Separation Processes with Two Recycles

RESEARCH NOTE pubs.acs.org/IECR

Heuristic Design of Reaction/Separation 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 and recycle flow rate during the preliminary conceptual process design of a reaction/separation process. The basic idea is to find the minimum recycle flow rate by designing the process to meet some specified conversion/yield/selectivity criterion, using a very large reactor. A heuristic of setting the actual recycle flow rate equal to 1.2 times the minimum then is used to obtain an approximate optimum design. The process studied had relative volatilities such that only one recycle stream was needed. The purpose of this paper is to extend this work to the case where two recycle streams are required. There is a reactor and three distillation columns with two recycle streams. The desired product C is produced via the reaction A þ B f C. An undesired product D is also produced. Two alternative reactions (A þ C f D or A þ B f D) mean that there is a large recycle of either B or A to achieve high selectivity. The relative volatilities are assumed to be RA > RC > RB > RD, so reactant A is recycled from the overhead of the first distillation column and reactant B is recycled from the overhead of the third column. Product C is the distillate of the second column, and product D is the bottoms of the third column. Results show that the more-complex separation section shifts the economics to favor a smaller heuristic ratio (1.05) of actual recycle to minimum recycle.

1. INTRODUCTION Heuristics are very useful at the conceptual design stage of process development, where the precision of a rigorous optimization method is not required. Common heuristics in distillation design are to set the actual number of trays equal to twice the minimum number of trays or to set the actual reflux ratio equal to 1.2 times the minimum reflux ratio. Other examples of important chemical engineering heuristics include selecting pressure drops over heat exchangers to achieve reasonable heat-transfer coefficients, selecting pressure drops over control valves to achieve dynamic rangeability, and choosing reasonable heat-transfer coefficients and temperature differential driving forces to find the area of heat exchangers. A recent paper1 suggested a new heuristic for establishing the optimum design of a reactor/separation process with recycle. There is a tradeoff between the size of the reactor and the amount of recycle required to achieve a specified design criterion, such as conversion, yield, or selectivity in the overall process. Major capital and operating costs are often in the separation section, but the performance of the reaction section is usually critical because of the dominant economic effect of raw material costs and product values. The intent of the proposed heuristic is to provide some guidance for initial flowsheet development at the conceptual process design stage. In the original paper, the process consisted of a reactor and two distillation columns. The relative volatilities were such that a single recycle stream was required. The heuristic developed proposed setting the actual recycle flow rate at ∼1.2 times the minimum recycle flow rate as determined by designing with a very large reactor. The purpose of this paper is to extend this work to consider a more complex separation section in which two recycles are required. Since the separation section is more complex and therefore more expensive, we expect the heuristic ratio of actual-to-minimum recycle flow rates to be smaller, which is indeed what the results of this paper show. There is no claim that this approach is applicable to all chemical kinetic reactions and reactor/separator systems. Although recycles r 2011 American Chemical Society

are very commonly used to affect selectivity, which is the situation in this study, recycles are sometimes used for other purposes. For example, a recycle stream is used in some adiabatic reactors to moderate the temperature change through the reactor. The recycle serves as a thermal sink whose sensible heat absorbs some of the heat of reaction. This technique is applied with both exothermic and endothermic reactions. Another application of recycle is to maintain the composition of one of the reactants below some hazardous level. Oxidation reactions often require operation below a lower explosive limit, so a recycle stream is used to keep the concentration of oxygen well below this limit. However, the use of recycle to affect selectivity is very common in industrial application, so we may expect that the proposed methodology should be widely applicable. A continuous stirred tank reactor (CSTR) has been used in this study, but the same situation occurs in tubular reactors since what affects selectivity is the ratios of reactants, and these ratios impact recycle flow rates. However, we offer no rigorous mathematical proof that a limiting recycle flow rate exists for all reactor types and chemical kinetics.

2. PROCESS STUDIED Figure 1 shows the flowsheet of the process considered in this paper with the more-complex separation section. The relative volatilities among the reactants A and B and the products C and D are RA > RC > RB > RD. Two fresh feed streams and two recycle streams are fed into a CSTR reactor. The reactor effluent is fed to a distillation column in which the light reactant A goes overhead and is recycled back to the reactor. The second column produces product C at the top. The third column produces a distillate of mostly reactant B, which is recycled back to the reactor. Product D is the bottoms of the third column. Received: September 14, 2010 Accepted: March 11, 2011 Revised: February 15, 2011 Published: March 22, 2011 4788

dx.doi.org/10.1021/ie101896v | Ind. Eng. Chem. Res. 2011, 50, 4788–4795

Industrial & Engineering Chemistry Research

RESEARCH NOTE

Figure 1. Two-recycle flowsheet; Case 1 (k1 = 25 h1, selectivity = 100, $10/kg, R = 2).

Two cases are explored. In the first, the undesired product consumes C and A, which leads to a large recycle of B and only a small recycle of A. In the second case, the undesired product consumes C and B, which leads to a large recycle of A and only a small recycle of B. The equipment sizes and conditions shown are the economic optimum for the first case that are developed later in this paper for the base-case conditions: a selectivity specification of 100 (kmol C produced divided by kmol D produced), kinetic parameters of k1 = 25 h1 and k2 = 1 h1, relative volatilities between adjacent components of 2, and catalyst price of $10 per kg. 2.1. Reactor. The molar holdup of the CSTR reactor is 90 kmol. Two irreversible reactions occur with specific reaction rates k1 and k2:

excess of B, and the concentrations of B and C must be kept small in Case 2 to achieve the desired selectivity by operating with an excess of A. Two fresh feed streams of pure A and pure B are fed to the reactor (F A0 and F B0 ), in addition to the two recycle streams from the top of the first column (D 1 ) and from the top of the third column (D 3 ). Note that, in Case 1, D 1 is small, compared to D 3 because of the excess of component B in the reactor. Selectivity is defined as the number of moles of the desired component C produced divided by the number of moles of the undesired component D produced:

AþB f C R 1 ¼ VR k1 zA zB

where D2 is the distillate from the second column, xD2C the mole fraction of desired component C in the distillate, B3 the bottoms from the third column, and xB3D is the mole fraction of the undesired product in the bottoms. It is important to note that the design criterion selected in this study is selectivity, not conversion. Selectivity is the important performance measure in processes with desirable and undesirable products, 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, which are set by the specified impurity levels. Low concentrations of reactant components A and B appear in the distillate product stream from the second column, and a low concentration of reactant B appears in the bottoms product stream from the third column. These specified compositions determine the conversions of reactants A and B for the overall process. The per-pass conversion of A in Case 1 is fairly high, while the perpass conversion of B is quite small. The reverse is true in Case 2. The fresh feed of reactant A is fixed at FA0 = 100 kmol/h in all cases. The fresh feed of B is calculated for each case by solving the

ð1Þ

Case 1: Reactant A and desired product C are consumed in an undesired reaction: AþC f D R 2 ¼ VR k2 zA zC

ð2AÞ

Case 2: Reactants B and desired product C are consumed in an undesired reaction: BþC f D R 2 ¼ VR k2 zB zC

ð2BÞ

where zj denotes the mole fraction component j in the reactor and VR is the reactor molar holdup. The desired product C is formed by the first reaction, but it can react further to produce an undesired product D. Therefore, the concentrations of A and C must be kept small in Case 1 to achieve the desired selectivity by operating with an

selectivity ¼

4789

number of moles of C D2 xD2 C ¼ number of moles of D B3 xB 3 D

ð3Þ

dx.doi.org/10.1021/ie101896v |Ind. Eng. Chem. Res. 2011, 50, 4788–4795


RESEARCH NOTE

17 nonlinear simultaneous algebraic equations that describe the reactor and the three columns for the specified conditions (reactor size, desired selectivity, and kinetic parameters). The equations that describe the reactor are FA0 þ D1 xD1 A ¼ F1 zA þ R 1 þ R 2

ð4Þ

FB0 þ D3 xD3 B ¼ F1 zB þ R 1

ð5Þ

D1 xD1 C þ D3 xD3 C ¼ F1 zC R 1 þ R 2

ð6Þ

D3 xD3 D ¼ F1 ð1 zA zB zC Þ R 2

ð7Þ

The composition of C in the D1 recycle is assumed to be xD1C = 0.001, which results in the composition of A being given as xD1A = 0.999, since we assume none of B or D goes overhead. The composition of D in the D3 recycle is assumed to be xD3D = 0.001. The six specified variables are FA0, VR, xD1C, xD3D, k1, and k2. The nine unknown variables in these four equations are FB0, zA, zB, zC, D1, D3, xD3C, xD3B, and F1. Note that the reactions are nonequimolar, so there is a reduction in the molar flows into and out of the reactor. Each reaction consumes two moles of reactants while making one mole of product. 2.2. Column C1. The reactor effluent is fed to a distillation column whose job is to recycle unreacted A back to the reactor and send a mixture of reactant B and products C and D downstream to the second distillation column. Constant relative volatilities are assumed with reactant A being the lightest, reactant C being the next lightest, product B being the next lightest, and product D being the heaviest component. RA > RC > RB > RD

ð8Þ

With these phase equilibria relationships, the separation section must have two recycles. The sizing and cost analysis for each column uses the Fenske equation to determine the minimum number of trays and the Underwood equations to determine the minimum reflux ratio. The separation in column C1 is between components A and C. All of components B and D are assumed to exit in the bottoms. The impurity of A in the bottoms is set at xB1A = 0.001.

Figure 2. Effect of k1 and reactor size on recycle D1: Case 1.

The number of trays then is set at twice the minimum, and the required reflux ratio is set at a factor of 1.1 times greater than the minimum to estimate the capital costs (column shell, condenser, and reboiler) and the energy cost (reboiler heat input at $7.78 per GJ). Standard column sizing and cost relationships are used.2,3 The capital cost of the column is based on the size of the vessel, getting the height from the number of theoretical trays with a 2-ft tray spacing and the diameter from Aspen’s Tray Sizing option. The equations describing the first distillation column C1 are given below. F1 ¼ D1 þ B1

ð9Þ

F1 zA ¼ D1 xD1 A þ B1 xB1 A

ð10Þ

F 1 z B ¼ B1 xB 1 B

ð11Þ

F1 zC ¼ D1 xD1 C þ B1 xB1 C

ð12Þ

The additional 3 unknown variables not in the previous list of 9 are B1, xB1B, and xB1C, bringing the total unknows to 12. Note that the variable xB1D can be calculated if the other 3 mole fractions are known (xB1A, xB1B, and xB1C). 2.3. Column C2. The bottoms B1 is fed to the second column whose job is to remove the desired product C overhead. The small amount of A that drops out the bottom of the first column also goes overhead. The separation in column C2 is between components C and B. All of component D is assumed to go out the bottom. The impurity of C in the bottoms is set at xB2C = 0.001. The impurity of B in the distillate is set at xD2B = 0.001. The equations describing the second distillation column C2 are given below. B1 ¼ D2 þ B2

ð13Þ

B1 xB1 A ¼ D2 xD2 A

ð14Þ

Figure 3. Effect of k1 and reactor size on total recycles D1 and D3: Case 1. 4790



RESEARCH NOTE

B1 xB1 B ¼ B2 xB2 B

ð15Þ

B1 xB1 C ¼ D2 xD2 C þ B2 xB2 C

ð16Þ

The additional 4 unknown variables not in the previous list of 12 are D2, B2, xD2A, and xB2B, bringing the total to 16. Note that xD2C can be calculated from eq 17. xD2 C ¼ 1 xD2 A xD2 B

from the bottom. The small amount of C that drops out the bottom of the second column also goes overhead. The separation in column C3 is between components B and D. The impurity of B in the bottoms is set at xB3B = 0.001. The impurity of D in the distillate is set at xD3D = 0.001. The equations that describe the third distillation column (column C3) are given below.

ð17Þ

2.4. Column C3. The bottoms B2 is fed into the third column, whose job is to recycle B from the top and produce product D

B2 ¼ D3 þ B3

ð18Þ

B2 xB2 B ¼ D3 xD3 B þ B3 xB3 B

ð19Þ

B2 xB 2 C ¼ D 3 xD 3 C

ð20Þ

Figure 4. Effect of k1 and reactor size on B1 and D3: Case 1.

Figure 5. Effect of k1 and reactor size on reactor composition: Case 1. 4791



RESEARCH NOTE

The additional unknown variable that was not in the previous lists is B3, which brings the final total number of unknown variables to 17. Note that xD3C can be calculated from eq 21. xD3 C ¼ 1 xD3 B xD3 D

ð21Þ

There are a total of 17 unknowns, so we need 17 equations. Equations 47, 916, and 1821 give a total of 16 equations that describe the system. We need one more equation. The final equation is provided by using the definition of selectivity given in eq 3. The resulting 17 equations are solved using the Matlab function fsolve for a given case of specified reactor size (VR), specific reaction rates (k1 and k2), and selectivity.

3. RESULTS 3.1. Case 1 (A þ C f D). Figure 2 shows results from these calculations for the case in which reactant A is consumed in the undesired reaction. In all of the cases shown in this paper, the selectivity is set at 100. Results for three different kinetic parameters are shown: k1 = 15, 25, and 50 h1. The value of k2 is 1 in all cases. The ordinate is the flow rate of recycle D1 from the first column. The abscissa is the reactor molar holdup. Figure 3 shows the sum of the two recycles D1 and D3. Since a large excess of B must be used in the reactor, the D3 recycle from the top of the third column is much larger than the D1 recycle from the top of the first column. More recycle is needed to achieve a specified selectivity for a fixed reactor size as the specific reaction rate k1 is reduced. Small values of k1 lead to larger concentrations of A in the reactor (zA) 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 flow rate level out at

some minimum value as the reactor size is made very large. We define the asymptotic recycle flow rate as the minimum recycle. It can be expressed as a ratio to the fresh feed of A to put it in dimensionless form. For example, for the k1 = 25 h1 case, the minimum total recycle is 409 kmol/h for a fresh feed of FA0 = 100 kmol/h. Thus, the minimum recycle ratio (Rmin) is 4.09. Figure 4 shows how the flow rate of the bottoms from the first column B1 and the D3 recycle change as reactor size is varied. Somewhat unexpectedly, the flow rates of the bottoms of all three columns and the distillates from the second and third column change very little with reactor size. The only flow rate that really changes significantly is the distillate of the first column, as shown in Figure 2. These other flow rates are strong functions of the reaction rate k1, but change little with reactor size. Figure 5 shows how reactor compositions change. Notice that the reactor compositions all level out as the reactor size is increased. The largest changes are in the composition reactant A (zA), which decreases as reactor size increases while the other three composition increase. Reactor composition zA decreases as specific reaction rate k1 increases, while zC and zD increase, since the desired reaction is more favorable. The curves shown in Figures 2 and 3 are similar to those seen in the classical plots of reflux ratio versus trays in distillation design. At any point on the curve, the products from the process are exactly the same, but equipment (reactor and columns) and energy (reboiler heat inputs) are different. So where is the optimum point on the curve? We address this question next for several different cases to determine if there is some simple relationship between the economic optimum recycle flow rates and the minimum. The minimum recycle flow rates can be easily determined by running a case with a very large reactor. 3.2. Case 2 (B þ C f D). Figure 6 gives results for the case in which reactant B is consumed in the undesired reaction. A

Figure 6. Effect of k1 and reactor size on recycles: Case 2. 4792



RESEARCH NOTE

Table 1A. Sizing and Economics Results for the k1 = 15 h1 Case parameter

Table 1B. Sizing and Economics Results for k1 = 25 h1 Case parameter

value

value VR

90 kmol

VR

140 kmol

recycle D1

30.12 kmol/h

recycle D1 recycle D3

45.3 kmol/h 661.1 kmol/h

recycle D3

396.5 kmol/h

reactor

$0.1134 106

reactor

$0.1499 106

catalyst

$0.3214 106

catalyst

$0.5000 106

value value

parameter

column C1

parameter

column C2

total trays total trays

32

column diameter 2.114 m

38

18

3.746 m

2.928 m

8.434

8.210

column vessel

$0.4908 10

$1.034 10

heat exchangers reboiler duty

$0.4263 10 2.693 MW

$0.7158 10 5.978 MW

energy

$0.6608 106/yr $1.467 106/yr $1.267 106/yr

6

0.2098 6 6

$0.4368 10

6

$0.6508 10 5.163 MW

6

38

18

3.112 m 5.511

2.495 m 0.4648

column vessel

$0.4245 106

$0.8486 106

$0.3683 106

heat exchangers

$0.3442 10

$0.5625 10

$0.5286 106

4.120 MW

3.750 MW

6

6

reboiler duty

1.938 MW

energy

$0.4754 106/yr $1.022 106/yr $0.9200 106/yr

TAC = $3.578 106/yr

TAC = $4.862 106/yr

Table 1C. Sizing and Economics Results for the k1 = 50 h1 Case value

VR

60 kmol

recycle D1

16.05 kmol/h

recycle D3

198.2 kmol/h

reactor catalyst

$0.08846 106 $0.2143 106 value

total trays

column C3

Total Energy = $2.408 106/yr

Total Energy = $3.394 106/yr

parameter

column C2

Total Capital = $3.512 106


parameter

33

column diameter 1.794 m reflux ratio 8.967

reflux ratio

6

column C1

column C3

column C1 35


column C2

column C3

38

18

2.531 m

1.918 m

reflux ratio

11.86

3.308

0.7321

column vessel

$0.3600 106

$0.6809 106

$0.2783 106

heat exchangers

$0.2698 106

$0.4300 106

$0.3766 106

reboiler duty energy

1.330 MW 2.730 MW 2.216 MW $0.3270 106/yr $0.6697 106/yr $0.5437 106/yr

annual cost of energy and capital. Therefore, most chemical process are designed for very high yields (99%) and selectivities (100). The precise “best” values for these criteria are strongly dependent on market prices for raw materials and finished products. Both are difficult to estimate with any precision. In order to avoid these uncertainties, we take the approach that the designer will specify a reasonable criterion, such as a selectivity of 100. A plant then can be designed that meets this criterion with the minimum total annual cost (TAC). Pricing of feed streams and products is avoided. TAC is the sum of the energy cost plus the annual cost of the capital investment using a payback period. In this work, a payback period of 3 years and the installed cost of equipment are used.

TAC ¼ energy cost þ

capital installed investment payback period

ð22Þ

Total Capital = $2.698 106 Total Energy = $1.540 106/yr TAC = $2.440 106/yr

large excess of A is required in the reactor to achieve the specified selectivity of 100. Therefore, the recycle D1 (from the top of the first column) is much larger than the D 3 recycle (from the top of the third column).

4. ECONOMIC OPTIMIZATION The annual cost of raw materials and the annual value of products are typically orders-of-magnitude larger than the

For the flowsheet considered in Figure 1, the reactor and all three columns change from case to case for a specified selectivity. Capital investment is required for the reactor vessel, catalyst, column vessels, reboilers and condensers. The energy cost depends on the reboiler duties. Tables 1A, 1B and 1C give sizing and cost results for Case 1 with three values of k1 . Tables 2A, 2B, and 2C give results for Case 2. The selectivity is 100, the cost of 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 TAC is found. 4793


Industrial & Engineering Chemistry Research Table 2A. Sizing and Economics Results for the k1 = 15 h1 Case; B þ C = D parameter

RESEARCH NOTE

Table 2B. Sizing and Economics Results for the k1 = 25 h1 Case; B þ C = D

value

parameter

value

VR

190 kmol

recycle D1

671.1 kmol/h

VR

125 kmol

recycle D3

33.83 kmol/h

reactor

$0.1813 10

recycle D1 recycle D3

401.5 kmol/h 21.76 kmol/h

catalyst

$0.6786 106

reactor

$0.1397 106

catalyst

$0.4465 106

6

value

value parameter

column C1

column C2

column C3

column

C1

C2

C3

total trays 37 column diameter 4.036 m

38 1.925 m

18 0.8635 m

total trays

38

18


1.870 m

0.6998 m

reflux ratio

1.266

1.466

1.056

$0.5077 106

$0.1189 106

1.377

1.329

1.100

column vessel

$1.100 106

reflux ratio

$0.3012 106

$0.1331 106

$0.8629 106

$0.4920 106

$0.0950 106

heat exchangers

$0.9881 106

column vessel

reboiler duty

9.815 MW

1.578 MW

0.4491 MW

$0.7299 106 6.160 MW

$0.2902 106 1.490 MW

$0.1012 106 0.295 MW

energy

$2.408 106/yr $0.3871 106/yr $0.1102 106/yr

heat exchangers reboiler duty energy

$1.511 106/yr $0.3656 106/yr $0.07238 106/yr


Total Capital = $3.157 106 Total Energy = $1.949 106/yr

Total Energy = $2.905 106/yr TAC = $4.242 106/yr

TAC = $3.002 106/yr

Table 2C. Sizing and Economics Results for the k1 = 50 h1 Case; B þ C = D parameter

value

VR

60 kmol

recycle D1

200.3 kmol/h

recycle D3

12.11 kmol/h

reactor

$0.1058 106

catalyst

$0.2857 106 value

parameter total trays

38

column C1 35

column C2

column C3

38

18


1.823 m

0.5294 m

reflux ratio column vessel

1.653 $0.6349 106

1.214 $0.4779 106

1.160 $0.0755 106

heat exchangers $0.4998 106

$0.2808 106

$0.07054 106

reboiler duty

3.431 MW

1.416 MW

0.168 MW

energy

$0.8417 106/yr $0.2475 106/yr $0.04142 106/yr

Total Capital = $2.425 106 Total Energy = $1.231 106/yr TAC = $2.039 106/yr

As expected, capital and energy costs decrease as the favorable specific reaction rate k1 increases because both the optimum reactor size and the optimum recycle flow rate decrease as k1 increases. 4.1. Case 1 (A þ C f D). The optimum designs are indicated by stars in Figures 2 and 3. Notice that the minimum total recycle

flow rates (D1 þ D3) for the three values of k1 are 691 kmol/h for k1 = 15 h1, 409 kmol/h for k1 = 25 h1, and 202 kmol/h for k1 = 50 h1. The economic optimum total recycle flow rates are 706 kmol/ h for k1 = 15 h1, 426 kmol/h for k1 = 25 h1, and 214 kmol/h for k1 = 50 h1. The three optimum-to-minimum ratios are 1.02, 1.04, and 1.06. 4.2. Case 2 (B þ C f D). The optimum designs are indicated by stars in Figures 7 and 8. Notice that the minimum total recycle flow rates (D1 þ D3) for the three values of k1 are 686.4 kmol/h for k1 = 15 h1, 407.8 kmol/h for k1 = 25 h1, and 202.5 kmol/h for k1 = 50 h1. These are essentially the same minimum total recycle flow rates as found in Case 1, but now the D1 recycle is large and D3 is small, which is the reverse of Case 1. The economic optimum total recycle flow rates are 704.9 kmol/h for k1 = 15 h1, 423.3 kmol/h for k1 = 25 h1, and 216 kmol/h for k1 = 50 h1. The three optimum-to-minimum ratios are 1.03, 1.04, and 1.07. Figure 9 shows the effect that k1 and reactor size has on reactor composition (zA, zB, zC, and zD) in Case 2. The results from both cases suggest that a heuristic of ∼1.05 may be valid for preliminary conceptual design of systems with more-complex separation sections. The heuristic for a separation section with only one recycle is 1.2.

5. CONCLUSION The results of this study illustrate that a simple design heuristic can be used at the early stages of conceptual design to develop chemical processes with reaction and separation sections connected by a recycle stream. 4794



Figure 7. Effect of k1 and reactor size on reactor compositions: Case 2.

RESEARCH NOTE

Figure 8. Effect of k1 and reactor size on total recycles: Case 2.

Figure 9. Effect of k1 and reactor size on reactor compositions; Case 2.

The economic optimum for flowsheets with complex multicolumn separation sections occurs at a low ratio of actual to minimum recycle flow rates.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: 610-758-4256. Fax: 610-758-5057. E-mail: [email protected].

’ REFERENCES (1) Luyben, W. L. Heuristic Design of Reaction/Separation Processes. Ind. Eng. Chem. Res., 2010, 49, 1156411571. (2) Douglas, J. M. Conceptual Design of Chemical Processes; McGrawHill: New York, 1988. (3) Turton, R., Bailie, R. C., Whiting, W. B., Shaelwitz, J. A. Analysis, Synthesis and Design of Chemical Processes, 2nd Edition; Prentice Hall: Upper Saddle River, NJ, 2003.

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Separation Processes with Two Recycles

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