Thermally Coupled Side-Column Configurations Enabling Distillation

Ind. Eng. Chem. Res. 2009, 48, 6387–6404

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Thermally Coupled Side-Column Configurations Enabling Distillation Boundary Crossing. 1. An Overview and a Solving Procedure Ilkka Malinen and Juha Tanskanen* Chemical Process Engineering Laboratory, Department of Process and EnVironmental Engineering, P.O. Box 4300, FI-90014, UniVersity of Oulu, Finland

In this paper, the thermally coupled side-rectifier and side-stripper configurations are studied in the separation of component sets with a curved distillation boundary. A solving procedure is introduced that can be used in the determination of the minimum total energy consumption for the studied complex separation structures. The results show that thermally coupled side-column configurations enable distillation boundary crossing with high product flow purities. In fact, the achievable purities are higher than is possible with conventional column sequences. It is also noted that in some methanol/ethanol/water separations the energy consumption of the thermally coupled side-stripper configuration may partly decrease with increasing methanol distillate purity. 1. Introduction Distillation is the most used separation technique in the chemical industry. Distillation is, however, a very energy intensive unit operation. Therefore, the increasing cost of energy has forced industry to reduce its energy consumption. In addition, the tendency to rationalize and reduce the usage of fossil energy resources, and the tighter environmental regulations caused by, for example, the effort to prevent climate change, have generated the need to adopt new and efficient separation methods. The energy usage in distillation can be reduced for instance by the thermal integration of distillation columns, appropriate integration of distillation columns with the overall process, and heat pumping techniques.1 In addition, the use of thermally coupled distillation arrangements as well as advanced control systems have been shown to be useful in decreasing energy consumption. Thermally coupled column configurations have been studied and compared to conventional ones in numerous papers during the last two decades.2–35 These studies have focused on energy consumption and control issues. The studies have shown that thermally coupled columns offer a great opportunity to reduce energy consumption by eliminating the remixing that occurs in conventional column sequences.35 In addition, mismatches between the composition of the column feed and the feed plate can be avoided. It is well-known that some component systems have one or more azeotropes, which may cause the formation of one or more distillation boundaries. This sets restrictions, which have to be taken into consideration when synthesizing feasible separation schemes. In general, azeotropic distillation operations have been found to present a complex but interesting behavior that is quite tedious to simulate. For example, Bossen et al.36 have stated that the accurate and reliable design of these processes needs accurate and reliable computation tools. It is known that the distillation boundary crossing is at least to a certain extent possible from the concave side with column sequences consisting of simple (one-feed, two-product) columns. The same is also possible to carry out, and even in a more flexible way, with thermally coupled distillation column configurations. Bauer and Stichlmair37 and Castillo et al.38,39 seem * To whom correspondence should be addressed. Tel.: +358-8-5532340. Fax: +358-8-553-2304. E-mail: [email protected].

to be the first ones, who found that it is possible to cross the distillation boundary with the thermally coupled side-column configurations. Castillo et al.39 showed that the total reflux boundary can be crossed at finite reflux by using a thermally coupled side-rectifier configuration with a single feed flow. They showed by simulation that crossing the distillation boundary of an acetone/chloroform/benzene component set is indeed possible, and that high product purities can be achieved. They suggested that complex designs may be improved without an excessive capital outlay with proper placement of intermediate reboilers or condensers. They also suggested that the scope for using complex column arrangements in the separation of azeotropic mixtures is greater than previously had been thought. Elsewhere, Bauer and Stichlmair37 studied the possibility to find an economically optimal process configuration for both zeotropic and homogeneous azeotropic mixtures. One of their case studies showed that the distillation boundary of methanol/ ethanol/water system can be crossed by using a thermally coupled side-stripper configuration. This configuration consisted of just two columns with partially recycling of the pure methanol flow. Later, Barttfeld et al.40 and Yeomans and Grossmann41 had synthesized methanol/ethanol/water separation with a thermally coupled side-stripper configuration based on the optimization of a superstructure embedding all possible alternative designs. This paper begins with an overview of thermally coupled column configurations. Distillation boundary crossing and separation feasibility issues are also considered in general. The rest of this paper focuses on simulation and solving aspects of thermally coupled side-rectifier and side-stripper column configurations in the separation of ternary component sets having a curved distillation boundary. To facilitate the determination of the operating conditions of minimum total reboiler duty, a procedure is introduced that consists of heuristic phases. In this procedure, an equation-oriented solving approach is utilized instead of a modular one. Modified bounded Newton homotopy42,43 is used in phases, where the “local” Newton-Raphson-based solving method does not offer a converged result within a tolerable number of iterations. On the basis of the simulation results, the performance of thermally coupled side-column configurations with respect to achievable product flow purities is compared with conventional direct and indirect column schemes.

10.1021/ie800817n CCC: $40.75  2009 American Chemical Society Published on Web 05/28/2009

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Ind. Eng. Chem. Res., Vol. 48, No. 13, 2009

Figure 1. Conventional schemes for ternary distillation: (a) direct, (b) indirect, and (c) prefractionator schemes.

2. Overview 2.1. Thermally Coupled Column Configurations. Figure 1 illustrates the conventional distillation schemes for ternary distillation. In the most basic ones, that is, in direct and indirect column sequences, there is a reboiler and a condenser in every distillation column. The number of product flows in the columns is always the same, namely, two. However, in a more novel distillation scheme, that is, in a prefractionator scheme (Figure 1c), there is one extra product flow, known as a sidestream, in the second column of the column sequence. In contrast to the conventional schemes, thermally coupled distillation configurations contain two-way material flow connections, that is, thermal links, between the first and the second column. As Figure 2 illustrates, in thermally coupled configurations the number of heat exchangers is also smaller than in conventional ones. The Petlyuk arrangement is a very attractive configuration because of its low energy requirement, and because of the configuration structure that requires just a single condenser and reboiler. This is also valid when the idea of the Petlyuk configuration is extended for any n component system. Therefore, the Petlyuk columns have been studied extensively in terms of both steady state and dynamic performance.2,3,13,19,21–25,27,35 On the basis of the studies, the energy consumption of the Petlyuk configuration may be of the order of 20-50% lower compared to the conventional column schemes. The low energy requirement leads to a smaller column diameter and low overall heat exchange area. Thus, in addition to lower operating costs, investment costs may also be lower.

Thermally coupled side-stripper and side-rectifier configurations have not been studied as extensively as the Petlyuk configuration. However, some papers have been published, which concentrate on the energy usage and controllability of thermally coupled side-column configurations.26,30,44–46 Agrawal and Fidkowski8,11 noticed that among the three thermally coupled column configurations (Figure 2), the thermally coupled side-rectifier and side-stripper configurations tend to provide thermodynamically the most efficient alternative more often than the Petlyuk configuration. The reason for this is primarily that thermally coupled side-column configurations possess the ability to either accept or reject heat at an intermediate temperature, and not just at the highest and the lowest temperature as in the Petlyuk system. Even though the Petlyuk configuration needs the lowest amount of heat, this heat is required at the highest temperature, and is rejected at the lowest temperature. In terms of thermodynamic efficiency, not only the heat duty, but also the temperature level at which the heat is exchanged should be considered. Despite the advantages of thermally coupled column configurations, industry and process designers have been reluctant to implement them in practice because of fear of control problems and lack of suitable design procedures. To reduce the control difficulties caused by two-way connections between thermally coupled columns, Agrawal4 and Agrawal and Fidkowski10 have proposed new thermally coupled distillation schemes. In these schemes, it is expected that the control properties will be improved with a reduced number of twoway connections, that is, when one or more two-way connections


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Figure 2. Thermally coupled configurations for ternary distillation. Thermally coupled (a) side-rectifier, (b) side-stripper, and (c) fully thermally coupled, i.e., the Petlyuk configurations.

have been replaced with one-way connections. On the other hand, it has been found that in several cases control properties of thermally coupled column configurations are similar or even better than more conventional ones.12,32,33,44,45,47 This should reduce the fear of control problems, and thus, promote applying thermally coupled column configurations in industrial separations. Even though research has mainly concentrated on ternary systems, methods to generate systematically all possible distillation configurations for a multicomponent separation have been presented.7,48–53 The energy consumption and controllability of thermally coupled distillation configurations for the separation of multicomponent systems have also been examined.18,32,47 It is noteworthy that despite its complicated character, there has been significant progress in the optimal synthesis of complex column configurations based on mixed-integer nonlinear programming (MINLP) with tray-by-tray models.16,17,37,40,41,54

2.2. Thermally Coupled Column Configurations in the Separation of Azeotropic Component Systems. Although the interest in the separation of zeotropic systems with thermally coupled column configurations has been extensive, separation of azeotropic systems with the same column configurations has been a relatively little examined topic. With azeotropic systems, the distillation boundaries set restrictions, which have to be taken into account. However, some pioneering work has been made in this area. For example, Timoshenko et al.55 have presented extractive distillation flowsheets, which use complex column arrangements with partially coupled heat and material flows to separate multicomponent azeotropic systems. Because the configurations become structurally closer to thermodynamically reversible distillation, a decrease in energy consumption may be achieved.

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It seems, however, that Bauer and Stichlmair56 and Castillo et al.38,39 were the first who found the possibility to cross a distillation boundary with the thermally coupled side-column configurations. Castillo et al.39 studied the separation of a ternary acetone/chloroform/benzene mixture and showed, based on the concept of operation leaves, that the total reflux boundary can be crossed at finite reflux by using a thermally coupled siderectifier configuration. They showed using simulation that the boundary crossing is indeed possible and that high product purities can be achieved. However, they did not optimize the system, and their objective was only to prove that a complex column arrangement can be used to cross the simple distillation boundary. Castillo et al.38,39 suggested that complex designs are helped without an excessive capital penalty with proper placement of intermediate reboilers and condensers. They also suggested that the scope for using complex column arrangements in the separation of azeotropic systems is greater than previously thought. Later on, Petlyuk and Danilov57 reported that the thermally coupled side-rectifier configuration is not comparable costwise to other alternatives for separating the acetone/chloroform/ benzene mixture. According to them, the thermally coupled side rectifier is not the worst, but average in costs compared to the flowsheets, which are based on the conventional distillation column sequences having a recycle flow. The major drawback of a thermally coupled side-rectifier configuration was found to be the high reflux ratio that is required in the side-rectifier column. Bauer and Stichlmair37 studied the possibility of finding the economically optimal (lowest annual costs) configuration for zeotropic and homogeneous azeotropic separations. They considered a ternary methanol/ethanol/water mixture with high (99 mol %) purity requirements for the product flows, and found that a complex column system consisting of three thermally coupled columns with methanol and azeotrope recycles yields the system with the lowest total annual costs. They also showed that the distillation boundary of the methanol/ethanol/water system could be crossed by using a thermally coupled sidestripper configuration, consisting of just two columns with partial recycling of the pure methanol. Later, at least Barttfeld et al.40 and Yeomans and Grossmann41 also utilized MINLP to synthesize the methanol/ethanol/water separation with a thermally coupled side-stripper configuration based on the optimization of the superstructure embedding all possible alternative designs as a form of a rigorous tray-by-tray model. 2.3. Distillation Boundary and Separation Feasibility. Azeotropes and distillation boundaries often place limitations on the degree of separation thus challenging the distillation sequence synthesis. Therefore, the determination of feasible product composition regions (separation regions) and possible separation sequences (feasible splits) have been actively studied.38,39,58–66 In addition to geometrical methods relying on the visualization of the behavior of three- and four-component systems, some references also propose fully equation-based feasibility study approaches. Both the residue curve maps36,58–61,64,67 and distillation line maps62 have been found to be useful tools in a separation sequence synthesis. Both maps illustrate well the thermodynamic complexity of azeotropic systems and display boundaries, which divide the composition space into distillation regions. A single distillation region can be understood as a family of curves connecting one unstable node to a stable node. Because of the importance of the location and shape of the distillation boundary in the separation sequence synthesis, algorithms to determine

distillation regions and separation boundaries have also recently been proposed.68,69 Although the fixed points (i.e., nodes of azeotropes and pure compounds) in the residue curve and distillation line maps are identical, the residue curves and distillation lines themselves do not coincide. This is because of the different definition basis and origin of the maps.70,71 A residue curve map is a diagram that shows residue curves, that is, composition trajectories of the residue liquid in an open equilibrium evaporator (simple distiller), for different initial compositions. A distillation line map is a diagram that consists of distillation lines, which describe the set of liquid compositions for which the vapor compositions in equilibrium lie on the same line. Thus, the residue curve boundaries (simple distillation boundaries) and distillation line boundaries (total reflux boundaries) do not coincide either. Even though the residue curve and distillation line boundaries have a solid theoretical background, neither of them can strictly predict the feasible product composition regions even for the simplest continuous distillation. There are several studies,36,58,64,66 which show that the distillation boundary (separatrix) is at least to some extent possible to be crossed from the concave side with a simple column (one-feed, two-product) with finite reflux. The significant curvature of the distillation boundary makes it easier to be crossed. Because the distillation boundary can be crossed from the concave side, two distillation regions partially overlap each other. This overlapping is encountered both with a simple distillation boundary (in the case of a packed column) and a total reflux boundary (in the case of a staged column). The pitchfork distillation boundary concept introduced by Davydyan et al.72 and later reviewed by Krolikowski68 may by utilized to predict the maximum extent of overlapping of the primary distillation regions. Distillation boundary crossing has been verified both with the equilibrium (EQ) and nonequilibrium (NEQ) stage models. Castillo and Towler73 found that the consideration of mass transfer in azeotropic distillation columns produces quantitative changes into the behavior of a liquid composition path for distillation columns at total reflux. In some cases, qualitative changes in product flows may also be observed. They73 also found that mass transfer effects tend to increase the curvature of distillation boundary, making it easier to be crossed. Springer et al.74 examined the influence of mass transfer on composition trajectories in multicomponent azeotropic distillation. They used a rigorous nonequilibrium (NEQ) stage model based on Maxwell-Stefan diffusion equations and noticed that the distillation boundary may be crossed even though the boundary is straight. In contrast to the general understanding presented in the literature, Springer et al.75 experimentally demonstrated that the crossing may be achieved even though the distillation boundary is nearly straight. In addition, based on a NEQ stage model, Springer and Krishna76 showed that the distillation boundary may be crossed even though the feed lies on the convex side of the boundary. However, the crossing seems to depend on the system and operating conditions. In addition, Baur et al.56 and Taylor et al.77 noticed the effect of mass transfer on the precise location of distillation boundaries, and thus on the feasibility and design of azeotropic distillation. Despite several academic examples of feasible distillation boundary crossings, industrial references seem to be rare. What Fidkowski et al.58 noticed is certainly true, namely that it is misleading to conclude that distillation boundaries can always be crossed to such an extent that it leads to an attractive


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Figure 3. Ternary component systems considered in the simulations: (a) acetone/chloroform/benzene and (b) methanol/ethanol/water systems.

application. They even recommended that it is a better engineering practice to explore all the other alternatives first and to attempt crossing a distillation boundary with distillation systems only when it is absolutely necessary. However, simply ignoring the sequences that are based on crossing a distillation boundary may lead to the exclusion of potential candidates in separation sequence synthesis. In the worst case, this may lead to the exclusion of notable benefits such as lower energy consumption (utility costs) and even lower investment costs. To avoid unjustified exclusions, it is worth increasing and deepening the knowledge of the capability and performance of complex column arrangements in the separation of azeotropic systems. In this paper, the issue is confronted by exploring the usability of thermally coupled side-column configurations in the separation of component sets having a curved distillation boundary. 3. Problem Definition and the Numerical Methods Utilized 3.1. The Component Sets Considered. Two ternary component systems having a curved distillation boundary were selected for the simulation studies. In the acetone/chloroform/ benzene system, the distillation boundary is formed between the maximum boiling azeotrope (saddle point between acetone and chloroform) and the pure benzene (stable node) according to Figure 3a. In the methanol/ethanol/water system, the distillation boundary is formed between the pure methanol (unstable node) and the minimum boiling azeotrope (saddle point between ethanol and water) according to Figure 3b. The selected component sets have been considered in several studies.37,39–41 These systems are also widely utilized in entrainer examinations. The column sequences separating acetone and chloroform using benzene as a heavy entrainer64,66 and column sequences separating ethanol and water using methanol as a light entrainer59,78,79 have both been studied. These separation configurations consist of conventional column sequences formed by two simple columns. The first column is an azeotropic (or an extractive) column and the second column is an entrainer recovery column from where the entrainer is recycled back to the first column. 3.2. Consideration of Thermally Coupled Side-Column Configurations. Figure 4 illustrates two thermodynamically equivalent structures for both thermally coupled side-rectifier

and side-stripper configurations. Even though the column configurations are structurally different, the basic character is the same. Every thermally coupled side-column configuration has thermal coupling between the main column and the side column. However, the molar flow ratios (SV/(V + SV) and SL/(L + SL)) expressed in Figure 4 are not identical between the thermodynamically equivalent configurations. For example, the values of the molar flow ratios SV1/(V1 + SV1) and SV2/(V2 + SV2) of the side rectifiers illustrated in Figure 4a follow the relation SV1/(V1 + SV1) ) 1 - SV2/(V2 + SV2), where V1 ) SV2 and V2 ) SV1. Correspondingly, the relation can be written for the thermally coupled side strippers illustrated in Figure 4b as SL1/(L1 + SL1) ) 1 - SL2/(L2 + SL2), where L1 ) SL2 and L2 ) SL1. The fulfillment of the relations requires that the number of column stages in various column sections (I, II, III, and IV) is the same in thermodynamically equivalent column configurations. After specifying the condition of the column feed, the number of stages, and the location of the feed and side draw stages, the total degrees of freedom of thermally coupled side-column configuration is four. If three degrees of freedom are utilized by specifying the mole fractions of key components in the product flows (one specified mole fraction in each product flow), one degree of freedom will be left. It can be utilized in the determination of the minimum energy operation point. Figure 5 illustrates the reboiler duty profile of thermally coupled side-rectifier configuration (Case 4 in Table 3) as a function of the molar flow ratio SV/(V + SV). The structure of the column configuration is illustrated in Figure 9a. It is found that the SV/(V + SV) ratio can be used in the determination of the minimum energy operation point (the operation point of minimum total reboiler duty) for a thermally coupled siderectifier configuration; the minimization function (reboiler duty) forms a convex profile with one global minimum point. In the same way, the SL/(L + SL) ratio can be used as an optimization variable in the determination of the minimum energy operation point for the thermally coupled side-stripper configuration. It is worth stressing that, as Figure 5 illustrates, the energy consumption increases considerably outside the minimum energy operation point. 3.3. Solving Procedure. Figure 6 illustrates the phases of the solving procedure that can be utilized when thermally coupled side-column configurations are considered. The procedure resembles the solving procedure proposed in Malinen

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Figure 4. Thermally coupled side-column configurations considered. Thermodynamically equivalent (a) side-rectifier and (b) side-stripper configurations.

and Tanskanen,42 where the aim was to determine the minimum energy operation point for a fully thermally coupled (i.e., the Petlyuk) distillation system. The procedure illustrated in Figure 6 is a heuristic approach that has been formulated into a computer algorithm. The procedure offers consecutive phases for the determination of a state distribution for a thermally coupled side-column configuration possessing the character of minimum energy usage. As a whole, all the phases shown in Figure 6 can be implemented in such a way that no manual intervention between the phases is necessary. At the beginning of the solving procedure, the column system structure (i.e., the number of stages, location of the feed and side draw stages, and reboiler and condenser types) is fixed together with the feed conditions (i.e., feed composition, pressure, and temperature). The column system structure and feed conditions can be fixed as desired. In the solving procedure, the target is simply to determine the minimum energy operation

conditions for the column system, rather than optimizing the structure of the system in terms of minimum investment and operating costs. Therefore, the column system structure is fixed and preserved together with the feed conditions throughout the phases of the minimum energy operation point determination procedure. Thus, the operation conditions determined with this procedure describe the minimum energy operation conditions specific for the column system structure and feed conditions under consideration. In the first phase of the solving procedure, the initial state distribution for the column configuration is calculated. Here, reflux and reboil ratios, and the molar flow ratio (either SV/(V + SV) or SL/(L + SL)) are used as specifications. To attain some kind of permanency, in the first phase, the molar flow ratio of 0.1 and the reflux and reboil ratio values of 1 have been utilized. In the second phase of the solving procedure, the state distribution for the column system is calculated with exact mole


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Figure 5. Reboiler duty profile of the thermally coupled side-rectifier as a function of the SV/(V + SV) ratio. The minimum reboiler duty is approached at the point 0.261. The figure on the right has been magnified from the figure on the left.

Figure 6. The minimum energy determination procedure for a thermally coupled side-column configuration that is capable of separating component sets having a curved distillation boundary.

fraction specifications. The initial state distribution obtained in the first phase of the solving procedure is utilized as a starting point for the calculation. The value 0.8 has been utilized for the molar flow ratio (SV/(V + SV) or SL/(L + SL)). The state distribution that fulfills the desired product purities is sought one column end at a time, starting from the end of the main column from where the component of the concave side is taken. In the case of the acetone/chloroform/benzene component system, the state distribution that fulfills the acetone purity in the distillate flow of the main column of the thermally coupled side-rectifier configuration is determined first. Correspondingly, in the case of the methanol/ethanol/water system, the state distribution that fulfills the water purity in the bottom product of the thermally coupled side-stripper configuration is determined first. After that, the state distribution that also fulfills the purity of another product flow of the main column is determined. Finally, the state distribution that also fulfills the purity requirement of the side column is determined. By searching the state distribution gradually, one column end at a time, the numerical solving of the column configuration model with exact mole fraction specifications is eased.

In the third phase of the solving procedure, the minimum energy operation point is finally determined. After specifying the three product flow purities, the thermally coupled sidecolumn configurations have one degree of freedom, which is utilized in the minimum energy operation point determination. In this paper, the minimum energy operation point, that is, the minimum total duty of the reboiler(s), is determined based on the molar flow ratio (SV/(V + SV) or SL/(L + SL)). In optimization terms, this means that the total duty of the reboilers is the objective function, which is minimized with respect to the molar flow ratio so that the constraints (the purity specifications) are fulfilled throughout the optimization phase. The state distribution obtained in the second phase of the solving procedure is used as a starting point for the optimization. 3.4. Consideration of Solving Methods. Due to the strong two-way couplings between the main and side column of the thermally coupled side-column configurations, the solving of equations describing the column configuration systems under consideration was carried out based on an equation-oriented solving approach rather than a modular solving approach. The local Newton-Raphson based solving method was often sufficient, offering a converged result in the solving procedure (Figure 6) phases. However, especially when determining the state distributions for the column configuration system in the second phase of the solving procedure, the modified bounded Newton homotopy was employed in order to improve robustness and to approach a converged result. This was done when the local Newton-Raphson based solving algorithm did not converge within 100 iterations. The modified bounded Newton homotopy method was also employed in the initial state distribution calculation and the optimization phase of the solving procedure when the state distributions were not achieved within 100 iterations. An in-depth introduction to the use and implementation of the homotopy continuation methods can be found in several books and articles.80–87 An introduction to bounded homotopies can be found in the papers of Paloschi,88–90 and to modified bounded homotopies in the papers of Malinen and Tanskanen.42,43 3.5. Consideration of the Optimization Method. In the optimization phase, the interpolation strategy was utilized in the determination of minimum energy operation conditions. The methods based on polynomial interpolation and extrapolation are simple and relatively fast methods when solving onedimensional optimization problems.91,92

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The implemented quadratic polynomial interpolation strategy is based on an approximation, in which the quadratic function is passed to run through three points. In this paper, these points represent the total duty of reboilers in the three molar flow ratio (SV/(V + SV) or SL/(L + SL)) points. At the beginning of the optimization phase, these points are selected around the molar flow ratio value utilized in the second phase of the solving procedure. The derivative of the quadratic polynomial equal to 0 yields the extreme point of the approximated quadratic function. From the set of four molar flow ratio points (the three points utilized in fitting the parameters of the quadratic polynomial and the interpolated point), the point that gives the highest value for the total duty of reboilers is discarded and the quadratic polynomial is passed to run through the three remaining points. The interpolation steps are continued until the minimum total duty of reboilers is attained. Polynomial approximation may be used with caution for extrapolation. In that case, care must be taken that the new point that is determined has a value less than the highest value offered by the three points utilized in the extrapolation. If this requirement is not met, the extrapolated point must be moved closer to the three points utilized in the extrapolation. In the third phase of the solving procedure, the optimization function is assumed to be continuous and convex with respect to the optimization variable (SV/(V + SV) or SL/(L + SL)) around the minimum energy operation point. This assumption has not been found to pose problems as local minima in the cases simulated in this paper. 3.6. Utilized Variables Mapping Method. In this paper, the mapped variables have been utilized in every phase of the solving procedure. This has been made in order to restrict variable values inside the reasonable problem domain, thus preventing error stops. All the problem variables have been mapped according to the following mapping equations introduced in Malinen and Tanskanen.42,43 Variable xi mapping from a finite space bounded by bmin and i max bi into an infinite space:

xinf i ) log10

xinf i ) log10

(

(

2(xi - bmin i ) bmax - bmin i i

)

bmax i

- xi

(1)

)

, when xi g 0.5(bmax + bmin i i ) (2)

Correspondingly, variable xinf i mapping from an infinite space into a finite space: inf

inf xi + 0.5(bmax - bmin xi ) bmin i i i )10 , when xi < 0

xi )

bmax i

- 0.5

(bmax - bmin i i ) xiinf

10

, when xinf i g 0

4. Simulation Cases In addition to the solving procedure and solving and optimization methods introduced in the previous sections, column models consisting of a full set of tray-by-tray MESH equations were implemented in the MATLAB environment. The MESH equation set for each stage j consists of an overall material balance Lj-1 + Vj+1 - (Lj + SLj ) - (Vj + SVj ) + FLj + FVj ) 0 (5) n material balances for the components (i ) 1... n) xi,j-1Lj-1 + yi,j+1Vj+1 - xi,j(Lj + SLj ) - yi,j(Vj + SVj ) + f V xfi,jFLj + yi.j Fj ) 0

(6)

n phase equilibrium relationships for the components (i ) 1... n) yi,j - xi,jKi,j ) 0

(7)

one summation equation for mole fractions n

(

∑y

i

i)1

n

-

∑x

i

) 0)

(8)

i)1

and a heat balance Lj-1hj-1 + Vj+1Hj+1 - (Lj + SLj )hj - (Vj + SVj )Hj + FLj hfj + FVj Hfj + Qj ) 0 (9)

, when xi < 0.5(bmax + bmin i i )

0.5(bmax - bmin i i )

them into the equations of the original equation set f(x). In the same way, when mapped variables are utilized in the calculations of the local Newton-Raphson based solving method, the variables must be mapped into a finite space before placing them into the equations of the original equation set. In the simulations carried out in this paper the mole fractions were bounded by [0 1], molar flows [0 1000], temperatures in Kelvins by [250 450], heat exchanger duties by [0 107], and reflux and reboil ratios by [0 1000].

(3)

(4)

The implemented variable mapping equations can be utilized with all solving methods. For example in the case of modified bounded homotopies, the homotopy path is tracked in an infinite space instead of a finite space bounded by the problem domain boundaries. Although the path is tracked in an infinite space, the variables are still mapped into a finite space before placing

The thermodynamic models and parameters implemented in the calculations are based on the database of the commercial simulation program HYSYS. The VLE parameters used in the calculations are shown in Tables 1 and 2. The Wilson model has been assumed to predict a less curved distillation boundary than other thermodynamic models.58,64 Thus, it is anticipated that when the simulations based on the Wilson model predict a successful crossing of a boundary, the distillation boundary crossing is also attainable in practice. Because the Jacobian matrix is approximated numerically, problem sparsity has been taken into account. By knowing the sparsity pattern of the Jacobian, the number of function evaluations needed to compute the Jacobian matrix columns has been reduced. 4.1. Case Example. Figure 7 presents mole fraction profiles for Case 4 of Table 3. The profiles illustrate how the state distribution that fulfills the purity requirements of the column system with minimum reboiler duty is sought in stages, according to the phases of the solving procedure of Figure 6. First, the initial state distribution (Figure 7a) is solved, having reflux and reboil ratios of 1 and a molar flow ratio SV/(V + SV) of 0.1. Then, the state distribution that fulfills the three product flow purities is sought sequentially (Figure 7b-d), as


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a

Table 1. Thermodynamic Parameters for the Acetone/Chloroform/Benzene System. Parameters Are from the HYSYS Database binary interaction parameters for the Wilson equation (cal mole-1) A11 ) 0 A21 ) -506.852 A31 ) -243.965

A12 ) 116.117 A22 ) 0 A32 ) -11.823

A13 ) 682.406 A23 ) -71.811 A33 ) 0

constants for the vapor pressure correlation component

A

B

C

D

E

F

molar volume (dm3 kmole-1)

acetone chloroform benzene

71.3031 73.7058 169.65

-5952 -6055.6 -10314.8

0 0 0

-8.53128 -8.9189 -23.5895

7.82393 × 10-6 7.74407 × 10-6 2.09442 × 10-5

2 2 2

74.4768 80.7314 89.5551

a

Pressure (kPa), temperature (K), ln(Psat) ) A + B/(T + C) + D ln(T) + E (TF).

Table 2. Thermodynamic Parameters for the Methanol/Ethanol/Water System. Parameters Are from the HYSYS Databasea binary interaction parameters for the Wilson equation (cal mole-1) A11 ) 0 A21 ) -132.058 A31 ) 620.631

A12 ) 135.811 A22 ) 0 A32 ) 975.486

A13 ) -52.605 A23 ) 276.756 A33 ) 0

constants for the vapor pressure correlation component

A

B

C

D

E

F

molar volume (dm3 kmole-1)

acetone chloroform benzene

59.8373 86.486 65.9278

-6282.89 -7931.1 -7227.53

0 0 0

-6.37873 -10.2498 -7.17695

4.61746 × 10-6 6.38949 × 10-6 4.0313 × 10-6

2 2 2

40.7622 58.4923 17.8834

a

Pressure (kPa), temperature (K), ln(Psat) ) A + B/(T + C) + Dln(T) + E(TF).

explained in section 3.3. The value 0.8 has been utilized as the molar flow ratio SV/(V + SV) specification. Finally, the state distribution of minimum reboiler duty (Figure 7e) has been determined by utilizing SV/(V + SV) as an optimization variable. It is worth noting that the local Newton-Raphson based solving method does not necessarily enable the approach of the state distribution (solution) for the phases of the solving procedure within a tolerable time, if indeed at all. For example, to achieve the state distribution shown in Figure 7c, the local Newton-Raphson based solving method of MATLAB requires 220 iterations altogether. This number of iterations is obtained by allowing the acetone mole fractions to receive negative values by restricting the values between -1 and 1. When the acetone mole fraction values are also restricted between 0 and 1, the converged result is not approached at all within 3000 iterations. Thus, when the problem domain is specified to have only meaningful variable values, the local Newton-Raphson based solving method may not be robust enough. Therefore, to increase the robustness and secure the solving, the Newton homotopy method has been utilized in this paper whenever the local Newton-Raphson based solving method fails to approach the solution within 100 iteration rounds. When homotopy continuation methods are utilized in solving, it may happen that the homotopy path runs outside the meaningful problem domain. Since several thermodynamic models cannot cope with unfeasible variable values such as negative mole fraction values, an error stop may result. To keep the homotopy path inside the meaningful problem domain, bounded homotopies can be utilized. In this paper, the modified bounded Newton homotopy method together with the variables mapping method have been utilized, thus enabling the bounded homotopy path to be tracked accurately and flexibly even though the bounding zone is narrow. This is illustrated in Figure 8, where in contrast to the unbounded Newton homotopy (-0-), the modified bounded Newton homotopy (-b-) enables the attainment of the desired state distribution for the column system without problem domain crossings. Figure 8 also illustrates how modified bounded homotopy together with mapped variables allow the homotopy path tracking inside the narrow bounding

zone that is vital when modified bounded homotopies are applied to solve chemical engineering problems.42,43 4.2. The Effect of Feed Composition and Product Purities on Energy Requirement. Tables 3 and 4 show the simulation results, which have been obtained based on the minimum energy determination procedure shown in Figure 6. The results illustrate the effect of the feed composition and product flow purities on the energy usage and operation conditions of the thermally coupled side-column configurations shown in Figure 9. The number of stages in the columns and the structure of the configurations are the same when distilling the same set of components. In the case of the acetone/ chloroform/benzene system, the separation is carried out with a thermally coupled side rectifier and in the case of the methanol/ ethanol/water system with a thermally coupled side-stripper configuration. Herein, the purpose has not been to optimize the structure of the column systems in terms of minimum total annual costs. Instead, the purpose has been to roughly screen how the column feed composition and product purity requirements affect the optimal operation conditions. Therefore, the results shown in Tables 3 and 4 do not represent the minimum energy (minimum reflux) conditions in general, but the minimum energy operation conditions of the column systems with the structure and product purity requirements specified in advance. On the basis of the results summarized in Table 3, it is found that when mole fraction specifications of the product flows are kept constant (i.e., 0.95), the energy consumption and molar flow ratio (SV/(V + SV) increase with the increasing acetone and chloroform portion in the feed. Thus, a constant product purity specification together with various feed compositions generates either relatively difficult or easy separations. The examination carried out demonstrates how significantly the feed composition affects the total energy requirement of thermally coupled side-column configurations. On the other hand, as cases 5 and 6 in Table 3 illustrate, both the energy consumption and reflux and reboil ratios increase with the increasing product purity requirements. When

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Figure 7. Liquid mole fraction profiles for acetone/chloroform/benzene separation (case 4 in Table 3). (a) Initial state distribution, (b) the state distribution where the distillate flow fulfills the purity specification, (c) the state distribution where the bottom product flow also fulfills the purity specification, (d) the state distribution where the distillate flow of the side rectifier also fulfills the purity specification, (e) the state distribution at the operation point of the minimum reboiler duty (SV/(V + SV) ) 0.261).

the molar flow ratio SV/(V + SV) increases, it indicates that the liquid and vapor flows inside the side-rectifier and the bottom

section of the main column increase. Thus, the reboiler duty and the molar flow ratio value together are able to characterize


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a

Table 3. Minimum Energy Operation Point for Various Acetone/Chloroform/Benzene Distillation Cases

no.

feed comp (mole fraction)

1

0.2/0.1/0.7

2

0.2/0.2/0.6

3

0.2/0.3/0.5

4

0.4/0.1/0.5

5

0.4/0.2/0.4

6

0.4/0.2/0.4

7

0.6/0.1/0.3

product comp: distillate (mole fraction) distillate C2 (mole fraction) bottom (mole fraction) 0.9500/0.0071/0.0429 0.0477/0.9500/0.0023 0.0000/0.0500/0.9500 0.9500/0.0297/0.0203 0.0500/0.9500/0.0000 0.0000/0.0500/0.9500 0.9500/0.0456/0.0044 0.0500/0.9500/0.0000 0.0002/0.0498/0.9500 0.9500/0.0028/0.0472 0.0499/0.9500/0.0001 0.0000/0.0500/0.9500 0.9000/0.0630/0.0370 0.1000/0.9000/0.0000 0.0009/0.0991/0.9000 0.9500/0.0309/0.0191 0.0500/0.9500/0.0000 0.0001/0.0499/0.9500 0.9500/0.0039/0.0461 0.0500/0.9500/0.0000 0.0001/0.0499/0.9500

search variable: SV/(V + SV) 0.327 0.485 0.831 0.261 0.536 0.696 0.504

reflux ratio C1 reboil ratio C1 reflux ratio C2

cond duty C1 reb duty C1 cond duty C2 (kJ mole-1 feed)

3.914 2.015 6.686 7.747 5.209 8.706 25.481 55.500 90.406 2.678 3.946 6.042 4.348 11.049 17.257 6.214 22.489 37.670 2.309 13.988 23.067

29.8 45.1 14.7 51.5 100.5 48.6 151.3 897.4 745.9 44.9 61.4 16.0 67.0 144.8 77.5 86.8 285.7 198.6 60.7 122.8 61.8

total heat duties: cond reb (kJ mole-1 feed) 44.5 45.1 100.2 100.5 897.2 897.4 60.9 61.4 144.5 144.8 285.4 285.7 122.5 122.8

a The product purity specifications are in bold. Pressure, 101.3 kPa; boiling liquid feed; reb, reboiler; cond, condenser; C1, main column; C2, side-rectifier.

the difficulty of the considered separation at the minimum energy operation point. The results in Table 4 present an interesting behavior. As cases 6-9 illustrate, energy consumption decreases when the purity requirements of the main column distillate and bottom product are increased. This is surprising, because in principle, the energy consumption should increase, not decrease, with increasing purity requirements. If, however, just the effect of a single distillate or bottom product purity requirement is considered, it can be recognized (based on the cases 6, 10 and 11) that just the increasing distillate purity has a lowering effect on the total energy requirement. If the purity of the bottom product is increased, the total energy requirement of the column configuration also increases. This raises the question as to why the increasing methanol product purity decreases the total energy requirement. This unexpected behavior can be discussed with the aid of Figure 10a, where the minimum total duty of reboilers is presented as the function of the methanol purity in the distillate. The energy requirement partly decreases with increasing distillate purity. However, when the purity requirement is tightened enough, the energy requirement begins to increase significantly. As Figure 10b illustrates, the molar flow ratio (SL/(L + SL)) also behaves illogically; the molar flow ratio does not increase as a function of distillate purity, but forms a multiplicity profile. This indicates that the nonideal behavior of the azeotropic system in question favors separation, offering relatively high methanol distillate purity with decreased energy requirement. Evidently, the product purity requirement in the side stripper and the closeness of the distillation boundary have a dramatic combined effect on the operation of this particular system. When cases 6 and 10 of Table 4 are compared, it can be recognized that when the purity of the methanol in the distillate is increased, the methanol portion in the side stripper bottom product clearly increases. In this case, the liquid mole fraction profile of the side stripper runs farther away from the distillation boundary. Consequently, the mole fraction profile does not run as close to the azeotrope (saddle) node. As Figure 11 illustrates, the mole

fraction profiles of these two cases (cases 6 and 10) clearly differ from each other. In the case of methanol/ethanol/water system, the distillation boundary is almost straight. Because of the minute distillation boundary curvature, a high amount of energy is needed to approach even relatively low purity requirements in the bottom product of the side-stripper. Thus, as cases 3 and 5 in Table 4 illustrate, when high ethanol product purity is sought, the energy requirement may grow to a high level. 4.3. Attainable Product Purities. To compare the highest middle component purity attainable with conventional column sequences and thermally coupled side-column configurations, the following examinations were carried out. The conventional column sequence schemes were simulated with a commercial simulation program HYSYS, and the thermally coupled sidecolumn configurations with the MATLAB based on the solving procedure presented in Figure 6. In both studies, the same thermodynamic model and database of HYSYS were utilized. The conventional column sequences and thermally coupled side-column configurations studied are shown in Figures 12 and 13. The structures of conventional column sequences were selected such that the maximum distillation boundary crossing was enabled. Therefore, the partial condenser in the first column of the methanol/ethanol/water system (Figure 12b) was utilized in the simulations. Since the aim was only to compare the attainable product flow purities between different column configurations, the number of column stages in the column sections was not defined congruently, but was high enough to avoid the limitations that may have resulted from a small number of column stages. First, the separation of acetone/chloroform/benzene mixture was considered according to Figure 12a. Both columns in the column sequence have 100 stages, a total condenser and a reboiler, and the feed is routed onto stage 50. On trial, the reflux ratio of the second column is set as high as 1000 to obtain the chloroform from the top of the second column as pure as possible. The acetone and benzene product purities are set

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Figure 8. The unbounded (-0-) and modified bounded (-b-) Newton homotopy paths for the acetone mole fraction in the bottom product flow when determining the state distribution of Figure 7c. Panels b and c have been magnified from panel a. A bounding zone width of 1×10-10 has been utilized. The starting point is (O) and the solution ( ×).

constant (either 0.95 or 0.99), and the chloroform product purity is studied as a function of the reboil ratio of the first column. As Figure 14 shows, the maximum attainable chloroform product purity is highly dependent on the reboil ratio of the first column of the direct column sequence. This is because the composition of the bottom product of the first column and thus the feed composition of the second column depend on the reboil ratio of the first column. The dependence is not straightforward. Certainly, an optimum reboil ratio can be obtained that gives the highest chloroform purity at the top of the second column. In this case, the direct column sequence consisting of two simple columns cannot produce a chloroform product having a purity higher than 0.907 and 0.908 in the case of purity specifications of 0.95 and 0.99 for the other product flows. As Figure 15 shows, the thermally coupled side-rectifier shown in Figure 13a is capable of producing a significantly higher chloroform product purity than the conventional direct column sequence. However, a high reflux ratio value is required in the side-rectifier column. The high reflux value indicates that the liquid and vapor flows inside and between the side rectifier and the bottom section of the main column become crucial when a high chloroform purity is required. The indirect column sequence shown in Figure 12b can be utilized in the separation of a boiling methanol/ethanol/water

mixture. The first column in the indirect column sequence has a partial condenser and the feed is routed to the second column in the vapor phase. The reboil ratio of the second column is set to 1000 to obtain ethanol from the bottom of the second column that is as pure as possible. The purities of the methanol and water products are specified (either 0.95 or 0.99), and the purity of the ethanol product is studied on the basis of the reflux ratio of the first column. As Figure 16 shows, the maximum attainable ethanol product purity is highly dependent on the reflux ratio of the first column of the conventional indirect column sequence (Figure 12b). However, the dependence is not straightforward. An optimum value of the reflux ratio exists, which gives the highest ethanol purity at the bottom of the second column. In this case, the indirect column sequence consisting of two simple columns cannot produce an ethanol product having a purity higher than 0.956 and 0.949 in the case of purity specifications 0.95 and 0.99 for other components. Note that the maximum ethanol product purity decreases when the purities of other product flows increase. As Figure 17 illustrates, the thermally coupled side-stripper column configuration shown in Figure 13b offers the means to achieve significantly higher ethanol product purity than is possible with the conventional indirect column sequence shown


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a

Table 4. Minimum Energy Operation Point for Various Methanol/Ethanol/Water Distillation Cases

no.

feed comp (mole fraction)

1

0.4/0.1/0.5

2

0.4/0.2/0.4

3

0.6/0.1/0.3

4

0.6/0.1/0.3

5

0.6/0.1/0.3

6

0.6/0.2/0.2

7

0.6/0.2/0.2

8

0.6/0.2/0.2

9

0.6/0.2/0.2

10

0.6/0.2/0.2

11

0.6/0.2/0.2

12

0.8/0.1/0.1

product comp: distillate (mole fraction) bottom C2 (mole fraction) bottom (mole fraction)

search variable: SL/(L + SL)

0.9500/0.0483/0.0017 0.0000/0.9100/0.0900 0.0004/0.0496/0.9500 0.9900/0.0098/0.0002 0.0000/0.9000/0.1000 0.0000/0.0500/0.9500 0.9500/0.0483/0.0017 0.0000/0.9300/0.0700 0.0001/0.0499/0.9500 0.9700/0.0292/0.0008 0.0000/0.9300/0.0700 0.0001/0.0299/0.9700 0.9500/0.0481/0.0019 0.0000/0.9500/0.0500 0.0001/0.0499/0.9500 0.9000/0.0951/0.0049 0.0000/0.9000/0.1000 0.0000/0.1000/0.9000 0.9500/0.0483/0.0017 0.0000/0.9000/0.1000 0.0000/0.0500/0.9500 0.9900/0.0099/0.0001 0.0005/0.9000/0.0995 0.0000/0.0100/0.9900 0.9990/0.0010/0.0000 0.0006/0.9000/0.0994 0.0000/0.0010/0.9990 0.9990/0.0010/0.0000 0.0006/0.9000/0.0994 0.0001/0.0999/0.9000 0.9000/0.0950/0.0050 0.0000/0.9000/0.1000 0.0000/0.0500/0.9500 0.9900/0.0099/0.0001 0.0004/0.9200/0.0796 0.0001/0.0799/0.9200

reflux ratio C1 reboil ratio C1 reboil ratio C2

cond duty C1 reb duty C1 reb duty C2 (kJ mole-1 feed)

6.016 3.489 13.279 15.476 7.713 14.304 5.854 7.935 23.435 6.777 8.317 21.896 8.700 9.014 46.510 6.673 16.502 9.145 5.931 16.420 3.925 5.124 14.224 3.012 5.152 13.855 3.456 4.671 11.270 3.706 7.344 18.240 10.019 2.563 20.747 4.713

104.8 74.6 30.5 235.2 126.8 108.7 153.6 101.1 52.7 170.4 104.1 66.5 217.4 115.3 102.4 182.6 136.9 45.9 155.4 128.5 27.1 131.1 106.4 25.0 130.4 101.0 29.7 120.2 91.6 28.7 198.6 143.8 55.0 101.7 85.2 16.7

0.365 0.526 0.419 0.468 0.536 0.320 0.256 0.303 0.351 0.368 0.346 0.276

total heat duties: cond reb (kJ mole-1 feed) 104.8 105.1 235.2 235.5 153.6 153.9 170.4 170.7 217.4 217.7 182.6 182.7 155.4 155.6 131.1 131.4 130.4 130.7 120.2 120.3 198.6 198.8 101.7 101.8

a The product purity specifications are in bold. Pressure, 101.3 kPa; boiling liquid feed; reb, reboiler; cond, condenser; C1, main column; C2, side-stripper.

Figure 9. Thermally coupled side-column configurations considered in section 4.2. Thermally coupled (a) side-rectifier and (b) side-stripper configurations.

in Figure 12b. However, a high reboil ratio value is needed in the side-stripper column. The high reboil ratio value indicates that the liquid and vapor flows inside and between the sidestripper and the top section of the main column become intensive when a high ethanol purity is required.

5. Discussion According to the simulation results, thermally coupled sidecolumn configurations enable a distillation boundary crossing in a more flexible way than do conventional direct and

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Figure 10. The unexpected behavior noticed in the methanol/ethanol/water separation with the thermally coupled side-stripper configuration: (a) the minimum total duty of reboilers and (b) the molar flow ratio (SL/(L + SL)) as a function of methanol purity in the distillate. The column configuration structure is shown in Figure 9b. The feed composition of 0.6/0.2/0.2 and mole fraction purity specifications of 0.9 for key components in the bottom products of the main and side columns have been utilized.

Figure 11. Liquid mole fraction profiles of the thermally coupled side-stripper column of case 6 (b) and case 10 ( ×) of Table 4.

Figure 12. Conventional column sequences considered in section 4.3: (a) the direct and (b) indirect column sequences.

indirect column sequences. This conclusion is based on the observation that in the situations where a curved distillation boundary is present, the thermally coupled side-column

configurations enable remarkably higher product purities to be achieved, that is, the feasible product composition area is wider than with conventional column sequences.


6401

Figure 13. Thermally coupled side column configurations considered in section 4.3: thermally coupled (a) side-rectifier and (b) side-stripper configurations.

Figure 14. Reboil ratio of the first column as a function of the chloroform purity in the distillate of the second column in the conventional direct column sequence shown in Figure 12a.

The disturbances in the first column of the conventional column sequence may easily disturb the operation of the second column. In the worst case, the disturbances may irreversibly ruin the purity of one or more product flows. In the case of a thermally coupled side-column configuration, however, a twoway connection between the main and side column offers a wide operation window that brings flexibility to the operation. This flexibility can be utilized to stabilize the column configuration, and thus the disturbances existing in one column do not necessarily definitely spoil the product purities of the other column. Therefore, simply based on the steady state simulations, it is expected that a wide operation window of thermally coupled side-column configurations may turn out to be invaluable for control. However, dynamic consideration would be required to confirm this. As Figure 5 illustrates, the energy consumption of thermally coupled side-column configurations increases sharply outside the minimum energy operation conditions. Therefore, the thermally coupled side-column configurations should be operated as close to the minimum energy operation point as possible. It is assumed that with a proper control strategy, the column

Figure 15. Reflux ratio of the side rectifier as a function of the chloroform purity in the product flow of the side rectifier in the thermally coupled siderectifier configuration shown in Figure 13a.

configuration may be operated close to the minimum energy operation point also during disturbances so that the product purity requirements are still fulfilled. Despite the benefits, there also seems to be one drawback. When the purity requirements of the product flows are increased, high internal flows in thermally coupled side-column configurations are required. This indicates a high energy consumption characteristic that may restrict the commercial use of these configurations. However, even though the energy usage of the thermally coupled side-column configurations in the separation of component systems having a curved distillation boundary may be considerable with high product purity requirements, the energy usage compared to conventional column schemes may nevertheless be lower. It is expected that, when taking into account the mass-transfer effects, that is, considering a nonequilibrium stage model (NEQ) in addition to an equilibrium stage model (EQ), the separation of component systems having a curved distillation boundary with thermally coupled side-column configurations may turn out to be more feasible in practice. In this case, a more curved distillation boundary makes it easier to cross it from the concave side. This would inevitably decrease the energy requirement.

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Figure 16. Reflux ratio of the first column as a function of the ethanol purity in the bottom product of the second column in the conventional indirect column sequence shown in Figure 12b.

column configurations to cross the curved distillation boundary from the concave side to attain separation with high product flow purity requirements. The results also show that the distillation boundary may have unexpected effects on the behavior of the column systems studied. This was noticed in methanol/ethanol/water separation, where the total duty of the reboilers in a thermally coupled side-stripper column configuration partly decreased with increasing methanol distillate purity. Despite the broadened insight and increased knowledge, there are still several interesting and important topics that deserve further study, including minimum energy (minimum reflux) examinations, consideration of mass transfer (NEQ column model) on the feasibility of the proposed separations, and experimental test runs to verify the validity of the presented results. In addition, the examination and development of procedures and strategies to optimize the structure of thermally coupled side-column configurations (number of stages, feed and side draw stage locations, etc.) with the objective of minimizing total annual costs are wide-ranging but important and interesting topics. In addition, the control and operation aspects (stability, start-ups and shut-downs, etc.) as well as possibilities to integrate the thermally coupled side-column configurations into larger process systems are topics which deserve attention. It is to be hoped that the examination and maturation phase concerning the practical usability of thermally coupled column configurations in the separation of azeotropic component systems will not take as long as for zeotropic systems. One step toward this has been made in Part 2 of this series of papers,94 which studies the effects of intermediate heat exchangers situated in thermally coupled side-column configurations. Acknowledgment

Figure 17. Reboil ratio of the side stripper as a function of the ethanol purity in the product flow of the side stripper in the thermally coupled sidestripper configuration shown in Figure 13b.

On the other hand, the reverse scenario is also possible. In that case, taking into account the mass-transfer effects, the distillation boundary may turn out to be less curved, indicating that the separation is more challenging in practice. As a recent work of Gutie´rrez-Antonio et al.93 illustrates, different thermodynamic models predict different locations for the distillation boundary. Thus, the selection of thermodynamic model has a considerable impact on the design of homogeneous azeotropic distillation columns. In addition, the location and shape of a distillation boundary predicted by the thermodynamic model is highly dependent on the quality of the thermodynamic data used in model regression. Therefore, because the curvature of a distillation boundary has a significant influence on the ability of the thermally coupled side-column configuration to carry out the separation feasibly, care should be taken to avoid uncertainties caused by an inappropriate thermodynamic model or erroneous thermodynamic data. 6. Conclusions In this paper, the general understanding and knowledge of the applicability and performance of the thermally coupled siderectifier and side-stripper configurations have been broadened in the separation of ternary systems having a curved distillation boundary. The results presented support the observation made in the literature about the ability of the thermally coupled side-

The postgraduate program Graduate School in Chemical Engineering (GSCE) and the financial support from the Tauno To¨nning and Emil Aaltonen Foundations are gratefully acknowledged. The helpful comments of Jani Kangas, University of Oulu, are highly appreciated. Nomenclature b ) boundary f ) equation set F ) feed flow h ) molar enthalpy of liquid flow H ) molar enthalpy of vapor flow K ) vapor-liquid equilibrium L ) liquid flow n ) number of components P ) pressure, kPa Q ) heat flow S ) sidestream flow T ) temperature, K V ) vapor flow x ) variable or mole fraction in liquid phase y ) mole fraction in vapor phase Subscripts i ) ith (variable) j ) jth (column stage) Superscripts f ) feed inf ) infinity L ) liquid phase max ) maximum

Ind. Eng. Chem. Res., Vol. 48, No. 13, 2009 min ) minimum V ) vapor phase

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ReceiVed for reView May 22, 2008 ReVised manuscript receiVed April 30, 2009 Accepted May 5, 2009 IE800817N

Thermally Coupled Side-Column Configurations Enabling Distillation

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