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8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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Published March 22 2011
r 2011 American Chemical Society 4788 dxdoiorg101021ie101896v | Ind Eng Chem Res 2011 50 4788ndash
4795
RESEARCH NOTE
pubsacsorgIECR
Heuristic Design of ReactionSeparation Processes with Two Recycles
William L Luyben
Department of Chemical Engineering Lehigh University Bethlehem Pennsylvania 18015 United States
ABSTRACT A recent paper presented a heuristic approach to quickly estimate the optimum tradeoff between reactor size andrecycle 1047298ow rate during the preliminary conceptual process design of a reactionseparation process The basic idea is to 1047297nd theminimum recycle 1047298ow rate by designing the process to meet some speci1047297ed conversionyieldselectivity criterion using a very largereactor A heuristic of setting the actual recycle 1047298ow rate equal to 12 times the minimum then is used to obtain an approximateoptimum design The process studied had relative volatilities such that only one recycle stream was needed The purpose of thispaper is to extend this work to the case where two recycle streams are required There is a reactor and three distillation columns withtwo recycle streams The desired product C is produced via the reaction A thornBfC An undesired product D is also produced Twoalternative reactions (A thorn CfD or A thorn BfD) mean that there is a large recycle of either B or A to achieve high selectivity Therelative volatilities are assumed to be R A gt RC gt RB gt RD so reactant A is recycled from the overhead of the 1047297rst distillation columnand reactant B is recycled from the overhead of the third column Product C is the distillate of the second column and product D isthe bottoms of the third column Results show that the more-complex separation section shifts the economics to favor a smallerheuristic ratio (105) of actual recycle to minimum recycle
1 INTRODUCTION
Heuristics are very useful at the conceptual design stage of processdevelopment where theprecision ofa rigorous optimizationmethod is notrequired Commonheuristics in distillation designareto set the actual number of trays equal to twice the minimumnumber of trays orto set the actual re1047298uxratio equal to12 times theminimum re1047298ux ratio Other examples of important chemicalengineering heuristics include selecting pressure drops over heat
exchangers to achievereasonable heat-transfer coeffi
cients selectingpressure drops over control valves to achieve dynamic rangeabilityand choosing reasonable heat-transfer coefficients and temperaturediff erential driving forces to 1047297nd the area of heat exchangers
A recent paper1 suggested a new heuristic for establishing theoptimumdesign of a reactorseparationprocess withrecycle Thereis a tradeoff between the size of the reactor and the amount of recycle required to achieve a speci1047297ed design criterion such asconversion yield or selectivity in the overall process Major capitaland operating costs are often in the separation section but theperformance of the reaction section is usually critical because of thedominant economic eff ect of raw material costs and product valuesThe intentof the proposed heuristic is to provide some guidance forinitial 1047298owsheet developmentat theconceptualprocessdesignstage
In the original paper the process consisted of a reactor and twodistillation columns The relative volatilities were such that a singlerecycle stream was required The heuristic developed proposedsetting the actual recycle 1047298ow rate at sim12 times the minimumrecycle1047298ow rate as determined by designing with a very large reactor
The purpose of this paper is to extend this work to consider amore complex separation section in which two recycles arerequired Since the separation section is more complex andtherefore more expensive we expect the heuristic ratio of actual-to-minimum recycle 1047298ow rates to be smaller which isindeed what the results of this paper show
There is no claim that this approach is applicable to all chemicalkinetic reactions and reactorseparator systems Although recycles
are very commonly used to aff ect selectivity which is the situation inthis study recycles are sometimes used for other purposes Forexample a recycle stream is used in some adiabatic reactors tomoderate the temperature change through the reactor The recycleserves as a thermal sink whose sensible heat absorbs some of the heatof reaction This technique is applied with both exothermic andendothermic reactions Another application of recycle is to maintainthe composition of one of the reactants below some hazardous levelOxidation reactions often require operation below a lower explosive
limit so a recycle stream is used to keep the concentration of oxygen well below this limitHowever theuse ofrecycle toaff ectselectivityis very common in industrial application so we may expect that theproposed methodology should be widely applicable A continuousstirredtankreactor (CSTR)hasbeen used inthis studybut thesamesituationoccurs in tubular reactors since what aff ects selectivity is theratios of reactants and these ratios impact recycle 1047298ow ratesHowever we off er no rigorous mathematical proof that a limitingrecycle 1047298ow rate exists for all reactor types and chemical kinetics
2 PROCESS STUDIED
Figure 1 shows the 1047298owsheet of the process considered in thispaper with the more-complex separation section The relative
volatilities among the reactants A and B and the products C andD are R A gt RC gt RB gt RD Two fresh feed streams and tworecycle streams are fed into a CSTR reactor The reactor effluentis fed to a distillation column in which the light reactant A goesoverhead and is recycled back to the reactor The second columnproduces product C at the top The third column produces adistillate of mostly reactant B which is recycled back to thereactor Product D is the bottoms of the third column
Received September 14 2010 Accepted March 11 2011Revised February 15 2011
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Two cases are explored In the 1047297rst the undesired productconsumes C and A which leads to a large recycle of B and only asmall recycle of A In the second case the undesired productconsumes C and B which leads to a large recycle of A and only asmall recycle of B
The equipment sizes and conditions shown are the economicoptimum for the 1047297rst case that are developed later in this paperfor the base-case conditions a selectivity speci1047297cation of 100(kmol C produced divided by kmol D produced) kineticparameters of k 1 = 25 h1 and k 2 = 1 h1 relative volatilities between adjacent components of 2 and catalyst price of $10per kg
21 Reactor The molar holdup of the CSTR reactor is 90kmol Two irreversible reactions occur with specific reactionrates k 1 and k 2
A thorn B f C
R 1 frac14 V R k 1 z A zBeth1THORN
Case 1 Reactant A and desired product C are consumed in anundesired reaction
A thornC f D
R 2 frac14 V R k 2 z A zCeth2A THORN
Case 2 Reactants B and desired product C are consumed in anundesired reaction
B thornC f D
R 2 frac14 V R k 2 zB zCeth2BTHORN
where z j denotes the mole fraction component j in the reactorand V R is the reactor molar holdup
The desired product C is formed by the 1047297rst reaction but itcan react further to produce an undesired product D There-fore the concentrations of A and C must be kept small inCase 1 to achieve the desired selectivity by operating with an
excess of B and the concentrations of B and C must be keptsmall in Case 2 to achieve the desired selectivity by operating with an excess of A Two fresh feed stre ams of pure A andpure B are fed to the reactor (F A0 and FB0) in addition to thetwo recycle streams from the top of the 1047297rst column (D1)andfrom the top of the third column (D3) Note that in Case 1D1 is small compared to D3 because of the excess of component B in the reactor
Selectivity is de1047297ned as the number of moles of the desiredcomponent C produced divided by the number of moles of theundesired component D produced
selectivity frac14 number of moles of C
number of moles of D frac14
D2xD2C
B3xB3Deth3THORN
where D2 is the distillate from the second column xD2C the mole
fraction of desired component C in the distillate B3 the bottomsfrom the third column and xB3D
is the mole fraction of theundesired product in the bottoms
It is important to note that the design criterion selected in thisstudy is selectivity not conversion Selectivity is the importantperformance measure in processeswith desirableand undesirableproducts such as those considered in this work The high overall
conversions of the reactants in the process are inherently set by the losses of the reactants in the two product streams whichare set by the speci1047297ed impurity levels Low concentrations of reactant components A and B appear in the distillate productstream from the second column and a low concentration of reactant B appears in the bottoms product stream from thethird column These speci1047297ed compositions determine theconversions of reactants A and B for the overall process Theper-pass conversion of A in Case 1 is fairly high while the per-pass conversion of B is quite small The reverse is true inCase 2
The fresh feed of reactant A is 1047297 xed at F A0 = 100 kmolh in allcasesThe fresh feed of B is calculated for eachcase bysolving the
Figure 1 Two-recycle 1047298owsheet Case 1 (k 1 = 25 h1 selectivity = 100 $10kg R = 2)
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8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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Industrial amp Engineering Chemistry Research RESEARCH NOTE
B1xB1B frac14 B2xB2B eth15THORN
B1xB1C frac14 D2xD2C thorn B2xB2C eth16THORN
The additional 4 unknown variables not in the previous list of 12are D2 B2 xD2 A
and xB2B bringing the total to 16 Note that xD2C
can be calculated from eq 17
xD2C frac14 1 xD2 A xD2B eth17THORN
24 Column C3 The bottoms B2 is fed into the third column whose job is to recycle B from the top and produce product D
from the bottom The small amount of C that drops out the bottom of the second column also goes overhead The separationin column C3 is between components B and D The impurity of B in the bottoms is set at xB3B
= 0001 The impurity of D in thedistillate is set at xD3D
= 0001The equations that describe the third distillation column
(column C3) are given below
B2 frac14 D3 thorn B3 eth18THORN
B2xB2B frac14 D3xD3B thorn B3xB3B eth19THORN
B2xB2C frac14 D3xD3C eth20THORN
Figure 4 Eff ect of k 1 and reactor size on B1 and D3 Case 1
Figure 5 Eff ect of k 1 and reactor size on reactor composition Case 1
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The additional unknown variable that was not in theprevious lists is B3 which brings the 1047297nal total number of unknown variables to 17 Note that xD3C
can be calculatedfrom eq 21
xD3C frac14 1 xD3B xD3D eth21THORN
There are a total of 17 unknowns so we need 17 equationsEquations 47 916 and 1821 give a total of 16 equationsthat describe the system We need one more equation
The 1047297nal equation is provided by using the de1047297nition of selectivity given in eq 3 The resulting 17 equations are solvedusing the Matlab function fsolve for a given case of speci1047297edreactor size (V R ) speci1047297c reaction rates (k 1 and k 2) andselectivity
3 RESULTS
31 Case 1 (A thorn Cf D) Figure 2 shows results from thesecalculations for the case in which reactant A is consumed in the
undesired reaction In all of the cases shown in this paper theselectivity is set at 100 Results for three different kineticparameters are shown k 1 = 15 25 and 50 h1 The value of k 2is 1 in all cases The ordinate is the flow rate of recycle D1 fromthe first column The abscissa is the reactor molar holdupFigure 3 shows the sum of the two recycles D1 and D3 Since alarge excess of B must be used in the reactor the D3 recycle fromthe top of the third column is much larger than the D1 recyclefrom the top of the first column
More recycle is needed to achieve a speci1047297ed selectivity fora1047297 xed reactor size as the speci1047297c reaction rate k 1 is reducedSmall values of k 1 lead to larger concentrations of A in thereactor ( z A ) but smaller concentrations of C ( zC) and D ( zD)
The key feature of these plots (and the basis for the heuristic
proposed) is that the required recycle 1047298ow rate level out at
some minimum value as the reactor size is made very large Wede1047297ne the asymptotic recycle 1047298ow rate as the minimumrecycle It can be expressed as a ratio to the fresh feed of A to put it in dimensionless form For example for the k 1 = 25h1 case the minimum total recycle is 409 kmolh for a freshfeed of F A0 = 100 kmolh Thus the minimum recycle ratio(R min) is 409
Figure 4 shows how the 1047298
ow rate of the bottoms from the1047297rst column B1 and the D3 recycle change as reactor size is varied Somewhat unexpectedly the 1047298ow rates of the bottomsof all three columns and the distillates from the second andthird column change very little with reactor size The only 1047298ow rate that really changes signi1047297cantly is the distillate of the1047297rst column as shown in Figure 2 These other 1047298ow rates arestrong functions of the reaction rate k 1 but change little withreactor size
Figure 5 shows how reactor compositions change Noticethat the reactor compositions all level out as the reactor size isincreased The largest changes are in the composition reactant A ( z A ) which decreases as reactor size increases while theother three composition increase Reactor composition z A
decreases as speci1047297c reaction rate k 1 increases while zC and zDincrease since the desired reaction is more favorable
The curves shown in Figures 2 and 3 are similar to those seenin the classical plots of re1047298ux ratio versus trays in distillationdesign At anypointon the curvethe productsfrom the processare exactly the same but equipment (reactor and columns)and energy (reboiler heat inputs) are diff erent So where is theoptimum point on the curve We address this question nextfor several diff erent cases to determine if there is some simplerelationship between the economic optimum recycle 1047298ow rates and the minimum The minimum recycle 1047298ow rates can be easily determined by running a case with a very largereactor
32 Case2 (BthornCfD) Figure 6 gives results for the case in
which reactant B is consumed in the undesired reaction A
Figure 6 Eff ect of k 1 and reactor size on recycles Case 2
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large excess of A is required in the reactor to achieve thespecified selectivity of 100 Therefore the recycle D1 (fromthe top of the first column)is much larger than the D3 recycle(from the top of the third column)
4 ECONOMIC OPTIMIZATION
The annual cost of raw materials and the annual valueof products are typically orders-of-magnitude larger than the
annual cost of energy and capital Therefore most chemicalprocess are designed for very high yields (99) and selectivities(100)
The precise ldquo bestrdquo values for these criteria are strongly dependent on market prices for raw materials and 1047297nishedproducts Both are difficult to estimate with any precisionIn order to avoid these uncertainties we take the
approach that the designer will specify a reasonable criterionsuch as a selectivity of 100 A plant then can be designedthat meets this criterion with the minimum total annualcost (TAC) Pricing of feed streams and products isavoided
TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period In this work apayback period of 3 years and the installed cost of equipmentare used
TAC frac14 energy cost thorncapital installed investment
payback period eth22THORN
For the 1047298owsheetconsideredin Figure 1 the reactor and all threecolumns change from case to case for a speci1047297ed selectivity Capitalinvestment is requiredfor thereactorvesselcatalyst columnvesselsreboilers and condensers The energy cost depends on the reboilerduties
Tables 1A 1B and 1C give sizing and cost results forCase 1 with three values of k 1 Tables 2A 2B and 2Cgive results for Case 2 The selectivity is 100 the costof catalyst is $10 per kg and the relative volatility between all adjacent components is 2 The reactor size is varied over a range until the reactor that minimized the TACis found
Table 1A Sizing and Economics Results for the k1 = 15 h1
Case
parameter value
V R 140 kmol
recycle D1 453 kmolh
recycle D3 6611 kmolh
reactor $01499 106
catalyst $05000 106
value
parameter column C1 column C2 column C3
total trays 32 38 18
column diameter 2114 m 3746 m 2928 m
re1047298ux ratio 8210 8434 02098
column vessel $04908 106 $1034 106 $04368 106
heat exchangers $04263 106 $07158 106 $06508 106
reboiler duty 2693 MW 5978 MW 5163 MW
energy $06608 106yr $1467 106yr $1267 106yr
Total Capital = $4404 106
Total Energy = $3394 106yr
TAC = $4862 106yr
Table 1B Sizing and Economics Results for k1 = 25 h1 Case
parameter value
V R 90 kmol
recycle D1 3012 kmolh
recycle D3 3965 kmolh
reactor $01134 106
catalyst $03214 106
value
parameter column C1 column C2 column C3
total trays 33 38 18
column diameter 1794 m 3112 m 2495 m
re1047298ux ratio 8967 5511 04648
column vessel $04245 106 $08486 106 $03683 106
heat exchangers $03442 106 $05625 106 $05286 106
reboiler duty 1938 MW 4120 MW 3750 MW
energy $04754 106yr $1022 106yr $09200 106yr
Total Capital = $3512 106
Total Energy = $2408 106yr
TAC = $3578 106yr
Table 1C Sizing and Economics Results for the k1 = 50 h1
Case
parameter value
V R 60 kmol
recycle D1 1605 kmolh
recycle D3 1982 kmolh
reactor $008846 106
catalyst $02143 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 1487 m 2531 m 1918 m
re1047298ux ratio 1186 3308 07321
column vessel $03600 106 $06809 106 $02783 106
heat exchangers $02698 106 $04300 106 $03766 106
reboiler duty 1330 MW 2730 MW 2216 MW
energy $03270 106yr $06697 106yr $05437 106yr
Total Capital = $2698 106
Total Energy = $1540 106yr
TAC = $2440 106yr
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As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
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The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
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Two cases are explored In the 1047297rst the undesired productconsumes C and A which leads to a large recycle of B and only asmall recycle of A In the second case the undesired productconsumes C and B which leads to a large recycle of A and only asmall recycle of B
The equipment sizes and conditions shown are the economicoptimum for the 1047297rst case that are developed later in this paperfor the base-case conditions a selectivity speci1047297cation of 100(kmol C produced divided by kmol D produced) kineticparameters of k 1 = 25 h1 and k 2 = 1 h1 relative volatilities between adjacent components of 2 and catalyst price of $10per kg
21 Reactor The molar holdup of the CSTR reactor is 90kmol Two irreversible reactions occur with specific reactionrates k 1 and k 2
A thorn B f C
R 1 frac14 V R k 1 z A zBeth1THORN
Case 1 Reactant A and desired product C are consumed in anundesired reaction
A thornC f D
R 2 frac14 V R k 2 z A zCeth2A THORN
Case 2 Reactants B and desired product C are consumed in anundesired reaction
B thornC f D
R 2 frac14 V R k 2 zB zCeth2BTHORN
where z j denotes the mole fraction component j in the reactorand V R is the reactor molar holdup
The desired product C is formed by the 1047297rst reaction but itcan react further to produce an undesired product D There-fore the concentrations of A and C must be kept small inCase 1 to achieve the desired selectivity by operating with an
excess of B and the concentrations of B and C must be keptsmall in Case 2 to achieve the desired selectivity by operating with an excess of A Two fresh feed stre ams of pure A andpure B are fed to the reactor (F A0 and FB0) in addition to thetwo recycle streams from the top of the 1047297rst column (D1)andfrom the top of the third column (D3) Note that in Case 1D1 is small compared to D3 because of the excess of component B in the reactor
Selectivity is de1047297ned as the number of moles of the desiredcomponent C produced divided by the number of moles of theundesired component D produced
selectivity frac14 number of moles of C
number of moles of D frac14
D2xD2C
B3xB3Deth3THORN
where D2 is the distillate from the second column xD2C the mole
fraction of desired component C in the distillate B3 the bottomsfrom the third column and xB3D
is the mole fraction of theundesired product in the bottoms
It is important to note that the design criterion selected in thisstudy is selectivity not conversion Selectivity is the importantperformance measure in processeswith desirableand undesirableproducts such as those considered in this work The high overall
conversions of the reactants in the process are inherently set by the losses of the reactants in the two product streams whichare set by the speci1047297ed impurity levels Low concentrations of reactant components A and B appear in the distillate productstream from the second column and a low concentration of reactant B appears in the bottoms product stream from thethird column These speci1047297ed compositions determine theconversions of reactants A and B for the overall process Theper-pass conversion of A in Case 1 is fairly high while the per-pass conversion of B is quite small The reverse is true inCase 2
The fresh feed of reactant A is 1047297 xed at F A0 = 100 kmolh in allcasesThe fresh feed of B is calculated for eachcase bysolving the
Figure 1 Two-recycle 1047298owsheet Case 1 (k 1 = 25 h1 selectivity = 100 $10kg R = 2)
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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B1xB1B frac14 B2xB2B eth15THORN
B1xB1C frac14 D2xD2C thorn B2xB2C eth16THORN
The additional 4 unknown variables not in the previous list of 12are D2 B2 xD2 A
and xB2B bringing the total to 16 Note that xD2C
can be calculated from eq 17
xD2C frac14 1 xD2 A xD2B eth17THORN
24 Column C3 The bottoms B2 is fed into the third column whose job is to recycle B from the top and produce product D
from the bottom The small amount of C that drops out the bottom of the second column also goes overhead The separationin column C3 is between components B and D The impurity of B in the bottoms is set at xB3B
= 0001 The impurity of D in thedistillate is set at xD3D
= 0001The equations that describe the third distillation column
(column C3) are given below
B2 frac14 D3 thorn B3 eth18THORN
B2xB2B frac14 D3xD3B thorn B3xB3B eth19THORN
B2xB2C frac14 D3xD3C eth20THORN
Figure 4 Eff ect of k 1 and reactor size on B1 and D3 Case 1
Figure 5 Eff ect of k 1 and reactor size on reactor composition Case 1
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4792 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The additional unknown variable that was not in theprevious lists is B3 which brings the 1047297nal total number of unknown variables to 17 Note that xD3C
can be calculatedfrom eq 21
xD3C frac14 1 xD3B xD3D eth21THORN
There are a total of 17 unknowns so we need 17 equationsEquations 47 916 and 1821 give a total of 16 equationsthat describe the system We need one more equation
The 1047297nal equation is provided by using the de1047297nition of selectivity given in eq 3 The resulting 17 equations are solvedusing the Matlab function fsolve for a given case of speci1047297edreactor size (V R ) speci1047297c reaction rates (k 1 and k 2) andselectivity
3 RESULTS
31 Case 1 (A thorn Cf D) Figure 2 shows results from thesecalculations for the case in which reactant A is consumed in the
undesired reaction In all of the cases shown in this paper theselectivity is set at 100 Results for three different kineticparameters are shown k 1 = 15 25 and 50 h1 The value of k 2is 1 in all cases The ordinate is the flow rate of recycle D1 fromthe first column The abscissa is the reactor molar holdupFigure 3 shows the sum of the two recycles D1 and D3 Since alarge excess of B must be used in the reactor the D3 recycle fromthe top of the third column is much larger than the D1 recyclefrom the top of the first column
More recycle is needed to achieve a speci1047297ed selectivity fora1047297 xed reactor size as the speci1047297c reaction rate k 1 is reducedSmall values of k 1 lead to larger concentrations of A in thereactor ( z A ) but smaller concentrations of C ( zC) and D ( zD)
The key feature of these plots (and the basis for the heuristic
proposed) is that the required recycle 1047298ow rate level out at
some minimum value as the reactor size is made very large Wede1047297ne the asymptotic recycle 1047298ow rate as the minimumrecycle It can be expressed as a ratio to the fresh feed of A to put it in dimensionless form For example for the k 1 = 25h1 case the minimum total recycle is 409 kmolh for a freshfeed of F A0 = 100 kmolh Thus the minimum recycle ratio(R min) is 409
Figure 4 shows how the 1047298
ow rate of the bottoms from the1047297rst column B1 and the D3 recycle change as reactor size is varied Somewhat unexpectedly the 1047298ow rates of the bottomsof all three columns and the distillates from the second andthird column change very little with reactor size The only 1047298ow rate that really changes signi1047297cantly is the distillate of the1047297rst column as shown in Figure 2 These other 1047298ow rates arestrong functions of the reaction rate k 1 but change little withreactor size
Figure 5 shows how reactor compositions change Noticethat the reactor compositions all level out as the reactor size isincreased The largest changes are in the composition reactant A ( z A ) which decreases as reactor size increases while theother three composition increase Reactor composition z A
decreases as speci1047297c reaction rate k 1 increases while zC and zDincrease since the desired reaction is more favorable
The curves shown in Figures 2 and 3 are similar to those seenin the classical plots of re1047298ux ratio versus trays in distillationdesign At anypointon the curvethe productsfrom the processare exactly the same but equipment (reactor and columns)and energy (reboiler heat inputs) are diff erent So where is theoptimum point on the curve We address this question nextfor several diff erent cases to determine if there is some simplerelationship between the economic optimum recycle 1047298ow rates and the minimum The minimum recycle 1047298ow rates can be easily determined by running a case with a very largereactor
32 Case2 (BthornCfD) Figure 6 gives results for the case in
which reactant B is consumed in the undesired reaction A
Figure 6 Eff ect of k 1 and reactor size on recycles Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4793 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
large excess of A is required in the reactor to achieve thespecified selectivity of 100 Therefore the recycle D1 (fromthe top of the first column)is much larger than the D3 recycle(from the top of the third column)
4 ECONOMIC OPTIMIZATION
The annual cost of raw materials and the annual valueof products are typically orders-of-magnitude larger than the
annual cost of energy and capital Therefore most chemicalprocess are designed for very high yields (99) and selectivities(100)
The precise ldquo bestrdquo values for these criteria are strongly dependent on market prices for raw materials and 1047297nishedproducts Both are difficult to estimate with any precisionIn order to avoid these uncertainties we take the
approach that the designer will specify a reasonable criterionsuch as a selectivity of 100 A plant then can be designedthat meets this criterion with the minimum total annualcost (TAC) Pricing of feed streams and products isavoided
TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period In this work apayback period of 3 years and the installed cost of equipmentare used
TAC frac14 energy cost thorncapital installed investment
payback period eth22THORN
For the 1047298owsheetconsideredin Figure 1 the reactor and all threecolumns change from case to case for a speci1047297ed selectivity Capitalinvestment is requiredfor thereactorvesselcatalyst columnvesselsreboilers and condensers The energy cost depends on the reboilerduties
Tables 1A 1B and 1C give sizing and cost results forCase 1 with three values of k 1 Tables 2A 2B and 2Cgive results for Case 2 The selectivity is 100 the costof catalyst is $10 per kg and the relative volatility between all adjacent components is 2 The reactor size is varied over a range until the reactor that minimized the TACis found
Table 1A Sizing and Economics Results for the k1 = 15 h1
Case
parameter value
V R 140 kmol
recycle D1 453 kmolh
recycle D3 6611 kmolh
reactor $01499 106
catalyst $05000 106
value
parameter column C1 column C2 column C3
total trays 32 38 18
column diameter 2114 m 3746 m 2928 m
re1047298ux ratio 8210 8434 02098
column vessel $04908 106 $1034 106 $04368 106
heat exchangers $04263 106 $07158 106 $06508 106
reboiler duty 2693 MW 5978 MW 5163 MW
energy $06608 106yr $1467 106yr $1267 106yr
Total Capital = $4404 106
Total Energy = $3394 106yr
TAC = $4862 106yr
Table 1B Sizing and Economics Results for k1 = 25 h1 Case
parameter value
V R 90 kmol
recycle D1 3012 kmolh
recycle D3 3965 kmolh
reactor $01134 106
catalyst $03214 106
value
parameter column C1 column C2 column C3
total trays 33 38 18
column diameter 1794 m 3112 m 2495 m
re1047298ux ratio 8967 5511 04648
column vessel $04245 106 $08486 106 $03683 106
heat exchangers $03442 106 $05625 106 $05286 106
reboiler duty 1938 MW 4120 MW 3750 MW
energy $04754 106yr $1022 106yr $09200 106yr
Total Capital = $3512 106
Total Energy = $2408 106yr
TAC = $3578 106yr
Table 1C Sizing and Economics Results for the k1 = 50 h1
Case
parameter value
V R 60 kmol
recycle D1 1605 kmolh
recycle D3 1982 kmolh
reactor $008846 106
catalyst $02143 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 1487 m 2531 m 1918 m
re1047298ux ratio 1186 3308 07321
column vessel $03600 106 $06809 106 $02783 106
heat exchangers $02698 106 $04300 106 $03766 106
reboiler duty 1330 MW 2730 MW 2216 MW
energy $03270 106yr $06697 106yr $05437 106yr
Total Capital = $2698 106
Total Energy = $1540 106yr
TAC = $2440 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 78
4794 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 88
4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 48
4791 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
B1xB1B frac14 B2xB2B eth15THORN
B1xB1C frac14 D2xD2C thorn B2xB2C eth16THORN
The additional 4 unknown variables not in the previous list of 12are D2 B2 xD2 A
and xB2B bringing the total to 16 Note that xD2C
can be calculated from eq 17
xD2C frac14 1 xD2 A xD2B eth17THORN
24 Column C3 The bottoms B2 is fed into the third column whose job is to recycle B from the top and produce product D
from the bottom The small amount of C that drops out the bottom of the second column also goes overhead The separationin column C3 is between components B and D The impurity of B in the bottoms is set at xB3B
= 0001 The impurity of D in thedistillate is set at xD3D
= 0001The equations that describe the third distillation column
(column C3) are given below
B2 frac14 D3 thorn B3 eth18THORN
B2xB2B frac14 D3xD3B thorn B3xB3B eth19THORN
B2xB2C frac14 D3xD3C eth20THORN
Figure 4 Eff ect of k 1 and reactor size on B1 and D3 Case 1
Figure 5 Eff ect of k 1 and reactor size on reactor composition Case 1
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4792 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The additional unknown variable that was not in theprevious lists is B3 which brings the 1047297nal total number of unknown variables to 17 Note that xD3C
can be calculatedfrom eq 21
xD3C frac14 1 xD3B xD3D eth21THORN
There are a total of 17 unknowns so we need 17 equationsEquations 47 916 and 1821 give a total of 16 equationsthat describe the system We need one more equation
The 1047297nal equation is provided by using the de1047297nition of selectivity given in eq 3 The resulting 17 equations are solvedusing the Matlab function fsolve for a given case of speci1047297edreactor size (V R ) speci1047297c reaction rates (k 1 and k 2) andselectivity
3 RESULTS
31 Case 1 (A thorn Cf D) Figure 2 shows results from thesecalculations for the case in which reactant A is consumed in the
undesired reaction In all of the cases shown in this paper theselectivity is set at 100 Results for three different kineticparameters are shown k 1 = 15 25 and 50 h1 The value of k 2is 1 in all cases The ordinate is the flow rate of recycle D1 fromthe first column The abscissa is the reactor molar holdupFigure 3 shows the sum of the two recycles D1 and D3 Since alarge excess of B must be used in the reactor the D3 recycle fromthe top of the third column is much larger than the D1 recyclefrom the top of the first column
More recycle is needed to achieve a speci1047297ed selectivity fora1047297 xed reactor size as the speci1047297c reaction rate k 1 is reducedSmall values of k 1 lead to larger concentrations of A in thereactor ( z A ) but smaller concentrations of C ( zC) and D ( zD)
The key feature of these plots (and the basis for the heuristic
proposed) is that the required recycle 1047298ow rate level out at
some minimum value as the reactor size is made very large Wede1047297ne the asymptotic recycle 1047298ow rate as the minimumrecycle It can be expressed as a ratio to the fresh feed of A to put it in dimensionless form For example for the k 1 = 25h1 case the minimum total recycle is 409 kmolh for a freshfeed of F A0 = 100 kmolh Thus the minimum recycle ratio(R min) is 409
Figure 4 shows how the 1047298
ow rate of the bottoms from the1047297rst column B1 and the D3 recycle change as reactor size is varied Somewhat unexpectedly the 1047298ow rates of the bottomsof all three columns and the distillates from the second andthird column change very little with reactor size The only 1047298ow rate that really changes signi1047297cantly is the distillate of the1047297rst column as shown in Figure 2 These other 1047298ow rates arestrong functions of the reaction rate k 1 but change little withreactor size
Figure 5 shows how reactor compositions change Noticethat the reactor compositions all level out as the reactor size isincreased The largest changes are in the composition reactant A ( z A ) which decreases as reactor size increases while theother three composition increase Reactor composition z A
decreases as speci1047297c reaction rate k 1 increases while zC and zDincrease since the desired reaction is more favorable
The curves shown in Figures 2 and 3 are similar to those seenin the classical plots of re1047298ux ratio versus trays in distillationdesign At anypointon the curvethe productsfrom the processare exactly the same but equipment (reactor and columns)and energy (reboiler heat inputs) are diff erent So where is theoptimum point on the curve We address this question nextfor several diff erent cases to determine if there is some simplerelationship between the economic optimum recycle 1047298ow rates and the minimum The minimum recycle 1047298ow rates can be easily determined by running a case with a very largereactor
32 Case2 (BthornCfD) Figure 6 gives results for the case in
which reactant B is consumed in the undesired reaction A
Figure 6 Eff ect of k 1 and reactor size on recycles Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4793 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
large excess of A is required in the reactor to achieve thespecified selectivity of 100 Therefore the recycle D1 (fromthe top of the first column)is much larger than the D3 recycle(from the top of the third column)
4 ECONOMIC OPTIMIZATION
The annual cost of raw materials and the annual valueof products are typically orders-of-magnitude larger than the
annual cost of energy and capital Therefore most chemicalprocess are designed for very high yields (99) and selectivities(100)
The precise ldquo bestrdquo values for these criteria are strongly dependent on market prices for raw materials and 1047297nishedproducts Both are difficult to estimate with any precisionIn order to avoid these uncertainties we take the
approach that the designer will specify a reasonable criterionsuch as a selectivity of 100 A plant then can be designedthat meets this criterion with the minimum total annualcost (TAC) Pricing of feed streams and products isavoided
TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period In this work apayback period of 3 years and the installed cost of equipmentare used
TAC frac14 energy cost thorncapital installed investment
payback period eth22THORN
For the 1047298owsheetconsideredin Figure 1 the reactor and all threecolumns change from case to case for a speci1047297ed selectivity Capitalinvestment is requiredfor thereactorvesselcatalyst columnvesselsreboilers and condensers The energy cost depends on the reboilerduties
Tables 1A 1B and 1C give sizing and cost results forCase 1 with three values of k 1 Tables 2A 2B and 2Cgive results for Case 2 The selectivity is 100 the costof catalyst is $10 per kg and the relative volatility between all adjacent components is 2 The reactor size is varied over a range until the reactor that minimized the TACis found
Table 1A Sizing and Economics Results for the k1 = 15 h1
Case
parameter value
V R 140 kmol
recycle D1 453 kmolh
recycle D3 6611 kmolh
reactor $01499 106
catalyst $05000 106
value
parameter column C1 column C2 column C3
total trays 32 38 18
column diameter 2114 m 3746 m 2928 m
re1047298ux ratio 8210 8434 02098
column vessel $04908 106 $1034 106 $04368 106
heat exchangers $04263 106 $07158 106 $06508 106
reboiler duty 2693 MW 5978 MW 5163 MW
energy $06608 106yr $1467 106yr $1267 106yr
Total Capital = $4404 106
Total Energy = $3394 106yr
TAC = $4862 106yr
Table 1B Sizing and Economics Results for k1 = 25 h1 Case
parameter value
V R 90 kmol
recycle D1 3012 kmolh
recycle D3 3965 kmolh
reactor $01134 106
catalyst $03214 106
value
parameter column C1 column C2 column C3
total trays 33 38 18
column diameter 1794 m 3112 m 2495 m
re1047298ux ratio 8967 5511 04648
column vessel $04245 106 $08486 106 $03683 106
heat exchangers $03442 106 $05625 106 $05286 106
reboiler duty 1938 MW 4120 MW 3750 MW
energy $04754 106yr $1022 106yr $09200 106yr
Total Capital = $3512 106
Total Energy = $2408 106yr
TAC = $3578 106yr
Table 1C Sizing and Economics Results for the k1 = 50 h1
Case
parameter value
V R 60 kmol
recycle D1 1605 kmolh
recycle D3 1982 kmolh
reactor $008846 106
catalyst $02143 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 1487 m 2531 m 1918 m
re1047298ux ratio 1186 3308 07321
column vessel $03600 106 $06809 106 $02783 106
heat exchangers $02698 106 $04300 106 $03766 106
reboiler duty 1330 MW 2730 MW 2216 MW
energy $03270 106yr $06697 106yr $05437 106yr
Total Capital = $2698 106
Total Energy = $1540 106yr
TAC = $2440 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 78
4794 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 88
4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4791 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
B1xB1B frac14 B2xB2B eth15THORN
B1xB1C frac14 D2xD2C thorn B2xB2C eth16THORN
The additional 4 unknown variables not in the previous list of 12are D2 B2 xD2 A
and xB2B bringing the total to 16 Note that xD2C
can be calculated from eq 17
xD2C frac14 1 xD2 A xD2B eth17THORN
24 Column C3 The bottoms B2 is fed into the third column whose job is to recycle B from the top and produce product D
from the bottom The small amount of C that drops out the bottom of the second column also goes overhead The separationin column C3 is between components B and D The impurity of B in the bottoms is set at xB3B
= 0001 The impurity of D in thedistillate is set at xD3D
= 0001The equations that describe the third distillation column
(column C3) are given below
B2 frac14 D3 thorn B3 eth18THORN
B2xB2B frac14 D3xD3B thorn B3xB3B eth19THORN
B2xB2C frac14 D3xD3C eth20THORN
Figure 4 Eff ect of k 1 and reactor size on B1 and D3 Case 1
Figure 5 Eff ect of k 1 and reactor size on reactor composition Case 1
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4792 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The additional unknown variable that was not in theprevious lists is B3 which brings the 1047297nal total number of unknown variables to 17 Note that xD3C
can be calculatedfrom eq 21
xD3C frac14 1 xD3B xD3D eth21THORN
There are a total of 17 unknowns so we need 17 equationsEquations 47 916 and 1821 give a total of 16 equationsthat describe the system We need one more equation
The 1047297nal equation is provided by using the de1047297nition of selectivity given in eq 3 The resulting 17 equations are solvedusing the Matlab function fsolve for a given case of speci1047297edreactor size (V R ) speci1047297c reaction rates (k 1 and k 2) andselectivity
3 RESULTS
31 Case 1 (A thorn Cf D) Figure 2 shows results from thesecalculations for the case in which reactant A is consumed in the
undesired reaction In all of the cases shown in this paper theselectivity is set at 100 Results for three different kineticparameters are shown k 1 = 15 25 and 50 h1 The value of k 2is 1 in all cases The ordinate is the flow rate of recycle D1 fromthe first column The abscissa is the reactor molar holdupFigure 3 shows the sum of the two recycles D1 and D3 Since alarge excess of B must be used in the reactor the D3 recycle fromthe top of the third column is much larger than the D1 recyclefrom the top of the first column
More recycle is needed to achieve a speci1047297ed selectivity fora1047297 xed reactor size as the speci1047297c reaction rate k 1 is reducedSmall values of k 1 lead to larger concentrations of A in thereactor ( z A ) but smaller concentrations of C ( zC) and D ( zD)
The key feature of these plots (and the basis for the heuristic
proposed) is that the required recycle 1047298ow rate level out at
some minimum value as the reactor size is made very large Wede1047297ne the asymptotic recycle 1047298ow rate as the minimumrecycle It can be expressed as a ratio to the fresh feed of A to put it in dimensionless form For example for the k 1 = 25h1 case the minimum total recycle is 409 kmolh for a freshfeed of F A0 = 100 kmolh Thus the minimum recycle ratio(R min) is 409
Figure 4 shows how the 1047298
ow rate of the bottoms from the1047297rst column B1 and the D3 recycle change as reactor size is varied Somewhat unexpectedly the 1047298ow rates of the bottomsof all three columns and the distillates from the second andthird column change very little with reactor size The only 1047298ow rate that really changes signi1047297cantly is the distillate of the1047297rst column as shown in Figure 2 These other 1047298ow rates arestrong functions of the reaction rate k 1 but change little withreactor size
Figure 5 shows how reactor compositions change Noticethat the reactor compositions all level out as the reactor size isincreased The largest changes are in the composition reactant A ( z A ) which decreases as reactor size increases while theother three composition increase Reactor composition z A
decreases as speci1047297c reaction rate k 1 increases while zC and zDincrease since the desired reaction is more favorable
The curves shown in Figures 2 and 3 are similar to those seenin the classical plots of re1047298ux ratio versus trays in distillationdesign At anypointon the curvethe productsfrom the processare exactly the same but equipment (reactor and columns)and energy (reboiler heat inputs) are diff erent So where is theoptimum point on the curve We address this question nextfor several diff erent cases to determine if there is some simplerelationship between the economic optimum recycle 1047298ow rates and the minimum The minimum recycle 1047298ow rates can be easily determined by running a case with a very largereactor
32 Case2 (BthornCfD) Figure 6 gives results for the case in
which reactant B is consumed in the undesired reaction A
Figure 6 Eff ect of k 1 and reactor size on recycles Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4793 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
large excess of A is required in the reactor to achieve thespecified selectivity of 100 Therefore the recycle D1 (fromthe top of the first column)is much larger than the D3 recycle(from the top of the third column)
4 ECONOMIC OPTIMIZATION
The annual cost of raw materials and the annual valueof products are typically orders-of-magnitude larger than the
annual cost of energy and capital Therefore most chemicalprocess are designed for very high yields (99) and selectivities(100)
The precise ldquo bestrdquo values for these criteria are strongly dependent on market prices for raw materials and 1047297nishedproducts Both are difficult to estimate with any precisionIn order to avoid these uncertainties we take the
approach that the designer will specify a reasonable criterionsuch as a selectivity of 100 A plant then can be designedthat meets this criterion with the minimum total annualcost (TAC) Pricing of feed streams and products isavoided
TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period In this work apayback period of 3 years and the installed cost of equipmentare used
TAC frac14 energy cost thorncapital installed investment
payback period eth22THORN
For the 1047298owsheetconsideredin Figure 1 the reactor and all threecolumns change from case to case for a speci1047297ed selectivity Capitalinvestment is requiredfor thereactorvesselcatalyst columnvesselsreboilers and condensers The energy cost depends on the reboilerduties
Tables 1A 1B and 1C give sizing and cost results forCase 1 with three values of k 1 Tables 2A 2B and 2Cgive results for Case 2 The selectivity is 100 the costof catalyst is $10 per kg and the relative volatility between all adjacent components is 2 The reactor size is varied over a range until the reactor that minimized the TACis found
Table 1A Sizing and Economics Results for the k1 = 15 h1
Case
parameter value
V R 140 kmol
recycle D1 453 kmolh
recycle D3 6611 kmolh
reactor $01499 106
catalyst $05000 106
value
parameter column C1 column C2 column C3
total trays 32 38 18
column diameter 2114 m 3746 m 2928 m
re1047298ux ratio 8210 8434 02098
column vessel $04908 106 $1034 106 $04368 106
heat exchangers $04263 106 $07158 106 $06508 106
reboiler duty 2693 MW 5978 MW 5163 MW
energy $06608 106yr $1467 106yr $1267 106yr
Total Capital = $4404 106
Total Energy = $3394 106yr
TAC = $4862 106yr
Table 1B Sizing and Economics Results for k1 = 25 h1 Case
parameter value
V R 90 kmol
recycle D1 3012 kmolh
recycle D3 3965 kmolh
reactor $01134 106
catalyst $03214 106
value
parameter column C1 column C2 column C3
total trays 33 38 18
column diameter 1794 m 3112 m 2495 m
re1047298ux ratio 8967 5511 04648
column vessel $04245 106 $08486 106 $03683 106
heat exchangers $03442 106 $05625 106 $05286 106
reboiler duty 1938 MW 4120 MW 3750 MW
energy $04754 106yr $1022 106yr $09200 106yr
Total Capital = $3512 106
Total Energy = $2408 106yr
TAC = $3578 106yr
Table 1C Sizing and Economics Results for the k1 = 50 h1
Case
parameter value
V R 60 kmol
recycle D1 1605 kmolh
recycle D3 1982 kmolh
reactor $008846 106
catalyst $02143 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 1487 m 2531 m 1918 m
re1047298ux ratio 1186 3308 07321
column vessel $03600 106 $06809 106 $02783 106
heat exchangers $02698 106 $04300 106 $03766 106
reboiler duty 1330 MW 2730 MW 2216 MW
energy $03270 106yr $06697 106yr $05437 106yr
Total Capital = $2698 106
Total Energy = $1540 106yr
TAC = $2440 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4794 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4792 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The additional unknown variable that was not in theprevious lists is B3 which brings the 1047297nal total number of unknown variables to 17 Note that xD3C
can be calculatedfrom eq 21
xD3C frac14 1 xD3B xD3D eth21THORN
There are a total of 17 unknowns so we need 17 equationsEquations 47 916 and 1821 give a total of 16 equationsthat describe the system We need one more equation
The 1047297nal equation is provided by using the de1047297nition of selectivity given in eq 3 The resulting 17 equations are solvedusing the Matlab function fsolve for a given case of speci1047297edreactor size (V R ) speci1047297c reaction rates (k 1 and k 2) andselectivity
3 RESULTS
31 Case 1 (A thorn Cf D) Figure 2 shows results from thesecalculations for the case in which reactant A is consumed in the
undesired reaction In all of the cases shown in this paper theselectivity is set at 100 Results for three different kineticparameters are shown k 1 = 15 25 and 50 h1 The value of k 2is 1 in all cases The ordinate is the flow rate of recycle D1 fromthe first column The abscissa is the reactor molar holdupFigure 3 shows the sum of the two recycles D1 and D3 Since alarge excess of B must be used in the reactor the D3 recycle fromthe top of the third column is much larger than the D1 recyclefrom the top of the first column
More recycle is needed to achieve a speci1047297ed selectivity fora1047297 xed reactor size as the speci1047297c reaction rate k 1 is reducedSmall values of k 1 lead to larger concentrations of A in thereactor ( z A ) but smaller concentrations of C ( zC) and D ( zD)
The key feature of these plots (and the basis for the heuristic
proposed) is that the required recycle 1047298ow rate level out at
some minimum value as the reactor size is made very large Wede1047297ne the asymptotic recycle 1047298ow rate as the minimumrecycle It can be expressed as a ratio to the fresh feed of A to put it in dimensionless form For example for the k 1 = 25h1 case the minimum total recycle is 409 kmolh for a freshfeed of F A0 = 100 kmolh Thus the minimum recycle ratio(R min) is 409
Figure 4 shows how the 1047298
ow rate of the bottoms from the1047297rst column B1 and the D3 recycle change as reactor size is varied Somewhat unexpectedly the 1047298ow rates of the bottomsof all three columns and the distillates from the second andthird column change very little with reactor size The only 1047298ow rate that really changes signi1047297cantly is the distillate of the1047297rst column as shown in Figure 2 These other 1047298ow rates arestrong functions of the reaction rate k 1 but change little withreactor size
Figure 5 shows how reactor compositions change Noticethat the reactor compositions all level out as the reactor size isincreased The largest changes are in the composition reactant A ( z A ) which decreases as reactor size increases while theother three composition increase Reactor composition z A
decreases as speci1047297c reaction rate k 1 increases while zC and zDincrease since the desired reaction is more favorable
The curves shown in Figures 2 and 3 are similar to those seenin the classical plots of re1047298ux ratio versus trays in distillationdesign At anypointon the curvethe productsfrom the processare exactly the same but equipment (reactor and columns)and energy (reboiler heat inputs) are diff erent So where is theoptimum point on the curve We address this question nextfor several diff erent cases to determine if there is some simplerelationship between the economic optimum recycle 1047298ow rates and the minimum The minimum recycle 1047298ow rates can be easily determined by running a case with a very largereactor
32 Case2 (BthornCfD) Figure 6 gives results for the case in
which reactant B is consumed in the undesired reaction A
Figure 6 Eff ect of k 1 and reactor size on recycles Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
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4793 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
large excess of A is required in the reactor to achieve thespecified selectivity of 100 Therefore the recycle D1 (fromthe top of the first column)is much larger than the D3 recycle(from the top of the third column)
4 ECONOMIC OPTIMIZATION
The annual cost of raw materials and the annual valueof products are typically orders-of-magnitude larger than the
annual cost of energy and capital Therefore most chemicalprocess are designed for very high yields (99) and selectivities(100)
The precise ldquo bestrdquo values for these criteria are strongly dependent on market prices for raw materials and 1047297nishedproducts Both are difficult to estimate with any precisionIn order to avoid these uncertainties we take the
approach that the designer will specify a reasonable criterionsuch as a selectivity of 100 A plant then can be designedthat meets this criterion with the minimum total annualcost (TAC) Pricing of feed streams and products isavoided
TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period In this work apayback period of 3 years and the installed cost of equipmentare used
TAC frac14 energy cost thorncapital installed investment
payback period eth22THORN
For the 1047298owsheetconsideredin Figure 1 the reactor and all threecolumns change from case to case for a speci1047297ed selectivity Capitalinvestment is requiredfor thereactorvesselcatalyst columnvesselsreboilers and condensers The energy cost depends on the reboilerduties
Tables 1A 1B and 1C give sizing and cost results forCase 1 with three values of k 1 Tables 2A 2B and 2Cgive results for Case 2 The selectivity is 100 the costof catalyst is $10 per kg and the relative volatility between all adjacent components is 2 The reactor size is varied over a range until the reactor that minimized the TACis found
Table 1A Sizing and Economics Results for the k1 = 15 h1
Case
parameter value
V R 140 kmol
recycle D1 453 kmolh
recycle D3 6611 kmolh
reactor $01499 106
catalyst $05000 106
value
parameter column C1 column C2 column C3
total trays 32 38 18
column diameter 2114 m 3746 m 2928 m
re1047298ux ratio 8210 8434 02098
column vessel $04908 106 $1034 106 $04368 106
heat exchangers $04263 106 $07158 106 $06508 106
reboiler duty 2693 MW 5978 MW 5163 MW
energy $06608 106yr $1467 106yr $1267 106yr
Total Capital = $4404 106
Total Energy = $3394 106yr
TAC = $4862 106yr
Table 1B Sizing and Economics Results for k1 = 25 h1 Case
parameter value
V R 90 kmol
recycle D1 3012 kmolh
recycle D3 3965 kmolh
reactor $01134 106
catalyst $03214 106
value
parameter column C1 column C2 column C3
total trays 33 38 18
column diameter 1794 m 3112 m 2495 m
re1047298ux ratio 8967 5511 04648
column vessel $04245 106 $08486 106 $03683 106
heat exchangers $03442 106 $05625 106 $05286 106
reboiler duty 1938 MW 4120 MW 3750 MW
energy $04754 106yr $1022 106yr $09200 106yr
Total Capital = $3512 106
Total Energy = $2408 106yr
TAC = $3578 106yr
Table 1C Sizing and Economics Results for the k1 = 50 h1
Case
parameter value
V R 60 kmol
recycle D1 1605 kmolh
recycle D3 1982 kmolh
reactor $008846 106
catalyst $02143 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 1487 m 2531 m 1918 m
re1047298ux ratio 1186 3308 07321
column vessel $03600 106 $06809 106 $02783 106
heat exchangers $02698 106 $04300 106 $03766 106
reboiler duty 1330 MW 2730 MW 2216 MW
energy $03270 106yr $06697 106yr $05437 106yr
Total Capital = $2698 106
Total Energy = $1540 106yr
TAC = $2440 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 78
4794 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 88
4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 68
4793 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
large excess of A is required in the reactor to achieve thespecified selectivity of 100 Therefore the recycle D1 (fromthe top of the first column)is much larger than the D3 recycle(from the top of the third column)
4 ECONOMIC OPTIMIZATION
The annual cost of raw materials and the annual valueof products are typically orders-of-magnitude larger than the
annual cost of energy and capital Therefore most chemicalprocess are designed for very high yields (99) and selectivities(100)
The precise ldquo bestrdquo values for these criteria are strongly dependent on market prices for raw materials and 1047297nishedproducts Both are difficult to estimate with any precisionIn order to avoid these uncertainties we take the
approach that the designer will specify a reasonable criterionsuch as a selectivity of 100 A plant then can be designedthat meets this criterion with the minimum total annualcost (TAC) Pricing of feed streams and products isavoided
TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period In this work apayback period of 3 years and the installed cost of equipmentare used
TAC frac14 energy cost thorncapital installed investment
payback period eth22THORN
For the 1047298owsheetconsideredin Figure 1 the reactor and all threecolumns change from case to case for a speci1047297ed selectivity Capitalinvestment is requiredfor thereactorvesselcatalyst columnvesselsreboilers and condensers The energy cost depends on the reboilerduties
Tables 1A 1B and 1C give sizing and cost results forCase 1 with three values of k 1 Tables 2A 2B and 2Cgive results for Case 2 The selectivity is 100 the costof catalyst is $10 per kg and the relative volatility between all adjacent components is 2 The reactor size is varied over a range until the reactor that minimized the TACis found
Table 1A Sizing and Economics Results for the k1 = 15 h1
Case
parameter value
V R 140 kmol
recycle D1 453 kmolh
recycle D3 6611 kmolh
reactor $01499 106
catalyst $05000 106
value
parameter column C1 column C2 column C3
total trays 32 38 18
column diameter 2114 m 3746 m 2928 m
re1047298ux ratio 8210 8434 02098
column vessel $04908 106 $1034 106 $04368 106
heat exchangers $04263 106 $07158 106 $06508 106
reboiler duty 2693 MW 5978 MW 5163 MW
energy $06608 106yr $1467 106yr $1267 106yr
Total Capital = $4404 106
Total Energy = $3394 106yr
TAC = $4862 106yr
Table 1B Sizing and Economics Results for k1 = 25 h1 Case
parameter value
V R 90 kmol
recycle D1 3012 kmolh
recycle D3 3965 kmolh
reactor $01134 106
catalyst $03214 106
value
parameter column C1 column C2 column C3
total trays 33 38 18
column diameter 1794 m 3112 m 2495 m
re1047298ux ratio 8967 5511 04648
column vessel $04245 106 $08486 106 $03683 106
heat exchangers $03442 106 $05625 106 $05286 106
reboiler duty 1938 MW 4120 MW 3750 MW
energy $04754 106yr $1022 106yr $09200 106yr
Total Capital = $3512 106
Total Energy = $2408 106yr
TAC = $3578 106yr
Table 1C Sizing and Economics Results for the k1 = 50 h1
Case
parameter value
V R 60 kmol
recycle D1 1605 kmolh
recycle D3 1982 kmolh
reactor $008846 106
catalyst $02143 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 1487 m 2531 m 1918 m
re1047298ux ratio 1186 3308 07321
column vessel $03600 106 $06809 106 $02783 106
heat exchangers $02698 106 $04300 106 $03766 106
reboiler duty 1330 MW 2730 MW 2216 MW
energy $03270 106yr $06697 106yr $05437 106yr
Total Capital = $2698 106
Total Energy = $1540 106yr
TAC = $2440 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 78
4794 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 88
4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 78
4794 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
As expected capital and energy costs decrease as the favorablespeci1047297c reaction rate k 1 increases because both the optimumreactor size and the optimum recycle 1047298ow rate decrease as k 1increases
41 Case 1 (A thorn CfD) The optimum designs are indicated by stars in Figures 2 and 3 Notice that the minimum total recycle
flow rates (D1thornD3) for the three values of k 1 are 691 kmolh fork 1 = 1 5 h1 409 kmolh for k 1 = 2 5 h1 and 202 kmolh for k 1 =50 h1
The economic optimum total recycle 1047298ow rates are 706 kmolhfor k 1 = 1 5 h1 426 kmolh for k 1 = 2 5 h1 and 214 kmolh fork 1 = 50 h1 The three optimum-to-minimum ratios are 102
104 and 10642 Case 2 (B thorn CfD) The optimum designs are indicated
by stars in Figures 7 and 8 Notice that the minimum totalrecycle flow rates (D1 thorn D3) for the three values of k 1 are6864 kmolh for k 1 = 15 h1 4078 kmolh for k 1 = 25 h1 and 2025 kmolh for k 1 = 50 h1 These are essentially thesame minimum total recycle flow rates as found in Case 1 butnowtheD1 recycle is large and D3 is small which is the reverse of Case 1
The economic optimum total recycle 1047298ow rates are 7049kmolh for k 1 = 15 h1 4233 kmolh for k 1 = 25 h1 and 216kmolh for k 1 = 50 h1 The three optimum-to-minimum ratiosare 103 104 and 107
Figure 9 shows the eff ect that k 1 and reactor size hason reactor
composition ( z A zB zC and zD) in Case 2The results from both cases suggest that a heuristic
of sim105 may be valid for preliminary conceptual designof systems with more-complex separation sections Theheuristic for a separation section with only one recycleis 12
5 CONCLUSION
The results of this study i llustrate that a s impledesign heuristic can be used at the early stages of con-ceptual design to develop chemical processes with reactionand separation sections connected by a recycle stream
Table 2A Sizing and Economics Results for the k1 = 15 h1
Case B thorn C = D
parameter value
V R 190 kmol
recycle D1 6711 kmolh
recycle D3 3383 kmolh
reactor $01813 106
catalyst $06786 106
value
parameter column C1 column C2 column C3
total trays 37 38 18
column diameter 4036 m 1925 m 08635 m
re1047298ux ratio 1266 1466 1056
column vessel $1100 106 $05077 106 $01189 106
heat exchangers $09881 106 $03012 106 $01331 106
reboiler duty 9815 MW 1578 MW 04491 MW
energy $2408 106yr $03871 106yr $01102 106yr
Total Capital = $4088 106
Total Energy = $2905 106yr
TAC = $4242 106yr
Table 2B Sizing and Economics Results for the k1 = 25 h1
Case B thorn C = D
parameter value
V R 125 kmol
recycle D1 4015 kmolh
recycle D3 2176 kmolh
reactor $01397 106
catalyst $04465 106
value
column C1 C2 C3
total trays 38 38 18
column diameter 3198 m 1870 m 06998 m
re1047298ux ratio 1377 1329 1100
column vessel $08629 106 $04920 106 $00950 106
heat exchangers $07299 106 $02902 106 $01012 106
reboiler duty 6160 MW 1490 MW 0295 MW
energy $1511 106yr $03656 106yr $007238 106yr
Total Capital = $3157 106
Total Energy = $1949 106yr
TAC = $3002 106yr
Table 2C Sizing and Economics Results for the k1 = 50 h1
Case B thorn C = D
parameter value
V R 60 kmol
recycle D1 2003 kmolh
recycle D3 1211 kmolh
reactor $01058 106
catalyst $02857 106
value
parameter column C1 column C2 column C3
total trays 35 38 18
column diameter 2386 m 1823 m 05294 m
re1047298ux ratio 1653 1214 1160
column vessel $06349 106 $04779 106 $00755 106
heat exchangers $04998 106 $02808 106 $007054 106
reboiler duty 3431 MW 1416 MW 0168 MW
energy $08417 106
yr $02475 106
yr $004142 106
yr
Total Capital = $2425 106
Total Energy = $1231 106yr
TAC = $2039 106yr
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 88
4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
8122019 Luyben_Heuristic Design of Reaction-separation Processes With Two Recycles
httpslidepdfcomreaderfullluybenheuristic-design-of-reaction-separation-processes-with-two-recycles 88
4795 dxdoiorg101021ie101896v |Ind Eng Chem Res 2011 50 4788ndash4795
Industrial amp Engineering Chemistry Research RESEARCH NOTE
The economic optimum for 1047298owsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle 1047298ow rates
rsquoAUTHOR INFORMATION
Corresponding AuthorTel 610-758-4256 Fax610-758-5057 E-mailWLL0Lehighedu
rsquoREFERENCES
(1) Luyben W L Heuristic Design of ReactionSeparation Pro-cesses Ind Eng Chem Res 2010 49 1156411571
(2) Douglas J M Conceptual Design of Chemical ProcessesMcGraw Hill New York 1988
(3) Turton R Bailie R C Whiting W B Shaelwitz J A AnalysisSynthesis and Design of Chemical Processes 2nd Edition Prentice HallUpper Saddle River NJ 2003
Figure 7 Eff ect of k 1 and reactor size on reactor compositions Case 2 Figure 8 Eff ect of k 1 and reactor size on total recycles Case 2
Figure 9 Eff ect of k 1 and reactor size on reactor compositions Case 2
