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of Combinatorial Analysis to Flowsheet Synthesis of Chemical PlantsMr. Lee R. Partin, P.E. Copyright 1994-2000 L R Partin Enterprises All Rights Reserved http://users.chartertn.net/lpartin

This worksheet demonstrates the use of Maple to generate Microsoft Visio flowsheets of a chemical plantThe following Maple techniques are highlighted:Developing custom functionsCreating a a flowVisualizing the flowExporting to a Visio diagram

The task is to synthesize chemical plant flowsheets to make specified products. The method requires a toolkit of information about the synthesis problem. The toolkit includes:a set of available raw materialsa set of required productsby-product specificationsa set of unit operation functions that convert inlet materials into outlet materialsThe first step is to determine the maximal structure which is the set of unit operation functions from the toolkit that assist in making the required products. Then, the maximal structure is analyzed for all feasible flowsheets.Ethanol - water mixtures can be separated using toluene in a distillation process. The following example shows the synthesis of feasible flowsheets for the process. A triangular composition diagram was prepared to show several potential unit operations for the process. The feed is located at point F. The desired products are pure ethanol (E) and pure water (W). Toluene (T) is a potential extraction agent for breaking the ethanol-water azeotrope.The defined unit operation functions are: 1) Mixing: F+T = A, F+B = J, K+G = L, D+G = O, K+C = M 2) Decanting: A -> B+C, H -> B+C 3) Distillation: B -> D+W, J -> K+W, L -> E+H, O -> E+H, M -> E+H, C -> G+TNote that materials are given names. A unit operation function is defined by its set of feed materials and its set of product materials. [{F,T},{A}] defines the first mixer.If you wish to read about the technology, here are some good references:F. Friedler, K. Tarjan, Y. W. Huang, and L. T. Fan, "Graph-Theoretic Approach to Process Synthesis: Polynomial Algorithm For Maximal Structure Generation," Computer Chem. Engng., Vol. 17, No. 9, 929-942, 1993.F. Friedler, K. Tarjan, Y. W. Huang, and L. T. Fan, "Combinatorial Algorithms for Process Synthesis," European Symposium on Computer Aided Process Engineering - 1, ESCAPE-1, May 24-28, 1992, S313-S320.F. Friedler, J. B. Varga and L. T. Fan, "Decision-Mapping for Design and Synthesis of Chemical Processes: Application to Reactor-Network Synthesis," Foundations of Computer Aided Process Design - 1994.

restart: interface( warnlevel=0 ): with( networks ): with( combinat ):

# Define the method for Psi- evaluation, Psi_minus:=proc(OpSet) local i, solution; solution:={}; for i from 1 to nops(OpSet) do solution:=solution union op(1,op(i,OpSet)) od; solution; end: # Define the method for Psi+ evaluation, Psi_plus:=proc(OpSet) local i, solution; solution:={}; for i from 1 to nops(OpSet) do solution:=solution union op(2,op(i,OpSet)) od; solution; end: # Define the method for phi- evaluation, phi_minus:=proc(mSet,OpSet) local i, solution, item; solution:={}; for i from 1 to nops(OpSet) do item:={op(i,OpSet)}; if (op(2,op(1,item)) intersect mSet) <> {} then solution:=solution union item fi; od; solution; end: # Define the method for phi+ evaluation, phi_plus:=proc(mSet,OpSet) local i, solution, item; solution:={}; for i from 1 to nops(OpSet) do item:={op(i,OpSet)}; if (op(1,op(1,item)) intersect mSet) <> {} then solution:=solution union item fi; od; solution; end: # Program MSG algorithm, MSG:=proc(OpSet,RM,Pr) local i, item, opset, Mat, o, r, p, m, ox; opset:=OpSet minus phi_minus(RM,OpSet); Mat:=Psi_minus(opset) union Psi_plus(opset); r:=Psi_minus(opset) minus (Psi_plus(opset) union RM); if nops(r) > 0 then while r <> {} do item:={op(1,r)}; Mat:=Mat minus item; o:=phi_plus(item,opset); opset:=opset minus o; r:=(r union (Psi_plus(o) minus Psi_plus(opset))) minus item; od; fi; if (Pr union Mat) <> Mat then lprint(`Error: No maximal structure exists!`); RETURN(`No maximal structure exists!`); fi; p:=Pr; m:={}; o:={}; while p <> {} do item:={op(1,p)}; m:=m union item; ox:=phi_minus(item,opset); o:=o union ox; p:=(p union Psi_minus(ox)) minus (RM union m); od; m:=Psi_minus(o) union Psi_plus(o); [m,o]; end: # Convert the Pgraph structure into a network, graph_network:=proc(Structure,naming) local i, j, rm, pr, mid, m, mat_order, listing, opset, Gr, mat_ins, mat_outs, el, unitnum, inset, outset, inset2, outset2, unit_order, unit_order2, unitname, location; global Raw_Materials, Products, OpData, LabelsList; m:=op(1,Structure); opset:=op(2,Structure); # check for material inlets and outlets of the structure mat_ins:=Psi_minus(opset); mat_outs:=Psi_plus(opset); # find all raw materials (they are only inlets to unit ops) rm:={}; # find all products (they are only outlets of unit ops) pr:={}; for el in m do if member(el,mat_ins) and member(el,mat_outs) = false then rm:=rm union {el} fi; if member(el,mat_ins) = false and member(el,mat_outs) then pr:=pr union {el} fi; od; mid:=m minus rm minus pr; mat_order:=[op(pr)],[op(mid)],[op(rm)]; # get labels from OpData information j:=0; for el in opset do j:=j+1; inset:=op(1,el); outset:=op(2,el); for i from 1 to nops(OpData) do inset2:={op(op(2,op(i,OpData)))}; outset2:={op(op(3,op(i,OpData)))}; if inset = inset2 and outset = outset2 then break fi; od; unitname:=op(1,op(i,OpData)); member(unitname,LabelsList,'location'); unitnum[j]:=location; od; unit_order:={}; if (naming = 'numbers') then unit_order:=[seq(unitnum[j],j=1..nops(opset))]; else unit_order:=[seq(cat(`:`,op(unitnum[j],LabelsList)), j=1..nops(opset))] fi; unit_order2:=convert(convert(unit_order,set),list); listing:=mat_order,unit_order2; new(Gr); addvertex(op(1,Structure),Gr); addvertex(unit_order,Gr); for i from 1 to nops(opset) do connect(op(1,op(i,opset)),[op(i,unit_order)],directed,Gr); connect([op(i,unit_order)],op(2,op(i,opset)),directed,Gr); od; Linear(listing),Gr; end: # Program SSG algorithm, SSG:=proc(by_prod) local mats, e, maps; global ox_vals, decision_map, by_prods, Op, Products; by_prods:=by_prod; mats:=Psi_minus(Op) union Psi_plus(Op); ox_vals:=table(); for e in mats do ox_vals[{e}]:=phi_minus({e},Op); od; SSGmethod(Products,{},{}); maps:=nops(decision_map); `# of decision maps found = `||maps end: SSGmethod:=proc(p,m,delta_m) local i, j, k, item_x, set_c, testing, item_c, item_y, ox, oy, delta_y, delta_m2, p2, m2, op_y, mat_outs, mat_ins, opmat, pr, el; global Raw_Materials, Products, Op, decision_map, ox_vals, by_prods; if nops(p) = 0 then if by_prods = true then # by-products are allowed; accept the solution decision_map:=decision_map union {delta_m} elif by_prods = false then # accept a solution if no by-products are present # check for material inlets and outlets of the decision map opmat:={seq(op(op(2,op(k,delta_m))),k=1..nops(delta_m))}; mat_ins:=Psi_minus(opmat); mat_outs:=Psi_plus(opmat); # subtract the raw materials and products mat_ins:=mat_ins minus Raw_Materials minus Products; mat_outs:=mat_outs minus Raw_Materials minus Products; # for a valid mapping, the intermediate materials must be both # inlet and outlet materials if ( (mat_ins minus mat_outs) = {} and (mat_outs minus mat_ins) = {} ) then decision_map:=decision_map union {delta_m}; fi; else # accept the solution if the by-products are within the input set # of allowed by-products. # check for material inlets and outlets of the structure opmat:={seq(op(op(2,op(k,delta_m))),k=1..nops(delta_m))}; mat_ins:=Psi_minus(opmat); mat_outs:=Psi_plus(opmat); # find all products (they are only outlets of unit ops) pr:={}; for el in (mat_ins union mat_outs) do if member(el,mat_ins) = false and member(el,mat_outs) then pr:=pr union {el} fi; od; # test that the by-products are contained in the by_prods set. # accept the solution if true. if ((pr minus Products) minus by_prods) = {} then decision_map:=decision_map union {delta_m} fi; fi; if (nops(decision_map) mod 100) = 0 and nops(decision_map) > 0 then lprint(nops(decision_map), ` decision maps found so far`) fi; RETURN(0); fi; item_x:={op(1,p)}; ox:=ox_vals[item_x]; set_c:=choose(ox) minus {{}}; for i from 1 to nops(set_c) do item_c:=op(i,set_c); testing:=0; for j from 1 to nops(m) do item_y:={op(j,m)}; oy:=ox_vals[item_y]; delta_y:={}; if nops(delta_m) > 0 then op_y:={seq(op(op(2,op(k,delta_m))),k=1..nops(delta_m))}; delta_y:=phi_minus(item_y,op_y); fi; if (item_c intersect (oy minus delta_y)) <> {} or ((ox minus item_c) intersect delta_y) <> {} then testing:=1; break; fi; od; if testing = 1 then next fi; delta_m2:=delta_m union {[item_x,item_c]}; p2:=p; for j from 1 to nops(item_c) do p2:=p2 union op(1,op(j,item_c)) od; p2:=p2 minus (Raw_Materials union m union item_x); m2:=m union item_x; SSGmethod(p2, m2, delta_m2); od; end: # Convert a decision mapping into a P graph, Pgraph:=proc(delta_m) local k, m, o; o:={seq(op(op(2,op(k,delta_m))),k=1..nops(delta_m))}; m:=Psi_minus(o) union Psi_plus(o); [m,o]; end: # updating the draw package to show different colors on the graph `draw/Linear`:= proc(partitions::specfunc(list,Linear),G::GRAPH, origin::list(numeric),xrng::name,yrng::name) local e,max_x,middle,n,nx,part,shift,t1,text,pos,x,y, t,vset,lines,points,i,j,v,center, a,b,c,d,a1,a2,a3,angle,dist; #** add new local vars options `Copyright 1993 by Waterloo Maple Software`; center := [origin[1 .. 2]]; vset := {}; n := 0; part := table(); shift := table(); for t in partitions do n := n+1; if not type(t,list) then ERROR(`partition should be a list`) fi; shift[n] := 0; t1 := select( hastype,t,'identical'('offset') = numeric) ; if t1 <> [] then shift[n] := subs({op(t1)},'offset'); t := select(proc(x) not hastype(x,`=`) end,t) else if {op(t)} intersect vset <> {} then ERROR( `intersecting partitions involving`,t ) fi fi; if not type(t,'list'('VERTEX'(G))) then ERROR(`not a list of vertices`,t) fi; part[n] := t; vset := vset union {op(t)} od; userinfo( 5,'networks',`allocated vertices:`,print(vset) ); if networks['vertices'](G) minus vset <> {} then n := n+1; t := sort([op(networks['vertices'](G) minus vset)]) ; part[n] := t; shift[n] := 0; userinfo( 1,'networks',`adding a new partition`,t) fi; max_x := origin[1]; for j to n do if max_x < nops(part[j]) then max_x := nops(part[j]) fi od; middle := 1/2*max_x-1/2+origin[1]; points := table(); text := table(); pos := table(); x := origin[1]; for j to n do vset := part[j]; nx := nops(vset); x := x+1; #** update to shift the alignment of columns y := middle-1/2*nx+1/2+shift[j]+origin[2]+0.2*((j mod 3) - 1); for i to nops(vset) do v := vset[i]; pos[v] := [x,y]; points[v] := POINTS(pos[v]); if j = n then text[v] := 'TEXT'( [pos[v][1]+1.6*10^(-1),pos[v][2]], convert(v,string)) else text[v] := 'TEXT'( [pos[v][1]-.1 ,pos[v][2]], convert(v,string)) fi; y := y+1 od od; lines := table(); for e in edges(G) do x := networks['ends'](e,G); if 1 < nops(x) then y := x[2]; x := x[1] else x := x[1] fi; if ( type(networks['head'](e,G),integer) or substring(convert(networks['head'](e,G),string),1..1) = `:` ) then lines[e] := #** update the line colour and linestyle CURVES([pos[x],pos[y]],COLOUR('RGB',1.0,0,0),LINESTYLE(0)) else lines[e] := #** update the line colour and linestyle CURVES([pos[x],pos[y]],COLOUR('RGB',0,0,1.0),LINESTYLE(3)) fi; od; t := map( op,{entries(points),entries(lines),entries(text)} ); xrng := origin[1]+1/2 .. origin[1]+n+1/2; yrng := origin[2]-1/2 .. origin[2]+max_x-1/2; RETURN(t) end: # Calculate statistics for a process network, netstats:=proc(first,Gr) local mat, mats, unitop, unitops, nodes, streams, systems, subsystems, loops; mat:=[op(op(1,op(1,[first]))), op(op(2,op(1,[first]))), op(op(3,op(1,[first])))]; mat; mats:=nops(mat); unitop:=[op(op(4,op(1,[first])))]; unitops:=nops(unitop); nodes:=mats+unitops; streams:=nops(edges(Gr)); systems:=components(Gr); subsystems:=nops(systems); loops:=streams-nodes+subsystems; `# of materials = `||mats, `# of unit ops = `||unitops, `# of network nodes (materials+unit ops) = `||nodes, `# of connections = `||streams, `# of subsystems = `||subsystems, `# of loops = `||loops; end: # Add routines related to generating a graphic flow diagram # of the process # Generate Op data structure on available unit operations from # the full unit operations set data. OpGen:=proc(OpData) local i, Op, count, Labels; global LabelsList; count:=nops(OpData); # setup unique list for the unit operation names Labels:={}; for i from 1 to count do Labels:=Labels union {op(1,op(i,OpData))} od; LabelsList:=convert(Labels,list); # check for the proper number of inlet ports for i from 1 to count do if nops(op(2,op(i,OpData))) <> nops(op(6,op(i,OpData))) then RETURN(`Error: Wrong number of inlet stream port values. Line=`,i) fi; od; # check for the proper number of outlet ports for i from 1 to count do if nops(op(3,op(i,OpData))) <> nops(op(7,op(i,OpData))) then RETURN(`Error: Wrong number of outlet stream port values. Line=`,i) fi; od; Op:={}; for i from 1 to nops(OpData) do Op := Op union {[ {op(op(2,op(i,OpData)))}, {op(op(3,op(i,OpData)))} ]}; od; Op; end: # Convert the Pgraph structure into data for a Visio flowsheet plot. Visio_data:=proc(PGraph,filename) local i, j, k, m, opset, rm, pr, mid, el, el2, mat_ins, mat_outs, unitnum, place, inset, outset, inset2, outset2, nextunit, unitname, matname, port1, port2, vals, max_els, unitprint, routes, route_count, Tree, AP, route_pair, max_route, table_data, route_value, route, Gr, Gr2, boxes, location, Streams, nextunitname, fileID; global OpData, LabelsList, none, numbers; boxes:={}; m:=op(1,PGraph); opset:=op(2,PGraph); # generate the network from the PGraph Gr:=op(2,[graph_network(PGraph,numbers)]); # check for material inlets and outlets of the structure mat_ins:=Psi_minus(opset); mat_outs:=Psi_plus(opset); # find all raw materials (they are only inlets to unit ops) rm:={}; # find all products (they are only outlets of unit ops) pr:={}; for el in m do if member(el,mat_ins) and member(el,mat_outs) = false then rm:=rm union {el} fi; if member(el,mat_ins) = false and member(el,mat_outs) then pr:=pr union {el} fi; od; mid:=m minus rm minus pr; # Print info for all boxes on the diagram, fileID:=fopen(`visio.dat`,WRITE,TEXT); fprintf(fileID,`%s %s\n`,`File:`, filename); # raw materials have the Feed icon for el in rm do vals[el]:=1; fprintf(fileID,`"%s" "towers" "Flowsheet Feed"\n`,el); boxes:=boxes union {el}; od; # mid materials use a box icon if they have multiple feeds for el in mid do Tree:=shortpathtree(Gr,el); if nops(daughter(el,Tree)) > 1 or nops(ancestor(el,Tree)) > 1 then vals[el]:=1; fprintf(fileID,`"%s" "towers" "Diamond"\n`,el); boxes:=boxes union {el}; else vals[el]:=0; fprintf(fileID,`"%s" "none" "none"\n`,el); fi; od; # products have the Product icon for el in pr do vals[el]:=1; fprintf(fileID,`"%s" "towers" "Flowsheet Feed"\n`,el); boxes:=boxes union {el}; od; # the unit ops have their special icons from OpData j:=0; for el in opset do j:=j+1; inset:=op(1,el); outset:=op(2,el); for i from 1 to nops(OpData) do inset2:={op(op(2,op(i,OpData)))}; outset2:={op(op(3,op(i,OpData)))}; if inset = inset2 and outset = outset2 then break fi; od; fprintf(fileID,`"%s" "%s" "%s"\n`,op(1,op(i,OpData)),op(4,op(i,OpData)), op(5,op(i,OpData)) ) ; member(op(1,op(i,OpData)),LabelsList,'location'); unitnum[j]:=i; boxes:=boxes union {location}; od; # print the stream connectivity data # source node, destination node, source port, dest. port, label fprintf(fileID,`Stream Data:\n`); # cycle through all units in the process Streams:={}; for i from 1 to nops(opset) do unitname:=op(1,op(unitnum[i],OpData)); # do inlets to the unit for el in op(1,op(i,opset)) do matname:=el; member(matname,op(2,op(unitnum[i],OpData)),'place'); port2:=op(place,op(6,op(unitnum[i],OpData))); if {el} intersect rm <> {} then Streams:=Streams union {[matname,unitname,1,port2,none]} elif vals[el] = 1 then Streams:=Streams union {[matname,unitname,5,port2,none]} else nextunit:=arrivals(el,Gr); nextunitname:=op(op(nextunit),LabelsList); for k from 1 to nops(OpData) do if op(1,op(k,OpData)) = nextunitname then if member(matname,op(3,op(k,OpData)),'place') then break fi; fi; od; port1:=op(place,op(7,op(k,OpData))); Streams:=Streams union {[nextunitname,unitname,port1,port2,matname]} fi; od; # do outlets of the unit for el in op(2,op(i,opset)) do matname:=el; member(matname,op(3,op(unitnum[i],OpData)),'place'); port1:=op(place,op(7,op(unitnum[i],OpData))); if {el} intersect pr <> {} then Streams:=Streams union {[unitname,matname,port1,2,none]} elif vals[el] = 1 then Streams:=Streams union {[unitname,matname,port1,3,none]} else NULL; # the connection was already made fi; od; od; # print the stored stream connectivities, for el in Streams do fprintf(fileID,`"%s" "%s" "%d" "%d" "%s"\n`,op(el)) od; # print the main route through the process followed by sets # with the other units. fprintf(fileID,`Routes:\n`); # find all routes from feeds to products, tag the longest one max_els:=0; for el in rm do Tree:=shortpathtree(Gr,el); for el2 in pr do # Note: path returns the vertices in reverse order routes[el,el2]:=path([el2,el],Tree); # count only the vertices that are part of the diagram route_count[el,el2]:= nops({op(routes[el,el2])} intersect boxes); # find the maximum pathway if route_count[el,el2] > max_els then route:=el,el2; max_els:=route_count[el,el2]; fi; od; od; # print the maximum route (it is in reverse order) fprintf(fileID,`%d\n`,max_els); k:=nops(routes[route]); for i from 1 to k do j:=k+1-i; if {op(j,routes[route])} intersect boxes <> {} then unitprint:=op(j,routes[route]); if whattype(unitprint) = integer then fprintf(fileID,`"%s"\n`,op(unitprint,LabelsList)) else fprintf(fileID,`"%s"\n`,unitprint); fi; fi; od; # if there are more than 1 box left, then find the longest path # through them and output it. boxes:=boxes minus {op(routes[route])}; if nops(boxes) > 1 then # get a new graph with only the remaining vertices new(Gr2); for el in boxes do Gr2:=gunion(Gr2,induce(incident(el,Gr),Gr),'SIMPLE'); od; # find the distances for all pairs AP:=allpairs(Gr2); # find the maximum distance route_pair:=0,0; max_route:=0; table_data:=op(op(AP)); for i from 1 to nops(table_data) do route_value:=op(2,op(i,table_data)); if route_value > max_route and route_value < infinity then max_route:=route_value; route_pair:=op(1,op(i,table_data)); fi; od; # find the route between the route_pair set Tree:=shortpathtree(Gr2,op(1,[route_pair])); route:=path([op(2,[route_pair]),op(1,[route_pair])],Tree); # print the number of units in the path and their names in reverse fprintf(fileID,`%d\n`,nops({op(route)} intersect boxes)); k:=nops(route); if k > 1 then for i from 1 to k do el:=op(k+1-i,route); if ({el} intersect boxes) <> {} then if whattype(el) = integer then fprintf(fileID,`"%s"\n`,op(el,LabelsList)) else fprintf(fileID,`"%s"\n`,el) fi; fi; od; else fprintf(fileID,`0\n`); route:=[]; fi; else fprintf(fileID,`0\n`) fi; # if there are more than 1 box left, then find the longest path # through them and output it. boxes:=boxes minus {op(route)}; if nops(boxes) > 1 then # get a new graph with only the remaining vertices new(Gr2); for el in boxes do Gr2:=gunion(Gr2,induce(incident(el,Gr),Gr),'SIMPLE'); od; # find the distances for all pairs AP:=allpairs(Gr2); # find the maximum distance route_pair:=0,0; max_route:=0; table_data:=op(op(AP)); for i from 1 to nops(table_data) do route_value:=op(2,op(i,table_data)); if route_value > max_route and route_value < infinity then max_route:=route_value; route_pair:=op(1,op(i,table_data)); fi; od; # find the route between the route_pair set Tree:=shortpathtree(Gr2,op(1,[route_pair])); route:=path([op(2,[route_pair]),op(1,[route_pair])],Tree); # print the number of units in the path and their names in reverse fprintf(fileID,`%d\n`,nops({op(route)} intersect boxes)); k:=nops(route); if k > 1 then for i from 1 to k do el:=op(k+1-i,route); if ({el} intersect boxes) <> {} then if whattype(el) = integer then fprintf(fileID,`"%s"\n`,op(el,LabelsList)) else fprintf(fileID,`"%s"\n`,el) fi; fi; od; else fprintf(fileID,`0\n`); route:=[]; fi; else fprintf(fileID,`0\n`) fi; # print the remaining units in the order of 1) raw materials # 2) mid materials, 3) unit ops, and 4) products boxes:=boxes minus {op(route)}; fprintf(fileID,`%d\n`,nops(boxes)); for el in boxes do if ({el} intersect rm) <> {} then fprintf(fileID,`"%s"\n`,el) fi od; for el in boxes do if ({el} intersect mid) <> {} then fprintf(fileID,`"%s"\n`,el) fi od; for el in boxes do if whattype(el) = integer then fprintf(fileID,`"%s"\n`,op(el,LabelsList)) fi od; for el in boxes do if ({el} intersect pr) <> {} then fprintf(fileID,`"%s"\n`,el) fi od; fprintf(fileID,`End:\n`); close(fileID); end: # calculate the rank value of a decision mapping rank_value:=proc(mapping) local el, i, m, opset, rankings, inset, outset, inset2, outset2, unitname, unitrank, PGr, tabledata, sumrank, mat_ins, mat_outs, rm, pr; global OpData, Material_Rank; # rankings is a table for storing the rank of each unit op rankings:=table(); # the inputted decision map is converted to a P graph (m,o) PGr:=Pgraph(mapping); m:=op(1,PGr); opset:=op(2,PGr); # check for material inlets and outlets of the structure mat_ins:=Psi_minus(opset); mat_outs:=Psi_plus(opset); # find all raw materials (they are only inlets to unit ops) rm:={}; # find all products (they are only outlets of unit ops) pr:={}; for el in m do if member(el,mat_ins) and member(el,mat_outs) = false then rm:=rm union {el} fi; if member(el,mat_ins) = false and member(el,mat_outs) then pr:=pr union {el} fi; od; # cycle through the unit ops within opset to find their location # within the OpData array; extract the name & rank for rankings table for el in opset do # match the unit op to its row within OpData inset:=op(1,el); outset:=op(2,el); for i from 1 to nops(OpData) do inset2:={op(op(2,op(i,OpData)))}; outset2:={op(op(3,op(i,OpData)))}; if inset = inset2 and outset = outset2 then break fi; od; # extract the name and rank unitname:=op(1,op(i,OpData)); unitrank:=op(8,op(i,OpData)); # store the info within the rankings table; use the highest # ranking that occurs for a given unit name if whattype(rankings[unitname]) = indexed then rankings[unitname]:=unitrank else if rankings[unitname] < unitrank then rankings[unitname]:=unitrank fi; fi; od; # Get the data from inside the rankings table tabledata:=op(2,op(1,rankings)); # Sum the ranks of the unit operations sumrank:=convert([seq(rhs(op(i,tabledata)),i=1..nops(tabledata))],`+`); # Add the ranks of the raw materials and products within the flowsheet m:=rm union pr; for el in m do if whattype(Material_Rank[el]) <> indexed then sumrank:=sumrank+Material_Rank[el] fi; od; sumrank; end: # provide the sort criteria for the flowsheets list; sort by # increasing rank value. sort_rank:=proc (a, b) # note: the rank is stored as the first element of the list if op(1,a) < op(1,b) then true else false fi; end: # add the rank to each decision mapping and sort it process_maps:=proc(dm) local j; global flowsheets; # create a list containing lists with the flowsheet rank and its # decision map. flowsheets:=[seq([rank_value(op(j,dm)),op(j,dm)], j=1..nops(dm))]; # sort the list by increasing rank; the sort_rank function provides # the boolean function for the sorting task. flowsheets:=sort(flowsheets,sort_rank); flowsheets; end: # use cycles in the flowsheet to determine key material # balance requirements, cycles:=proc(first,Gr,rootVertex) local el, el2, edgeset, Grund, G2, eset, G3, cyc, G4, cycleVertices, chords, numberChords, units, cycleFeeds, cycleProducts; global LabelsList, Raw_Materials; # first, generate an undirected graph from Gr edgeset:={}; for el in edges(Gr) do edgeset:=edgeset union {{head(el,Gr),tail(el,Gr)}}; od; Grund:=graph(vertices(Gr),edgeset); # find a spanning tree of Grund rooted at a raw material, G2:=spantree(Grund,rootVertex); # find the chords of the spanning tree, chords:=edges(Grund) minus edges(G2); # if there are no chords then stop, numberChords:=nops(chords); if numberChords = 0 then RETURN(`No loops found.`) fi; # loop through all fundamental cycles, for el in chords do # add a chord to the edge set eset:={el} union edges(G2); # find the fundamental cycle cyc:=fundcyc(eset,Grund); # create a subgraph from the cycle G3:=induce(cyc,Grund); # find the vertices in the graph cycleVertices:=vertices(G3); # delete any vertices that are raw materials or products for el2 in cycleVertices do if nops(arrivals(el2,Gr)) = 0 then cycleVertices:=cycleVertices minus {el2} fi; if nops(departures(el2,Gr)) = 0 then cycleVertices:=cycleVertices minus {el2} fi; od; # create a new graph from the original Gr with # the condensation of the cycleVertices, G4:=duplicate(Gr); shrink(cycleVertices,G4,new_vertex); # print results, units:={}; for el2 in cycleVertices do if whattype(el2) = integer then units:=units union {op(el2,LabelsList)} else units:=units union {el2} fi; od; cycleFeeds:={}; for el2 in arrivals(new_vertex,G4) do if whattype(el2) = integer then cycleFeeds:=cycleFeeds union {op(el2,LabelsList)} else cycleFeeds:=cycleFeeds union {el2} fi; od; cycleProducts:={}; for el2 in departures(new_vertex,G4) do if whattype(el2) = integer then cycleProducts:=cycleProducts union {op(el2,LabelsList)} else cycleProducts:=cycleProducts union {el2} fi; od; lprint(`Cycle found:`); lprint(`Fundamental cycle vertices (w/o RM's and Pr's) = `, units); lprint(`Feeds from =`,cycleFeeds); lprint(`Products to =`,cycleProducts); od; `# of cycles processed = `||numberChords; end:

All materials are given unique identifying names and listed by their functions.

Input the set of raw materialsRaw_Materials:={F}:

Input the set of required productsProducts:={W,E}:

The unit operation functions are entered as lists within OpData. OpData handlesseveral tasks:It gives a name for each unit operation function to be used as identifiers in flowsheet plots.It defines the inlet and outlet materials of each unit operation function.It provides data for plotting the flowsheet as a Visio drawing.Each unit operation function is linked to a shape within a Visio stencil.The inlet and outlet materials are attached to connection ports on the Visio shapes as defined in the connection section of the Visio shape.Each unit operation function is given a rank. The rank should be a positive number (or zero) that sets its relative cost when compared to the other unit functions in the list. The individual ranks are summed and added with ranks based on materials to give an overall ranking for each generated flowsheet. The flowsheet ranks are then used to sort the list by increasing rank.Note: The same unit label can be given for multiple unit operation functions. In the example OpData, `Decant1` is used twice to produce the products of B and C from either A or H as feeds. The flowsheet plot then shows `Decant1` with A, H or A & H as the feed(s) to the shape. For the case with A & H as feeds, the overall rank is calculated using the higher rank of the two functions. Definitions:unit label = a name given to the unit operation function for plotting purposesfeeds = a list of its inlet materialsproducts = a list of its outlet materialsstencil = the Visio stencil to be used for its shape on the flowsheet drawing. The VB program for plotting Visio flowsheets recognizes the several stencils. Enterpumps for 'Process Flow - Pumps and Compressors' stencil; enter heateq for'Process Flow - Heat Equipment' stencil; enter vessels for 'Process Flow - Vessels'stencil; enter equip for 'Process Flow - Equipment' stencil; enter towers for 'Towers' stencil.icon name = the icon name within the Visio Stencilfeed ports = a list of integers giving the corresponding connector ports for each feedproduct ports = a list of integers giving the corresponding connector ports for each productrank = a rank factor for the given unit operation function

[unit label, feeds, products, stencil, icon name, feed ports, product ports, rank ] OpData:= [ [`Mix1`,[F,T],[A],`towers`,`Mixer`,[3,1],[5], 0 ] , [`Decant1`,[A],[B,C],`towers`,`Decanter`,[1],[2,3],1], [`Distill1`,[B],[D,W],`towers`,`Full Column 2 Sections`,[1],[7,8], 10], [`Distill2`,[C],[G,T],`towers`,`Full Column 2 Sections`,[1],[7,8], 10], [`Mix2`,[G,D],[O],`towers`,`Mixer`,[3,1], [5], 0 ], [`Distill3`,[O],[H,E],`towers`,`Full Column 2 Sections`,[1],[7,8], 10], [`Decant1`,[H],[B,C],`towers`,`Decanter`,[1],[2,3], 1 ], [`Mix3`,[F,B],[J],`towers`,`Mixer`,[3,1], [5], 0 ], [`Distill4`,[J],[K,W],`towers`,`Full Column 2 Sections`,[1],[7,8], 10], [`Mix4`,[G,K],[L],`towers`,`Mixer`,[3,1], [5], 0 ], [`Distill3`,[L],[H,E],`towers`,`Full Column 2 Sections`,[1],[7,8], 10], [`Mix5`,[C,K],[M],`towers`,`Mixer`,[3,1], [5], 0 ], [`Distill3`,[M],[H,E],`towers`,`Full Column 2 Sections`,[1],[7,8], 10] ]:Op:=OpGen(OpData):

The flowsheet ranking can also include rank factors for the materials that are present in the flowsheet. The rank factors only apply to materials that are either raw materials or products in the given flowsheet. The raw materials must be within the Raw_Materials set as defined previously. The products are either from the Products set as defined previously or they are by-products. Note that the internal material streams can become by-products in some generated flowsheets. An input flag to the SSG procedure controls the presence of by-products.The material rank can be positive for a cost such as a raw material or a by-product that requires disposal. It can be negative for a product.

Material_Rank:=table(): # required to define the tableMaterial_Rank[F]:=0: # example entry for material F

The maximal structure (if it exists) is the collection of unit operation functions from the toolkit that are valid for making the required products from the available raw materials. It is a feasible flowsheet solution to the synthesis task. The maximal structure may contain several smaller flowsheets that are also solutions to the synthesis task.

The MSG procedure generates a P graph for the maximal structure that contains all of the useful unit operation functions for the synthesis task. The procedure requires three sets defining the unit operation functions, the raw materials and the required products. The sets were calculated in the previous sections of the worksheet.maximal_structure:=MSG(Op,Raw_Materials,Products);

The network draw capabilities of Maple provide a simple method of plotting the flowsheet diagrams. The draw procedure was modified to allow show the feed streams to a unit as solid red lines and the products from a unit as dashed blue lines. The network for the maximal structure is drawn next.draw(graph_network(maximal_structure,names));

The SSG procedure finds all of the individual flowsheets from within the maximal structure that meet the criteria. Op is the set of unit operation functions that were accepted into the maximal structure. decision_map is initialized to the null set. The SSG procedure adds decision maps to decision_map as it finds them. Decision maps store flowsheet connectivity data.SSG has one input value. Its values are defined as:true = allow internal materials to become byproductsfalse = do not allow internal materials to become byproductsset of materials = allow the materials in the set to be byproducts, (i.e., { H } )Op:=op(2,maximal_structure):decision_map:={}:SSG(false); # false for no by-product

The following Maple code calculates the ranking of each flowsheet, sorts the results in ascending order and prints a listing of the ranks.FlowsheetRankings:=process_maps(decision_map): lprint(`Flowsheet Rankings`); lprint(`# Rank`); for i from 1 to nops(FlowsheetRankings) do lprint(i,FlowsheetRankings[i][1]) od;

The flowsheets were ordered by the cost ranking in the previous section. You select a given flowsheet from the ranking by its order number (1, 2, etc) in the ranking of the results.selection:= 1;PGr:=Pgraph(FlowsheetRankings[selection][2]):rank_value:=FlowsheetRankings[selection][1];

draw(graph_network(PGr,names));

The `Visio_data` procedure extracts the required information from the flowsheet for drawing it as a process flow diagram. The data are printed to an ASCII file called `VISIO.DAT`. A VBA macro within Visio can then read the data file and plot the process flowsheet within a Visio drawing.

Visio_data(PGr,`fsheet`||selection);

Next, start the Visio program and create a new drawing based on the Chemical_Flowsheet template within the Industrial Process directory. You need Visio Technical 4.5 or higher to execute the template. Instructions are provided within the template. Two Visio files are used for the software:Chemical Flowsheet.vst & Towers.vssPlace the two files within the Visio\Solutions\Industrial Process subdirectory.

netstats(graph_network(PGr,numbers));

The cycles procedure analyzes the flowsheet for special material balance constraints. It uses graph theory to analyze an undirected graph of the flowsheet for fundamental cycles. The results give information on important material balance constraints. A process will not be feasible if the constraints can not be met. The feeds must equal the products for each cycle. The first input to cycles gives the P-graph of the given flowsheet. The second input is a raw material or product that is used as the root of a spanning tree of the undirected graph.

Define NiMlKU1hdGVyaWFsRw== as a material from either the NiMlLVJhd19NYXRlcmlhbEc= or NiMlKVByb2R1Y3RzRw== sets. The material is used as the root in spanning tree analysis. You can repeat the cycle determinations with different root materials.Material:=Products[1];Next, calculate `cycles` to determine the material balance constraints that are related to the cycles that it finds. The Feeds must equal Products for each of the cycles to maintain the material balance.cycles(graph_network(PGr,numbers),Material);

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