Driving Force Based Design of Cyclic Distillation - ACS Publications

Article pubs.acs.org/IECR

Driving Force Based Design of Cyclic Distillation Rasmus Fjordbak Nielsen, Jakob Kjøbsted Huusom, and Jens Abildskov* PROSYS Research Centre, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Building 229, DK-2800 Kongens Lyngby, Denmark S Supporting Information *

ABSTRACT: Driving force based design is adopted from conventional continuous distillation to cyclic distillation. This leads to a definition of the operating line representation for the cyclic distillation process. A possible realization of the driving force design is presented, which implies operation with mixed phase feeds. A range of binary test cases, benzene−toluene, methanol−water, and ethanol−water, are evaluated. The advantage of the design approach in cyclic distillation is shown to be analogous to the advantages obtained in conventional continuous distillation, including a minimal utility consumption of the column and likely less sensitivity to feed composition changes.

1. INTRODUCTION Distillation is the most common separation technique in the chemical industry. Distillation columns in use today account for 40−55% of the operating cost in chemical plants.1,2 With over 40 000 distillation columns in operation worldwide,3 even small improvements in the technology of distillation will substantially reduce both operating and possibly also capital costs of separation processes. One of the technologies that has been discussed as a promising example of process intensification is cyclic distillation,4 also known as periodic distillation.3 Cyclic distillation has several features in common with conventional distillation. Both employ a stripping and rectifying section located below and above a feed stage, respectively. Both employ a condenser and a reboiler at the top/bottom. Both employ counter-current internal flows of vapor and liquid phases. However, conventional distillation implies continuous flows, with values which at stationary operating conditions are (nearly) constant and independent of time. Cyclic distillation has an operating cycle consisting of two key operational steps of separate (cyclically repeated) flow periods. There is a vapor flow period (VFP), where the liquid remains in the same position on trays without overflow. In the classical form, there is a liquid flow period (LFP) where the vapor flow is interrupted and (ideally) all liquid moves down one tray. The cyclic mode of operating distillation columns has the advantage that the tray efficiency is substantially higher than that of trays in conventional columns. This has long been theoretically established. More and more experimental demonstrations are also coming along. Thus, there are several indications that a separation accomplished with a conventional column should be possible using a not nearly as tall cyclic column. Among the barriers to be overcome for more widespread implementation of cyclic separation are the development of simpler/ cheaper trays, elimination of inconveniences of operation, and availability of modeling and simulation tools. Parts of this have ̂ been reviewed by Bildea et al.5 © XXXX American Chemical Society

For application, options for process design are essential. Since the group of Cannon6,7 in the 1950s demonstrated cyclic operation of distillation, a number of papers have proposed different algorithms for designing cyclic distillation columns, to obtain the number of trays and the feed location. In 1977, Rivas8 suggested an analytical way of obtaining the number of trays needed for a given separation of a binary mixture, including the feed tray location. He employed a method resembling the Kremser−Souders−Brown equation for the ordinary separation. The algorithm was based on an approximated concentration profile over a period consisting of a linear combination of a linear and an exponentially decreasing term. One limitation was that, as for the Kremser−Souders−Brown equation, the vapor−liquid equilibrium relationship has to be linear. Rivas stated that for nonlinear VLE relationships the calculation can be made by dividing the column into sections, in which the equilibrium curve is approximated by straight lines. This can, however, cause large errors, as Toftegård and Jørgensen9 later demonstrated. With the method of Rivas, the internal flows (a variation in internal flows is accomplished by a simultaneous variation of L and V, while keeping the product rates, D and B, constant) were specified in addition to the separation of components in the feed stream. The feed location was found where the liquid composition xNF matched the feed composition xF. In 1987, Toftegård and Jørgensen9 proposed a stage-to-stage design algorithm for binary mixtures. That method only required specification of the separation (product and feed compositions and flows) and internal flows, without restriction to any particlular VLE relation. A characteristic feature was to integrate mass balances backward in time numerically, on each stage of Received: Revised: Accepted: Published: A

March 17, 2017 June 12, 2017 August 24, 2017 August 24, 2017 DOI: 10.1021/acs.iecr.7b01116 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Best established design algorithms for cyclic distillation columns.

Figure 2. Driving-force diagram example for constant relative volatility of α = 3.5. For xi = Dx the driving force is the largest, where the operating lines have been adjusted to intersect.

of the following vapor flow period. This operation is consistent with the commercially available Maleta trays.12 At the same time Toftegård and Jørgensen9 contemplated charging of liquid feed during the vapor flow period. Using the COPS trays and the sequential draining principle of operation of Toftegård et al.,13 vapor flow does not need to be interrupted during the liquid flow period. Therefore, there is no reason why two-phase feed streams should be excluded from consideration. With the feed restriction, in the three above-mentioned design algorithms, the feed tray has been placed according to where the composition in the liquid phase differs the least from the feed composition. With the design algorithm by Pǎtruţ et al.10 and Liţǎ et al.,11 the feed tray is where the following crite9 (L) rion is obtained: x(V) NF+1 < xF < xNF+1. Toftegård and Jørgensen would calculate on which tray the value of the feed composition was reached (xNF = xF). The tray where this occurred was designated to be the feed tray. The difference between the two feed tray criteria is subtle but due to the difference in how the feed tray is defined. By relaxing the feed state assumption, additional modes of operation become possible for the cyclic distillation column. This makes it possible to use a driving force design approach, previously suggested for design of conventional distillation columns. The driving force design approach results in minimum utility consumption within the column, for the separation to be carried out with a given number of stages in a conventional continuous distillation column.14 Recently, the driving force principle has been adapted to reactive distillation15, resulting a design that leads to a process less sensitive to feed disturbances, in both conventional continuous distillation and reactive distillation.16,17

the column, beginning from the specified bottom composition and integrating upward stage by stage. This can then be used to find the number of required stages and a feed location, which was where the liquid phase tray composition differed the least from the feed composition. Toftegård and Jørgensen9 considered the options to introduce the feed both in the LFP and in the VFP. With introduction during the LFP, they would introduce the feed at the tray, where the tray liquid differed the least from the feed, whereas with introduction during the VFP, the feed amount per cycle would be introduced at the time, during the VFP, where the tray liquid of the feed tray differs the least from the feed. In recent years, Pǎtruţ et al.10 and Liţǎ et al.11 employed a design algorithm resembling that of Toftegård and Jørgensen,9 with the extension to multicomponent mixtures. With the method of Pǎtruţ et al., the internal flows were also specified in addition to the separation of components in the feed stream. Here, however, the feed was introduced in the liquid flow period, on the stage below that where the liquid composition xNF matched the feed composition xF, i.e., on stage NF + 1. It seems to be the most generalized design algorithm for cyclic distillation columns currently available in the literature. The development of design algorithms is summarized in Figure 1. All of the mentioned design algorithms have assumed singlephase feed streams of saturated liquid. This limitation makes sense, when interruption of the vapor flow is necessary during the liquid flow period. According to the model of Pǎtruţ et al.10 and Liţǎ et al.,11 the liquid feed stream is introduced during the liquid flow period, where it is mixed with the holdup on the feed stage and transferred to the stage below, before initiation B

DOI: 10.1021/acs.iecr.7b01116 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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be the reflux ratio where a pinch point occurs between the operating lines and the equilibrium line.

The contribution of this paper is to show how cyclic distillation can be modeled in terms of operating lines, to develop a driving force based design approach. The design approach is based on a mass-balance-only model, utilizing the backwardintegration method by Pǎtruţ et al.10 The method enables a design of cyclic distillation columns, which will be an optimized design, which has the lowest utility consumption within the column. The driving force method is illustrated by a number of examples of binary separations and compared to the existing design method of Pǎtruţ et al.10 The paper is organized as follows: In Section 2, the driving force operation in a conventional continuous distillation column is briefly summarized. In Section 3, representation of cyclic distillation operating lines is developed resembling the McCabe− Thiele operating lines known from conventional continuous distillation, and the analogy with conventional continuous distillation is presented in detail. The modeling and methodology used in the paper is then presented in Section 4 including the modified mass balance models for two-phase feeds. The models are subsequently used to obtain operating parameters for the driving force design and designs obtained with previously proposed design methods. The results are presented in Section 5, where three separations of binary mixtures are evaluated; benzene−toluene, methanol−water, and ethanol− water. Finally, the results are discussed in Section 6 and conclusions are summarized in Section 7.

3. OPERATING LINES IN CYCLIC DISTILLATION To establish the analogy of the driving force operation in the cyclic case, a representation of the operating lines in the cyclic case must be used. We use the nomenclature of Figure 3. Liţǎ et al.11

2. DRIVING FORCE OPERATION FOR CONVENTIONAL DISTILLATION The McCabe−Thiele method for classical distillation (and the previous cyclic distillation design methods) require feed and products compositions and internal flows to determine a feed location that minimizes the number of ideal stages. The design approach for conventional continuous distillation columns, based on driving forces, by Gani and Bek-Pedersen,14,18 was shown to minimize the utility consumption for the column. To realize this operation, the state of the feed, given as the q-value, must be adjusted, such that the q-line intersects the operating lines where the driving force is largest, irrespective of the feed composition. The utility consumption will be minimized, when both the product purities and the number of ideal stages are kept constant. The driving force is defined as FDi = yi − xi, where i is the light key component (LK). The point of maximum driving force is located at xi = Dx in the driving force diagram, shown in Figure 2. The operating lines intersect with the q-line at Dx. On all stages, material and phase equilibrium relationships are satisfied, consistent with the operating lines. The feed stage is where the entering liquid has x > Dx and the exiting liquid has x < Dx. The total number of stages is a specification, and the product compositions are satisfied exactly by the adjustment of operating line slopes. With the driving force design approach, the minimal reflux ratio would be the reflux ratio where the operating lines create a pinch point with the equilibrium line, where the operating lines intersect at x = Dx. Thus, the reflux ratio adjustment, in the driving force diagram, would be done by simply moving the intersection point of the two operating lines along the vertical Dx-line. This is in contrast to how the minimal reflux ratio would be found for a fixed q-value, where the reflux ratio would be adjusted by moving the intersection of the two operating lines along the fixed q-line, where the minimal reflux ratio will

Figure 3. Nomenclature used for the cyclic distillation column, with the numbering of stages.

Table 1. Separation Specifications for Example Shown with Different Operating Line Representations operating parameter

value

constant relative volatility, α F V·tvap reboiler holdup, M(L) NP NP NF q zF(LK) xB(LK) xD(LK)

3.5 0.375 kmol/cycle 0.442 kmol/cycle 1.525 kmol 8 4 1 0.500 0.003 0.997

presented a representation, resembling the classical McCabe− Thiele operating lines for the conventional continuous distillation, including a time dependency. With their representation, the mole fraction of vapor entering a tray n (from tray n + 1), denoted yn+1, is plotted against the liquid mole fraction on tray n, denoted xn, at various times during the VFP. As the concentration in liquid and vapor changes during a cycle in the cyclic distillation column, this representation results in cyclic distillation operating lines that are not straight. An example of their operating line representation for an equimolar feed mixture with the separation specifications given in Table 1 is reproduced in Figure 4. The superscript (L) denotes the end of the LFP. Our notation is consistent with that of Pǎtruţ et al.,10 with the vapor flow period duration, tvap (time/cycle), relating flows in kmol/cycle to flows in kmol/time. The points on the operating curve are the liquid mole fraction on one tray, xn(t), and the vapor mole fraction on the C


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Figure 4. Reproduced example from Liţǎ et al. of operating lines, using the operating parameters listed in Table 1. The operating lines are shown for the VFP, for times ranging from t = 0 to t = tvap. Reboiler is stage 8.

Figure 5. Present cyclic distillation operating line representation, for the separation specified in Table 1. The reboiler is stage 8, which can be drawn as a normal stage, that does not exceed the equilibrium line for M(L) NP ≫ Vtvap. λ is the ratio of slopes of equilibrium and operating lines.

Table 2. Theoretical Tray Efficiency, ET, of a Lewis Case 2 Distillation Tray for a Given λa

a

λ

ET/EP

>1 =1 2 ≈2 1, and Table 2 shows that the tray efficiency is greater than 2. On the contrary, on tray 3, the

4. METHOD With the new definition of operating lines for the cyclic distillation, the same principles used in the driving force design approach for conventional continuous distillation can be used for cyclic distillation. In the following section, the driving force E


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Figure 6. Feed tray model used by Pǎtruţ et al.10 and Liţǎ et al.11

design approach for cyclic distillation is presented together with the mass balance modeling for two-phase feeds. First, the mass balance model by Pǎtruţ et al.10 is adapted to account for situations when 0 < q < 1, i.e., two-phase feeds. The driving force design approach could in some cases require q < 0 or q > 1. This paper shows examples of the effects of the design method for 0 < q < 1. The general design approach presented in the following is however applicable to all situations; only the mass balance model would have to be adapted to deal with these situations as well. Furthermore, only binary separation examples will be presented, but the design method will be applicable to multicomponent mixtures as well, where the driving force composition will be found between the light and heavy key components, as it would be done in the conventional continuous distillation.18 Both design approaches use the assumptions listed in the developed operating line representation, shown in Section 3. 4.1. Modeling of Cyclic Distillation Column. To realize the cyclic distillation with a two-phase feed, where 0 < q < 1, with both the commercially available Maleta trays12 and the COPS trays by Toftegård et al.,13 it is decided to introduce the feed during the VFP, as earlier proposed by Toftegård et al.9 In the model by Pǎtruţ et al.10 and Liţǎ et al.,11 the feed was introduced in the LFP, where the saturated liquid feed would mix with the tray liquid on tray NF, which then would be transferred to tray NF + 1 when the next VFP was initiated. The vapor flow would be interrupted during this process. The feed tray model can be seen in Figure 6.

Figure 8. Procedure for designing cyclic distillation column using a driving force approach.

If a mixed phase feed mixture was introduced in the same fashion, a vapor flow would be created during the LFP. This could disrupt the tray drainage process, when using cyclic trays controlled by the vapor flow, such as the Maleta trays.12 This can be avoided by introducing the feed during the VFP. Here, the vapor fraction of the feed will mix with the internal vapor and will not cause problems when it comes to the tray drainage process. In analogy with the McCabe−Thiele modeling of the feed tray,19 the feed tray is defined, in the modified mass balance model, as the tray where the feed is introduced during the VFP. The total liquid part of the feed (q·F [mol/cycle] with composition xF) is introduced just as the VFP initiates (t = 0) where it will mix with the tray liquid. The vapor part of the feed ((1 − q)·F [mol/cycle] with composition yF) is introduced with a constant vapor flow VF [mol/s] and a constant composition yF over the VFP. The liquid and vapor fractions of the feed will be in equilibrium when introduced to the column and follow the mass balance zF = q·xF + (1−q)·yF. Thus, with this feed tray

Figure 7. Feed tray model for two phase feeds. F


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Figure 9. Operating lines for the driving force design. dM n , j

modeling, all the feed with quality q is introduced during the VFP, where the vapor part is introduced continuously and the liquid part is introduced just as the VFP begins. The feed tray model is shown in Figure 7. Note that the feed tray definition is different from that of Pǎtruţ et al.,10 when using this model. For q = 1, the only difference between the two models is the definition of the feed tray location. With the definition by Pǎtruţ et al.10 and Liţǎ et al.,11 the feed is exposed to its first VFP on tray NF + 1. In the modified model presented in this paper, this happens on tray NF. Thus, to directly compare the feed location in the two models, one would have to subtract a stage from the feed location, to go from the definition by Pǎtruţ et al.10 and Liţǎ et al.11 to the definition presented in this paper. The constant vapor flow coming from the feed is defined as VF =

(1 − q) ·F [mol/s] tvap

dt dM n , j dt

= V ·(yn + 1, j − yn , j )

(L) (V) MNF, j = MNF − 1, j + L F · x F, j

n = 1 ... NP − 1 (4.3)

LFP (L) (V) MNF + 1, j = MNF, j + F · x F, j

(4.4)

The feed tray model, opening up for the possibility of a two phase feed, will result in the following modified mass balance model: VFP dM n , j dt

= V ·(yn + 1, j − yn , j )

for

for

n = 1 ... NF − 2

(4.8)

Note that if q = 1 in the modified mass balance equations for VFP, they reduce to those of Pǎtruţ et al.10 The LFP balance will not be the same, due to the two ways of defining the feed tray, as previously mentioned. The rest of the mass balances by Pǎtruţ et al.10 are retained in the design approach. Using these mass balances, it is possible to design the cyclic distillation column, by integrating backward in time, as in the design algorithms by Pǎtruţ et al. and Toftegård and Jørgensen. The only changes from the previously suggested algorithms are the modification of the mass balances and a new feed tray criterion. The criterion used by Pǎtruţ et al.10 is to place the feed tray one tray above the tray N where x(L) N > xF. Likewise, for driving force design, the feed tray can be placed one tray above the tray N where x(L) N > Dx. 4.2. Design Procedure. With the modified mass balance model and the definition of operating lines for cyclic distillation, the cyclic distillation column can be designed based on the driving force principle together with the backward-integration method. The procedure for designing the cyclic distillation column using the driving force principle can be seen in Figure 8. In the backward-integration design algorithm, as described by Liţǎ et al.11 and Pǎtruţ et al.,10 the separation specifications F, zF, xD, xB, D, B, V, and tvap would be known. The algorithm would then result in a number of needed stages NP and a feed location NF. The number of needed stages will be determined as the stage number where the tray-liquid composition of the upper tray (tray 1) at the beginning of the VFP (x(L) 1 ) exceeds the specified distillate composition xD. To apply the driving force concept to cyclic distillation, one will have to supply almost the same separation specifications,

(4.2)

for

= (VF + V )·(yn + 1, j − yn , j )

LFP

The mass balances as originally given by Pǎtruţ et al., for a point efficiency of unity, are10 VFP dt

n = NF − 1

(4.7)

The liquid contribution from the feed is defined as

dM n , j

for

(4.6)

(4.1)

L F = q·F [mol/cycle]

= V ·yn + 1, j + VF·yF, j − (VF + V )·yn , j

n = NP − 1 ... NF (4.5) G


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The tray liquid composition of the upper tray (tray 1) at the beginning of the VFP (x(L) 1 ) can now be used to check whether the distillate composition can be obtained using the operating specifications. For a correctly designed distillation column, the composition x(L) 1 equals the specified distillate composition xD. If not, the reflux ratio must be adjusted (by adjusting V·tvap), and the corresponding q-value and the feed compositions, xF and yF, must be recalculated. The procedure is repeated until x(L) 1 converges to xD.

Table 4. Case Specifications with Thermodynamic Models and Purity Specifications feed mixture (1)/(2)

liquid phase model

vapor phase model

xF,1

xB,1

xD,1

benzene/toluene methanol/water ethanol/water

ideal solution Wilson Wilson

ideal gas ideal gas ideal gas

0.50 0.40 0.35

0.005 0.005 0.005

0.995 0.995 0.800

Table 5. Wilson Parameters and Molar Volumes26,27 Used for VLE Predictiona binary pair (1)/(2)

a12 [J/mole]

a21 [J/mole]

Vm,1 [cm3/mol]

Vm,2 [cm3/mol]

methanol/water ethanol/water

833.67 1651.14

2345.48 4172.69

44.87 58.69

18.07 18.07

5. RESULTS In the following section, the results obtained for the driving force design of cyclic distillation are presented and compared to designs obtained with the method of Pǎtruţ et al.10 First, the driving force design approach is shown explicitly for the separation covered in Section 3. Then, three separations are shown with their optimal feed locations. 5.1. Driving Force Design Approach Example. A driving force-based design is now obtained for the separation covered in Section 3. As before, 8 equilibrium plates (NP = 8, including reboiler) form the basis of the design. The operating specifications can be found in Table 1. The fraction of liquid in the feed is first to be calculated, as the q-value where the operating lines intersect at x = Dx which for this separation is Dx = 0.348 (for α = 3.5). For a given fixed feed location, NF, and a fixed number of equilibrium plates NP, the backward integration can be used to obtain the composition in plate 1 at (L) the end of the VFP x(L) 1 . If the composition x1 does not match exactly the distillate composition xD, the vapor flow V·tvap is adjusted, and a new q-value is calculated, using the criterion of intersect of operating lines where x = Dx. This procedure is carried out until the purity has converged to the objective distillate purity xD. The operating conditions where the distillate composition is obtained for NP = 8 are for this case V·tvap = 0.295 kmol/cycle and q = 0.307. These operating conditions result in a sum of reflux and boilup ratio of RR + BR = 3.53, whereas with the design approach by Pǎtruţ et al.,10 the sum of reflux and boilup ratio was RR + BR = 3.715. This is a 5% reduction of the sum of ratios, BR + RR, using the driving force design, which

The Wilson parameters were obtained from fitting to experimental data by Kurihara et al.28. a

Table 6. Antoine Parameters Used,29 Where the Pressure Is in Bar and Temperature is in K (log10(P) = A − (B/(T + C))) A B [K] C [K]

benzene

toluene

methanol

ethanol

water

4.0306 1211.033 −52.36

4.0782 1343.943 −53.77

5.15853 1569.613 −34.846

5.24677 1598.673 −46.424

5.40221 1838.675 −31.737

but instead of specifying the vapor flow rate V and the duration of the vapor flow period tvap, one specifies the number of stages NP instead. Thus, the specifications needed for this algorithm are F, zF, xD, xB, D, B, and NP. One will then find the driving force composition Dx by creating a driving force diagram for the separation. A value of V·tvap is chosen (or a reflux ratio), so RR > RRmin, together with a q-value, where the operating lines, as presented in Section 3, intersect at x = Dx. After finding the appropriate value of q, the feed compositions xF and yF are calculated using the equilibrium condition and the mass balance zF = q·xF + (1 − q)·yF. The backward integration design method is then run for the number of equilibrium plates NP. The feed tray location is set to be the tray where the tray liquid differs the least from the driving force composition Dx.

Figure 10. Driving force diagrams for the three binary mixtures. H


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To compare the two design methods, the two designs were made for various feed-stage locations, for all three separations, to ensure that the operating conditions used in the comparison were found for the optimal feed location. The designs were verified afterwards, using a full simulation of the column. 5.3. Optimal Feed Location. For the three separations, the boil up ratio is plotted against the feed location. The boil up ratios are calculated using the method presented in Figure 8. Here, different feed stages NF are chosen, which results in different magnitudes of V·tvap for fixed feed and product compositions and a fixed number of stages, which then can be used to calculate the boil up ratio using eq 3.7. The driving force composition for the three mixtures was found to be the following (with respect to the light key): Dx(Benzene/Toluene) = 0.402, Dx(Methanol/Water) = 0.202, and Dx(Ethanol/Water) = 0.128. The driving force diagrams for the three binary mixtures can be seen in Figure 10. The three plots of boilup ratio versus feed location can be seen in Figure 11. 5.4. Reduction of Utility Exchange. By using the optimal feed location found in the previous section, the driving force approach can now be compared to the designs that would result from Pǎtruţ’s design method. The operating parameters for the three case studies can be seen in Table 7. Notice that the feed tray definitions are different for the Pǎtruţ method and for the model used for driving force design approach, according to the definitions in Section 4.1. It can be seen that, for the benzene−toluene separation, a 3.5% reduction of the sum of ratios can be obtained. For the methanol−water separation, a 29.5% reduction in sum of ratios can be obtained, and a reduction of 43.7% is seen in the ethanol−water separation. All these reductions can directly be translated into a percentage of reduction in utility consumption of the column. When assuming the feed to be saturated liquid, a preparation of the feed, for the driving force based design, must be carried out to get a feed mixture of liquid and vapor. The duties for reboiler, condenser, and preheating can be seen in Table 8. From Table 8, it can be seen that when assuming a saturated liquid feed, the driving force design will end up having an overall larger utility consumption in the BT and MW separations, only showing a small reduction in overall utility consumption in the EW separation. The internal utility consumptions do, however, show a reduction using the driving force design in all three cases, as already seen in Table 7. If one has a sequence of distillation columns, the products coming from one column to the next do not necessarily have to be single phased, which can open up the possibility of using this method for reducing the overall utility consumption of the separation train, using this driving force method. However, for single columns, the method does not provide a significant utility consumption. This is consistent with the analysis of Mathias.30

Figure 11. Boilup ratio vs feed tray location NF for the three cases. The circle marks the optimal feed-stage position.

directly translates into a reduction in utility consumption within the column. The operating lines obtained for the driving force design are shown in Figure 9. 5.2. Cases for Driving Force Approach. Three case studies are shown. The specifications are shown in Table 4. The molar holdup in the reboiler was in all three cases set to be M(L) NP ≫ V·tvap, which implies that the change of xNP during the VFP will be negligible. With this assumption, the reboiler behavior will approach that of an infinite reboiler. The pressure of the cyclic distillation column was in all three cases set to 1 atm. The Wilson parameters25 and molar volumes used can be seen in Table 5, and the Antoine parameters used can be seen in Table 6.

6. DISCUSSION By designing a cyclic distillation column using the principle of maximum driving force, the utility consumption can be reduced. This conclusion resembles the conclusions previously reached for conventional columns. This will minimize the sum of needed heating and cooling, in the reboiler and condenser, respectively. However, the driving force-based designs will require the q-values to be reduced to numbers less than unity, for zF > Dx. As discussed by Mathias,30 this may not be preferred in all situations. Therefore, the preferred design procedure will depend upon a range of considerations, ultimately combined I


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Industrial & Engineering Chemistry Research Table 7. Operating Parameters for the Three Cases with the Pǎtruţ Method and the Driving Force Designa BT separation approach

EW separation

DF

Pǎtruţ et al.

DF

Pǎtruţ et al.

DF

1

0.518

1

0.432

1

0.24

1.25

0.976

0.865

0.339

1.00

0.242

1.67 1.92 1.95 3.87 14 8 0.50 0.995 0.005 0.402 96.5%

0.90 1.17 1.44 2.61 14 11 0.40 0.995 0.005 0.202 100%

1.13 1.27 0.56 1.84 14 12 0.40 0.995 0.005 0.202 70.5%

q V ·tvap

F RRmin RR BR RR + BR NP NF zF,1 xD,1 xB,1 Dx,1 %-UE

MW separation

Pǎtruţ et al.

1.32 1.50 2.50 4.01 14 7 0.50 0.995 0.005 0.402 100%

0.79 1.31 1.77 3.08 14 12 0.35 0.800 0.005 0.128 100%

1.14 1.31 0.43 1.73 14 13 0.35 0.800 0.005 0.128 56.3%

a

UE is short for utility exchange, where 100% is given by the utility exchange in the method of Pǎtruţ. Feed tray number is presented for the respective feed tray definition, as described in Section 4.1. The minimal reflux ratio was estimated using the operating lines, as explained in Section 2.

the control performance. A multi-input mult-output (MIMO) controller should be able to take into account the interactions between all measurements and all manipulated variables. Furthermore, a MIMO controller designed from a properly formulated model automatically may include a feed forward component, such that some fluctuations are reduced if not eliminated. However, to design a MIMO controller places stronger demands on the adequacy of the process dynamics ̂ model. In later years, the paper of Bildea controls the temperatures in the lower and upper parts of the column, using the vapor flow rate and the amount of liquid reflux as the manipulated variable, with promising results. Thus, developments are still coming along, as also indicated in the more ̂ detailed review of Bildea et al.5 With the feed tray model used to show the effect of driving force design in cyclic distillation, the feed was to be introduced in the beginning of the VFP (t = 0). It is possible that the effect of the driving force design could be further enhanced, if the feed would be introduced at a point in time during the VFP, as earlier suggested by Toftegård et al.,9 when the driving force composition is obtained.

Table 8. Utility duties for the three separations, assuming total condenser. The internal duty includes reboiler and condenser. The external duty includes the internal duty and the feed preheat Duty [kJ/mol feed] Reboiler Condenser Feed preheat Internal External

BT-separation

MW-separation

EW-separation

Pǎtruţ et al.

DF

Pǎtruţ et al.

DF

Pǎtruţ et al

DF

41.4 38.4 0 79.9 79.9

32.4 44.8 15.3 77.2 92.4

35.0 30.5 0 65.5 65.5

13.7 32.0 21.4 45.7 67.0

40.5 39.0 0 79.5 79.5

9.81 39.1 30.2 48.9 79.1

in an economic model of the situation. However, the fact that a driving force-based design is possible expands the range of options available for employing cyclic distillation in different contexts. Furthermore, using the driving force design in cyclic distillation, the column will be likely to effectively reject feed disturbances. With the operating line representation for cyclic distillation, presented in Section 3, an analogous proof for the improved ability of rejecting feed disturbance using a driving force design, as shown for conventional distillation and reactive distillation by Abd Hamid,16,17 can be carried out. This shows that a column designed with the maximum driving force design will have the best disturbance rejection,17 which will result in a cyclic distillation column that might be easier to control in comparison to using the design obtained using the method by Pǎtruţ et al.10 Reports on quite a few industrial applications of cyclic separations have appeared in recent years.31 Maleta mentions the need for developments of control systems for such cases, though this does not seem to be prohibitive. Although the advantages of cyclic operation have been demonstrated experimentally, how to control cyclic distillation columns seems less established. Some noteworthy efforts of the 1970−1980s were those of Matsubara et al.32 and of Dale and ̂ Furzer.33 In recent years Bildea et al.34 have published work on automatic control of cyclic distillation. Both the controllers of Matsubara et al. and of Dale and Furzer were single-input single-output (SISO) controllers. This gives some limits in

7. CONCLUSIONS In this work, it has been shown how the driving force design approach can be applied to design of cyclic distillation columns. By establishing a similar representation of operating lines in cyclic distillation, the analogy of conventional distillation to cyclic distillation has been illustrated and justified using the driving force operation in the cyclic case. The driving force design has shown a clear reduction in the sum of ratios in comparison to the earlier proposed designs, for three binary separation cases: benzene−toluene, methanol− water, and ethanol−water, ranging from reductions in the sum of ratios from 3.5% to 43.7%, which directly translates into a reduction in utility consumption within the column. With introduction of feed in the VFP, the driving force design can be realized with both the currently commercially available cyclic trays by Maleta12 and the newly suggested COPS-trays by Toftegård et al.,13 which makes the driving force design a potential approach to designing cyclic distillation columns. J


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ASSOCIATED CONTENT

LK OL UE VFP

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b01116. Proof of linear operating line representation (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(J.A.) E-mail: [email protected].

REFERENCES

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ORCID

Rasmus Fjordbak Nielsen: 0000-0002-3830-8743 Jens Abildskov: 0000-0003-1187-8778 Notes

The authors declare no competing financial interest.

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NOMENCLATURE a Wilson parameter [J/mole] A, B, C Antoine parameters [−], [K], [K] α Relative volatility [−] B Bottoms [mol/cycle] BR Boilup ratio [−] c Constant defined in Supporting Information [−] D Distillate [mol/cycle] Dx Driving force composition [−] Dy Driving force FD at Dx [−] EP Local point efficiency [−] ET Theoretical Murphree tray efficiency [−] F Feed [mol/cycle] FD Driving force [−] L Liquid flow [mol/cycle] λ Ratio of slopes of equilibrium and operating line [−] M Holdup [mol] m Slope of equilibrium curve [−] NF Feed stage [−] NP Number of equilibrium plates [−] q Feed state [−] RR Reflux ratio [−] RRmin Minimal reflux ratio [−] t Time [s] tliq Duration of liquid flow period [s] tvap Duration of vapor flow period [s] V Vapor flow [mol/s] Vm Molar volume [cm3/mol] x Mole fraction, liquid phase [−] y Mole fraction, vapor phase [−] y Time averaged mole fraction [−] z Mole fraction, overall [−] Superscripts

(V) End of the vapor flow period (L) End of the liquid flow period Subscripts

B D F i n r s

Light key Operating line Utility exchange Vapor flow period

Bottoms Distillate Feed Component Tray number from the top Rectifying section Stripping section

Abbrevations

DF Driving force LFP Liquid flow period K


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Driving Force Based Design of Cyclic Distillation - ACS Publications

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