Python Gekko 流程图对象中有哪些方程？

Question

What are the equations and other details of the built-in Python Gekko flowsheet objects such as the reactor model? Gekko has the compounds that I need for an industrial application of nonlinear Model Predictive Control (MPC) to a gas-phase fluidized-bed polymer (polyethylene) reactor.

from gekko import GEKKO, chemical
m = GEKKO(remote=False)
c = chemical.Properties(m)
c.compound('ethylene')    # primary monomer reactant
c.compound('propylene')   # co-polymer monomer reactant
c.compound('hydrogen')    # melt-index modifier
c.compound('ethane')      # inert
c.compound('propane')     # inert
c.compound('cyclohexene') # density modifier
c.compound('isopentane')  # condensing agent
c.compound('nitrogen')    # pressure control
f = chemical.Flowsheet(m)
r = f.reactor(ni=2)
m.options.SOLVER = 1
m.solve()

This simple reactor model produces the following output:

 --------- APM Model Size ------------
 Each time step contains
   Objects      :  1
   Constants    :  0
   Variables    :  12
   Intermediates:  0
   Connections  :  12
   Equations    :  0
   Residuals    :  0

 Number of state variables:    29
 Number of total equations: -  10
 Number of slack variables: -  0
 ---------------------------------------
 Degrees of freedom       :    19

 ----------------------------------------------
 Steady State Optimization with APOPT Solver
 ----------------------------------------------

 Iter    Objective  Convergence
    0  2.55529E-16  1.38889E+00
    1  2.38753E-25  1.23358E-16
    2  2.38753E-25  1.23358E-16
 Successful solution

 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :  0.026300000000000004 sec
 Objective      :  0.
 Successful solution
 ---------------------------------------------------

How can I find more details about the 10 equations and 29 variables? I am interested in property control (melt index and density) and maximize production rate by adjusting catalyst, hydrogen, and co-monomer (propylene, iso-butene, etc).

Answer 1

Gekko outputs a LaTeX file rto_4_latex.tex (or {mode}_4_latex.tex} for other modes ) with the model details about equations and variables when you set m.options.DIAGLEVEL to 4 or higher.

from gekko import GEKKO, chemical
m = GEKKO(remote=False)
c = chemical.Properties(m)
c.compound('ethylene')    # primary monomer reactant
c.compound('propylene')   # co-polymer monomer reactant
c.compound('hydrogen')    # melt-index modifier
c.compound('ethane')      # inert
c.compound('propane')     # inert
c.compound('cyclohexene') # density modifier
c.compound('isopentane')  # condensing agent
c.compound('nitrogen')    # pressure control
f = chemical.Flowsheet(m)
r = f.reactor(ni=2)
m.options.SOLVER = 1
m.options.DIAGLEVEL = 4
m.solve()
m.open_folder()

You can also see more information in the many files that it produces when you solve locally with remote=False and open the run directory with m.open_folder() .

\documentclass[8pt]{article}
\begin{document}
\title{Model Title}
\author{John D. Hedengren}
\maketitle
\section{equations}

\subsection{Equation 1 }
\texttt{ ss.reactor1.overall\_mole\_balance }
\begin{equation}
0 = {\dot n}_{in} + {\dot r}_{gen} - {\dot n}_{out} - \frac{\partial n}{\partial t}
\end{equation}
Variables
\begin{enumerate}
\item \texttt{ 0.60000E+00 kmol/sec    ss.reactor1.inlet[1].ndot * 2}
\item \texttt{ 0.60000E+00 kmol/sec    ss.reactor1.inlet[2].ndot * 11}
\item \texttt{ 0.12000E+01 kmol/sec    ss.reactor1.outlet.ndot * 19}
\item \texttt{ 0.00000E+00 kmol/sec    ss.v1 * 29}
\end{enumerate}

You can get a PDF document if you compile the LaTeX document with call pdflatex main if you are in Windows and have downloaded texlive . Otherwise, you could put it into the online OverLeaf editor to convert to a PDF. Here are the first two equations of the 7 page document that is created.