = m.Preb # Initial given pressure value [bar] + m.Ti = {} # Initial known temperature values [K] + + ## Initial values for pressure, temperature, flowrates, composition, and enthalpy + for sec in m.section: + for n_tray in m.tray: + m.P0[sec, n_tray] = m.Pi + + for sec in m.section: + for n_tray in m.tray: + for comp in m.comp: + m.L0[sec, n_tray, comp] = m.Li + m.V0[sec, n_tray, comp] = m.Vi + + for sec in m.section: + for n_tray in m.tray: + m.Ltotal0[sec, n_tray] = sum(m.L0[sec, n_tray, comp] for comp in m.comp) + m.Vtotal0[sec, n_tray] = sum(m.V0[sec, n_tray, comp] for comp in m.comp) + + for n_tray in m.tray_total: + if n_tray == m.reb_tray: + m.Ti[n_tray] = m.Treb + elif n_tray == m.num_total: + m.Ti[n_tray] = m.Tcon + else: + m.Ti[n_tray] = m.Tbot + (m.Ttop - m.Tbot) * (n_tray - 2) / (m.num_total - 3) + + for n_tray in m.tray_total: + if n_tray <= m.num_trays: + m.T0[1, n_tray] = m.Ti[n_tray] + elif n_tray >= m.num_trays and n_tray <= m.num_trays * 2: + m.T0[2, n_tray - m.num_trays] = m.Ti[n_tray] + m.T0[3, n_tray - m.num_trays] = m.Ti[n_tray] + elif n_tray >= m.num_trays * 2: + m.T0[4, n_tray - m.num_trays * 2] = m.Ti[n_tray] + + ## Initial vapor and liquid composition of the feed and activity coefficients + for sec in m.section: + for n_tray in m.tray: + for comp in m.comp: + m.x0[sec, n_tray, comp] = m.xfi[comp] + m.actv0[sec, n_tray, comp] = 1 + m.y0[sec, n_tray, comp] = m.xfi[comp] + + ## Assigns the enthalpy boundary values, heat capacity, heat of vaporization calculation, temperature bounds, and light and heavy key components. + hlb = {} # Liquid enthalpy [J/mol] + hvb = {} # Vapor enthalpy [J/mol] + cpb = {} # Heact capacity [J/mol/K] + dHvapb = {} # Heat of vaporization [J/mol] + Tbounds = {} # Temperature bounds [K] + kc = {} # Light and heavy key components + Tbounds[1] = m.Tcon # Condenser temperature [K] + Tbounds[2] = m.Treb # Reboiler temperature [K] + kc[1] = m.lc + kc[2] = m.hc + + ## Heat of vaporization calculation for each component in the feed. + for comp in m.comp: + dHvapb[comp] = -( + m.Rgas + * m.prop[comp, 'TC'] + * ( + m.prop[comp, 'vpA'] * (1 - m.Tref / m.prop[comp, 'TC']) + + m.prop[comp, 'vpB'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 1.5 + + m.prop[comp, 'vpC'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 3 + + m.prop[comp, 'vpD'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 6 + ) + + m.Rgas + * m.Tref + * ( + m.prop[comp, 'vpA'] + + 1.5 * m.prop[comp, 'vpB'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 0.5 + + 3 * m.prop[comp, 'vpC'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 2 + + 6 * m.prop[comp, 'vpD'] * (1 - m.Tref / m.prop[comp, 'TC']) ** 5 + ) + ) + + ## Boundary values for heat capacity and enthalpy of liquid and vapor phases for light and heavy key components in the feed. + for b in m.bounds: + for cp in m.cplv: + cpb[b, cp] = m.cpc[cp] * ( + (Tbounds[b] - m.Tref) * m.prop[kc[b], 'cpA', cp] + + (Tbounds[b] ** 2 - m.Tref**2) + * m.prop[kc[b], 'cpB', cp] + * m.cpc2['A', cp] + / 2 + + (Tbounds[b] ** 3 - m.Tref**3) + * m.prop[kc[b], 'cpC', cp] + * m.cpc2['B', cp] + / 3 + + (Tbounds[b] ** 4 - m.Tref**4) * m.prop[kc[b], 'cpD', cp] / 4 + ) + hlb[b] = cpb[b, 1] + hvb[b] = cpb[b, 2] + dHvapb[b] + + m.hllo = ( + (1 - copysign(0.2, hlb[1])) * hlb[1] / m.Hscale + ) # Liquid enthalpy lower bound + m.hlup = ( + (1 + copysign(0.2, hlb[2])) * hlb[2] / m.Hscale + ) # Liquid enthalpy upper bound + m.hvlo = ( + (1 - copysign(0.2, hvb[1])) * hvb[1] / m.Hscale + ) # Vapor enthalpy lower bound + m.hvup = ( + (1 + copysign(0.2, hvb[2])) * hvb[2] / m.Hscale + ) # Vapor enthalpy upper bound + # copysign is a function that returns the first argument with the sign of the second argument + + ## Heat of vaporization for each component in the feed scaled by Hscale + for comp in m.comp: + m.dHvap[comp] = dHvapb[comp] / m.Hscale + + ## Heat capacity calculation for liquid and vapor phases using Ruczika-D method for each component in the feed, section, and tray + for sec in m.section: + for n_tray in m.tray: + for comp in m.comp: + for cp in m.cplv: + m.cpdT0[sec, n_tray, comp, cp] = ( + m.cpc[cp] + * ( + (m.T0[sec, n_tray] - m.Tref) * m.prop[comp, 'cpA', cp] + + (m.T0[sec, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', cp] + * m.cpc2['A', cp] + / 2 + + (m.T0[sec, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', cp] + * m.cpc2['B', cp] + / 3 + + (m.T0[sec, n_tray] ** 4 - m.Tref**4) + * m.prop[comp, 'cpD', cp] + / 4 + ) + / m.Hscale + ) + + ## Liquid and vapor enthalpy calculation using Ruczika-D method for each component in the feed, section, and tray + for sec in m.section: + for n_tray in m.tray: + for comp in m.comp: + m.hl0[sec, n_tray, comp] = m.cpdT0[sec, n_tray, comp, 1] + m.hv0[sec, n_tray, comp] = m.cpdT0[sec, n_tray, comp, 2] + m.dHvap[comp] + + #### Side feed + m.cpdTf = {} # Heat capacity for side feed [J/mol K] + m.hlf = {} # Liquid enthalpy for side feed [J/mol] + m.hvf = {} # Vapor enthalpy for side feed [J/mol] + m.F0 = {} # Side feed flowrate per component [mol/s] + + ## Heat capacity in liquid and vapor phases for side feed for each component using Ruczika-D method + for comp in m.comp: + for cp in m.cplv: + m.cpdTf[comp, cp] = ( + m.cpc[cp] + * ( + (m.Tf - m.Tref) * m.prop[comp, 'cpA', cp] + + (m.Tf**2 - m.Tref**2) + * m.prop[comp, 'cpB', cp] + * m.cpc2['A', cp] + / 2 + + (m.Tf**3 - m.Tref**3) + * m.prop[comp, 'cpC', cp] + * m.cpc2['B', cp] + / 3 + + (m.Tf**4 - m.Tref**4) * m.prop[comp, 'cpD', cp] / 4 + ) + / m.Hscale + ) + + ## Side feed flowrate and liquid and vapor enthalpy calculation using Ruczika-D method for each component in the feed + for comp in m.comp: + m.F0[comp] = ( + m.xfi[comp] * m.Fi + ) # Side feed flowrate per component computed from the feed composition and flowrate Fi + m.hlf[comp] = m.cpdTf[ + comp, 1 + ] # Liquid enthalpy for side feed computed from the heat capacity for side feed and liquid phase + m.hvf[comp] = ( + m.cpdTf[comp, 2] + m.dHvap[comp] + ) # Vapor enthalpy for side feed computed from the heat capacity for side feed and vapor phase and heat of vaporization + + m.P = Var( + m.section, + m.tray, + doc="Pressure at each potential tray in bars", + domain=NonNegativeReals, + bounds=(m.Pcon, m.Preb), + initialize=m.P0, + ) + m.T = Var( + m.section, + m.tray, + doc="Temperature at each potential tray [K]", + domain=NonNegativeReals, + bounds=(m.Tlo, m.Tup), + initialize=m.T0, + ) + + m.x = Var( + m.section, + m.tray, + m.comp, + doc="Liquid composition", + domain=NonNegativeReals, + bounds=(0, 1), + initialize=m.x0, + ) + m.y = Var( + m.section, + m.tray, + m.comp, + doc="Vapor composition", + domain=NonNegativeReals, + bounds=(0, 1), + initialize=m.y0, + ) + + m.dl = Var( + m.dw, + doc="Liquid distributor in the dividing wall sections", + bounds=(0.2, 0.8), + initialize=m.dl0, + ) + m.dv = Var( + m.dw, + doc="Vapor distributor in the dividing wall sections", + bounds=(0, 1), + domain=NonNegativeReals, + initialize=m.dv0, + ) + + m.V = Var( + m.section, + m.tray, + m.comp, + doc="Vapor flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.V0, + ) + m.L = Var( + m.section, + m.tray, + m.comp, + doc="Liquid flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.L0, + ) + m.Vtotal = Var( + m.section, + m.tray, + doc="Total vapor flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Vtotal0, + ) + m.Ltotal = Var( + m.section, + m.tray, + doc="Total liquid flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Ltotal0, + ) + + m.D = Var( + m.comp, + doc="Distillate flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Ddes, + ) + m.B = Var( + m.comp, + doc="Bottoms flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Bdes, + ) + m.S = Var( + m.so, + m.comp, + doc="Product 2 and 3 flowrates [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Sdes, + ) + m.Dtotal = Var( + doc="Distillate flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Ddes, + ) + m.Btotal = Var( + doc="Bottoms flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Bdes, + ) + m.Stotal = Var( + m.so, + doc="Total product 2 and 3 side flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, m.flow_max), + initialize=m.Sdes, + ) + + m.hl = Var( + m.section, + m.tray, + m.comp, + doc='Liquid enthalpy [J/mol]', + bounds=(m.hllo, m.hlup), + initialize=m.hl0, + ) + m.hv = Var( + m.section, + m.tray, + m.comp, + doc='Vapor enthalpy [J/mol]', + bounds=(m.hvlo, m.hvup), + initialize=m.hv0, + ) + m.Qreb = Var( + doc="Reboiler heat duty [J/s]", + domain=NonNegativeReals, + bounds=(0, m.Qmax), + initialize=1, + ) + m.Qcon = Var( + doc="Condenser heat duty [J/s]", + domain=NonNegativeReals, + bounds=(0, m.Qmax), + initialize=1, + ) + + m.rr = Var( + doc="Internal reflux ratio in the column", + domain=NonNegativeReals, + bounds=(0.7, 1), + initialize=m.rr0, + ) + m.bu = Var( + doc="Boilup rate in the reboiler", + domain=NonNegativeReals, + bounds=(0.7, 1), + initialize=m.bu0, + ) + + m.F = Var( + m.comp, + doc="Side feed flowrate [mol/s]", + domain=NonNegativeReals, + bounds=(0, 50), + initialize=m.F0, + ) + m.q = Var( + doc="Vapor fraction in side feed", + domain=NonNegativeReals, + bounds=(0, 1), + initialize=1, + ) + + m.actv = Var( + m.section, + m.tray, + m.comp, + doc="Liquid activity coefficient", + domain=NonNegativeReals, + bounds=(0, 10), + initialize=m.actv0, + ) + + m.errx = Var( + m.section, + m.tray, + doc="Error in liquid composition [mol/mol]", + bounds=(-1e-3, 1e-3), + initialize=0, + ) + m.erry = Var( + m.section, + m.tray, + doc="Error in vapor composition [mol/mol]", + bounds=(-1e-3, 1e-3), + initialize=0, + ) + m.slack = Var( + m.section, + m.tray, + m.comp, + doc="Slack variable", + bounds=(-1e-8, 1e-8), + initialize=0, + ) + + m.tray_exists = Disjunct( + m.section, + m.tray, + doc="Disjunct that enforce the existence of each tray", + rule=_build_tray_equations, + ) + m.tray_absent = Disjunct( + m.section, + m.tray, + doc="Disjunct that enforce the absence of each tray", + rule=_build_pass_through_eqns, + ) + + @m.Disjunction( + m.section, m.tray, doc="Disjunction between whether each tray exists or not" + ) + def tray_exists_or_not(m, sec, n_tray): + """ + Disjunction between whether each tray exists or not. + + Parameters + ---------- + m : Pyomo ConcreteModel + The Pyomo model object. + sec : int + The section index. + n_tray : int + The tray index. + + Returns + ------- + Disjunction + The disjunction between whether each tray exists or not. + """ + return [m.tray_exists[sec, n_tray], m.tray_absent[sec, n_tray]] + + @m.Constraint(m.section_main) + def minimum_trays_main(m, sec): + """ + Constraint that ensures the minimum number of trays in the main section. + + Parameters + ---------- + m : Pyomo ConcreteModel + The model object for the GDP Kaibel Column. + sec : Set + The section index. + + Returns + ------- + Constraint + A constraint expression that enforces the minimum number of trays in the main section to be greater than or equal to the minimum number of trays. + """ + return ( + sum( + m.tray_exists[sec, n_tray].binary_indicator_var + for n_tray in m.candidate_trays_main + ) + + 1 + >= m.min_num_trays + ) + + @m.Constraint() + def minimum_trays_feed(m): + """ + Constraint function that ensures the minimum number of trays in the feed section is met. + + Parameters + ---------- + m : Pyomo ConcreteModel + The Pyomo model object. + + Returns + ------- + Constraint + The constraint expression that enforces the minimum number of trays is greater than or equal to the minimum number of trays. + """ + return ( + sum( + m.tray_exists[2, n_tray].binary_indicator_var + for n_tray in m.candidate_trays_feed + ) + + 1 + >= m.min_num_trays + ) + + # TOCHECK: pyomo.GDP Syntax + + @m.Constraint() + def minimum_trays_product(m): + """ + Constraint function to calculate the minimum number of trays in the product section. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint expression that enforces the minimum number of trays is greater than or equal to the minimum number of trays. + """ + return ( + sum( + m.tray_exists[3, n_tray].binary_indicator_var + for n_tray in m.candidate_trays_product + ) + + 1 + >= m.min_num_trays + ) + + ## Fixed trays + enforce_tray_exists(m, 1, 1) # reboiler + enforce_tray_exists(m, 1, m.num_trays) # vapor distributor + enforce_tray_exists(m, 2, 1) # dividing wall starting tray + enforce_tray_exists(m, 2, m.feed_tray) # feed tray + enforce_tray_exists(m, 2, m.num_trays) # dividing wall ending tray + enforce_tray_exists(m, 3, 1) # dividing wall starting tray + enforce_tray_exists(m, 3, m.sideout1_tray) # side outlet 1 for product 3 + enforce_tray_exists(m, 3, m.sideout2_tray) # side outlet 2 for product 2 + enforce_tray_exists(m, 3, m.num_trays) # dividing wall ending tray + enforce_tray_exists(m, 4, 1) # liquid distributor + enforce_tray_exists(m, 4, m.num_trays) # condenser + + #### Global constraints + @m.Constraint( + m.dw, m.tray, doc="Monotonic temperature in the dividing wall sections" + ) + def monotonic_temperature(m, sec, n_tray): + """This function returns a constraint object representing the monotonic temperature constraint. + + The monotonic temperature constraint ensures that the temperature on each tray in the distillation column + is less than or equal to the temperature on the top tray. + + Parameters + ---------- + m : Pyomo ConcreteModel + The Pyomo model object. + sec : Set + The set of sections in the dividing wall sections. + n_tray : Set + The set of trays in the distillation column. + + Returns + ------- + Constraint + The monotonic temperature constraint specifying that the temperature on each tray is less than or equal to the temperature on the top tray of section 1 which is the condenser. + """ + return m.T[sec, n_tray] <= m.T[1, m.num_trays] + + @m.Constraint(doc="Liquid distributor") + def liquid_distributor(m): + """Defines the liquid distributor constraint. + + This constraint ensures that the sum of the liquid distributors in all sections is equal to 1. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The liquid distributor constraint that enforces the sum of the liquid flow rates in all sections is equal to 1. + + """ + return sum(m.dl[sec] for sec in m.dw) - 1 == 0 + + @m.Constraint(doc="Vapor distributor") + def vapor_distributor(m): + """ + Add a constraint to ensure that the sum of the vapor distributors is equal to 1. + + Parameters + ---------- + m : Pyomo ConcreteModel + The Pyomo model object. + + Returns + ------- + Constraint + The vapor distributor constraint. + """ + return sum(m.dv[sec] for sec in m.dw) - 1 == 0 + + @m.Constraint(doc="Reboiler composition specification") + def heavy_product(m): + """ + Reboiler composition specification for the heavy component in the feed. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the reboiler composition is greater than or equal to the specified composition xspechc final liquid composition for butanol, the heavy component in the feed. + """ + return m.x[1, m.reb_tray, m.hc] >= m.xspec_hc + + @m.Constraint(doc="Condenser composition specification") + def light_product(m): + """ + Condenser composition specification for the light component in the feed. + + Parameters + ---------- + m : Model + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the condenser composition is greater than or equal to the specified final liquid composition for ethanol, xspeclc , the light component in the feed. + """ + return m.x[4, m.con_tray, m.lc] >= m.xspec_lc + + @m.Constraint(doc="Side outlet 1 final liquid composition") + def intermediate1_product(m): + ''' + This constraint ensures that the intermediate 1 final liquid composition is greater than or equal to the specified composition xspec_inter1, which is the final liquid composition for ethanol. + + Parameters + ---------- + m : Pyomo ConcreteModel. + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the intermediate 1 final liquid composition is greater than or equal to the specified composition xspec_inter1, which is the final liquid composition for ethanol. + ''' + return m.x[3, m.sideout1_tray, 3] >= m.xspec_inter3 + + @m.Constraint(doc="Side outlet 2 final liquid composition") + def intermediate2_product(m): + """ + This constraint ensures that the intermediate 2 final liquid composition is greater than or equal to the specified composition xspec_inter2, which is the final liquid composition for butanol. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the intermediate 2 final liquid composition is greater than or equal to the specified composition xspec_inter2, which is the final liquid composition for butanol. + """ + return m.x[3, m.sideout2_tray, 2] >= m.xspec_inter2 + + @m.Constraint(doc="Reboiler flowrate") + def _heavy_product_flow(m): + """ + Reboiler flowrate constraint that ensures the reboiler flowrate is greater than or equal to the specified flowrate Bdes, which is the flowrate of butanol. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the reboiler flowrate is greater than or equal to the specified flowrate Bdes, which is the flowrate of butanol. + """ + return m.Btotal >= m.Bdes + + @m.Constraint(doc="Condenser flowrate") + def _light_product_flow(m): + """ + Condenser flowrate constraint that ensures the condenser flowrate is greater than or equal to the specified flowrate Ddes, which is the flowrate of ethanol. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the condenser flowrate is greater than or equal to the specified flowrate Ddes, which is the flowrate of ethanol. + """ + return m.Dtotal >= m.Ddes + + @m.Constraint(m.so, doc="Intermediate flowrate") + def _intermediate_product_flow(m, so): + """ + Intermediate flowrate constraint that ensures the intermediate flowrate is greater than or equal to the specified flowrate Sdes, which is the flowrate of the intermediate side product 2 and 3. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + so : int + The side product outlet index. + + Returns + ------- + Constraint + The constraint that enforces the intermediate flowrate is greater than or equal to the specified flowrate Sdes, which is the flowrate of the intermediate side product 2 and 3. + """ + return m.Stotal[so] >= m.Sdes + + @m.Constraint(doc="Internal boilup ratio, V/L") + def _internal_boilup_ratio(m): + """ + Internal boilup ratio constraint that ensures the internal boilup ratio is equal to the boilup rate times the liquid flowrate on the reboiler tray is equal to the vapor flowrate on the tray above the reboiler tray. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the boilup rate times the liquid flowrate on the reboiler tray is equal to the vapor flowrate on the tray above the reboiler tray. + """ + return m.bu * m.Ltotal[1, m.reb_tray + 1] == m.Vtotal[1, m.reb_tray] + + @m.Constraint(doc="Internal reflux ratio, L/V") + def internal_reflux_ratio(m): + """ + Internal reflux ratio constraint that ensures the internal reflux ratio is equal to the reflux rate times the vapor flowrate on the tray above the condenser tray is equal to the liquid flowrate on the condenser tray. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the reflux rate times the vapor flowrate on the tray above the condenser tray is equal to the liquid flowrate on the condenser tray. + """ + return m.rr * m.Vtotal[4, m.con_tray - 1] == m.Ltotal[4, m.con_tray] + + @m.Constraint(doc="External boilup ratio relation with bottoms") + def _external_boilup_ratio(m): + """ + External boilup ratio constraint that ensures the external boilup ratio times the liquid flowrate on the reboiler tray is equal to the bottoms flowrate. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the external boilup ratio times the liquid flowrate on the reboiler tray is equal to the bottoms flowrate. + """ + return m.Btotal == (1 - m.bu) * m.Ltotal[1, m.reb_tray + 1] + + @m.Constraint(doc="External reflux ratio relation with distillate") + def _external_reflux_ratio(m): + """ + External reflux ratio constraint that ensures the external reflux ratio times the vapor flowrate on the tray above the condenser tray is equal to the distillate flowrate. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the external reflux ratio times the vapor flowrate on the tray above the condenser tray is equal to the distillate flowrate. + """ + return m.Dtotal == (1 - m.rr) * m.Vtotal[4, m.con_tray - 1] + + @m.Constraint(m.section, m.tray, doc="Total vapor flowrate") + def _total_vapor_flowrate(m, sec, n_tray): + """ + Constraint that ensures the total vapor flowrate is equal to the sum of the vapor flowrates of each component on each tray. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + sec : int + The section index. + n_tray : int + The tray index. + + Returns + ------- + Constraint + The constraint that enforces the total vapor flowrate is equal to the sum of the vapor flowrates of each component on each tray on each section. + """ + return sum(m.V[sec, n_tray, comp] for comp in m.comp) == m.Vtotal[sec, n_tray] + + @m.Constraint(m.section, m.tray, doc="Total liquid flowrate") + def _total_liquid_flowrate(m, sec, n_tray): + """ + Constraint that ensures the total liquid flowrate is equal to the sum of the liquid flowrates of each component on each tray on each section. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + sec : int + The section index. + n_tray : int + The tray index. + + Returns + ------- + Constraint + The constraint that enforces the total liquid flowrate is equal to the sum of the liquid flowrates of each component on each tray on each section. + """ + return sum(m.L[sec, n_tray, comp] for comp in m.comp) == m.Ltotal[sec, n_tray] + + @m.Constraint(m.comp, doc="Bottoms and liquid relation") + def bottoms_equality(m, comp): + """ + Constraint that ensures the bottoms flowrate is equal to the liquid flowrate of each component on the reboiler tray. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint that enforces the bottoms flowrate is equal to the liquid flowrate of each component on the reboiler tray. + """ + return m.B[comp] == m.L[1, m.reb_tray, comp] + + @m.Constraint(m.comp) + def condenser_total(m, comp): + """ + Constraint that ensures the distillate flowrate in the condenser is null. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + comp : int + The component index. + Returns + ------- + Constraint + The constraint that enforces the distillate flowrate is equal to zero in the condenser. + """ + return m.V[4, m.con_tray, comp] == 0 + + @m.Constraint() + def total_bottoms_product(m): + """ + Constraint that ensures the total bottoms flowrate is equal to the sum of the bottoms flowrates of each component. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the total bottoms flowrate is equal to the sum of the bottoms flowrates of each component. + """ + return sum(m.B[comp] for comp in m.comp) == m.Btotal + + @m.Constraint() + def total_distillate_product(m): + """ + Constraint that ensures the total distillate flowrate is equal to the sum of the distillate flowrates of each component. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint that enforces the total distillate flowrate is equal to the sum of the distillate flowrates of each component. + """ + return sum(m.D[comp] for comp in m.comp) == m.Dtotal + + @m.Constraint(m.so) + def total_side_product(m, so): + """ + Constraint that ensures the total side product flowrate is equal to the sum of the side product flowrates of each component. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + so : int + The side product index, 2 or 3 for the intermediate side products. + + Returns + ------- + Constraint + The constraint that enforces the total side product flowrate is equal to the sum of the side product flowrates of each component. + """ + return sum(m.S[so, comp] for comp in m.comp) == m.Stotal[so] + + # Considers the number of existent trays and operating costs (condenser and reboiler heat duties) in the column. To ensure equal weights to the capital and operating costs, the number of existent trays is multiplied by a weight coefficient of 1000. + + m.obj = Objective( + expr=(m.Qcon + m.Qreb) * m.Hscale + + 1e3 + * ( + sum( + sum( + m.tray_exists[sec, n_tray].binary_indicator_var + for n_tray in m.candidate_trays_main + ) + for sec in m.section_main + ) + + sum( + m.tray_exists[2, n_tray].binary_indicator_var + for n_tray in m.candidate_trays_feed + ) + + sum( + m.tray_exists[3, n_tray].binary_indicator_var + for n_tray in m.candidate_trays_product + ) + + 1 + ), + sense=minimize, + doc="Objective function to minimize the operating costs and number of existent trays in the column", + ) + + @m.Constraint( + m.section_main, m.candidate_trays_main, doc="Logic proposition for main section" + ) + def _logic_proposition_main(m, sec, n_tray): + """ + Apply a logic proposition constraint to the main section and candidate trays to specify the order of trays in the column is from bottom to top provided the condition is met. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + sec : int + The section index. + n_tray : int + The tray index. + + Returns + ------- + Constraint or NoConstraint + The constraint expression or NoConstraint if the condition is not met. + """ + + if n_tray > m.reb_tray and (n_tray + 1) < m.num_trays: + return ( + m.tray_exists[sec, n_tray].binary_indicator_var + <= m.tray_exists[sec, n_tray + 1].binary_indicator_var + ) + else: + return Constraint.NoConstraint + # TOCHECK: Update the logic proposition constraint for the main section with the new pyomo.gdp syntax + + @m.Constraint(m.candidate_trays_feed) + def _logic_proposition_feed(m, n_tray): + """ + Apply a logic proposition constraint to the feed section and candidate trays to specify the order of trays in the column is from bottom to top provided the condition is met. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + n_tray : int + The tray index. + + Returns + ------- + Constraint or NoConstraint + The constraint expression or NoConstraint if the condition is not met. + """ + if n_tray > m.reb_tray and (n_tray + 1) < m.feed_tray: + return ( + m.tray_exists[2, n_tray].binary_indicator_var + <= m.tray_exists[2, n_tray + 1].binary_indicator_var + ) + elif n_tray > m.feed_tray and (n_tray + 1) < m.con_tray: + return ( + m.tray_exists[2, n_tray + 1].binary_indicator_var + <= m.tray_exists[2, n_tray].binary_indicator_var + ) + else: + return Constraint.NoConstraint + # TODO: Update the logic proposition constraint for the feed section with the new pyomo.gdp syntax + + @m.Constraint(m.candidate_trays_product) + def _logic_proposition_section3(m, n_tray): + """ + Apply a logic proposition constraint to the product section and candidate trays to specify the order of trays in the column is from bottom to top provided the condition is met. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + n_tray : int + The tray index. + + Returns + ------- + Constraint or NoConstraint + The constraint expression or NoConstraint if the condition is not met. + """ + if n_tray > 1 and (n_tray + 1) < m.num_trays: + return ( + m.tray_exists[3, n_tray].binary_indicator_var + <= m.tray_exists[3, n_tray + 1].binary_indicator_var + ) + else: + return Constraint.NoConstraint + # TODO: Update the logic proposition constraint for the product section with the new pyomo.gdp syntax + + @m.Constraint(m.tray) + def equality_feed_product_side(m, n_tray): + """ + Constraint that enforces the equality of the binary indicator variables for the feed and product side trays. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + n_tray : int + The tray index. + + Returns + ------- + Constraint + The constraint expression that enforces the equality of the binary indicator variables for the feed and product side trays. + """ + return ( + m.tray_exists[2, n_tray].binary_indicator_var + == m.tray_exists[3, n_tray].binary_indicator_var + ) + + # TODO: Update the equality constraint for the feed and product side trays with the new pyomo.gdp syntax + + @m.Constraint() + def _existent_minimum_numbertrays(m): + """ + Constraint that enforces the minimum number of trays in the column. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + + Returns + ------- + Constraint + The constraint expression that enforces the minimum number of trays in each section and each tray to be greater than or equal to the minimum number of trays. + """ + return sum( + sum(m.tray_exists[sec, n_tray].binary_indicator_var for n_tray in m.tray) + for sec in m.section + ) - sum( + m.tray_exists[3, n_tray].binary_indicator_var for n_tray in m.tray + ) >= int( + m.min_tray + ) + + return m + + +def enforce_tray_exists(m, sec, n_tray): + """ + Enforce the existence of a tray in the column. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + sec : int + The section index. + n_tray : int + The tray index. + """ + m.tray_exists[sec, n_tray].indicator_var.fix(True) + m.tray_absent[sec, n_tray].deactivate() + + +def _build_tray_equations(m, sec, n_tray): + """ + Build the equations for the tray in the column as a function of the section when the tray exists. + Points to the appropriate function to build the equations for the section in the column. + + Parameters + ---------- + m : Pyomo ConcreteModel + The optimization model. + sec : int + The section index. + n_tray : int + The tray index. + + Returns + ------- + None + """ + build_function = { + 1: _build_bottom_equations, + 2: _build_feed_side_equations, + 3: _build_product_side_equations, + 4: _build_top_equations, + } + build_function[sec](m, n_tray) + + +def _build_bottom_equations(disj, n_tray): + """ + Build the equations for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + n_tray : int + The tray index. + + Returns + ------- + None + """ + m = disj.model() + + @disj.Constraint(m.comp, doc="Bottom section 1 mass per component balances") + def _bottom_mass_percomponent_balances(disj, comp): + """ + Mass per component balances for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the mass balance per component in the bottom section of the column. + """ + return (m.L[1, n_tray + 1, comp] if n_tray < m.num_trays else 0) + ( + m.L[2, 1, comp] if n_tray == m.num_trays else 0 + ) + (m.L[3, 1, comp] if n_tray == m.num_trays else 0) - ( + m.L[1, n_tray, comp] if n_tray > m.reb_tray else 0 + ) + ( + m.V[1, n_tray - 1, comp] if n_tray > m.reb_tray else 0 + ) - ( + m.V[1, n_tray, comp] * m.dv[2] if n_tray == m.num_trays else 0 + ) - ( + m.V[1, n_tray, comp] * m.dv[3] if n_tray == m.num_trays else 0 + ) - ( + m.V[1, n_tray, comp] if n_tray < m.num_trays else 0 + ) - ( + m.B[comp] if n_tray == m.reb_tray else 0 + ) == m.slack[ + 1, n_tray, comp + ] + + @disj.Constraint(doc="Bottom section 1 energy balances") + def _bottom_energy_balances(disj): + """ + Energy balances for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the energy balance for the bottom section in the column. + """ + return ( + sum( + ( + m.L[1, n_tray + 1, comp] * m.hl[1, n_tray + 1, comp] + if n_tray < m.num_trays + else 0 + ) + + (m.L[2, 1, comp] * m.hl[2, 1, comp] if n_tray == m.num_trays else 0) + + (m.L[3, 1, comp] * m.hl[3, 1, comp] if n_tray == m.num_trays else 0) + - ( + m.L[1, n_tray, comp] * m.hl[1, n_tray, comp] + if n_tray > m.reb_tray + else 0 + ) + + ( + m.V[1, n_tray - 1, comp] * m.hv[1, n_tray - 1, comp] + if n_tray > m.reb_tray + else 0 + ) + - ( + m.V[1, n_tray, comp] * m.dv[2] * m.hv[1, n_tray, comp] + if n_tray == m.num_trays + else 0 + ) + - ( + m.V[1, n_tray, comp] * m.dv[3] * m.hv[1, n_tray, comp] + if n_tray == m.num_trays + else 0 + ) + - ( + m.V[1, n_tray, comp] * m.hv[1, n_tray, comp] + if n_tray < m.num_trays + else 0 + ) + - (m.B[comp] * m.hl[1, n_tray, comp] if n_tray == m.reb_tray else 0) + for comp in m.comp + ) + * m.Qscale + + (m.Qreb if n_tray == m.reb_tray else 0) + == 0 + ) + + @disj.Constraint(m.comp, doc="Bottom section 1 liquid flowrate per component") + def _bottom_liquid_percomponent(disj, comp): + """ + Liquid flowrate per component in the bottom section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid flowrate per component in the bottom section of the column. + """ + return m.L[1, n_tray, comp] == m.Ltotal[1, n_tray] * m.x[1, n_tray, comp] + + @disj.Constraint(m.comp, doc="Bottom section 1 vapor flowrate per component") + def _bottom_vapor_percomponent(disj, comp): + """ + Vapor flowrate per component in the bottom section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor flowrate per component in the bottom section of the column. + """ + return m.V[1, n_tray, comp] == m.Vtotal[1, n_tray] * m.y[1, n_tray, comp] + + @disj.Constraint(doc="Bottom section 1 liquid composition equilibrium summation") + def bottom_liquid_composition_summation(disj): + """ + Liquid composition equilibrium summation for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid composition equilibrium summation for the bottom section in the column. + It ensures the sum of the liquid compositions is equal to 1 plus the error in the liquid composition. + """ + return sum(m.x[1, n_tray, comp] for comp in m.comp) - 1 == m.errx[1, n_tray] + + @disj.Constraint(doc="Bottom section 1 vapor composition equilibrium summation") + def bottom_vapor_composition_summation(disj): + """ + Vapor composition equilibrium summation for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition equilibrium summation for the bottom section in the column. + It ensures the sum of the vapor compositions is equal to 1 plus the error in the vapor composition. + """ + return sum(m.y[1, n_tray, comp] for comp in m.comp) - 1 == m.erry[1, n_tray] + + @disj.Constraint(m.comp, doc="Bottom section 1 vapor composition") + def bottom_vapor_composition(disj, comp): + """ + Vapor composition for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition for the bottom section in the column. + The equation is derived from the vapor-liquid equilibrium relationship. + """ + return ( + m.y[1, n_tray, comp] + == m.x[1, n_tray, comp] + * ( + m.actv[1, n_tray, comp] + * ( + m.prop[comp, 'PC'] + * exp( + m.prop[comp, 'TC'] + / m.T[1, n_tray] + * ( + m.prop[comp, 'vpA'] + * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) + + m.prop[comp, 'vpB'] + * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) ** 1.5 + + m.prop[comp, 'vpC'] + * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) ** 3 + + m.prop[comp, 'vpD'] + * (1 - m.T[1, n_tray] / m.prop[comp, 'TC']) ** 6 + ) + ) + ) + ) + / m.P[1, n_tray] + ) + + @disj.Constraint(m.comp, doc="Bottom section 1 liquid enthalpy") + def bottom_liquid_enthalpy(disj, comp): + """ + Liquid enthalpy for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid enthalpy for the bottom section in the column. + """ + return m.hl[1, n_tray, comp] == ( + m.cpc[1] + * ( + (m.T[1, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] + + (m.T[1, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 1] + * m.cpc2['A', 1] + / 2 + + (m.T[1, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 1] + * m.cpc2['B', 1] + / 3 + + (m.T[1, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 + ) + / m.Hscale + ) + + @disj.Constraint(m.comp, doc="Bottom section 1 vapor enthalpy") + def bottom_vapor_enthalpy(disj, comp): + """ + Vapor enthalpy for the bottom section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor enthalpy for the bottom section in the column. + """ + return m.hv[1, n_tray, comp] == ( + m.cpc[2] + * ( + (m.T[1, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] + + (m.T[1, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 2] + * m.cpc2['A', 2] + / 2 + + (m.T[1, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 2] + * m.cpc2['B', 2] + / 3 + + (m.T[1, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 + ) + / m.Hscale + + m.dHvap[comp] + ) + + @disj.Constraint(m.comp, doc="Bottom section 1 liquid activity coefficient") + def bottom_activity_coefficient(disj, comp): + """ + Liquid activity coefficient for the bottom section in the column equal to 1. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the bottom section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid activity coefficient for the bottom section for each component and tray in the column to be equal to 1. + """ + return m.actv[1, n_tray, comp] == 1 + + +def _build_feed_side_equations(disj, n_tray): + """ + Build the equations for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + n_tray : int + The tray index. + + Returns + ------- + None + """ + m = disj.model() + + @disj.Constraint(m.comp, doc="Feed section 2 mass per component balances") + def _feedside_masspercomponent_balances(disj, comp): + """ + Mass per component balances for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the mass balance per component in the feed side section of the column. + """ + return (m.L[2, n_tray + 1, comp] if n_tray < m.num_trays else 0) + ( + m.L[4, 1, comp] * m.dl[2] if n_tray == m.num_trays else 0 + ) - m.L[2, n_tray, comp] + ( + m.V[1, m.num_trays, comp] * m.dv[2] if n_tray == 1 else 0 + ) + ( + m.V[2, n_tray - 1, comp] if n_tray > 1 else 0 + ) - m.V[ + 2, n_tray, comp + ] + ( + m.F[comp] if n_tray == m.feed_tray else 0 + ) == 0 + + @disj.Constraint(doc="Feed section 2 energy balances") + def _feedside_energy_balances(disj): + """ + Energy balances for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the energy balance for the feed side section in the column. + """ + return ( + sum( + ( + m.L[2, n_tray + 1, comp] * m.hl[2, n_tray + 1, comp] + if n_tray < m.num_trays + else 0 + ) + + ( + m.L[4, 1, comp] * m.dl[2] * m.hl[4, 1, comp] + if n_tray == m.num_trays + else 0 + ) + - m.L[2, n_tray, comp] * m.hl[2, n_tray, comp] + + ( + m.V[1, m.num_trays, comp] * m.dv[2] * m.hv[1, m.num_trays, comp] + if n_tray == 1 + else 0 + ) + + ( + m.V[2, n_tray - 1, comp] * m.hv[2, n_tray - 1, comp] + if n_tray > 1 + else 0 + ) + - m.V[2, n_tray, comp] * m.hv[2, n_tray, comp] + for comp in m.comp + ) + * m.Qscale + + sum( + ( + m.F[comp] * (m.hlf[comp] * (1 - m.q) + m.hvf[comp] * m.q) + if n_tray == m.feed_tray + else 0 + ) + for comp in m.comp + ) + * m.Qscale + == 0 + ) + + @disj.Constraint(m.comp, doc="Feed section 2 liquid flowrate per component") + def _feedside_liquid_percomponent(disj, comp): + """ + Liquid flowrate per component in the feed side section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid flowrate per component in the feed side section of the column is equal to the total liquid flowrate times the liquid composition. + """ + return m.L[2, n_tray, comp] == m.Ltotal[2, n_tray] * m.x[2, n_tray, comp] + + @disj.Constraint(m.comp, doc="Feed section 2 vapor flowrate per component") + def _feedside_vapor_percomponent(disj, comp): + """ + Vapor flowrate per component in the feed side section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor flowrate per component in the feed side section of the column is equal to the total vapor flowrate times the vapor composition. + """ + return m.V[2, n_tray, comp] == m.Vtotal[2, n_tray] * m.y[2, n_tray, comp] + + @disj.Constraint(doc="Feed section 2 liquid composition equilibrium summation") + def feedside_liquid_composition_summation(disj): + """ + Liquid composition equilibrium summation for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid composition equilibrium summation for the feed side section in the column. + It ensures the sum of the liquid compositions is equal to 1 plus the error in the liquid composition. + """ + return sum(m.x[2, n_tray, comp] for comp in m.comp) - 1 == m.errx[2, n_tray] + + @disj.Constraint(doc="Feed section 2 vapor composition equilibrium summation") + def feedside_vapor_composition_summation(disj): + """ + Vapor composition equilibrium summation for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition equilibrium summation for the feed side section in the column. + It ensures the sum of the vapor compositions is equal to 1 plus the error in the vapor composition. + """ + return sum(m.y[2, n_tray, comp] for comp in m.comp) - 1 == m.erry[2, n_tray] + + @disj.Constraint(m.comp, doc="Feed section 2 vapor composition") + def feedside_vapor_composition(disj, comp): + """ + Vapor composition for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition for the feed side section in the column. + The equation is derived from the vapor-liquid equilibrium relationship. + """ + return ( + m.y[2, n_tray, comp] + == m.x[2, n_tray, comp] + * ( + m.actv[2, n_tray, comp] + * ( + m.prop[comp, 'PC'] + * exp( + m.prop[comp, 'TC'] + / m.T[2, n_tray] + * ( + m.prop[comp, 'vpA'] + * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) + + m.prop[comp, 'vpB'] + * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) ** 1.5 + + m.prop[comp, 'vpC'] + * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) ** 3 + + m.prop[comp, 'vpD'] + * (1 - m.T[2, n_tray] / m.prop[comp, 'TC']) ** 6 + ) + ) + ) + ) + / m.P[2, n_tray] + ) + + @disj.Constraint(m.comp, doc="Feed section 2 liquid enthalpy") + def feedside_liquid_enthalpy(disj, comp): + """ + Liquid enthalpy for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid enthalpy for the feed side section in the column. + """ + return m.hl[2, n_tray, comp] == ( + m.cpc[1] + * ( + (m.T[2, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] + + (m.T[2, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 1] + * m.cpc2['A', 1] + / 2 + + (m.T[2, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 1] + * m.cpc2['B', 1] + / 3 + + (m.T[2, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 + ) + / m.Hscale + ) + + @disj.Constraint(m.comp, doc="Feed section 2 vapor enthalpy") + def feedside_vapor_enthalpy(disj, comp): + """ + Vapor enthalpy for the feed side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor enthalpy for the feed side section in the column. + """ + return m.hv[2, n_tray, comp] == ( + m.cpc[2] + * ( + (m.T[2, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] + + (m.T[2, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 2] + * m.cpc2['A', 2] + / 2 + + (m.T[2, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 2] + * m.cpc2['B', 2] + / 3 + + (m.T[2, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 + ) + / m.Hscale + + m.dHvap[comp] + ) + + @disj.Constraint(m.comp, doc="Feed section 2 liquid activity coefficient") + def feedside_activity_coefficient(disj, comp): + """ + Liquid activity coefficient for the feed side section in the column equal to 1. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the feed side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid activity coefficient for the feed side section for each component and tray in the column to be equal to 1. + This is an assumption for the feed side section, since the feed is assumed to be ideal. + """ + return m.actv[2, n_tray, comp] == 1 + + +def _build_product_side_equations(disj, n_tray): + """ + Build the equations for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + n_tray : int + The tray index. + + Returns + ------- + None + """ + m = disj.model() + + @disj.Constraint(m.comp, doc="Product section 3 mass per component balances") + def _productside_masspercomponent_balances(disj, comp): + """ + Mass per component balances for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the mass balance per component in the product side section of the column. + """ + return (m.L[3, n_tray + 1, comp] if n_tray < m.num_trays else 0) + ( + m.L[4, 1, comp] * m.dl[3] if n_tray == m.num_trays else 0 + ) - m.L[3, n_tray, comp] + ( + m.V[1, m.num_trays, comp] * m.dv[3] if n_tray == 1 else 0 + ) + ( + m.V[3, n_tray - 1, comp] if n_tray > 1 else 0 + ) - m.V[ + 3, n_tray, comp + ] - ( + m.S[1, comp] if n_tray == m.sideout1_tray else 0 + ) - ( + m.S[2, comp] if n_tray == m.sideout2_tray else 0 + ) == 0 + + @disj.Constraint(doc="Product section 3 energy balances") + def _productside_energy_balances(disj): + """ + Energy balances for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the energy balance for the product side section in the column. + """ + return ( + sum( + ( + m.L[3, n_tray + 1, comp] * m.hl[3, n_tray + 1, comp] + if n_tray < m.num_trays + else 0 + ) + + ( + m.L[4, 1, comp] * m.dl[3] * m.hl[4, 1, comp] + if n_tray == m.num_trays + else 0 + ) + - m.L[3, n_tray, comp] * m.hl[3, n_tray, comp] + + ( + m.V[1, m.num_trays, comp] * m.dv[3] * m.hv[1, m.num_trays, comp] + if n_tray == 1 + else 0 + ) + + ( + m.V[3, n_tray - 1, comp] * m.hv[3, n_tray - 1, comp] + if n_tray > 1 + else 0 + ) + - m.V[3, n_tray, comp] * m.hv[3, n_tray, comp] + - ( + m.S[1, comp] * m.hl[3, n_tray, comp] + if n_tray == m.sideout1_tray + else 0 + ) + - ( + m.S[2, comp] * m.hl[3, n_tray, comp] + if n_tray == m.sideout2_tray + else 0 + ) + for comp in m.comp + ) + * m.Qscale + == 0 + ) + + @disj.Constraint(m.comp, doc="Product section 3 liquid flowrate per component") + def _productside_liquid_percomponent(disj, comp): + """ + Liquid flowrate per component in the product side section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid flowrate per component in the product side section of the column is equal to the total liquid flowrate times the liquid composition. + """ + return m.L[3, n_tray, comp] == m.Ltotal[3, n_tray] * m.x[3, n_tray, comp] + + @disj.Constraint(m.comp, doc="Product section 3 vapor flowrate per component") + def _productside_vapor_percomponent(disj, comp): + """ + Vapor flowrate per component in the product side section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor flowrate per component in the product side section of the column is equal to the total vapor flowrate times the vapor composition. + """ + return m.V[3, n_tray, comp] == m.Vtotal[3, n_tray] * m.y[3, n_tray, comp] + + @disj.Constraint(doc="Product section 3 liquid composition equilibrium summation") + def productside_liquid_composition_summation(disj): + """ + Liquid composition equilibrium summation for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid composition equilibrium summation for the product side section in the column. + It ensures the sum of the liquid compositions is equal to 1 plus the error in the liquid composition. + """ + return sum(m.x[3, n_tray, comp] for comp in m.comp) - 1 == m.errx[3, n_tray] + + @disj.Constraint(doc="Product section 3 vapor composition equilibrium summation") + def productside_vapor_composition_summation(disj): + """ + Vapor composition equilibrium summation for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition equilibrium summation for the product side section in the column. + It ensures the sum of the vapor compositions is equal to 1 plus the error in the vapor composition. + """ + return sum(m.y[3, n_tray, comp] for comp in m.comp) - 1 == m.erry[3, n_tray] + + @disj.Constraint(m.comp, doc="Product section 3 vapor composition") + def productside_vapor_composition(disj, comp): + """ + Vapor composition for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition for the product side section in the column. + The equation is derived from the vapor-liquid equilibrium relationship. + """ + return ( + m.y[3, n_tray, comp] + == m.x[3, n_tray, comp] + * ( + m.actv[3, n_tray, comp] + * ( + m.prop[comp, 'PC'] + * exp( + m.prop[comp, 'TC'] + / m.T[3, n_tray] + * ( + m.prop[comp, 'vpA'] + * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) + + m.prop[comp, 'vpB'] + * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) ** 1.5 + + m.prop[comp, 'vpC'] + * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) ** 3 + + m.prop[comp, 'vpD'] + * (1 - m.T[3, n_tray] / m.prop[comp, 'TC']) ** 6 + ) + ) + ) + ) + / m.P[3, n_tray] + ) + + @disj.Constraint(m.comp, doc="Product section 3 liquid enthalpy") + def productside_liquid_enthalpy(disj, comp): + """ + Liquid enthalpy for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid enthalpy for the product side section in the column. + """ + return m.hl[3, n_tray, comp] == ( + m.cpc[1] + * ( + (m.T[3, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] + + (m.T[3, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 1] + * m.cpc2['A', 1] + / 2 + + (m.T[3, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 1] + * m.cpc2['B', 1] + / 3 + + (m.T[3, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 + ) + / m.Hscale + ) + + @disj.Constraint(m.comp, doc="Product section 3 vapor enthalpy") + def productside_vapor_enthalpy(disj, comp): + """ + Vapor enthalpy for the product side section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor enthalpy for the product side section in the column. + """ + return m.hv[3, n_tray, comp] == ( + m.cpc[2] + * ( + (m.T[3, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] + + (m.T[3, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 2] + * m.cpc2['A', 2] + / 2 + + (m.T[3, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 2] + * m.cpc2['B', 2] + / 3 + + (m.T[3, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 + ) + / m.Hscale + + m.dHvap[comp] + ) + + @disj.Constraint(m.comp, doc="Product section 3 liquid activity coefficient") + def productside_activity_coefficient(disj, comp): + """ + Liquid activity coefficient for the product side section in the column equal to 1. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the product side section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid activity coefficient for the product side section for each component and tray in the column to be equal to 1. + This is an assumption for the product side section, since the product is assumed to be ideal. + """ + return m.actv[3, n_tray, comp] == 1 + + +def _build_top_equations(disj, n_tray): + """ + Build the equations for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + n_tray : int + The tray index. + + Returns + ------- + None + """ + m = disj.model() + + @disj.Constraint(m.comp, doc="Top section 4 mass per component balances") + def _top_mass_percomponent_balances(disj, comp): + """ + Mass per component balances for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the mass balance per component in the top section of the column. + """ + return (m.L[4, n_tray + 1, comp] if n_tray < m.con_tray else 0) - ( + m.L[4, n_tray, comp] * m.dl[2] if n_tray == 1 else 0 + ) - (m.L[4, n_tray, comp] * m.dl[3] if n_tray == 1 else 0) - ( + m.L[4, n_tray, comp] if n_tray > 1 else 0 + ) + ( + m.V[2, m.num_trays, comp] if n_tray == 1 else 0 + ) + ( + m.V[3, m.num_trays, comp] if n_tray == 1 else 0 + ) + ( + m.V[4, n_tray - 1, comp] if n_tray > 1 else 0 + ) - ( + m.V[4, n_tray, comp] if n_tray < m.con_tray else 0 + ) - ( + m.D[comp] if n_tray == m.con_tray else 0 + ) == 0 + + @disj.Constraint(doc="Top scetion 4 energy balances") + def _top_energy_balances(disj): + """ + Energy balances for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the energy balance for the top section in the column. + """ + return ( + sum( + ( + m.L[4, n_tray + 1, comp] * m.hl[4, n_tray + 1, comp] + if n_tray < m.con_tray + else 0 + ) + - ( + m.L[4, n_tray, comp] * m.dl[2] * m.hl[4, n_tray, comp] + if n_tray == 1 + else 0 + ) + - ( + m.L[4, n_tray, comp] * m.dl[3] * m.hl[4, n_tray, comp] + if n_tray == 1 + else 0 + ) + - (m.L[4, n_tray, comp] * m.hl[4, n_tray, comp] if n_tray > 1 else 0) + + ( + m.V[2, m.num_trays, comp] * m.hv[2, m.num_trays, comp] + if n_tray == 1 + else 0 + ) + + ( + m.V[3, m.num_trays, comp] * m.hv[3, m.num_trays, comp] + if n_tray == 1 + else 0 + ) + + ( + m.V[4, n_tray - 1, comp] * m.hv[4, n_tray - 1, comp] + if n_tray > 1 + else 0 + ) + - ( + m.V[4, n_tray, comp] * m.hv[4, n_tray, comp] + if n_tray < m.con_tray + else 0 + ) + - (m.D[comp] * m.hl[4, n_tray, comp] if n_tray == m.con_tray else 0) + for comp in m.comp + ) + * m.Qscale + - (m.Qcon if n_tray == m.con_tray else 0) + == 0 + ) + + @disj.Constraint(m.comp, doc="Top section 4 liquid flowrate per component") + def _top_liquid_percomponent(disj, comp): + """ + Liquid flowrate per component in the top section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid flowrate per component in the top section of the column is equal to the total liquid flowrate times the liquid composition. + """ + return m.L[4, n_tray, comp] == m.Ltotal[4, n_tray] * m.x[4, n_tray, comp] + + @disj.Constraint(m.comp, doc="Top section 4 vapor flowrate per component") + def _top_vapor_percomponent(disj, comp): + """ + Vapor flowrate per component in the top section of the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor flowrate per component in the top section of the column is equal to the total vapor flowrate times the vapor composition. + """ + return m.V[4, n_tray, comp] == m.Vtotal[4, n_tray] * m.y[4, n_tray, comp] + + @disj.Constraint(doc="Top section 4 liquid composition equilibrium summation") + def top_liquid_composition_summation(disj): + """ + Liquid composition equilibrium summation for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid composition equilibrium summation for the top section in the column. + It ensures the sum of the liquid compositions is equal to 1 plus the error in the liquid composition. + """ + return sum(m.x[4, n_tray, comp] for comp in m.comp) - 1 == m.errx[4, n_tray] + + @disj.Constraint(doc="Top section 4 vapor composition equilibrium summation") + def top_vapor_composition_summation(disj): + """ + Vapor composition equilibrium summation for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition equilibrium summation for the top section in the column. + It ensures the sum of the vapor compositions is equal to 1 plus the error in the vapor composition. + """ + return sum(m.y[4, n_tray, comp] for comp in m.comp) - 1 == m.erry[4, n_tray] + + @disj.Constraint(m.comp, doc="Top scetion 4 vapor composition") + def top_vapor_composition(disj, comp): + """ + Vapor composition for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition for the top section in the column. + The equation is derived from the vapor-liquid equilibrium relationship. + """ + return ( + m.y[4, n_tray, comp] + == m.x[4, n_tray, comp] + * ( + m.actv[4, n_tray, comp] + * ( + m.prop[comp, 'PC'] + * exp( + m.prop[comp, 'TC'] + / m.T[4, n_tray] + * ( + m.prop[comp, 'vpA'] + * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) + + m.prop[comp, 'vpB'] + * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) ** 1.5 + + m.prop[comp, 'vpC'] + * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) ** 3 + + m.prop[comp, 'vpD'] + * (1 - m.T[4, n_tray] / m.prop[comp, 'TC']) ** 6 + ) + ) + ) + ) + / m.P[4, n_tray] + ) + + @disj.Constraint(m.comp, doc="Top section 4 liquid enthalpy") + def top_liquid_enthalpy(disj, comp): + """ + Liquid enthalpy for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid enthalpy for the top section in the column. + """ + return m.hl[4, n_tray, comp] == ( + m.cpc[1] + * ( + (m.T[4, n_tray] - m.Tref) * m.prop[comp, 'cpA', 1] + + (m.T[4, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 1] + * m.cpc2['A', 1] + / 2 + + (m.T[4, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 1] + * m.cpc2['B', 1] + / 3 + + (m.T[4, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 1] / 4 + ) + / m.Hscale + ) + + @disj.Constraint(m.comp, doc="Top section 4 vapor enthalpy") + def top_vapor_enthalpy(disj, comp): + """ + Vapor enthalpy for the top section in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor enthalpy for the top section in the column. + """ + return m.hv[4, n_tray, comp] == ( + m.cpc[2] + * ( + (m.T[4, n_tray] - m.Tref) * m.prop[comp, 'cpA', 2] + + (m.T[4, n_tray] ** 2 - m.Tref**2) + * m.prop[comp, 'cpB', 2] + * m.cpc2['A', 2] + / 2 + + (m.T[4, n_tray] ** 3 - m.Tref**3) + * m.prop[comp, 'cpC', 2] + * m.cpc2['B', 2] + / 3 + + (m.T[4, n_tray] ** 4 - m.Tref**4) * m.prop[comp, 'cpD', 2] / 4 + ) + / m.Hscale + + m.dHvap[comp] + ) + + @disj.Constraint(m.comp, doc="Top section 4 liquid activity coefficient") + def top_activity_coefficient(disj, comp): + """ + Liquid activity coefficient for the top section in the column equal to 1. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the top section in the column. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid activity coefficient for the top section for each component and tray in the column to be equal to 1. + This is an assumption for the top section, since the product is assumed to be ideal. + """ + return m.actv[4, n_tray, comp] == 1 + + +def _build_pass_through_eqns(disj, sec, n_tray): + """ + Build the equations for the pass through section in the column when a given tray in the disjunct is not active if it is the first or last tray. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through section in the column. + sec : int + The section index. + n_tray : int + The tray index. + + Returns + ------- + None + """ + m = disj.model() + + # If the tray is the first or last tray, then the liquid and vapor flowrates, compositions, enthalpies, and temperature are passed through. + if n_tray == 1 or n_tray == m.num_trays: + return + + @disj.Constraint(m.comp, doc="Pass through liquid flowrate") + def pass_through_liquid_flowrate(disj, comp): + """ + Pass through liquid flowrate for the given tray in the column. + The constraint enforces the liquid flowrate for the given tray is equal to the liquid flowrate for the tray above it. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid flowrate for the given tray is equal to the liquid flowrate for the tray above it. + """ + return m.L[sec, n_tray, comp] == m.L[sec, n_tray + 1, comp] + + @disj.Constraint(m.comp, doc="Pass through vapor flowrate") + def pass_through_vapor_flowrate(disj, comp): + """ + Pass through vapor flowrate for the given tray in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor flowrate for the given tray is equal to the vapor flowrate for the tray below it. + """ + return m.V[sec, n_tray, comp] == m.V[sec, n_tray - 1, comp] + + @disj.Constraint(m.comp, doc="Pass through liquid composition") + def pass_through_liquid_composition(disj, comp): + """ + Pass through liquid composition for the given tray in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid composition for the given tray is equal to the liquid composition for the tray above it. + """ + return m.x[sec, n_tray, comp] == m.x[sec, n_tray + 1, comp] + + @disj.Constraint(m.comp, doc="Pass through vapor composition") + def pass_through_vapor_composition(disj, comp): + """ + Pass through vapor composition for the given tray in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor composition for the given tray is equal to the vapor composition for the tray below it. + """ + return m.y[sec, n_tray, comp] == m.y[sec, n_tray + 1, comp] + + @disj.Constraint(m.comp, doc="Pass through liquid enthalpy") + def pass_through_liquid_enthalpy(disj, comp): + """ + Pass through liquid enthalpy for the given tray in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the liquid enthalpy for the given tray is equal to the liquid enthalpy for the tray above it. + """ + return m.hl[sec, n_tray, comp] == m.hl[sec, n_tray + 1, comp] + + @disj.Constraint(m.comp, doc="Pass through vapor enthalpy") + def pass_through_vapor_enthalpy(disj, comp): + """ + Pass through vapor enthalpy for the given tray in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + comp : int + The component index. + + Returns + ------- + Constraint + The constraint expression that enforces the vapor enthalpy for the given tray is equal to the vapor enthalpy for the tray below it. + """ + return m.hv[sec, n_tray, comp] == m.hv[sec, n_tray - 1, comp] + + @disj.Constraint(doc="Pass through temperature") + def pass_through_temperature(disj): + """ + Pass through temperature for the given tray in the column. + + Parameters + ---------- + disj : Disjunct + The disjunct object for the pass through when the tray is inactive. + + Returns + ------- + Constraint + The constraint expression that enforces the temperature for the given tray is equal to the temperature for the tray below it. + """ + return m.T[sec, n_tray] == m.T[sec, n_tray - 1] + + +if __name__ == "__main__": + model = build_model() diff --git a/gdplib/kaibel/main_gdp.py b/gdplib/kaibel/main_gdp.py index 5b130eb..3a66121 100644 --- a/gdplib/kaibel/main_gdp.py +++ b/gdplib/kaibel/main_gdp.py @@ -1,246 +1,289 @@ -""" - KAIBEL COLUMN: Modeling, Optimization, and - Conceptual Design of Multi-product Dividing Wall Columns - (written by E. Soraya Rawlings, esoraya@rwlngs.net, - in collaboration with Qi Chen) - - Case study: separation of a mixture of a quaternary mixture: - 1 = methanol - 2 = ethanol - 3 = propanol - 4 = butanol - - The scheme of the Kaibel Column is shown in Figure 1: - ____ - --|Cond|--- - | ---- | - -------------- | - | sect 4 |<------> D mostly 1 - | ---------- | - | | - | ----- |----- | - | | |-------> S2 - Fj ------>| sect | sect | - | 2 | 3 | - | | |-------> S1 - | ----- |----- | - | | - | ---------- | - | sect 1 |<------> B mostly 4 - -------------- | - | ____ | - ---|Reb |--- - ---- - Figure 1. Kaibel Column scheme -""" - -from __future__ import division - -from math import fabs - -import matplotlib.pyplot as plt -from pyomo.environ import * - -from kaibel_solve_gdp import build_model - - -def main(): - m = build_model() - - m.F[1].fix(50) - m.F[2].fix(50) - m.F[3].fix(50) - m.F[4].fix(50) - m.q.fix(m.q_init) - m.dv[2].fix(0.394299) - - for sec in m.section: - for n_tray in m.tray: - m.P[sec, n_tray].fix(m.Preb) - - ## Initial values for the tray existence or absence - for n_tray in m.candidate_trays_main: - for sec in m.section_main: - m.tray_exists[sec, n_tray].indicator_var.set_value(1) - m.tray_absent[sec, n_tray].indicator_var.set_value(0) - for n_tray in m.candidate_trays_feed: - m.tray_exists[2, n_tray].indicator_var.set_value(1) - m.tray_absent[2, n_tray].indicator_var.set_value(0) - for n_tray in m.candidate_trays_product: - m.tray_exists[3, n_tray].indicator_var.set_value(1) - m.tray_absent[3, n_tray].indicator_var.set_value(0) - - intro_message(m) - - results = SolverFactory('gdpopt').solve( - m, - strategy='LOA', - tee=True, - time_limit=3600, - mip_solver='gams', - mip_solver_args=dict(solver='cplex'), - ) - - m.calc_nt = sum( - sum(m.tray_exists[sec, n_tray].indicator_var.value for n_tray in m.tray) - for sec in m.section - ) - sum(m.tray_exists[3, n_tray].indicator_var.value for n_tray in m.tray) - m.dw_start = ( - sum(m.tray_exists[1, n_tray].indicator_var.value for n_tray in m.tray) + 1 - ) - m.dw_end = sum( - m.tray_exists[1, n_tray].indicator_var.value for n_tray in m.tray - ) + sum(m.tray_exists[2, n_tray].indicator_var.value for n_tray in m.tray) - - display_results(m) - - print(' ', results) - print(' Solver Status: ', results.solver.status) - print(' Termination condition: ', results.solver.termination_condition) - - -def intro_message(m): - print( - """ - -If you use this model and/or initialization strategy, you may cite the following: -Rawlings, ES; Chen, Q; Grossmann, IE; Caballero, JA. Kaibel Column: Modeling, -optimization, and conceptual design of multi-product dividing wall columns. -Comp. and Chem. Eng., 2019, 125, 31-39. -DOI: https://doi.org/10.1016/j.compchemeng.2019.03.006 - - - """ - ) - - -def display_results(m): - print('') - print('Components:') - print('1 methanol') - print('2 ethanol') - print('3 butanol') - print('4 propanol') - print(' ') - print('Objective: %s' % value(m.obj)) - print('Trays: %s' % value(m.calc_nt)) - print('Dividing_wall_start: %s' % value(m.dw_start)) - print('Dividing_wall_end: %s' % value(m.dw_end)) - print(' ') - print( - 'Qreb: {: >3.0f}kW B_1: {: > 2.0f} B_2: {: >2.0f} B_3: {: >2.0f} B_4: {: >2.0f} Btotal: {: >2.0f}'.format( - value(m.Qreb / m.Qscale), - value(m.B[1]), - value(m.B[2]), - value(m.B[3]), - value(m.B[4]), - value(m.Btotal), - ) - ) - print( - 'Qcon: {: >2.0f}kW D_1: {: >2.0f} D_2: {: >2.0f} D_3: {: >2.0f} D_4: {: >2.0f} Dtotal: {: >2.0f}'.format( - value(m.Qcon / m.Qscale), - value(m.D[1]), - value(m.D[2]), - value(m.D[3]), - value(m.D[4]), - value(m.Dtotal), - ) - ) - print(' ') - print('Reflux: {: >3.4f}'.format(value(m.rr))) - print('Reboil: {: >3.4f} '.format(value(m.bu))) - print(' ') - print('Flowrates[mol/s]') - print( - 'F_1: {: > 3.0f} F_2: {: >2.0f} F_3: {: >2.0f} F_4: {: >2.0f} Ftotal: {: >2.0f}'.format( - value(m.F[1]), - value(m.F[2]), - value(m.F[3]), - value(m.F[4]), - sum(value(m.F[comp]) for comp in m.comp), - ) - ) - print( - 'S1_1: {: > 1.0f} S1_2: {: >2.0f} S1_3: {: >2.0f} S1_4: {: >2.0f} S1total: {: >2.0f}'.format( - value(m.S[1, 1]), - value(m.S[1, 2]), - value(m.S[1, 3]), - value(m.S[1, 4]), - sum(value(m.S[1, comp]) for comp in m.comp), - ) - ) - print( - 'S2_1: {: > 1.0f} S2_2: {: >2.0f} S2_3: {: >2.0f} S2_4: {: >2.0f} S2total: {: >2.0f}'.format( - value(m.S[2, 1]), - value(m.S[2, 2]), - value(m.S[2, 3]), - value(m.S[2, 4]), - sum(value(m.S[2, comp]) for comp in m.comp), - ) - ) - print(' ') - print('Distributors:') - print('dl[2]: {: >3.4f} dl[3]: {: >3.4f}'.format(value(m.dl[2]), value(m.dl[3]))) - print('dv[2]: {: >3.4f} dv[3]: {: >3.4f}'.format(value(m.dv[2]), value(m.dv[3]))) - print(' ') - print(' ') - print(' ') - print(' Kaibel Column Sections ') - print('__________________________________________') - print(' ') - print(' Tray Bottom Feed ') - print('__________________________________________') - for t in reversed(list(m.tray)): - print( - '[{: >2.0f}] {: >9.0g} {: >18.0g} F:{: >3.0f} '.format( - t, - ( - fabs(value(m.tray_exists[1, t].indicator_var)) - if t in m.candidate_trays_main - else 1 - ), - ( - fabs(value(m.tray_exists[2, t].indicator_var)) - if t in m.candidate_trays_feed - else 1 - ), - sum(value(m.F[comp]) for comp in m.comp) if t == m.feed_tray else 0, - ) - ) - print(' ') - print('__________________________________________') - print(' ') - print(' Product Top ') - print('__________________________________________') - for t in reversed(list(m.tray)): - print( - '[{: >2.0f}] {: >9.0g} S1:{: >2.0f} S2:{: >2.0f} {: >8.0g}'.format( - t, - ( - fabs(value(m.tray_exists[3, t].indicator_var)) - if t in m.candidate_trays_product - else 1 - ), - ( - sum(value(m.S[1, comp]) for comp in m.comp) - if t == m.sideout1_tray - else 0 - ), - ( - sum(value(m.S[2, comp]) for comp in m.comp) - if t == m.sideout2_tray - else 0 - ), - ( - fabs(value(m.tray_exists[4, t].indicator_var)) - if t in m.candidate_trays_main - else 1 - ), - ) - ) - print(' 1 = trays exists, 0 = absent tray') - - -if __name__ == "__main__": - main() +""" + KAIBEL COLUMN: Modeling, Optimization, and + Conceptual Design of Multi-product Dividing Wall Columns + (written by E. Soraya Rawlings, esoraya@rwlngs.net, + in collaboration with Qi Chen) + +This is a dividing wall distillation column design problem to determine the optimal minimum number of trays and the optimal location of side streams for the separation of a quaternary mixture: + 1 = methanol + 2 = ethanol + 3 = propanol + 4 = butanol +while minimizing its capital and operating costs. + + The scheme of the Kaibel Column is shown in Figure 1: + ____ + --|Cond|--- + | ---- | + -------------- | + | sect 4 |<------> D mostly 1 + | ---------- | + | | + | ----- |----- | + | | |-------> S2 + Fj ------>| sect | sect | + | 2 | 3 | + | | |-------> S1 + | ----- |----- | + | | + | ---------- | + | sect 1 |<------> B mostly 4 + -------------- | + | ____ | + ---|Reb |--- + ---- + Figure 1. Kaibel Column scheme + +Permanent trays: +- Reboiler and vapor distributor in the bottom section (sect 1) +- Liquid distributor and condenser in the top section (sect 4) +- Side feed tray for the feed side and dividing wall starting and and ening tray in the feed section (sect 2). +- Side product trays and dividing wall starting and ending tray in the product section (sect 3). + +The trays in each section are counted from bottom to top, being tray 1 the bottom tray in each section and tray np the top tray in each section, where np is a specified upper bound for the number of possible trays for each section. +Each section has the same number of possible trays. + +Six degrees of freedom: the reflux ratio, the product outlets (bottom, intermediate, and distillate product flowrates), and the liquid and vapor flowrates between the two sections of the dividing wall, controlled by a liquid and vapor distributor on the top and bottom section of the column, respectively. +including also the vapor and liquid flowrate and the energy consumption in the reboiler and condenser. +The vapor distributor is fixed and remain constant during the column operation. + +Source paper: +Rawlings, E. S., Chen, Q., Grossmann, I. E., & Caballero, J. A. (2019). Kaibel Column: Modeling, optimization, and conceptual design of multi-product dividing wall columns. *Computers and Chemical Engineering*, 125, 31–39. https://doi.org/10.1016/j.compchemeng.2019.03.006 + +""" + +from math import fabs + +import matplotlib.pyplot as plt +from pyomo.environ import * + +# from kaibel_solve_gdp import build_model +from gdplib.kaibel.kaibel_solve_gdp import build_model + + +def main(): + """ + This is the main function that executes the optimization process. + + It builds the model, fixes certain variables, sets initial values for tray existence or absence, + solves the model using the 'gdpopt' solver, and displays the results. + + Returns: + None + """ + m = build_model() + + # Fixing variables + m.F[1].fix(50) # feed flowrate in mol/s + m.F[2].fix(50) + m.F[3].fix(50) + m.F[4].fix(50) + m.q.fix( + m.q_init + ) # vapor fraction q_init from the feed set in the build_model function + m.dv[2].fix(0.394299) # vapor distributor in the feed section + + for sec in m.section: + for n_tray in m.tray: + m.P[sec, n_tray].fix(m.Preb) + + ## Initial values for the tray existence or absence + for n_tray in m.candidate_trays_main: + for sec in m.section_main: + m.tray_exists[sec, n_tray].indicator_var.set_value(1) + m.tray_absent[sec, n_tray].indicator_var.set_value(0) + for n_tray in m.candidate_trays_feed: + m.tray_exists[2, n_tray].indicator_var.set_value(1) + m.tray_absent[2, n_tray].indicator_var.set_value(0) + for n_tray in m.candidate_trays_product: + m.tray_exists[3, n_tray].indicator_var.set_value(1) + m.tray_absent[3, n_tray].indicator_var.set_value(0) + + intro_message(m) + + results = SolverFactory('gdpopt').solve( + m, + strategy='LOA', + tee=True, + time_limit=3600, + mip_solver='gams', + mip_solver_args=dict(solver='cplex'), + ) + + m.calc_nt = sum( + sum(m.tray_exists[sec, n_tray].indicator_var.value for n_tray in m.tray) + for sec in m.section + ) - sum(m.tray_exists[3, n_tray].indicator_var.value for n_tray in m.tray) + m.dw_start = ( + sum(m.tray_exists[1, n_tray].indicator_var.value for n_tray in m.tray) + 1 + ) + m.dw_end = sum( + m.tray_exists[1, n_tray].indicator_var.value for n_tray in m.tray + ) + sum(m.tray_exists[2, n_tray].indicator_var.value for n_tray in m.tray) + + display_results(m) + + print(' ', results) + print(' Solver Status: ', results.solver.status) + print(' Termination condition: ', results.solver.termination_condition) + + +def intro_message(m): + """ + Display the introduction message. + + + + """ + print( + """ + +If you use this model and/or initialization strategy, you may cite the following: +Rawlings, ES; Chen, Q; Grossmann, IE; Caballero, JA. Kaibel Column: Modeling, +optimization, and conceptual design of multi-product dividing wall columns. +Comp. and Chem. Eng., 2019, 125, 31-39. +DOI: https://doi.org/10.1016/j.compchemeng.2019.03.006 + + + """ + ) + + +def display_results(m): + """ + Display the results of the optimization process. + + Parameters + ---------- + m : Pyomo ConcreteModel + The Pyomo model object containing the results of the optimization process. + """ + print('') + print('Components:') + print('1 methanol') + print('2 ethanol') + print('3 butanol') + print('4 propanol') + print(' ') + print('Objective: %s' % value(m.obj)) + print('Trays: %s' % value(m.calc_nt)) + print('Dividing_wall_start: %s' % value(m.dw_start)) + print('Dividing_wall_end: %s' % value(m.dw_end)) + print(' ') + print( + 'Qreb: {: >3.0f}kW B_1: {: > 2.0f} B_2: {: >2.0f} B_3: {: >2.0f} B_4: {: >2.0f} Btotal: {: >2.0f}'.format( + value(m.Qreb / m.Qscale), + value(m.B[1]), + value(m.B[2]), + value(m.B[3]), + value(m.B[4]), + value(m.Btotal), + ) + ) + print( + 'Qcon: {: >2.0f}kW D_1: {: >2.0f} D_2: {: >2.0f} D_3: {: >2.0f} D_4: {: >2.0f} Dtotal: {: >2.0f}'.format( + value(m.Qcon / m.Qscale), + value(m.D[1]), + value(m.D[2]), + value(m.D[3]), + value(m.D[4]), + value(m.Dtotal), + ) + ) + print(' ') + print('Reflux: {: >3.4f}'.format(value(m.rr))) + print('Reboil: {: >3.4f} '.format(value(m.bu))) + print(' ') + print('Flowrates[mol/s]') + print( + 'F_1: {: > 3.0f} F_2: {: >2.0f} F_3: {: >2.0f} F_4: {: >2.0f} Ftotal: {: >2.0f}'.format( + value(m.F[1]), + value(m.F[2]), + value(m.F[3]), + value(m.F[4]), + sum(value(m.F[comp]) for comp in m.comp), + ) + ) + print( + 'S1_1: {: > 1.0f} S1_2: {: >2.0f} S1_3: {: >2.0f} S1_4: {: >2.0f} S1total: {: >2.0f}'.format( + value(m.S[1, 1]), + value(m.S[1, 2]), + value(m.S[1, 3]), + value(m.S[1, 4]), + sum(value(m.S[1, comp]) for comp in m.comp), + ) + ) + print( + 'S2_1: {: > 1.0f} S2_2: {: >2.0f} S2_3: {: >2.0f} S2_4: {: >2.0f} S2total: {: >2.0f}'.format( + value(m.S[2, 1]), + value(m.S[2, 2]), + value(m.S[2, 3]), + value(m.S[2, 4]), + sum(value(m.S[2, comp]) for comp in m.comp), + ) + ) + print(' ') + print('Distributors:') + print('dl[2]: {: >3.4f} dl[3]: {: >3.4f}'.format(value(m.dl[2]), value(m.dl[3]))) + print('dv[2]: {: >3.4f} dv[3]: {: >3.4f}'.format(value(m.dv[2]), value(m.dv[3]))) + print(' ') + print(' ') + print(' ') + print(' Kaibel Column Sections ') + print('__________________________________________') + print(' ') + print(' Tray Bottom Feed ') + print('__________________________________________') + for t in reversed(list(m.tray)): + print( + '[{: >2.0f}] {: >9.0g} {: >18.0g} F:{: >3.0f} '.format( + t, + ( + fabs(value(m.tray_exists[1, t].indicator_var)) + if t in m.candidate_trays_main + else 1 + ), + ( + fabs(value(m.tray_exists[2, t].indicator_var)) + if t in m.candidate_trays_feed + else 1 + ), + sum(value(m.F[comp]) for comp in m.comp) if t == m.feed_tray else 0, + ) + ) + print(' ') + print('__________________________________________') + print(' ') + print(' Product Top ') + print('__________________________________________') + for t in reversed(list(m.tray)): + print( + '[{: >2.0f}] {: >9.0g} S1:{: >2.0f} S2:{: >2.0f} {: >8.0g}'.format( + t, + ( + fabs(value(m.tray_exists[3, t].indicator_var)) + if t in m.candidate_trays_product + else 1 + ), + ( + sum(value(m.S[1, comp]) for comp in m.comp) + if t == m.sideout1_tray + else 0 + ), + ( + sum(value(m.S[2, comp]) for comp in m.comp) + if t == m.sideout2_tray + else 0 + ), + ( + fabs(value(m.tray_exists[4, t].indicator_var)) + if t in m.candidate_trays_main + else 1 + ), + ) + ) + print(' 1 = trays exists, 0 = absent tray') + + +if __name__ == "__main__": + main() diff --git a/gdplib/small_batch/README.md b/gdplib/small_batch/README.md new file mode 100644 index 0000000..837d76e --- /dev/null +++ b/gdplib/small_batch/README.md @@ -0,0 +1,15 @@ +## gdp_small_batch.py + +The gdp_small_batch.py module contains the GDP model for the small batch problem based on the Kocis and Grossmann (1988) paper. + +The problem is based on the Example 4 of the paper. + +The objective is to minimize the investment cost of the batch units. + +The solution is 167427.65711. + +### References + +[1] Kocis, G. R.; Grossmann, I. E. Global Optimization of Nonconvex Mixed-Integer Nonlinear Programming (MINLP) Problems in Process Synthesis. Ind. Eng. Chem. Res. 1988, 27 (8), 1407-1421. https://doi.org/10.1021/ie00080a013 + +[2] Ovalle, D., Liñán, D. A., Lee, A., Gómez, J. M., Ricardez-Sandoval, L., Grossmann, I. E., & Bernal Neira, D. E. (2024). Logic-Based Discrete-Steepest Descent: A Solution Method for Process Synthesis Generalized Disjunctive Programs. arXiv preprint arXiv:2405.05358. https://doi.org/10.48550/arXiv.2405.05358 diff --git a/gdplib/small_batch/gdp_small_batch.py b/gdplib/small_batch/gdp_small_batch.py new file mode 100644 index 0000000..b7d2b48 --- /dev/null +++ b/gdplib/small_batch/gdp_small_batch.py @@ -0,0 +1,435 @@ +""" +gdp_small_batch.py +The gdp_small_batch.py module contains the GDP model for the small batch problem based on the Kocis and Grossmann (1988) paper. +The problem is based on the Example 4 of the paper. +The objective is to minimize the investment cost of the batch units. + +References +---------- +[1] Kocis, G. R.; Grossmann, I. E. Global Optimization of Nonconvex Mixed-Integer Nonlinear Programming (MINLP) Problems in Process Synthesis. Ind. Eng. Chem. Res. 1988, 27 (8), 1407-1421. https://doi.org/10.1021/ie00080a013 +[2] Ovalle, D., Liñán, D. A., Lee, A., Gómez, J. M., Ricardez-Sandoval, L., Grossmann, I. E., & Bernal Neira, D. E. (2024). Logic-Based Discrete-Steepest Descent: A Solution Method for Process Synthesis Generalized Disjunctive Programs. arXiv preprint arXiv:2405.05358. https://doi.org/10.48550/arXiv.2405.05358 +""" + +import os +import pyomo.environ as pyo +from pyomo.core.base.misc import display +from pyomo.core.plugins.transform.logical_to_linear import ( + update_boolean_vars_from_binary, +) +from pyomo.gdp import Disjunct, Disjunction +from pyomo.opt.base.solvers import SolverFactory + + +def build_small_batch(): + """ + Build the GDP model for the small batch problem. + + Returns + ------- + m : Pyomo.ConcreteModel + The GDP model for the small batch problem is created. + + References + ---------- + [1] Kocis, G. R.; Grossmann, I. E. (1988). Global Optimization of Nonconvex Mixed-Integer Nonlinear Programming (MINLP) Problems in Process Synthesis. Ind. Eng. Chem. Res., 27(8), 1407-1421. https://doi.org/10.1021/ie00080a013 + [2] Ovalle, D., Liñán, D. A., Lee, A., Gómez, J. M., Ricardez-Sandoval, L., Grossmann, I. E., & Neira, D. E. B. (2024). Logic-Based Discrete-Steepest Descent: A Solution Method for Process Synthesis Generalized Disjunctive Programs. arXiv preprint arXiv:2405.05358. https://doi.org/10.48550/arXiv.2405.05358 + """ + NK = 3 + + # Model + m = pyo.ConcreteModel() + + # Sets + m.i = pyo.Set( + initialize=["a", "b"], doc="Set of products" + ) # Set of products, i = a, b + m.j = pyo.Set( + initialize=["mixer", "reactor", "centrifuge"] + ) # Set of stages, j = mixer, reactor, centrifuge + m.k = pyo.RangeSet( + NK, doc="Set of potential number of parallel units" + ) # Set of potential number of parallel units, k = 1, 2, 3 + + # Parameters and Scalars + + m.h = pyo.Param( + initialize=6000, doc="Horizon time [hr]" + ) # Horizon time (available time) [hr] + m.vlow = pyo.Param( + initialize=250, doc="Lower bound for size of batch unit [L]" + ) # Lower bound for size of batch unit [L] + m.vupp = pyo.Param( + initialize=2500, doc="Upper bound for size of batch unit [L]" + ) # Upper bound for size of batch unit [L] + + # Demand of product i + m.q = pyo.Param( + m.i, + initialize={"a": 200000, "b": 150000}, + doc="Production rate of the product [kg]", + ) + # Cost coefficient for batch units + m.alpha = pyo.Param( + m.j, + initialize={"mixer": 250, "reactor": 500, "centrifuge": 340}, + doc="Cost coefficient for batch units [$/L^beta*No. of units]]", + ) + # Cost exponent for batch units + m.beta = pyo.Param( + m.j, + initialize={"mixer": 0.6, "reactor": 0.6, "centrifuge": 0.6}, + doc="Cost exponent for batch units", + ) + + def coeff_init(m, k): + """ + Coefficient for number of parallel units. + + Parameters + ---------- + m : Pyomo.ConcreteModel + The small batch GDP model. + k : int + The number of parallel units. + + Returns + ------- + pyomo.Param + Coefficient for number of parallel units. logarithm of k is applied to convexify the model. + """ + return pyo.log(k) + + # Represent number of parallel units + m.coeff = pyo.Param( + m.k, initialize=coeff_init, doc="Coefficient for number of parallel units" + ) + + s_init = { + ("a", "mixer"): 2, + ("a", "reactor"): 3, + ("a", "centrifuge"): 4, + ("b", "mixer"): 4, + ("b", "reactor"): 6, + ("b", "centrifuge"): 3, + } + + # Size factor for product i in stage j [kg/L] + m.s = pyo.Param( + m.i, m.j, initialize=s_init, doc="Size factor for product i in stage j [kg/L]" + ) + + t_init = { + ("a", "mixer"): 8, + ("a", "reactor"): 20, + ("a", "centrifuge"): 4, + ("b", "mixer"): 10, + ("b", "reactor"): 12, + ("b", "centrifuge"): 3, + } + + # Processing time of product i in batch j [hr] + m.t = pyo.Param( + m.i, m.j, initialize=t_init, doc="Processing time of product i in batch j [hr]" + ) + + # Variables + m.Y = pyo.BooleanVar(m.k, m.j, doc="Stage existence") # Stage existence + m.coeffval = pyo.Var( + m.k, + m.j, + within=pyo.NonNegativeReals, + bounds=(0, pyo.log(NK)), + doc="Activation of Coefficient", + ) # Activation of coeff + m.v = pyo.Var( + m.j, + within=pyo.NonNegativeReals, + bounds=(pyo.log(m.vlow), pyo.log(m.vupp)), + doc="Colume of stage j [L]", + ) # Volume of stage j [L] + m.b = pyo.Var( + m.i, within=pyo.NonNegativeReals, doc="Batch size of product i [L]" + ) # Batch size of product i [L] + m.tl = pyo.Var( + m.i, within=pyo.NonNegativeReals, doc="Cycle time of product i [hr]" + ) # Cycle time of product i [hr] + # Number of units in parallel stage j + m.n = pyo.Var( + m.j, within=pyo.NonNegativeReals, doc="Number of units in parallel stage j" + ) + + # Constraints + + # Volume requirement in stage j + @m.Constraint(m.i, m.j) + def vol(m, i, j): + """ + Volume Requirement for Stage j. + Equation + -------- + v_j \geq log(s_ij) + b_i for i = a, b and j = mixer, reactor, centrifuge + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + i : str + Index of Product. + j : str + Stage. + + Returns + ------- + Pyomo.Constraint + A Pyomo constraint object representing the volume requirement for a given stage. + """ + return m.v[j] >= pyo.log(m.s[i, j]) + m.b[i] + + # Cycle time for each product i + @m.Constraint(m.i, m.j) + def cycle(m, i, j): + """ + Cycle time for each product i. + + Equation + -------- + n_j + tl_i \geq log(t_ij) for i = a, b and j = mixer, reactor, centrifuge + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + i : str + Index of Product. + j : str + Index of Stage. + + Returns + ------- + Pyomo.Constraint + A Pyomo constraint object representing the cycle time requirement for each product in each stage. + """ + return m.n[j] + m.tl[i] >= pyo.log(m.t[i, j]) + + # Constraint for production time + @m.Constraint() + def time(m): + """ + Production time constraint. + Equation: + sum_{i \in I} q_i * \exp(tl_i - b_i) \leq h + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + + Returns + ------- + Pyomo.Constraint + A Pyomo constraint object representing the production time constraint. + """ + return sum(m.q[i] * pyo.exp(m.tl[i] - m.b[i]) for i in m.i) <= m.h + + # Relating number of units to 0-1 variables + @m.Constraint(m.j) + def units(m, j): + """ + Relating number of units to 0-1 variables. + Equation: + n_j = sum_{k \in K} coeffval_{k,j} for j = mixer, reactor, centrifuge + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + j : str + Index of Stage. + + Returns + ------- + Pyomo.Constraint + A Pyomo constraint object representing the relationship between the number of units and the binary variables. + """ + return m.n[j] == sum(m.coeffval[k, j] for k in m.k) + + # Only one choice for parallel units is feasible + @m.LogicalConstraint(m.j) + def lim(m, j): + """ + Only one choice for parallel units is feasible. + Equation: + sum_{k \in K} Y_{k,j} = 1 for j = mixer, reactor, centrifuge + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + j : str + Index of Stage. + + Returns + ------- + Pyomo.LogicalConstraint + A Pyomo logical constraint ensuring only one choice for parallel units is feasible. + """ + return pyo.exactly(1, m.Y[1, j], m.Y[2, j], m.Y[3, j]) + + # _______ Disjunction_________ + + def build_existence_equations(disjunct, k, j): + """ + Build the Logic Disjunct Constraints (equation) for the existence of the stage. + + Parameters + ---------- + disjunct : Pyomo.Disjunct + Disjunct block for the existence of the stage. + k : int + Number of parallel units. + j : str + Index of Stage. + + Returns + ------- + None + None, the constraints are built inside the disjunct. + """ + m = disjunct.model() + + # Coefficient value activation + @disjunct.Constraint() + def coeffval_act(disjunct): + """ + Coefficien value activation. + + Equation + -------- + m.coeffval[k,j] = m.coeff[k] = log(k) + + Parameters + ---------- + disjunct : Pyomo.Disjunct + Disjunct block for the existence of the stage. + + Returns + ------- + Pyomo.Constraint + A Pyomo constraint object representing the activation of the coefficient value. + """ + return m.coeffval[k, j] == m.coeff[k] + + def build_not_existence_equations(disjunct, k, j): + """ + Build the Logic Disjunct Constraints (equations) for the absence of the stage. + + Parameters + ---------- + disjunct : Pyomo.Disjunct + Disjunct block for the absence of the stage. + k : int + Number of parallel units. + j : str + Index of Stage. + + Returns + ------- + None + None, the constraints are built inside the disjunct.. + """ + m = disjunct.model() + + # Coefficient value deactivation + @disjunct.Constraint() + def coeffval_deact(disjunct): + """ + Coefficient value deactivation. + + Equation + -------- + m.coeffval[k,j] = 0 + + Parameters + ---------- + disjunct : Pyomo.Disjunct + Disjunct block for the absence of the stage. + + Returns + ------- + Pyomo.Constraint + A Pyomo constraint object representing the deactivation of the coefficient value. + """ + return m.coeffval[k, j] == 0 + + # Create disjunction block + m.Y_exists = Disjunct( + m.k, m.j, rule=build_existence_equations, doc="Existence of the stage" + ) + m.Y_not_exists = Disjunct( + m.k, m.j, rule=build_not_existence_equations, doc="Absence of the stage" + ) + + # Create disjunction + + @m.Disjunction(m.k, m.j) + def Y_exists_or_not(m, k, j): + """ + Build the Logical Disjunctions of the GDP model for the small batch problem. + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + k : int + Number of parallel units. + j : str + Index of Stage. + + Returns + ------- + list + List of disjuncts. The disjunction is between the existence and absence of the stage. + """ + return [m.Y_exists[k, j], m.Y_not_exists[k, j]] + + # Associate Boolean variables with with disjunction + for k in m.k: + for j in m.j: + m.Y[k, j].associate_binary_var(m.Y_exists[k, j].indicator_var) + + # ____________________________ + + # Objective + def obj_rule(m): + """ + Objective: minimize the investment cost [$]. + + Equation + -------- + min z = sum(alpha[j] * exp(n[j] + beta[j]*v[j])) for j = mixer, reactor, centrifuge + + Parameters + ---------- + m : pyomo.ConcreteModel + The small batch GDP model. + + Returns + ------- + Pyomo.Objective + Objective function to minimize the investment cost [$]. + """ + return sum(m.alpha[j] * (pyo.exp(m.n[j] + m.beta[j] * m.v[j])) for j in m.j) + + m.obj = pyo.Objective(rule=obj_rule, sense=pyo.minimize) + + return m + + +if __name__ == "__main__": + m = build_small_batch() + pyo.TransformationFactory("core.logical_to_linear").apply_to(m) + pyo.TransformationFactory("gdp.bigm").apply_to(m) + pyo.SolverFactory("gams").solve( + m, solver="baron", tee=True, add_options=["option optcr=1e-6;"] + ) + display(m)