Distillation profiles in ternary heterogeneous mixtures with distillation boundaries

chemical engineering research and design 8 9 ( 2 0 1 1 ) 879–893

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Distillation profiles in ternary heterogeneous mixtures with distillation boundaries Andrzej R. Królikowski a,∗ , Lechosław J. Królikowski b , Stanisław K. Wasylkiewicz c a b c

Cargill Sweeteners, Cargill (Polska) Sp. z o.o., ul. MacMillan 1, Bielany Wrocławskie, 55-040 Kobierzyce, Poland ˙ Politechnika Wrocławska, Zakład Inzynierii Chemicznej, ul. Norwida 4/6, 50-373 Wrocław, Poland Aspen Technology Inc., 900, 125-9th Avenue SE, Calgary, Alberta T2G 0P6, Canada

a b s t r a c t Distillation boundaries are created by saddle azeotropes and divide the composition space into distillation regions. In this study, the behavior of rectification profiles was investigated in the following heterogeneous systems: benzene, tert-butanol, water and ethanol, water, toluene. These systems were chose in order to scrutinize whether distillation regions overlapped. The experiments were performed using Distil (afterwards Conceptual Engineering) software from AspenTech, Inc. For each type of distillation column (staged and packed), a different pair of distillation boundaries is referred (TRB & PDB and SDB & PDB accordingly). Similar to homogeneous mixtures, distillation regions were found to overlap each other in heterogeneous mixtures. As a consequence, their common part was parametrically sensitive. © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Distillation; Distillation boundaries; SDB; TRB; PDB; Heterogeneous mixtures; Packed column

1.

Introduction

In industrial practices, the design process of distillation systems for the separation of non-ideal mixtures with mutual immiscible liquid regions and many distillation regions is a complex issue. Examining separability and selecting feasible processing conditions through extensive simulation studies is tedious and very time-consuming, despite the development of modern computational techniques. Only a small selection of promising process alternatives and internal degrees of freedom can be analyzed at a time, forcing other potentially attractive alternatives are dismissed. In the trial-and-error technique, all of the input variables and process parameters are specified and the composition and flows of the products are calculated. In contrast, designing methods through simulation is a robust technique for ascertaining the performance of existing columns. The synthesis of distillation systems engages the consecutive design of individual columns, the assignment of a system structure (intermediate stream connections between columns) and the choice of entrainers and the selection of appropriate operating parameters (such as pressure, reflux ratio, number of stages and feed stage location). The above

∗

parameters are estimated through guessing, extrapolation of existing separation systems or by applying short-cut methods, e.g. Fenske (1932), Tongberg et al. (1936), Gilliland (1940), Underwood (1948), Van Wijk (1949), Henley and Seader (1981), Wasylkiewicz (1992), Fien and Liu, 1994, Matias et al. (1995), Bausa et al. (1998), von Watzdorf et al. (1999), Brüggemann and Marquardt (2004) and Liu et al. (2004). In this situation, only these design methods are useful, that take the analysis and examination of the entire composition space into account as well as stationary points (azeotropes), distillation boundaries, residue curves, distillation lines and composition profiles in the distillation column. By using these specific methods, infeasible designs can be removed early in the design process, which saves valuable time and resources. Several researchers have attempted to develop methods for assessing the feasibility studies for azeotropic homogeneous mixtures (see Petlyuk et al., 1965; Petlyuk and Serafimov, 1983). In turn, Thompson and King (1972) reported their efforts to automate the synthesis of separation processes by using heuristic and algorithmic programming. Rathore et al. (1974) solved the problem of synthesizing an optimal multicomponent separation system that was energy integrated by using a combined decomposition and dynamic programming tech-

Corresponding author. Tel.: +48 502 005 429; fax: +48 713 110 250. E-mail address: [email protected] (A.R. Królikowski). Received 7 September 2008; Received in revised form 24 October 2010; Accepted 26 November 2010 0263-8762/$ – see front matter © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2010.11.016

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Nomenclature A, B, C, D, E, F parameters in extended Antoine equation R reflux ratio R gas constant Aij , Aji parameters in NRTL model Gij , Gji binary parameters in NRTL model parameter in NRTL Model ˛ij = ˛ji  ij ,  ji binary parameters in NRTL model n number of components p operating pressure x vector of mole fractions in liquid phase x bifurcation point of locus of pinch y vector of mole fractions in vapor phase z vector of mole fractions in product  nonlinear, dimensionless evaporating time  parameter Y = (∂yi /∂xi ) Jacobian matrix for vapor–liquid equilibrium mapping CBR case based reasoning PDB pitchfork distillation boundary SDB simple distillation boundary TRB total reflux boundary [sa] saddle [sn] stable node [un] unstable node Subscripts and superscripts i component number j component number j stage number B bottom D distillate P product

nique. Hohmann et al. (1982) presented a new approach for the synthesis of multicomponent separation schemes and they proved that the total number of column sections that were used was also indicative of the amount of computational work required to design the separation scheme. Julka and Doherty (1990) developed a simple algebraic method for calculating the minimum flows in a distillation column. The method was based on an analysis of the geometry of composition profiles in the composition space. They provided an example of a mixture that exhibited a simple distillation boundary. Bernot et al. (1990, 1991) used residue curve maps and global material balances to identify the boundaries and distillation regions at infinite reflux ratios and at the infinite number of stages. Koehler et al. (1991) reported a new method that used the reversible distillation model for calculating minimum flows in a simple distillation column. This method was suitable for the evaluation of a large number of distillation sequences in terms of energy consumption at the early stages of process design. Laroche et al. (1992) analyzed the profiles of distillation columns that were operated at finite and infinite reflux. They showed that the separabilities were not equivalent and must be examined independently. They also demonstrated that under necessary and sufficient conditions, separations are always feasible. Rev (1992) calculated, presented and theoretically discussed residue curves, simple distillation boundaries and rectification column liquid composition profiles of several ternary mixtures. In turn, Wahnschafft et al. (1992) explained

how the limiting operating conditions, total reflux and thermodynamically optimal operation could be used to determine the feasibility of a desired separation in continuous, singlefeed azeotropic distillation columns. They also demonstrated total reflux boundaries and the possibility of crossing the boundaries. Wahnschafft and Westerberg (1993) generalized a method that was developed in 1992 (Wahnschafft et al., 1992) for multiple-feed columns by carrying out a graphical analysis. Their analysis used pinch point trajectories to establish separation feasibility. Stichlmair and Herguijuela (1992) presented a method for the easy determination of feasible processes. This method was especially useful in the first steps of process synthesis and design because impossible separations can be determined and excluded from further analysis. Fidkowski et al. (1993) examined feasible separations for the distillation of non-ideal ternary mixtures with distillation boundaries, which may give rise to additional restrictions on product compositions. Pöllmann et al. (1994) designed an algebraic approximate criterion for calculating the minimum reflux of non-ideal multicomponent distillation by using eigenvalue theory. In 1994, a method for the calculation of multicomponent distillation from stage to stage, which was based on the balances around the product end of the cascade of equilibrium stages, was developed by Pöllmann and Blass (1994). They also provided an excellent review of the literature about the product boundaries of homoazeotropic distillation. In turn, Jobson et al. (1995) focused on the feasible vapor–liquid separation of homogeneous ternary mixtures in processes that involve separation and mixing. Jaksland et al. (1995) developed a methodology where they employed physiochemical properties and the relationships between the properties in their separation techniques. Their tactic involved a wide range of separation problems and consisted of selecting and identifying separation techniques, the sequencing of the separation tasks and determining the appropriate and consistent conditions for the operation. In 1996, Ahmad and Barton (1996) extended a method created by Bernot et al. (1990, 1991) for homogeneous systems with an arbitrary number of components. In turn, Safrit and Westerberg (1997) developed an algorithm for generating distillation regions for azeotropic multicomponent mixtures. They determined the continuous and batch distillation boundaries and regions. These regions provided information about the types of feasible products that can be obtained by using either continuous or batch distillation. Rooks et al. (1998) described a generalized geometric method for the conceptual design and assessment of feasibility and alternative separations of non-ideal and azeotropic distillation systems for mixtures with a large number of components. In the same year, Sargent (1998) proposed a general framework, which was represented by a statetask-network and feasible networks, for systematic implicit enumeration and the evaluation of feasible designs with successive model refinement that led to a final detailed design. In a series of papers, Lelkes et al. (1998a) presented a simple method to study the feasibility of extractive distillation in a batch rectifier by calculating the feasible profiles of different column sections and studying them in a triangular diagram. Furthermore, Lelkes et al. (1998b) elaborated, analyzed and studied several operational policies for the batch realization of extractive distillation using experimental and simulation methods. Afterwards (Lelkes et al., 1998c), they developed a method for assessing the feasibility and the sequencing of homoazeotropic distillation in a batch rectifier under continuous entrainer feeding. In turn, Lang et al.

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(1999) extended their feasibility studies for batch rectification (Lelkes et al., 1998c) to include the condition where a light entrainer is fed continuously into a rectifier or stripper. Subsequently, Lang et al. (2000a) expanded a previous method to investigate the separation of maximum boiling homoazeotropes. Next, they examined their method with rigorous simulations (Lang et al., 2000b). In turn, Wasylkiewicz et al. (2000) published an extended version of a paper from 1996 (Wasylkiewicz et al., 1996) where geometric methods for optimal process synthesis and the design of complex azeotropic distillation columns were presented. These tools provided a graphical representation of azeotropes, residue curves and distillation boundaries (in this case, simple distillation boundaries) and provided a wealth of knowledge about the entire composition space. Westerberg et al. (2000) demonstrated how to synthesize alternative distillation-based separation processes by using boundary curvatures, solvent addition, extractive agents, liquid–liquid behavior and strategically placed reactions to cross distillation boundaries. Tyner and Westerberg (2001a) demonstrated a novel approach for generating preliminary designs for a multi-period azeotropic design problem based on asynchronous-teams. In their second study (Tyner and Westerberg, 2001b), the authors focused on developing simplified models for azeotropic distillation designs that relied on parameters derived from distillation simulations that involved rigorous thermodynamic models. ˜ Manan and Banares-Alcántara (2001) presented a systematic procedure for generating a new catalog of the most promising separation sequences for homogeneous azeotropic mixtures without boundary crossing. Pajula et al. (2000, 2001) developed a new approach to chemical process synthesis based on the reuse of proven process solutions, which were used for solving new problems through case-based reasoning (CBR). Thong and Jobson (2001a) produced a method for estimating the feasibility of a pair of product compositions from a single-feed, two-product distillation column. Feasibility was determined by using geometric principles, which were expressed numerically. Afterwards (Thong and Jobson, 2001b), they proposed a new design tool with which many feasible combinations of design parameters could be determined rapidly, and the combinations could be represented conveniently in a feasibility matrix. Finally, Thong and Jobson (2001c) designed an algorithmic distillation column sequence synthesis procedure for multicomponent azeotropic mixtures. Urdaneta et al. (2002) investigated feasibility analysis for a ternary heteroazeotropic distillation process by using tray-bytray algorithms and minimum-energy calculations. In turn, Thong et al. (2004) developed an automatic procedure for the synthesis of sequences in distillation columns for separating azeotropic homogeneous mixtures by using sets of compositions or product regions to specify product compositions. Brüggemann and Wolfgang (2004) introduced a method for rapid screening of different process alternatives for nonideal multiproduct distillation by ranking their overall energy demand, energy consumption or utility cost. Seuranen et al. (2005) extended the method developed by Pajula et al. (2000, 2001) to cover the synthesis of more complicated systems. The method was based on reusing existing design cases that were created through case-based reasoning (CBR). Skouras et al. (2005) presented a theoretical feasibility analysis and entrainer selection rules for heteroazeotropic batch distillation. They formulated two feasibility conditions based on information that came solely from the distillation line map along with the binodal curve of the ternary mixture. Ji and Liu

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(2007) proposed a graphical method for analyzing the feasibility of split, crossing distillation compartment boundaries. The proposed method was simpler than the existing tools, which were based on residue curve maps, and had the same efficiency. The disadvantage of their method was that fact that it could only be applied to ternary mixtures. In turn, Lucia et al. (2008) proposed a short stripping line approach to find the minimum energy requirements for distillation, processes with multiple units and to identify the proper processing targets in multi-unit processes. Linninger (2009) developed an automatic procedure for generating and evaluating all possible optimal column sequences based on a thermodynamic problem transformation called temperature collocation. Królikowski (2009) proposed a new construction method for feasible separation regions for non-ideal ternary homogenous mixtures with Sshaped distillation lines. He found two separate regions for rectifying and stripping sections, which had not been identified until then. Modla et al. (2009, 2010) investigated the feasibility of pressure swing batch distillation separation for ternary homoazeotropic mixtures by assuming maximal separation. Despite numerous techniques and methods available for the assessment of the feasibility studies, a complete solution for ternary mixtures with distillation boundaries has not yet been found. Rev (1992) proved that valleys and ridges on the boiling temperature surface are not the simple distillation boundaries because they run along different paths from the residue curve trajectories. Fidkowski et al. (1993) devised a method for calculating feasible distillation regions for ternary zeotropic mixtures. They found that for azeotropic mixtures, distillation boundaries might give rise to additional restrictions on product compositions. Jobson et al. (1995) proved that separation boundaries depend on the equipment that is used. In turn, Safrit and Westerberg (1997) developed an algorithm for generating the distillation regions for azeotropic n-component mixtures and described basic distillation boundaries, continuous distillation boundaries and batch distillation boundaries. Castillo and Towler (1998), Springer and Krishna (2001, 2002), Springer et al. (2002a,b,c), Taylor et al. (2004), Mortaheb and Kosuge (2004) and Baur et al. (2005) illustrated the influence of mass transfer on distillation boundaries. Pöpken and Gmehling (2003) presented a simple method for calculating the exact location of distillation region boundaries in quaternary systems. They used residue curve maps with distillation boundaries (without designating the boundaries as simple distillation boundaries) as a representation of the phase behavior, then extended this procedure to quaternary systems. Teixeira et al. (2009) showed that simple distillation boundaries are sensitive to the application of an irreversible model. In order to analyze this observation, residue curves were calculated by using the equilibrium and the irreversible model with initial compositions that were similar to the simple distillation boundary. Observations led to the conclusion that the residue curve constructed by the irreversible model crosses the distillation boundary. Additionally, Doherty and Caldarola (1985) stated that an individual residue curve cannot cross a simple distillation boundary. In turn, Bossen et al. (1993) refined this statement by showing that residue curves cannot cross straight simple distillation boundaries. However, the curved boundaries can be crossed (on the concave side). In contrast, Springer et al. (2003) undertook an analysis of the composition paths calculated by the non-equilibrium stage model generated by Krishnamurthy and Taylor (1985), and Springer and colleagues determined that, in some cases, it

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was possible to cross a straight simple distillation boundary on the convex side through the residue curve. However, the nature of distillation boundaries was still ambiguous until a study that was published by Królikowski (2006). He reflected on the determination of all three types of distillation boundaries, including using a bifurcation theory to track all of the pinch points of rectifying and stripping profiles, mapping the branches of solutions and checking for a jump of composition profiles at bifurcation points. He demonstrated precise methods for computing distillation boundaries. One of the main products of that study was an algorithm for determining distillation regions, which took into account the properties of the presented distillation boundaries. At the same time, Lucia and Taylor (2006) published a study about the geometry of separation boundaries. They determined various attributes for the optimization formulation required to compute separation boundaries and provided steps for a feasible path optimization strategy for finding separation boundaries. They showed that geometric methodology was generalized to mixtures with four and more components, reactive systems, crystallization and other processes as well. They observed that separation boundaries corresponded to local maxima in the line integral within a given separation region for ternary liquid mixtures. Local maxima in the line integral corresponded to one-sided cusps, and several local maxima could exist within any separation region. As such, global optimization methodology was necessary for finding all of the separation boundaries. The geometric technique for defining separation boundaries could be easily translated into computer program and be used to correctly locate precise separation boundaries in a reliable manner. However, this was not a novel method. This method has been already implemented in a software program by Hyprotech called Distil (which was later called Conceptual Engineering (AspenTech, 2010)) to compute ternary diagrams with residue curves and simple distillation boundaries. Subsequently, Lucia and Taylor (2007) provided mathematical proof that distillation boundaries corresponded to local maxima in the line integral from any unstable node to all of the reachable stable nodes (residue curves and distillation lines at maximum reflux or reboil ratio). The mathematical conditions were based on the following inputs: (1) the assumption that trajectories were continuously differentiable and did not cross, (2) the comparison of neighboring trajectories that converged on the same stable node, (3) the existence and placement of a proper focal point and (4) local congruence. Lucia and Taylor showed that when distillation boundaries acted as trajectories, they did not stop at saddle points. Instead, they just ran from unstable to stable nodes along integral curves. This statement was incorrect because saddle points do actually create distillation boundaries (distillation boundaries originate from saddle points) (Brüggemann and Marquardt, 2010a; Królikowski, 2006). The authors also considered residue curves as boundaries as well as distillation lines at total reflux as boundaries without providing names for particular types of distillation boundaries. Therefore, boundaries created by residue curves should be designated as simple distillation boundaries, and the boundaries created by distillation lines should be categorized as total reflux boundaries. In latest studies on distillation boundaries, Brüggemann and Marquardt (2010a,b) presented a fully automated conceptual design methodology for finding an optimal recycle policy for the separation of mixtures exhibiting distillation boundaries (which was not limited to ternary mixtures only). In the first article, the authors introduced a fully computational

geometric split feasibility test based on bifurcation analysis. In the second paper, a novel optimization-based conceptual design framework for azeotropic distillation processes (for the rapid screening of process alternatives) was presented. Previous authors have described three types of distillation boundaries: simple distillation boundaries, continuous distillation boundaries and pinch distillation boundaries. These boundaries were abbreviated as SDB, CDB and PDB, respectively. Using the nomenclature provided by Królikowski (2006), a continuous distillation boundary is the counterpart of a total reflux boundary, and a pinch distillation boundary is equivalent to a pitchfork distillation boundary.

2.

Distillation boundaries

In some azeotropic mixtures, distillation boundaries border the reachable products of distillation columns. These mixtures cannot be separated by a sequential series of columns. Instead, processes in which the columns are coupled by one or more recycle streams must be utilized. In the scientific literature, these boundaries are primarily determined based on limiting residue curves. Nevertheless, two additional formulations for distillation boundaries have been acknowledged. These formulations are based on the limiting conditions of tray-by-tray profiles (distillation lines) and pinch point curves (pinch branches). Distillation boundaries are created by saddle azeotropes. They divide the composition space into distillation regions. In homogeneous mixtures, there are three types of distillation boundaries (which depend on the type of distillation column): simple distillation boundaries (SDB), total reflux boundaries (TRB) and pitchfork distillation boundaries (PDB). An analysis of the distillation boundaries trajectory in a composition space allows an investigator to identify which products are obtainable. When these boundaries are incorporated in geometrical methods for distillation column design, the analysis facilitates, simplifies and accelerates the design process. The best technique for visualizing and evaluating distillation boundaries is to display them on a triangle composition space. Mixtures with four or more components can form surfaces and multidimensional hypersurfaces. With very sophisticated visualization techniques, at most quaternary mixtures can be visualized with high definition. Additionally, many state-of-the-art algorithms for checking the feasibility of multicomponent splits use some approximation of the distillation boundaries (e.g. Foucher et al., 1991; Peterson and Partin, 1997; Rooks et al., 1998; Pöpken and Gmehling, 2003). For example, Rooks et al. (1998) have linearly connected all of the singular points of a residue curve map to obtain a two-dimensional illustration of the distillation boundaries. This method is robust and computationally productive. But this method also has faults and unequivocally eliminates potentially attractive processing alternatives, which could exploit the strongly curved boundaries. Fortunately, the current approximation methods apply nonlinear hypersurfaces based on spheres, ellipsoids or polynomials, which are capable of surmounting some of the limitations of linear surfaces. On the subject of heteroazeotropic mixtures, the structure of the residue curve mapping is not different from the map for any homogeneous solution with the same singular points. The properties of heteroazeotropic mixtures are the same as the properties for homogeneous systems. Similar results are obtained with a distillation line map structure and the trajectories of pitchfork distillation boundaries.

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Saddle Unstable Node Residue Curve Distillate Curve Distillation Line Condensation Curve Condensate Curve

Fig. 1 – Relationship between residue curves, distillation lines and condensation curves (based on Kiva et al., 2003).

2.1.

Simple distillation boundary

A simple distillation process for n-component homogeneous solution can be described by the n − 1 system of ordinary differential equations: dx = x − y(x) d

(1)

By solving these equations, a composition curve of the liquid, which is still left in the boiler, is obtained. The formed curvatures will be referred to as residue curves. A vapor with a composition that is in equilibrium with the liquid is removed as soon as it is formed. Some researchers (e.g. Doherty and Malone, 2001) interpret residue curves as the composition profile along the height of a packed column, whereas the composition profiles of tray columns are called rectification lines (or distillation lines) (Vogelpohl, 1993; Widagdo and Seider, 1996; Pelkonen et al., 1997). Often, the slight difference between residue curves and rectification lines are neglected. For this reason, the conceptual design of a distillation column is usually based on a study of a residue curve map regardless of the type of the distillation column that is being used (staged or packed). Nevertheless, this assumption is often incorrect because the difference, for certain mixtures, may be significant. In general, residue curves begin and end at nodes. However, for a mixture containing a saddle azeotrope, there is one residue curve linking it to a node-type singular point, which is either a pure component or an azeotrope. This trajectory divides the composition space into different parts, and it has been called a simple distillation boundary (SDB). According to Eq. (1), residue curves have a valuable property in which they only depend on the column pressure p and the initial composition x. Therefore, the structure of the residue curve map only depends on the column pressure. The same argument applies for the simple distillation boundaries.

2.2.

Total reflux boundary

In a continuous distillation process performed in a tray column with theoretical plates, products that are at a boiling point, constant pressure and equimolar flow rates in each column section, and with conditions of total reflux or a reboil

Fig. 2 – Rectifying profiles for the heterogeneous distillate zD = (0.3455, 0.4000, 0.2545). (a) R = 0.76 and (b). R = 0.77.

ratio (Królikowski, 2002), the mass balance equations can be simplified to the equilibrium between vapor and liquid flows as well as the composition of both phases between the stages: xj+1 = yj

(2)

Since balance between liquid and vapor at each stage was assumed, these equations described the vapor–liquid equilibrium: yj = f (xj )

(3)

These equations can be solved (from a certain initial composition) for the upwards or downwards direction in the column, for either a finite or an infinite number of stages, by calculating only the boiling or condensation points (tray-by-tray

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Fig. 3 – Rectifying profiles for the heterogeneous distillate zD = (0.5079, 0.2914, 0.2007). (a) R = 2.0 and (b) R = 8.298.

Fig. 4 – Rectifying profiles for the heterogeneous distillate zD = (0.2575, 0.1771, 0.5654). (a) R = 0.03 and (b) R = 0.5.

profiles). Each formed curve is called a discrete distillation line (which previously referred to finite differences curve). Similarly, in the residue curve map, a finite difference mapping produces an invariant curve beginning at the azeotropic saddle point that links exactly the same singular points and ends at the node. This curve, which divides the composition space into different parts, is called a total reflux boundary (TRB). TRB for a staged column is the equivalent of SDB for a packed column, and TRB possesses similar properties. Because SDB and TRB are often close to each other, SDB is sometimes regarded as an approximation of TRB. Nevertheless, this assumption is incorrect. The difference for certain mixtures, especially heterogeneous mixtures, may often be significant quantitatively or qualitatively (Urdaneta et al., 2002). In general, it can be assumed that residue curves and the finite difference curves have the same starting point and

link the same nodes, which represent pure components or azeotropes.

2.3.

Pitchfork distillation boundary

Because the column concentration profiles have been observed to cross the simple distillation boundary on its convex side, a new distillation boundary has been investigated. This new boundary was defined by Davydian et al. (1997). This boundary was defined by the minimal separation energy expenditures in the theoretical process of reversible distillation, which was performed on an infinitely long column with continuous heat exchange along its entire length and running everywhere at the pinch point. This type of distillation boundary is called a pitchfork distillation boundary (PDB). In order to determine PDB, a set of bifurcation points for pinch curves has to be found. By changing the value of 

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azeotrope or a pure component vertex, but crosses a composition space edge at another point, which provides additional opportunities for distillation boundaries crossing. Pitchfork distillation boundary trajectories, similar to SDBs and TRBs, divide the composition space into separate distillation regions. A summary of the application of bifurcation analysis for the determination of distillation regions can be found in work of Królikowski (2006). In contrast to total reflux boundaries and simple distillation boundaries, the pitchfork distillation boundary does not depend on the type of distillation column that is used. However, together with TRB or SDB, PDB forms a pair of boundaries that define the common areas of distillation regions.

3.

Fig. 5 – Rectifying profiles for the heterogeneous distillate zD = (0.5857, 0.1670, 0.2473). (a) R = 3.0 and (b) R = 80.0. parameter in the equation: (x − y(x)) + (1 − ) det(Y)Y −1 (x − y(x)) = 0

(4)

the bifurcation points curve can be obtained. Each point of this curve corresponds to a certain product composition zP , which can be calculated from the following equation: x + (1 − )y(x) = zP

(5)

A set of obtained product composition points defines the pitchfork distillation boundary (PDB). Pöllmann and Blass (1994) illustrated the graphical construction of zP by using the inflection points of the pinch branches. Unlike the previously discussed distillation boundaries, PDB does not always link saddle azeotropes with another singular node-type point. However, PDB is often not aimed at

Behavior of distillation profiles

On the subject of homogeneous mixtures, problems associated with distillation boundaries and crossing of boundaries were systematized by Królikowski (1999, 2002). Jobson et al. (1995) have also demonstrated that distillation boundaries are dependent on the equipment used in the experiments. In turn, Królikowski showed that the simple distillation boundary (SDB) is associated with a packed column, and its counterpart for the staged column is the total reflux boundary (TRB), while the pitchfork distillation boundary (PDB) works with either column type. Thus, a different pair of distillation boundaries is associated with each type of the distillation column. As a consequence, distillation regions are not inseparable, but they do overlap. Their common part, which is contained between the pair of matching distillation boundaries, is parametrically sensitive (Królikowski, 2003). The nature of the composition profile within the section of the column, which product is located between the corresponding pair of distillation boundaries (and the assignment of the pinch point of given concentration profile of a specific distillation region), depends either on the reflux value or on the reboil ratio. Distillation boundaries, created by different azeotropes, exert mutual effects on each other. These interactions induce a change in the behavior of distillation profiles, which can cause a significant change in the shape of distillation regions (Królikowski, 2003, 2009). Fidkowski et al. (1993) presented a methodology for constructing the feasible regions of separations for ternary azeotropic mixtures. Whereas, Królikowski (2006) has demonstrated, for homogeneous azeotropic systems, that this construction should be modified because distillation regions overlap. Concerning homogeneous solutions, the common part of distillation regions is located between SDB and PDB for packed columns and between TRB and PDB for staged columns. Simple distillation boundaries exist in heterogeneous mixtures with saddle azeotropes. Similar to homogeneous mixtures, heterogeneous solution saddle azeotrope also create total reflux boundaries and pitchfork distillation boundaries. In order to verify whether distillation regions overlap in heterogeneous mixtures, evidence has to be found with the trial-and-error method, such as composition points for products with distillation profiles that end in different distillation regions. Studies have been performed for the following threecomponent mixtures: • Benzene–tert-butanol–water, and • Ethanol–water–toluene.

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Fig. 6 – Rectifying profiles for the heterogeneous distillate zD = (0.5314, 0.2000, 0.2686). (a) R = 1.0, (b) R = 8.0, (c) R = 84.0 and (d) denotation of distillation boundaries. All of the simple distillation boundaries in these mixtures were unstable separatrices linking the saddle point with the unstable node. It was assumed that the relations between distillation boundaries were the same as the boundaries for homogeneous mixtures (Kiva et al., 2003; Królikowski, 2002, 2006). Thus, there is TRB on the convex side of SDB with PDB located farther on. Because neither the trajectory of TRB nor the trajectory of PDB was known, the distillate composition was selected on the convex side of SDB and different distances from the boundary were considered (Fig. 1).Distillation profiles for staged columns were determined using the Distil (afterwards Conceptual Engineering) program from AspenTech, Inc. (2010) with the following assumptions:

• The column has theoretical stages. • Flows in the column were equimolar. • The pressure along the column was constant at 1 atm.

• The vapor phase was described by the ideal gas model with the Antoine equation (Antoine, 1888). • The liquid phase was described by the NRTL model (Renon and Prausnitz, 1968, 1969). • The simulations were performed using a one-feed staged column. • The column was equipped with a total condenser (zero stage). • The column has no decanter on the top. • The column was equipped with an evaporator (last stage). • The distillate and reflux streams were diphase.

All of the thermodynamic data (including the binary interaction parameters for the NRTL equation and the coefficients for the Antoine equation) can be found in Appendix A.

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(a)

887

0

X

X

(b)

0

11

27

(c)

0

8

16 Fig. 7 – Distillation designs for the examples shown in Fig. 6a–c. The numbers represent the number of stages in the column. X denotes an unfeasible design.

3.1.

Benzene–tert-butanol–water mixture

The benzene–tert-butanol–water mixture forms a mixture that, at p = 1 atm, has three binary saddle azeotropes: benzene–tert-butanol, tert-butanol–water and benzene–water, and the last one is a heteroazeotrope. There is also one ternary heteroazeotrope that is the only unstable node with respect to Eq. (1). The azeotropic compositions and temperatures are shown in Table A4 in Appendix A. For the heterogeneous distillate, zD = (0.3455, 0.4000, 0.2545) located on the convex side of the unstable SDB, which linked the benzene– water and tert-butanol–water azeotropes, the rectification profile for the reflux ratio R = 0.76 ran towards the stable water node, while the rectification profile for the reflux ratio R = 0.77 was close to the stable tert-butanol node (Fig. 2). As a result, the distillate composition point was located in the common part of the two distillation regions. A similar situation existed for the heterogeneous distillate zD = (0.5079, 0.2914, 0.2007), which was located on the con-

Fig. 8 – Rectifying profiles for the heterogeneous distillate zD = (0.5300, 0.2000, 0.2700), which was localized in the cut-off distillation region. (a) R = 1.0 and (b) R = 84.0.

vex side of the simple distillation boundary that connects the ternary heteroazeotrope with the binary homoazeotrope benzene–tert-butanol. In this condition, the rectification profile for the reflux ratio R = 2.0 ran in the direction of the stable tert-butanol vertex, while the rectification profile for the reflux ratio R = 8.298 ran towards the stable benzene node (Fig. 3). Accordingly, the distillate point was located in the common part of the distillation regions. In turn, for the heterogeneous distillate zD = (0.2575, 0.1771, 0.5654), which was situated on the convex side of SDB that links heteroazeotropes such as saddle benzene–water with unstable node benzene–tert-butanol–water, the rectification profile, for the reflux ratio R = 0.03 ran towards the stable water node, while the rectification profile for the reflux ratio R = 0.5 came close to the stable benzene vertex (Fig. 4). Thus, in this

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chemical engineering research and design 8 9 ( 2 0 1 1 ) 879–893

Fig. 9 – Influence of the change in reflux ratio on feed stage and the total number of stages in the distillation column. The distillate was located in an immiscible region. Table 1 – Streams for the distillation designs shown in Fig. 7. Stream specification

Temperature [K] Pressure [atm] XETHANOL XWATER XTOLUENE

Feed

Reflux

394.14 1.00 0.8000 0.0858 0.1142

346.24 1.00 0.5314 0.2000 0.2686

condition, the distillate point was also located in the common part of the two distillation regions.

3.2.

Distillate

Bottom

346.24 1.00 0.5314 0.2000 0.2686

351.22 1.00 0.9900 0.0050 0.0050

fore, this point was also located in the common part of the two distillation regions. While the heterogeneous distillate zD = (0.5314, 0.2000, 0.2686) was placed on the convex side of SDB that links the ternary heteroazeotrope with the binary homoazeotrope ethanol–toluene, the rectification profile could end in three different distillation regions (Fig. 6). In this condition, the distillate point was located in the common part of the two distillation regions. The regions were determined by pairs of SDB I + PDB I and SDB II + PDB II. As shown above, common area of distillation regions was parametrically sensitive and it determined the possibilities of crossing the distillation boundaries. For the given reflux ratios, distillation columns were designed using Distil. The specific products and separation goals for every column were the same (see Table 1). In two cases (R = 8 and R = 84), feasible separations were obtained. In the condition where the rectifying profile was running in the direction of the toluene vertex, it was unfeasible to design a distillation column. Fig. 7 shows the total number of stages and the feed stage. However, these columns could be difficult to start-up and control. With the heterogeneous distillate point zD = (0.5300, 0.2000, 0.2700), which was localized in the distillation region determined by SDB I + PDB I and was cut-off by SDB II, the changing

Ethanol–water–toluene mixture

The ethanol–water–toluene mixture, at pressure p = 1 atm, has three binary azeotropes: ethanol–water, ethanol–toluene and water–toluene as well as a ternary heteroazeotrope, which are shown in Table A5 in Appendix A. Similar to the previous liquid mixture, the ternary azeotrope in this system is the lowest boiling mixture and the only unstable node with respect to Eq. (1). The three binary azeotropes are saddle nodes, whereas the pure component vertices are stable nodes. Simple distillation boundaries for this mixture run from each of the binary azeotropes and end at the ternary heteroazeotrope node. The trajectory of one pitchfork distillation boundary was determined in this mixture. The boundary that links the binary homoazeotrope ethanol–water with the water–toluene edge in the composition space. For the heterogeneous distillate zD = (0.5857, 0.1670, 0.2473), which was located between simple distillation boundaries that linked ternary heteroazeotropes with the binary azeotropes ethanol–water and ethanol–toluene, the rectification profiles for the reflux ratios R = 3.0 and R = 80.0 ran to the stable water and ethanol vertices, respectively (Fig. 5). There-

Table 2 – Stream for the distillation designs shown in Fig. 9. Streams specification

Temperature [K] Pressure [atm] XETHANOL XWATER XTOLUENE

Feed

Reflux

394.17 1.00 0.8000 0.0964 0.1036

346.90 1.00 0.5857 0.1670 0.2473

Distillate

Bottom

346.90 1.00 0.5857 0.1670 0.2473

351.18 1.00 0.9500 0.0470 0.0003

chemical engineering research and design 8 9 ( 2 0 1 1 ) 879–893

889

Fig. 10 – Influence of the change in reflux ratio on feed stages and the total number of stages in the distillation column. The distillate was located in the homogenous region. Table 3 – Stream for the distillation designs shown in Fig. 10. Streams specification

Temperature [K] Pressure [atm.] XETHANOL XWATER XTOLUENE

Feed

Reflux

394.14 1.00 0.8000 0.0899 0.1101

347.35 1.00 0.6229 0.1430 0.2341

Distillate

Bottom

347.35 1.00 0.6229 0.1430 0.2341

351.14 1.00 0.9500 0.0450 0.0050

reflux ratio was not in the appropriate sequence to observe the end of the rectifying profiles in different distillation regions (Fig. 8). While the reflux ratio was being changed, the rectifying profile was aimed towards the toluene vertex in the composition space. In this condition, the cut-off effect occurs due to the other simple distillation boundary. Otherwise, the rectifying profile would leap to the entire area assigned by SDB I + PDB I. The influence of changing the reflux ratio on the constructional and operational parameters of a distillation column was examined. These fixed separation goals (with fixed compositions of product) were selected in order to obtain column configuration and generate feasible separations. The reflux ratio was changed from R = 2.48 to R = 100. The distillate point composition zD = (0.5857, 0.1670, 0.2473) was selected in the heterogeneous area. Compositions of feed and bottom products were located in the homogenous area. The exact streams specifications are shown in Table 2. It was observed (Fig. 9) that for the reflux ratio R = 71.53, the rectification profile jumped into another distillation region, and the number of feed stages as well as the total number of stages in the distillation column drastically increased. For distillate xD = (0.6229, 0.1430, 0.2341), which was located in the homogenous area, no increase in the column was indicated (Table 3, Fig. 10). In this condition, the rectification profile jumped into another distillation region at R = 49.2.

singular node types (stable or unstable). It was observed that:

4.

Appendix A.

Conclusions

For heteroazeotropic mixtures, the behavior of distillation profiles, which started in the vicinity of the distillation boundaries, was examined. The examined distillation boundaries were unstable separatrices that linked saddle nodes with other

• for the heterogeneous distillate point located close to the convex side of a simple distillation boundary (SDB), the rectification profiles may end at different distillation regions (which depends on the reflux ratio value); • for the heterogeneous distillate composition point situated in the vicinity of two SDBs, the rectification profile may end in three different distillation regions; • the compositions of stripping profiles ended in the same region where the bottom product point was localized; • for the heterogeneous distillate located in the region with the cut-off effect, the rectifying profile ended in the same distillation region where the distillate was localized. It was concluded that the distillation regions overlap in heteroazeotropic mixtures in a manner that was similar to homogeneous systems, and the common area of the distillation regions was parametrically sensitive.

Acknowledgements The first author is grateful to his future wife, Ms. Dominika Wójtowicz, for inspiring and motivating him to write this article. He also acknowledges Dr. Eng. Lechosław Królikowski for the support and guidance he has provided over the years.

To describe the vapor–(liquid)–liquid equilibria of mixtures in this study, the set of binary interaction parameters for the NRTL activity coefficient model (Renon and Prausnitz, 1968, 1969), and the constants used to calculate standard state

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Table A1 – Pure component constants for the extended Antoine equation. Component Benzene tert-Butanol Water Ethanol Toluene

A

B

C

D

E

F

76.1992 14.8401 65.9278 86.4860 76.4511

−6486.20 −2658.29 −7227.53 −7931.10 −6995.00

0.000000 −95.5000 0.000000 0.000000 0.000000

−9.21940 0.000000 −7.17695 −10.2498 −9.16350

6.98440e−006 0.000000 4.03130e−006 6.38949e−006 6.22500e−006

2.00000 2.00000 2.00000 2.00000 2.00000

Table A2 – Binary interaction parameters for the NRTL model. Component i

Component j

Benzene Benzene tert-Butanol Ethanol Ethanol Toluene

tert-Butanol Water Water Toluene Water Water

Distillate

Feed

theoretical stages flows are equimolar pressure p=1 atm. total condenser no decanter on top evaporator

Bottom

fugacities were required. The standard component fugacities can be obtained by using the temperature dependent property-extended Antoine equation:



B + D ln X + EXF C+X

 (A1)

where f0 is in units of atm and X has units of ◦ C. The additional parameters increased the flexibility of the standard Antoine equation (Antoine, 1888) and allowed for the entire vapor pressure curve to be described. The extended equation form could be reduced to the original form by setting the additional parameters D, E and F to zero. All of the relevant numerical values of the pure component constants in Eq. (A1) are provided in Table A1. All of the parameters were taken from the Distil internal database (AspenTech, 2008) (Fig. A1). The temperature-dependent interaction parameters  ij and  ji as well as Gij and Gji , for the model invented by Renon and Prausnitz (1968) are expressed in the form:

 ij = exp

Aij RT

 + Bij

 and

ji = exp

Aji RT

 + Bji

(A2)

and Gij = exp(aij ij )

and

Gji = exp(aji ji )

15.0277 3719.3950 2304.0920 1137.0620 1332.3120 4293.9370

753.0446 4843.3760 828.8162 396.2090 -109.6339 5642.3700

0.2958 0.2000 0.533698 0.2933 0.303099 0.2000

Component i

Component j

Benzene Benzene tert-Butanol Ethanol Ethanol Toluene

tert-Butanol Water Water Toluene Water Water

Literature reference Aleykutty and Srinivasan (1975) AspenTech (2008) AspenTech (2008) Govindaswamy et al. (1977) Stabnikov et al. (1972) AspenTech (2008)

Table A4 – Pure components and azeotropic compositions as well as temperatures for (1) benzene, (2) tert-butanol, (3) water mixture at p = 1 atm.

Fig. A1 – Block diagram of the distillation column used in the simulation for a heterogeneous mixture split.

f 0 = exp A +

Aji

Table A3 – Literature references for the binary interaction parameters for the NRTL model.

Reflux • • • • • •

␣ij

Aij

(A3)

Composition

Temperature Node type (◦ C)

(1, 0, 0) 80.13 (0, 1, 0) 82.41 (0, 0, 1) 100 (0.496834, 0.243642, 66.36 0.259524) (0.703649, 0, 0.296351) 69.14 (0.612265, 0.387735, 0) 74.55 (0, 0.681364, 0.318636) 78.49

Type

[sn] [sn] [sn] [un]

Homogeneous Homogeneous Homogeneous Heterogeneous

[sa] [sa] [sa]

Heterogeneous Homogeneous Homogeneous

Table A5 – Pure components and azeotropic compositions as well as temperatures for (1) ethanol, (2) water, (3) toluene mixture at p = 1 atm. Composition

Temperature (◦ C)

Node type

(1, 0, 0) (0, 1, 0) (0, 0, 1) (0.448702, 0.273257, 0.278041) (0.789914, 0, 0.210086) (0.918679, 0.081321, 0) (0, 0.555927, 0.444073)

78.17 100 110.64 73.51

[sn] [sn] [sn] [un]

Homogeneous Homogeneous Homogeneous Heterogeneous

76.66 78.09 84.34

[sa] [sa] [sa]

Homogeneous Homogeneous Heterogeneous

Type

chemical engineering research and design 8 9 ( 2 0 1 1 ) 879–893

where Aij and Aji as well as Bij and Bji act as the binary interaction parameters and R is the gas constant. In this study, all Bij and Bji values were set to zero. Table A2 shows the binary interaction parameters for the chemical species that were used in this study. Table A3 provides the relevant literature references. Tables A4 and A5 provide basic information about the investigated liquid mixtures.

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