ALGORITHMIC FLOWSHEET GENERATION
A series of executable codes is provided in this section
so that users can follow the implementation of an algorithmic method for flowsheet
synthesis, i.e., process-network synthesis (PNS), based on process graphs
(P-graphs) on a computer. The demonstration program for each algorithm of
this method is provided in the website.
Fundamentals of Algorithmic Process-Network
Synthesis
The framework of the method, as depicted in Figure 4-8
of the text, is reproduced below:
Figure 4-8. Major steps for the algorithmic process-network
synthesis based on graph theory.
Application of Algorithmic Process-Network Synthesis
to Vinyl Chloride Production
The steps in Figure 4-8 can be demonstrated with the
executable codes provided by applying them to corresponding steps of flowsheet
synthesis for the manufacture of vinyl chloride according to the so-called
balanced process described in the text.
The balanced process for vinyl-chloride synthesis involves
three reactions r1, r2 and r3, which collectively
lead to the overall reaction.
Reaction-Network Synthesis
In the first major step, feasible reaction networks are synthesized as the
precursors to process networks. This first major step comprises three
substeps. The maximal reaction network is synthesized in the first of these
three substeps.
Generation of the Maximal Structure Corresponding
to the Maximal Reaction Network with Algorithm MSG
The maximal-reaction network is synthesized by means
of algorithm MSG. The information necessary for preparing the inputs
is specified in conjunction with the problem definition and Figure 4-10 in
the text. Figure WA-1 illustrates the flowchart for executing algorithm MSG
to generate the maximal reaction network of the balanced process for synthesizing
vinyl chloride. What follows describe the procedure.
Figure WA-1. Flowchart for algorithm MSG as applied to the generation of
the maximal reaction network of the balanced process for vinyl-chloride synthesis.
Demonstration programs for algorithm MSG
Two implementations of algorithm MSG can be downloaded, the
Command-line implementation of algorithm MSG
A command-line implementation of algorithm MSG can be
downloaded
here. The input
to this program is a plain text
file including the formal definition of the synthesis problem. This input
file can be created by any plain text-editor, e.g., Microsoft Notepad. Other
examples together with the
demonstration programs are available in
www.p-graph.com.
The file has a clear hierarchical structure defined as follows:
At the highest level, a list of objects separated by
commas is established; these objects may have attributes. If an object defined
in this formal language has a single attribute, it is followed by a colon
and the attribute. If the object has multiple attributes, the colon is followed
by curly braces. In each of the braces, the attribute is separated by a comma.
Any attribute can be regarded as an object and may also have its own attributes.
For the problem of concern, keyword “pns_problem” is
at the highest level, i.e., level one, indicating that a synthesis problem
is defined. The set of materials (reactants, or reacting species, for reaction-network
synthesis, i.e., rns) and operating units, (individual reactions, or reaction
steps, for rns) are at the second level as the attributes of the “pns_problem”
at level one. A list of materials’ names defines the set of materials, each
of which can be a desired product (final reaction product for rns) or raw
material (starting reactant for rns) indicated by keywords “product” and
“raw” as attributes of the material (reacting species for rns). The operating
units (reactions steps for rns) are defined by the list of their input and
output materials’ names. Note that letters, numbers, plus and minus signs,
stars, and underscores, are allowed in names, e.g., O2-, Cl-, H+, hydrogen_chloride,
CH3*. The input to the executable code for algorithm MSG for reaction-network
synthesis (rns) is given in the following.
Input for implementation of algorithm MSG (file rns.in):
pns_problem :
{
materials :
{
C2H4 : raw,
Cl2 : raw,
O2 : raw,
C2H3Cl : product,
H2O,
C2H4Cl2,
HCl
},
operating_units :
{
r1 : {
input : {
C2H4,
Cl2
},
output : {
C2H4Cl2
}
},
r2 : {
input : {
C2H4,
HCl,
O2
},
output : {
C2H4Cl2,
H2O
}
},
r3 : {
input : {
C2H4Cl2
},
output : {
C2H3Cl,
HCl
}
}
}
}
The program can be executed in a command prompt by entering
its name, i.e., pns, followed by MSG and the names of the input file and the
output file, i.e., rns.in rnsmsg.out. Thus,
The parameters are separated by spaces.
The output from the program is the synthesis problem
given in the input and the list of materials (reacting species) and operating
units (reactions) included in the maximal structure representing the maximal
reaction network shown in step 5 of Figure 4-12 in the text. Note that the
input structure containing all the input information in the form of P-graphs
as given in Figure 4-11 is internally generated. The output from the executable
code for algorithm MSG for reaction-network synthesis is given in the following.
Output from the implementation of algorithm MSG (file rnsmsg.out):
#rns.in
pns_problem :
{
materials :
{
C2H4 : raw,
Cl2 : raw,
O2 : raw,
C2H3Cl : product,
H2O,
C2H4Cl2,
HCl
},
operating_units :
{
r1 :
{
input :
{
C2H4,
Cl2
},
output : C2H4Cl2
},
r2 :
{
input :
{
C2H4,
HCl,
O2
},
output :
{
C2H4Cl2,
H2O
}
},
r3 :
{
input : C2H4Cl2,
output :
{
C2H3Cl,
HCl
}
}
}
},
#output
maximal_structure :
{
materials :
{
C2H4,
Cl2,
O2,
C2H3Cl,
H2O,
C2H4Cl2,
HCl
},
operating_units :
{
r1,
r2,
r3
}
}
As noted earlier, the output manifests itself as the
maximal reaction network for vinyl-chloride synthesis according to the balanced
process as given in step 5 on Figure 4-12 of the text.
Implementation of algorithm MSG with graphical user
interface
A graphical user interface is also
downloadable for manipulating a PNS problem and
calling combinatorial algorithms, e.g., algorithms MSG and SSG. It is termed
Combinatorial PNS Editor; the main window
of this editor is divided into two parts; see Figure WA-1a.
Figure WA-1a
The upper part lists materials (starting reactants, final
reaction products, and intermediates or reacting species, for reaction-network
synthesis, i.e., rns) and the bottom part lists operating units (individual
reaction steps for rns) defining a PNS problem. A material can be added to
the list of materials by pressing button Add on the right-hand side of the
list. A small window titled Material properties appears; see Figure WA-1b.
Figure WA-1b
After entering the name of the material and selecting
whether it is a raw material (a starting reactant for rns), product (a final
reaction product for rns), or neither, the material can be added to the problem
by pressing button OK; see Figure WA-1c.
Figure WA-1c
The name and type of the material appears in the list
of materials. All of the remaining materials can be defined similarly.
After having a list of materials the operating units
can be added to the PNS problem being considered by pressing button Add..
on the right hand side of the list of operating units in the main window shown
in Figure WA-1a. A window titled Operating unit properties appears; see
Figure WA-1d.
Figure WA-1d
After entering the name of the operating unit (individual
reaction step for rns) its input and output materials (reactants and products
of an individual reaction step for rns) can be given one-by-one by selecting
them in the list of materials on the right-hand side and pressing button <<
Add on the right-hand side of the lists of input and output materials labeled
by Input and Output; see Figure WA-1e.
Figure WA-1e
When the name of an operating unit (individual reaction
step for rns) and all of its input and output materials (reactants and products
of individual reaction step for rns) are given, the operating unit can be
added to the problem by pressing OK in the window; see Figure WA-1e.
All of the remaining operating units can be defined similarly. At this stage,
the problem is ready to be solved but it should be saved first by selecting
menu item File/Save in the main window; see Figure WA-1f.
Figure WA-1f
Then, a filename, e.g., rns.in, is entered and Save
is pressed in the window; see Figure WA-1g.
Figure WA-1g
As a result, the name of the problem appears in the title
bar of the main window; see Figure WA-1h.
Figure WA-1h
To call algorithm MSG, menu item Generate/MSG is selected; see Figure WA-1i.
Figure WA-1i
Subsequently, the graphical interface calls the command
line program, pns. The output from this program is converted into an easy-to-read
format containing the lists of materials (reactants and products of individual
reaction steps for rns) and operating units included in the maximal-structure,
which appear in the succeeding window; see Figure WA-1j.
Figure WA-1j
Generation of the Solution-Structure Corresponding
to the Combinatorially Feasible Reaction Networks with Algorithm SSG
The combinatorially feasible reaction networks, i.e.,
synthetic routes, for vinyl-chloride synthesis are generated by algorithm
SSG with the aforementioned maximal reaction network in Figure 4-12 of the
text as its input. The implementation of algorithm SSG for reaction-network
synthesis (rns) is diagrammatically illustrated in Tables 4-2a through 4-2c
of the text. Figure WA-2 shows the flowchart for executing this algorithm
on a computer.
Figure WA-2. Flowchart for algorithm SSG as applied to
the generation of the combinatorially feasible reaction networks of the balanced
process for vinyl-chloride synthesis.
Algorithm SSG for reaction-network synthesis (rns) can be executed by the
same program as that for algorithm MSG for reaction-network synthesis (rns)
by entering the SSG instead of MSG as indicated below.
The output from executing algorithm SSG for reaction-network
synthesis (rns), as given in the following, contains three sets of materials
(reacting species) and operating units (reactions) representing the three
solution structures (combinatorially feasible reaction networks) illustrated
in Figure 4-14 of the text.
Output from the implementation of algorithm SSG (file rnsssg.out):
#rns.in
pns_problem :
{
materials :
{
C2H4 : raw,
Cl2 : raw,
O2 : raw,
C2H3Cl : product,
H2O,
C2H4Cl2,
HCl
},
operating_units :
{
r1 :
{
input :
{
C2H4,
Cl2
},
output : C2H4Cl2
},
r2 :
{
input :
{
C2H4,
HCl,
O2
},
output :
{
C2H4Cl2,
H2O
}
},
r3 :
{
input : C2H4Cl2,
output :
{
C2H3Cl,
HCl
}
}
}
},
#output
solution_structures :
{
1 :
{
materials :
{
C2H4,
Cl2,
C2H3Cl,
C2H4Cl2,
HCl
},
operating_units :
{
r1,
r3
}
},
2 :
{
materials :
{
C2H4,
O2,
C2H3Cl,
H2O,
C2H4Cl2,
HCl
},
operating_units :
{
r2,
r3
}
},
3 :
{
materials :
{
C2H4,
Cl2,
O2,
C2H3Cl,
H2O,
C2H4Cl2,
HCl
},
operating_units :
{
r1,
r2,
r3
}
}
}
As mentioned earlier, this output manifests itself as
the three combinatorially feasible reaction networks for vinyl-chloride synthesis
according to the balanced process as given in Figure 4-14 of the text.
Identification of the Feasible Reaction Network
Among the Combinatorially Feasible Ones by Linear Programming
The feasible reaction networks (synthetic routes) are
to be determined among the three combinatorially feasible networks.
As described in the text, this is accomplished by minimizing the sum of the
unknown multipliers for individual reactions in each of the three combinatorially
feasible reaction networks by means of linear programming (LP), specifically
integer linear programming (ILP). The results indicate that only network
(c) in Figure 4-14 of the text yields the solution, thus indicating that it
is the only feasible reaction network (synthetic route).
Process-Network Synthesis
The resultant feasible reaction network guides the initial
selection of major operating units, which are reacting units. Each of these
reacting units is followed by a separating unit.
Identification of the Plausible Operating Units
The initially selected operating units in conjunction
with additional technical information available makes it possible to identify
all plausible operating units whose P-graph representations are given in Figure
4-19 of the text. These operating units are designated as R1, R2,
R3, S1, S2, S3and M1.
Thus, process-network synthesis (pns) can now proceed as indicated in the
second major block in Figure 4-8.
Generation of the Maximal Structure with Algorithm
MSG
Figure WA-3 illustrates the flowchart for executing algorithm
MSG for process-network synthesis to generate the maximal structure of the
balanced process for vinyl-chloride synthesis. The procedure to execute this
algorithm is identical to that for generating the maximal-reaction network,
as shown in Figure WA-1, except that the input given in the following specifically
indicates that it is for generating the maximal structure for process-network.
Figure WA-3. Flowchart for algorithm MSG as applied to
the generation of the maximal structure of the balanced process for vinyl-chloride
synthesis.
The program can be executed in a command prompt by entering
its name, i.e., pns, followed by MSG and the names of the input file and the
output file, i.e., pns.in and pnsmsg.out; thus,
The parameters are separated by spaces. What follows
is the input to executable code for algorithm MSG for process-network synthesis.
Input for the implementation of algorithm MSG (file pns.in):
pns_problem :
{
materials :
{
S01 : raw,
S02 : raw,
S03 : raw,
S04,
S05,
S06,
S07,
S08,
S09,
S10,
S11,
S12,
S13,
S14 : product
},
operating_units :
{
R-1 : {
input : {
S01,
S02
},
output : {
S04
}
},
R-2 : {
input : {
S02,
S03,
S12
},
output : {
S05
}
},
R-3 : {
input : {
S10
},
output : {
S11
}
},
S-1 : {
input : {
S08
},
output : {
S09,
S10
}
},
S-2 : {
input : {
S05
},
output : {
S06,
S07
}
},
S-3 : {
input : {
S11
},
output : {
S12,
S13,
S14
}
},
M-1 : {
input : {
S04,
S06,
S13
},
output : {
S08
}
}
}
}
The output from the program is the synthesis problem
given in the input as well as the list of materials and operating units included
in the maximal structure shown in Figure 4-6 of the text. The output from
the executable code for algorithm MSG for process-network synthesis (pns)
is given in the following.
Output from the implementation of algorithm MSG (file pnsmsg.out):
#pns.in
pns_problem :
{
materials :
{
S01 : raw,
S02 : raw,
S03 : raw,
S04,
S05,
S06,
S07,
S08,
S09,
S10,
S11,
S12,
S13,
S14 : product
},
operating_units :
{
R-1 :
{
input :
{
S01,
S02
},
output : S04
},
R-2 :
{
input :
{
S02,
S03,
S12
},
output : S05
},
R-3 :
{
input : S10,
output : S11
},
S-1 :
{
input : S08,
output :
{
S09,
S10
}
},
S-2 :
{
input : S05,
output :
{
S06,
S07
}
},
S-3 :
{
input : S11,
output :
{
S12,
S13,
S14
}
},
M-1 :
{
input :
{
S04,
S06,
S13
},
output : S08
}
}
},
#output
maximal_structure :
{
materials :
{
S01,
S02,
S03,
S04,
S05,
S06,
S07,
S08,
S09,
S10,
S11,
S12,
S13,
S14
},
operating_units :
{
R-1,
R-2,
R-3,
S-1,
S-2,
S-3,
M-1
}
}
Generation of the Solution-Structure Corresponding
to the Cominatorially Feasible Process Networks with Algorithm SSG
The combinatorially feasible process networks, i.e.,
flowsheets, for vinyl-chloride synthesis, are generated by algorithm SSG with
the aforementioned maximal structure in Figure 4-16 of the text as its input.
The implementation of algorithm SSG for process-network synthesis (pns) is
diagrammatically illustrated in Table 4-4 of the text. Figure WA-4 illustrates
the flowchart for executing this algorithm on a computer.
Figure WA-4. Flowchart for algorithm SSG as applied to
the generation of the solution structures (combinatorially feasible flowsheets)
of the balanced process for vinyl-chloride synthesis.
Algorithm SSG for process-network synthesis (pns) can
be executed by the same program as that for algorithm MSG for pns by selecting
SSG instead of MSG as indicated below.
The output from executing algorithm SSG for process-network
synthesis (pns) as given in the following contains one set of materials and
operating units representing the single solution structure (cominatorially
feasible process network, i.e., flowsheet) illustrated in Figure 4-18 of the
text.
Output from the implementation of algorithm SSG (file pnsssg.out):
#pns.in
pns_problem :
{
materials :
{
S01 : raw,
S02 : raw,
S03 : raw,
S04,
S05,
S06,
S07,
S08,
S09,
S10,
S11,
S12,
S13,
S14 : product
},
operating_units :
{
R-1 :
{
input :
{
S01,
S02
},
output : S04
},
R-2 :
{
input :
{
S02,
S03,
S12
},
output : S05
},
R-3 :
{
input : S10,
output : S11
},
S-1 :
{
input : S08,
output :
{
S09,
S10
}
},
S-2 :
{
input : S05,
output :
{
S06,
S07
}
},
S-3 :
{
input : S11,
output :
{
S12,
S13,
S14
}
},
M-1 :
{
input :
{
S04,
S06,
S13
},
output : S08
}
}
},
#output
solution_structures : 1 :
{
materials :
{
S01,
S02,
S03,
S04,
S05,
S06,
S07,
S08,
S09,
S10,
S11,
S12,
S13,
S14
},
operating_units :
{
R-1,
R-2,
R-3,
S-1,
S-2,
S-3,
M-1
}
}
As indicated earlier, the output manifests itself as
the only combinatorially feasible process network (flowsheet) for vinyl-chloride
synthesis according to the balanced process as given in Figure 4-18 of the
text. Naturally, this combinatorially feasible flowsheet is expected to be
the feasible flowsheet as can be verified through the material balances.
No demonstration programs are provided here for size
and cost estimation of individual operating units or for the optimization
of the objective function in terms of the annualized cost according to Eq.
(4-2). These are subjects treated elsewhere in the text.
An
additional example
for vinyl-chloride synthesis is given in
www.p-graph.com linked to this website
to demonstrate process-network synthesis when the production of HCl is allowed. Readers
can also carry out the flowsheet synthesis of a process with the executable
code of the demonstration program given in
this
website as long as the synthesis does not involve more than 15 operating
units. A wealth of information on P-graphs and their applications is contained
in the latter website which will eventually include P-graph based treatment
of some of the other topics covered in the text.
