The production zone method: A non-ideal shortcut method for the design of distillation columns

Accepted Manuscript The production zone method: a non-ideal shortcut method for the design of distillation columns Worms Guillaume, Meyer Michel, Rouzineau David, Brehelin Mathias PII: DOI: Reference:

S1383-5866(16)32742-3 http://dx.doi.org/10.1016/j.seppur.2017.04.019 SEPPUR 13681

To appear in:

Separation and Purification Technology

Received Date: Revised Date: Accepted Date:

16 December 2016 6 April 2017 17 April 2017

Please cite this article as: W. Guillaume, M. Michel, R. David, B. Mathias, The production zone method: a nonideal shortcut method for the design of distillation columns, Separation and Purification Technology (2017), doi: http://dx.doi.org/10.1016/j.seppur.2017.04.019

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The production zone method: a non-ideal shortcut method for the design of distillation columns WORMS Guillaumea,b, MEYER Michela, ROUZINEAU Davida*, BREHELIN Mathiasb a: UNIVERSITE DE TOULOUSE, ENSIACET—INP de Toulouse, Laboratoire de Génie Chimique, UMR CNRS 5503, 4 allée Emile Monso, BP 44362, 31432 Toulouse Cedex 4, France b: SOLVAY — Research and Innovation Center of Lyon, 85 Avenue des Frères Perret, BP62, 69192 Saint-Fons Cedex, France

Abstract Graphical shortcut methods are useful tools for the design of distillation columns. The proposed nonideal shortcut method includes a graphical representation and is based on the concept of operation leaves. This new method uses a production segment rather than a completely specified product, which eliminates any sensitivity to the composition of the minor product. Concerning phase equilibria, no restrictive assumptions are made. The study aimed 1) to determine whether a specified separation respects the mass balance and thermodynamic feasibility and 2) to find the minimum reflux ratio for a preliminary design of the column. Designs obtained with this new method for ideal, non-ideal, and azeotropic mixtures give purity and recovery rates close to the specifications, which might be impossible to obtain with a conventional ideal shortcut like the well-known Fenske– Underwood–Gilliland shortcut method. The distillation boundaries of azeotropic mixtures are taken into account thanks to a non-ideal thermodynamic model applied to the calculation, which is not the case with a conventional ideal shortcut. The paper examines the following mixtures: an ideal mixture of ethanol, n-propanol, and n-butanol; a non-ideal mixture of acetone, water, and acetic acid; and an azeotropic mixture of acetone, isopropanol, and water. Keywords: Distillation, Shortcut method, Non-ideal mixture

1.

Introduction

As one of the most important fields in process engineering, distillation column design has been researched extensively and is used in a wide range of industrial applications [3]. From a practical engineering standpoint, good distillation column design is the result of a complex process. First, certain operating and structural parameters such as the reflux ratio, feed position, and number of stages must be specified. Additionally, rigorous simulations and optimization are necessary. Finally, the column sizing must be established in accordance with the simulation. In fact, distillation column design can be divided into three steps. The first step seeks to determine whether the desired separation is feasible from a mass balance and a thermodynamic point of view. Provided the separation is thermodynamically feasible, the aim of the second step is to obtain a preliminary design of the column and define certain key parameters such as the minimum reflux ratio (rmin), the total number of stages, and the feed location. Calculating the minimum energy demand of a separation is often a good way to identify the final column design with the lowest operating cost. The third and last step consists in running a rigorous simulation with a software process that uses the shortcut parameters for initialization. Optimizing this simulation provides a good compromise between capital cost and energy demand. 1

Based on the operation leaves concept described by Castillo [1], the proposed method applies to the first two steps: the feasibility of the separation and the acquisition of the key parameters required to run a rigorous simulation. A detailed description of the new method is presented in the following. The proposed method uses data easily obtained in an industrial= environment and provides a good estimation of the key parameters for ideal, non-ideal, and azeotropic mixtures. Only one specification is required for each product. 2.

Literature review

Several methods exist that aim to define composition surfaces to determine the feasibility of a separation. A short review of the most common methods is given below. Developed by Levy [4,5] in 1985, the boundary value method (BVM) is based on the plate-to-plate calculation of column profiles. To determine these profiles, the compositions of the distillate and the residue and the reflux ratio are specified. Because rmin is not known a priori, there is a significant probability of choosing a reflux ratio smaller than rmin. Consequently, the obtained profiles do not need to correspond to a feasible separation. An intersection between the profiles is necessary to provide a feasible separation, and the intersection point is the feed tray. rmin is the smallest reflux ratio which provides an intersection between the profiles of each section: the profiles do not intersect, but merely touch. The method is very sensitive to the product composition and was developed for three component mixtures but can be applied to multicomponent systems. The intersection can be verified through a 3-D graphical representation for mixtures of up to four components. Based on the BVM, the zero-volume criterion (ZVC) is an algebraic criterion proposed by Julka and Doherty [6,7]. Instead of using the plate-to-plate calculation, the ZVC method relies on pinch-points to approximate a profile. These pinch-points must be known at the beginning, which means that the ZVC method works for direct and indirect cuts only. The recommended formulation of the criterion requires the point x, the pinch s2, and the pinch r1 to be on the same straight line to obtain the rmin configuration. Another method, the minimum angle criterion (MAC) is an application of the ZVC for an unrestricted number of components. It was proposed by Köhler [8,9] and requires the angle that is formed by xF and one pinch point in each column section to be minimal at rmin. The difficulty lies in choosing the appropriate two pinch points because there are multiple solutions. Given that the number of solution branches increases with the number of components, selecting the right solution can become very complicated for multicomponent mixtures. Moreover, the method works only if there is a pinch at the feed stage when the feed is not a boiling liquid. Consequently, configurations with side columns cannot be taken into consideration. Several new methods were introduced in the mid-1990s. The eigenvalue criterion, proposed by Pöllmann [10,11], only calculates the part of the profile after the actual pinch point. Again, rmin is the smallest reflux ratio that provides an intersection, although which pinch point must be used is not always easily to determine. Introduced by Bausa [12,13], the rectification body method (RBM) is a geometrical analysis of plate-to-plate profiles. The method orders the pinch points to propose several paths from an unstable to a stable node. The thermodynamic consistency of these paths is verified to ensure that entropy increases strictly monotonously along the profiles. The relevant profiles are approximated by straight lines joining the pinch points: the thermodynamic of the system is not completely taken into consideration. These lines form an area (the body) of the attainable compositions for a column section. The method is not constrained by the number of components, but the intersection can only be verified through a 3-D graphical representation for mixtures of up to four components. As for the previous methods, rmin corresponds to the smallest reflux providing an intersection between the bodies of each column section. At the end of the 1990s, the operation leaves concept was developed by Castillo and Thong [1,2,14] and Castillo and Sutton [15]. An operation leaf is a surface that includes all compositions that can be obtained for any given specification—for instance, a distillate or a residue composition—in a distil2

lation section. This surface is defined by two curves: the pinch-point curve and the distillation line. Each point of the leaf can be reached with an appropriate reflux or reboil ratio: each ratio provides a specific profile included in the leaf. Each section of the column has its own leaf, and the separation is feasible if the leaves overlap. If this overlap exists, then it is possible to graphically access rmin, the number of theoretical stages, and other parameters. As with the RBM, the operation leaves method is not constrained by the number of components, but the intersection can only be verified graphically with a 3-D representation for mixtures of up to four components. In 2000, Thong [16–18] developed a method that replaces one of the composition profiles with a composition area: each plate of the profile is no longer a point, but an area of the attainable compositions for this plate. This modification provides greater flexibility because one of the products is not specified completely, but is only defined by one specification. Moreover, this type of data is particularly relevant because it usually corresponds to the reality of a separation problem: process engineers often look for the minimal purity of a product A, rarely for the complete specified compositions of A, B, and C. Finally, the method offers a higher probability of finding a solution. Because the method relies on a composition area, it can be used for more than four components without theoretical limits. Nevertheless, as with the previous methods, graphical representation remains limited to a maximum of four components. To define the surface composition, the method calculates the profile from an intersection point between the boundaries of the ternary diagram and the specification area. The points corresponding to the same plate number are then joined with straight lines. The thermodynamics of the system is therefore not considered completely. However, the authors have proposed to correct the results with a tuning method. The assumptions and data of the methods presented here are summarized in Table 1. Because all presented methods were developed for non-ideal mixtures, no assumptions are made for the thermodynamic model. The user is free to choose the most appropriate model in accordance with the target application. These graphical methods share the same benefit: they enable the user to identify quickly and graphically the feasibility of a separation. The additional value of the operation leaves concept lies in how the leaf limits are defined. The limits are physical curves that consider the thermodynamics of the studied mixture depending on the chosen model. This is not the case for most of the graphical methods because the limits are a geometrical approximation and may differ from the real physical limits. Nevertheless, the operation leaves method shares an inconvenience with the other methods: it is very sensitive to the product composition because of the plate-to-plate calculation. A small change in the composition of the starting point may lead to considerable changes in the dimensions and shape of the area, resulting in a very different solution. A substantial iterative procedure is required to find the exact composition that provides a solution. The operation leaves method has another more practical inconvenience. Engineers seeking a distillation column design know the composition, flow, and heat condition of the feed and some specification for each outlet flow. However, engineers rarely know the exact outlet flow compositions. Yet graphical methods require precisely these data: they are therefore difficult to use in an industrial context. The method proposed here is based on the operation leaves concept and aims to eliminate its negative aspects. To better understand the method, the concept of operation leaves is first presented in detail.

Table 1. Assumptions and data of presented methods 3

Methods

Assumptions

Data

Boundary value method

Saturated liquid feed

Pressure

Equilibrium stage

Feed composition

Constant molar overflow

Three of the four independent mole fractions , , ,

Equilibrium stage

Pressure

Constant molar overflow

Feed composition

Components with very small amounts in each product are neglected

Feed heat condition

Zero volume criterion

Full product compositions Minimum angle criterion

Concept of reversible distillation:

Pressure

Heat transfer without temperature change

Feed composition

No pressure drop and constant pressure

Full product compositions

Each point in the column verifies the L–V equilibrium Only the light component can be removed from the residue and the heavy one from the distillate Eigenvalue criterion

The composition of the non-key component of each product set to zero

Pressure Feed composition Reboiler or condenser duty Full product compositions

Rectification body method

Limits of the composition surfaces are straight lines

Pressure Feed composition Full product compositions

Operation leaves

Thong’s method

3.

Equilibrium stage

Pressure

Constant molar overflow

Full product compositions

One feed, two-product column

Pressure

Composition area is a plane

One product with one specification and the other completely specified

Operation leaves

An operation leaf is a surface that includes all compositions that can be obtained from a precise starting composition—for instance, a distillate or a residue composition—in a section of a distillation column. This surface is defined by two curves: the pinch-point curve and the distillation line (Figure 1). In this paper, the following assumptions are made: -

Equilibrium stages Constant liquid and vapor molar overflow Total condenser without under cooling 4

For each equation, i is the component index ( and j is the stage index. In the rectifying section, ; in the stripping section, . In the rectifying section, the stage 1 is the top stage and the stage n is the first stage above the feed stage. In the stripping section, the stage 1 is the bottom stage and the stage m is the first stage below the feed stage. 3.1.

Composition profile

Each point included in a leaf can be reached by a single composition profile which corresponds to a single reflux or reboil ratio. Figure 1 shows several profiles obtained for different reboil ratio.

Figure 1. Product W operation leaf with several profiles obtained for different reboil ratio Each profile is determined with plate-to-plate calculations. A set of 2NC+1 equations (Equations (1)-(3)) which are respectively equilibrium, partial mass balance and summation equations are solved on each stage j to obtain profiles in the rectifying section: (1) (2) (3) A set of 2NC+1 equations (Equations (4)-(6)) which are respectively equilibrium, partial mass balance and summation equations are solved on each stage j to obtain profiles in the stripping section: (4) (5) (6)

3.2. Operation leaf limits 3.2.1. Pinch point curve

Each profile reaches a particular point called the pinch-point. At this point, the vapor from stage j+1 is in equilibrium with the liquid from stage j. Because stage j is in equilibrium, the vapor from stage 5

j is in equilibrium with the liquid from stage j. Therefore, the compositions of the vapors j and j+1 are the same and so are the composition of the liquid j and j+1: the number of necessary stages to proceed and continue to move along the profile is infinite. All the pinch points form the pinch-point curve, and each pinch point comes from a different profile, which comes from a different reflux (reboil) ratio. This curve is therefore the liquid profile in the column section for an infinite number of stages. To determine the pinch-point, each profile is calculated until the value of the criterion defined by Equation (7) is less than 1.10-8. The last calculated point is then considered to be the pinch-point. (7)

3.2.2. Distillation line

The liquid composition profile at infinite reflux, which is the profile with the minimum number of stages, defines the second boundary of the operation leaf. Two curves can be used to describe this profile: The first is the distillation line [19] which is the result of a plate-to-plate calculation with a reflux (reboil) ratio close to infinite. A set of 2NC+1 equations (Equations (8)-(10)) which are respectively equilibrium, partial mass balance and summation equations are solved on each stage j to obtain the distillation line. The second is the residue curve [20], which represents the evolution over time of the composition of a liquid in equilibrium with its vapor for a simple distillation (Rayleigh’s distillation). Castillo suggests using the residue curve for a packing column and the distillation line for a staged column. In general, the difference between distillation lines and residue curves is negligible. Nevertheless, for wide boiling systems and regions of high curvature, distillation lines are slightly more bulged than residue curves [21]. For this reason, and to ensure the entire composition zone is considered, distillation lines are used as boundaries in the present study. (8) (9) or

(10)

The operation leaf is therefore defined, on the one hand, by the pinch-point curve representing the end of all profiles and, on the other hand, by the distillation line representing the total reflux profile. All points located between these two boundaries are part of a profile defined by a finite reflux (reboil) ratio. The profiles provided by a reboil ratio are shown in Figure 1. At first, these profiles tend to follow the distillation line before turning off to the pinch-point curve. The higher the reflux (reboil) ratio, the farther away from the starting composition this change of direction will occur.

3.2.3. The operation leaves method

The operation leaves method aims to determine the feasibility of a separation through distillation and to design a column for a specific separation, proposing some key parameters such as rmin or the number of theoretical stages. To determine whether the separation is feasible or not, the operation leaves of the distillate and the residue (whose compositions have been defined completely) are plotted in a ternary diagram identical to the one given in Figure 2. Separation is feasible only if a distillate composition profile intersects a residue composition profile—that is, if the distillate and the residue leaf overlap each other at least partially. In Figure 2, the separation of the products D and W2 is feasible because their leaves overlap. Conversely, the separation of the products D and W1 is infeasible because their leaves do not overlap. The intersection point between a specific distillate and a specific residue profile corresponds to the composition of 6

their corresponding feed plate. Given that the aim is to find rmin, the method must determine the reflux ratio linked to the first distillate profile that intersects a residue profile, which is the first distillate profile that intersects the residue operation leaf, as shown in Figure 3. For a smaller reflux ratio, there is no intersection between the distillate profile and the residue profile, and thus the separation is infeasible. If the aim is to find the number of theoretical stages for a specific pair of distillate and residue profiles, then the method has to count the number of trays, which is the number of calculated points on each profile between the starting point and the intersection (Figure 4). The number of calculated points on the distillate profile corresponds to the number of trays in the rectifying section, and the number of calculated points on the residue profile corresponds to the number of trays in the stripping section. The total number of stages is the sum of these two numbers plus the feed plate.

Figure 2. Feasible and infeasible separation: separation of D and W2 is feasible, but separation of D and W1 is infeasible

7

Figure 3. The profile provided by rmin is the first profile that intersects the residue operation leaf

Figure 4. Number of theoretical stages: six stages in the rectifying section (yellow triangle), three stages in the stripping section (green square), and the feed plate (purple diamond) gives a total of 12 stages, including the condenser and the reboiler 8

4. 4.1.

The production zone method Required data and assumptions

The proposed method is called the production zone method (PZ method) and was developed for a column with one feed and two product streams. Its aim is to overcome the inconveniences of the operation leaves method while retaining its advantages. To this end, the following data are required: -

Liquid vapor thermodynamic model

-

Column pressure

-

Composition, flow rate, temperature and pressure of the feed

-

Specification of one distillate composition

-

Specification of one residue composition

The following assumptions are made: -

Equilibrium stages

-

Constant liquid and vapor molar overflow

-

Total condenser without under cooling

The method is illustrated in this paper for mixtures of three components. Although the method can be used for more complex systems, the graphical representation quickly becomes useless.

4.2.

Graphical representation

Having only one specification for the distillate and another for the residue constitutes a serious problem for the definition of the operation leaves starting point. Graphically, in a ternary diagram, a product specification corresponds to a production segment. Figure 5b shows the production segment for a specification of xA= 0.7. This segment and the vertex to which the specification refers, delimits a triangle that corresponds to the production zone, that is, the area where the specification is respected. Figure 5a shows the zone where the specification xA= 0.7 is respected, so the zone where xA 0.7. In this second configuration, the product must be at least on his production segment. Each point of this segment or this zone can be a potential starting point of an operation leaf. Then, instead of specifying a precise starting point, all points of the segment or the zone will be used as starting points. In the case of a distillation column, each associated couple of distillate and residue points defines a couple of operation leaves which will be evaluated to find the best configuration. However, specifications for pollutant compositions can also be set. As more compositions are specified, the production zone and segment gets smaller. Figure 5c-f illustrate this evolution. Thus, the more the problem is constrained, the more PZ method is simplified and takes less computational time. The borderline case appears if all compositions are specified: in this situation presented in Figure 5f, there is a single starting point: PZ method is equivalent to the operation leaves method. In the following, the method will be applied to a production segment (Figure 5b). The latter must respect two constraints: -

The mass balance feasibility The thermodynamic feasibility

9

Figure 5. Production a,c,e) zone and b,d,f) segment according to the number of specifications

4.3. Separation feasibility 4.3.1. Mass balance feasibility

Mass balance is calculated with Equations (11)-(13) which are respectively partial mass balance and equations of summation of distillate and residue compositions (11) (12) (13) Graphically for a ternary mixture, the composition points tions (11)-(13), are on the same line.

,

and

, which verify the Equa-

To determine the mass balance feasibility, the method solves the mass balance for both extreme points of the distillate production segment. These two points must be aligned with the feed composition point and a calculated residue composition point. Each calculated residue composition point must also be on the residue production segment. Several configurations are possible. 10

Figure 6 illustrates one of the most common configurations: a mixture of A, B, and C, where A is the lighter component and C the heavier one. The product specifications are 70 n% in A for the distillate and 80 n% in C for the residue. The point F on the diagram represents the feed composition. The segment [D1,D2] is the production segment of the distillate, and the segment [W1,W2] is the production segment of the residue. The mass balance is calculated from the points D1 and D2, and the points W1’ and W2’ are found. Only the point W1’ is on the residue production segment. This means that the point W2’ does not respect the specification. The closest point that respects the mass balance and the specification is the point W2. A new mass balance is calculated from this point, and the point D2’ is obtained. Finally, segments [D1,D2’] and [W2,W1’] are identified as the production segments that respect the mass balance and the specifications.

Figure 6. Common configuration: one residue provided by the first mass balance is not on the residue production segment There is a specific case of this configuration in which the point W1’ corresponds to the point W2 (as shown in Figure 7). In this case, there is only one solution to the mass balance. Other configurations exist: -

Both residues found are on the residue production segment (Figure 8). This is the easier case. No residue is on the residue production segment. In this situation, there are two possibilities: o Calculated residue points are on the same side of the residue production segment. In this configuration, there is no solution to the mass balance (Figure 9). To find a solution, either the specifications or the feed composition must be changed. o Calculated residue points are on either side of the residue production segment. In this configuration, there is a solution to the mass balance, and the procedure applied above can be used to find the production segment that respects the mass balance, as shown in Figure 10.

11

Figure 7. Specific case with only one solution

Figure 8. Both residues are on the residue production segment

Figure 9. Infeasible configuration

12

Figure 10. No residue from the mass balance is on the residue production segment

4.3.2. Thermodynamic feasibility

Thermodynamic feasibility is obtained if the distillate and the residue operation leaf overlap. If they do not overlap, then it is impossible to “find a way” from the distillate to the residue. The separation is thus infeasible. The method must check whether both extreme points of the production segment that respect the mass balance also ensure thermodynamic feasibility. In other words, the method looks for the first intersection between the leaves—for both extremities if necessary—and the production segments are modified accordingly. In Figure 11, the extreme points D and W respect the masse balance, but they do not respect the thermodynamic feasibility because the operation leaves do not overlap. The first couple of points that respects both feasibilities is the couple D’ and W’ in Figure 12. These points form the new extremities of their production segment.

Figure 11. Configuration respecting the mass balance feasibility, but not the thermodynamic feasibility 13

Figure 12. Configuration respecting both the mass balance and thermodynamic feasibility

4.4. Providing a preliminary design of the column 4.4.1. Procedure

In this second step of the method, the distillate production segment is scanned to identify the distillate and residue composition couple that provides the smallest rmin to achieve the separation. Once this couple is found, the method can easily obtain the number of theoretical stages for a design reflux ratio r = a.rmin, where the arbitrarily chosen value of a is 1.3. These parameters can be used to initialize a rigorous simulation. Figure 13 illustrates the second step of the method.

Figure 13. The second step of the procedure

4.4.2. Determining rmin

For each couple of operation leaves, the procedure is as follows. For each couple of distillate and residue points respecting the mass balance, the operation leaves are calculated and plotted, and the intersections between them are found. The nearest intersection from the distillate is retained: this is the thermodynamic minimum reflux ratio. If the reflux ratio is smaller, then no intersection exists between the distillate and residue profile.

14

In Equation (14), which is derived from the overall mass balance (see Appendix A), zF, xD, xW, and q are known, and r and s are unknown. Solving this equation thus involves an additional requirement: the distillate and residue profiles must intersect. (14)

The first step of this procedure thus seeks to determine the minimum value of the reflux ratio that provides an intersection between both distillate and residue profiles and ensures that the specified value of the feed heat condition is respected by the mass balance through Equation (14). Once rmin is found, the method moves on to the next couple of distillate and residue operation leaves and looks for the corresponding rmin. The whole distillate segment is scanned in this way, retaining the configuration that provides the smallest rmin. The example in Figure 14 shows two couples of operation leaves plotted with their minimum reflux profiles. The value of r1, the minimum reflux ratio of couple (D1,W1), is smaller than that of r2 , the minimum reflux ratio of couple (D2,W2). Thus, couple (D1,W1) will be retained.

Figure 14. Two couples of operation leaves and their minimum reflux profiles

4.4.3. Providing a preliminary design

To obtain the design reflux, the smallest rmin is multiplied by a factor; the present study used the common value 1.3. Based on this actual reflux ratio and on the feed heat condition, the associated reboil ratio is calculated with Equation (16), and then the profiles (which will intersect) are plotted. The number of theoretical stages in the rectifying section is equal to the number of calculation points between the distillate and the intersection, whereas the number of theoretical stages in the stripping section is equal to the number of calculation points between the residue and the intersection. The feed plate (corresponding to the intersection) must be added to obtain the total number of theoretical stages. Figure 4 shows a feasible final result.

15

5.

Case studies

The method was applied to three different mixtures: an ideal mixture of ethanol, n-propanol, and nbutanol; a non-ideal, non-azeotropic mixture of acetone, water, and acetic acid; and an azeotropic mixture of acetone, isopropanol, and water. The Matlab software package was used to implement the method, and the thermodynamic calculations were performed with the Prosim Simulis application. The thermodynamic model is NRTL and the parameters used can be found in Appendix B, Table 6, Table 7 and Table 8. The method was run for 18 different cases and 3 different mixtures (Table 2) by combining the feed compositions and product specifications described in Table 3 and

16

Table 4, respectively. Table 5 presents the data set used for each case with a sequence of four couples of one letter and one number. The first couple indicates the mixture (M1, M2 or M3), the second one indicates the feed composition (F1, F2 or F3), the third indicates the specifications (S1, S2, S3, S4, S5 or S6) and the forth indicates if the feed is at its boiling (q1) or dew (q0) point. The feed flow rate was 100 mol/s for all cases. Table 2. The three studied mixtures M1

M2

M3

Component 1

Ethanol

Acetone

Acetone

Component 2

n-Butanol

Water

Isopropanol

Component 3

n-Propanol

Acetic acid

Water

Table 3. Molar feed compositions F1

M3

F3

Component 1

0.27 0.2

Component 2

0.03 0.005 0.56

Component 3

0.7

0.795 0.4

Component 1

0.5

0.6

Component 2

0.01 0.37

0.395

Component 3

0.49 0.03

0.005

M1 M2

F2

0.04

0.6

17

Table 4. Molar composition specifications S1 Component 1 xD = 0.95

S2

S3

xD = 0.99

Component 2

S4

S5

S6

xD = 0.95

xD = 0.95

xD = 0.99

xW = 0.95

xW = 0.99

xD = 0.9

Component 3 xW = 0.95

xW = 0.99

xW = 0.99

xW = 0.99

Table 5. Data set used for each case Case

01

02

03

04

05

06

Data set M1F1S1q0 M1F1S1q1 M1F2S2q0 M1F2S2q1 M1F3S3q0 M1F3S3q1 Case

07

08

09

10

11

12

Data set M2F1S1q0 M2F1S1q1 M2F2S2q0 M2F2S2q1 M2F3S3q0 M2F3S3q1 In the two following studies, the results obtained with the proposed method were compared with results obtained with the well-known FUG shortcut based on the Fenske [22], Underwood [23], and Gilliland [24] equations.

5.1.

Relative gap study for the specifications

The results thus obtained were then used to initialize rigorous simulations with the ProsimPlus software package. In these simulations, the reflux ratio, the distillate flow rate, the feed plate, and the number of stages were fixed by the shortcut results, and no complementary specifications were made: the outlet compositions therefore differed for each case depending of the shortcut method used. A comparison of the various results can be found in Appendix D, Table 9, Table 11 and Table 13. Figure 15 shows the relative gap between the results of the simulation and the desired specification for the recovery rate of the light in the distillate and of the heavy in the residue for the three studied mixtures. Results show that the gap was generally smaller when the simulation was initialized with the PZ method than when the simulation was initialized with the FUG shortcut. Most of the time, when the simulation was initialized with the PZ method, the relative gap was smaller than 1% in absolute value; the largest gap was 6.08% (case 15). When the simulation was initialized with the FUG shortcut, in several cases, the relative gap was larger than 4% in absolute value and the largest gap was −21.47%. These results show that the recovery ratios were close to their input values with the column design obtained with PZ initialization, and the relative gaps were of the same order of magnitude. With the column design obtained with FUG initialization, relative gap sizes varied considerably from case to case. In conclusion, the PZ method seems to be more precise than the FUG method.

18

Figure 15. Relative gap between the results of the simulation and the desired specification for the recovery rate of the light in the distillate and of the heavy in the residue The relative gaps for the purity of the light in the distillate and of the heavy in the residue followed the same trend. Figure 16 illustrates this in the case of an ideal mixture of ethanol/n-propanol/nbutanol. Most of the time, when the simulation was initialized with the PZ method, the relative gap was also smaller than 1% in absolute value whereas when the simulation was initialized with the FUG shortcut, most of the time, the relative gap was larger than 1% in absolute value. In both cases, results appear to show a larger relative gap for the distillate than for the residue. No explication has been found to explain this particularity. 19

Figure 16. Relative gaps between desired specifications and results provide by the simulation for the purity and the recovery rate of the light in the distillate and of the heavy in the residue

5.2.

Cost study

A detailed comparison between energy consumption and total annual cost (TAC) for each designed column is described in the following. In these simulations, the feed plate and the number of plates were fixed, whereas the reflux ratio and the reboiler duty were adjusted to obtain the distillate and residue specifications presented in

20

Table 4. TAC calculations were based on the equations and values recommended by Kiss [25] (see Appendix C). The packing properties correspond to those of Mellapack 250Y. Results can be found in Appendix D, Table 10, Table 12 and Table 14.

5.2.1. Ideal mixture: ethanol, n-propanol, and n-butanol

For the ideal mixture M1, the comparison showed that the PZ method was advantageous (Figure 17). For cases 1, 3, and 5, the feed temperature corresponded to the dew temperature, whereas for cases 2, 4, and 6 the feed temperature corresponded to the bubble temperature. The characteristics of cases 1 and 2 were F1S1, the characteristics of cases 2 and 3 were F2S2, and the characteristics of cases 5 and 6 were F3S3. For the first four cases, the PZ design is more interesting. Bigger differences between the results of the two shortcuts were observed for case 2. The PZ method yielded a TAC of around $1,300,000 with an energy consumption of 2.81 MW, whereas the FUG shortcut gave a TAC of around $2,600,000—twice the amount determined with the PZ method—with an energy consumption of 6.33 MW— more than double the value obtained with the PZ method. For cases 5 and 6, the designs obtained with the two methods (see Table 9) were quite similar, as were the TAC and energy consumption values.

Figure 17. a) TAC ($) and b) Energy consumption (MW) for ideal mixture M1

5.2.2. Non-ideal mixture: acetone, water, and acetic acid

For the non-ideal mixture M2 (Figure 18), the feed temperature for cases 7, 9, and 11 corresponded to the dew temperature, whereas the feed temperature for cases 8, 10, and 12 corresponded to the bubble temperature. The characteristics of cases 7 and 8 were F1S1, the characteristics of cases 9 and 10 were F2S2, and the characteristics of cases 11 and 12 were F3S3. The results obtained with both methods were equivalent for cases 7 and 8, but the energy consumption for case 7 was higher with the PZ method: 410 kW compared with only 97.9 kW (indiscernible on the graph) for the FUG design. The FUG shortcut performed better for cases 9 and 10. For case 10, the TAC ($1,800,000) obtained for the PZ design was almost double the TAC obtained with the FUG design ($993,000). For case 9, the TAC of the PZ design was nearly five times higher than that of the FUG design ($2,370,000 compared with $476,000). In fact, these cases illustrate the current limitation of the PZ method: the precision of the curve interpolation. When the operation leaves cover only a small part of the ternary diagram, this imprecision can have a significant impact on the results. Results for the PZ design without simulation specifications (see Table 12) came very close to the design specifications. However, because there were 30% fewer stages, obtaining the specifications required more energy and thus resulted in a higher TAC. For cases 11 and 12, the PZ design performed better than the FUG design. For example, the FUG design TAC ($6,077,000) for case 11 was almost twice that of the PZ design ($3,365,000). The same observations were made concerning the energy consumption.

21

Figure 18. a) TAC ($) and b) Energy consumption (MW) for non-ideal mixture M2 ($)

5.2.3. Azeotropic mixture: acetone, isopropanol, and water

For the azeotropic mixture M3, the PZ method proved superior (Figure 19). For cases 13, 15, and 17, the feed temperature corresponded to the dew temperature, whereas for cases 14, 16, and 18 the feed temperature corresponded to the bubble temperature. The characteristics of cases 13 and 14 were F1S4, the characteristics of cases 15 and 16 were F2S5, and the characteristics of cases 17 and 18 were F3S6. For cases 13 and 14, the FUG design revealed a non-convergence. For the other four cases, the PZ design provided lower TAC and energy consumption values. Case 15 showed the biggest difference: the FUG design TAC was $1,593,000 compared with $1,075,000 for the PZ design, a difference of 32%. Case 16 showed the smallest difference: the FUG design TAC was $1,961,000 compared with $1,727,000 for the PZ design, a difference of 12%. The same observations were made concerning the energy consumption.

Figure 19. a) TAC ($) and b) Energy consumption (MW) for azeotropic mixture M3 ($) Moreover, the FUG shortcut enabled a solution that consisted of a separation with a respective feed composition of 0.05/0.45/0.5 in acetone/isopropanol/water and respective specifications of 0.9/0.99 and 0.9/0.9 in isopropanol/water at the distillate/residue. Thermodynamic feasibility prohibits these solutions because in both cases the two production segments are located in different distillation areas, as shown in Figure 20 for the case with a specification of 0.9/0.9. The PZ method did not identify this predicted incorrect result as a solution because the feasibility study failed.

22

Figure 20. The distillate with 90% isopropanol and residue with 99% water are located in different distillation areas 6.

Conclusion

The study proposes a new graphical shortcut method for the design of distillation columns. This method makes it possible to determine the mass balance and thermodynamic feasibility of the separation and of rmin when the separation is feasible. Based on this rmin value, a preliminary design can be obtained and used to initialize a rigorous simulation. The results of several rigorous simulations for ideal, non-ideal, and azeotropic systems showed that the method provides a good approximation of the rigorous results and is more precise than the FUG shortcut. Moreover, the designs proposed by the new method are more energy- and cost-efficient than those proposed by the FUG shortcut. The method requires the following data: the compositions, the heat condition, the flow of the feed, and one specification for each outlet stream. These quantities were chosen because they are more easily obtained than other types of data. In fact, the feed properties are usually known. Consequently, this method promises a greater ease of use for industrial and engineering applications than other previously proposed methods. The method uses the given specification to build a production segment for each outlet, which is scanned during the search for rmin to obtain the other outlet compositions. This enables fixing the mass balance of the column only after the most energy- and cost-efficient design has been determined. Future work will focus on adapting this method to unconventional column design, beginning with an investigation of the dividing wall column design.

Corresponding Author * To whom correspondence should be addressed. E-mail: [email protected]

ABBREVIATIONS A: Light component B: Intermediate component C: Heavy component D: Distillate molar flow rate (mol/s) F: Feed molar flow rate (mol/s)

23

K: Equilibrium constant L: Liquid molar flow rate at the top of the column (mol/s) m: Total number of stages in the stripping section n: Total number of stages in the rectifying section NC: Total number of components q: Feed heat condition QB: Energy of the reboiler (kW) r: Reflux ratio s: Reboil ratio T: Temperature (K) V: Vapor molar flow rate at the top of the column (mol/s) V’: Vapor molar flow rate at the bottom of the column (mol/s) W: Residue molar flow rate (mol/s) x: Liquid mole composition y: Vapor mole composition y*: Equilibrium vapor mole composition zF: Feed mole composition Greek symbol Recovery rate Superscript i: Component index , j: Stage index,

in the rectifying section;

in the stripping section

Subscripts D: Distillate W: Residue F: Feed min: Minimum

REFERENCES [1] F.J.L. Castillo, D.Y.-C. Thong, G.P. Towler, Homogeneous azeotropic distillation. 1. design procedure for single-feed columns at nontotal reflux, Ind. Eng. Chem. Res. 37 (1998) 987–997. [2] F.J. Castillo, D.Y.-C. Thong, G.P. Towler, Homogeneous azeotropic distillation. 2. Design procedure for sequences of columns, Ind. Eng. Chem. Res. 37 (1998) 998–1008. [3] Ö. Yildirim, A.A. Kiss, E.Y. Kenig, Dividing wall columns in chemical process industry: A review on current activities, Sep. Purif. Technol. 80 (2011) 403–417. [4] S.G. Levy, D.B. Van Dongen, M.F. Doherty, Design and synthesis of homogeneous azeotropic distillations. 1. Problem formulation for a single column, Ind. Eng. Chem. Fundam. 24 (1985) 454–463. 24

[5] S.G. Levy, D.B. Van Dongen, M.F. Doherty, Design and synthesis of homogeneous azeotropic distillations. 2. Minimum reflux calculations for nonideal and azeotropic columns, Ind. Eng. Chem. Fundam. 24 (1985) 463–474. [6] V. Julka, M.F. Doherty, Geometric behavior and minimum flows for nonideal multicomponent distillation, Chem. Eng. Sci. 45 (1990) 1801–1822. [7] V. Julka, M.F. Doherty, Geometric nonlinear analysis of multicomponent nonideal distillation: a simple computer-aided design procedure, Chem. Eng. Sci. 48 (1993) 1367–1391. [8] J. Koehler, P. Aguirre, E. Blass, Minimum reflux calculations for nonideal mixtures using the reversible distillation model, Chem. Eng. Sci. 46 (1991) 3007–3021. [9] J. Koehler, P. Poellmann, E. Blass, A review on minimum energy calculations for ideal and nonideal distillations, Ind. Eng. Chem. Res. 34 (1995). [10] P. Pöllmann, S. Glanz, E. Blass, Calculating minimum reflux of nonideal multicomponent distillation using eigenvalue theory, Comput. Chem. Eng. 18 (1994) S49–S53. [11] P. Pöllmann, M.H. Bauer, E. Blass, Investigation of vapour-liquid equilibrium of non-ideal multicomponent systems, Gas Sep. Purif. 10 (1996) 225–241. [12] J. Bausa, R. v. Watzdorf, W. Marquardt, Minimum energy demand for nonideal multicomponent distillations in complex columns, Comput. Chem. Eng. 20 (1996) S55–S60. [13] J. Bausa, R. v. Watzdorf, W. Marquardt, Shortcut methods for nonideal multicomponent distillation: I. Simple columns, AIChE J. 44 (1998) 2181–2198. [14] D.Y.-C. Thong, F.J.L. Castillo, G.P. Towler, Distillation design and retrofit using stagecomposition lines, Chem. Eng. Sci. 55 (2000) 625–640. [15] F.J.L. Castillo, C.C. Sutton, Azeotropic distillation simulation package, Department of Process Integration, UMIST, 1996. [16] D.Y.-C. Thong, M. Jobson, Multicomponent homogeneous azeotropic distillation 1. Assessing product feasibility, Chem. Eng. Sci. 56 (2001) 4369–4391. [17] D.Y.-C. Thong, M. Jobson, Multicomponent homogeneous azeotropic distillation 2. Column design, Chem. Eng. Sci. 56 (2001) 4393–4416. [18] D.Y.-C. Thong, Multicomponent azeotropic distillation design, Ph.D., University of Manchester : UMIST, 2000. [19] J. Stichlmair, Distillation and rectification, in: Ullmanns Encycl. Ind. Chem., 5th ed., 1987: p. 4.1-4.94. [20] D.B. Van Dongen, M.F. Doherty, Design and synthesis of homogeneous azeotropic distillations. 1. Problem formulation for a single column, Ind. Eng. Chem. Fundam. 24 (1985) 454– 463. [21] O.M. Wahnschafft, J.W. Koehler, E. Blass, A.W. Westerberg, The product composition regions of single-feed azeotropic distillation columns, Ind. Eng. Chem. Res. 31 (1992) 2345–2362. [22] M.R. Fenske, Fractionation of Straight-Run Pennsylvania Gasoline, Ind. Eng. Chem. 24 (1932) 482–485. [23] A.J.V. Underwood, Fractional distillation of multicomponent mixtures, Ind. Eng. Chem. 41 (1949) 2844–2847. [24] E.R. Gilliland, Multicomponent rectification optimum feed–plate composition, Ind. Eng. Chem. 32 (1940) 918–920. [25] A.A. Kiss, Advanced distillation technologies: design, control and applications, John Wiley & Sons, Ltd, Chichester, UK, 2013.

APPENDIX A: Overall mass balance The overall partial mass balance of a distillation column is described by Equation (I): (I) The overall total mass balance of a distillation column is described by Equation (II): (II) 25

Combining Equations (I) and (II) leads to Equation (III): (III) If V is the molar flow rate of the vapor at the top of the column and V’ is the molar flow rate of the vapor at the bottom of the column, and if the vapor molar overflow is constant in each column section, then Equations (IV)-(VI) can be obtained, where r is the reflux ratio and s is the reboil ratio: (IV) (V) (VI) Combining Equations (II), (IV)-(VI) leads to Equation (VII): (VII) Then, Equation (VIII) is obtained by combining and rearranging Equations (III) and (VII): (VIII)

26

APPENDIX B: NRTL parameters Table 6. NRTL parameters for the ideal mixture (cal/mol)

M1

(cal/mol/K)

(cal/mol)

(cal/mol/K)

(1/K)

Ethanol/n-Propanol

0.0000

180.7384

0.0197

0

0

0.0937

Ethanol/n-Butanol

38.0762

-32.9413

0.3000

0.5141

-0.2320

0.0298

n-Propanol/n-Butanol

0

0

0.3077

0

1.6135

1.9017

Table 7. NRTL parameters for the non-ideal mixture (cal/mol)

M2

(cal/mol)

(cal/mol/K)

(cal/mol/K)

(1/K)

Acetone/Water

750.2256

1299.2627

4.9956

-3.8962

-8.031

-0.0773

Water/Acetic acid

13859.0794

541.9444

1.6487

0.0005

0.00071

0.0000

Acetone/Acetic acid

0.0000

0

0.906810316

0

32.9389

0.0001

Table 8. NRTL parameters for the azeotropic mixture M3

(cal/mol)

(cal/mol)

(cal/mol/K)

(cal/mol/K)

(1/K)

Acetone/Water 628.2471

1198.1984

0.5341

0

0

0

IPA/Water

252.8925

1483.2122

0.4369

0

0

0

Acetone/IPA

369.3416

0

0

0

0

0

NRTL equation applied in Prosim:

with

APPENDIX C: Total annual cost 27

All values and equations are taken from Kiss [25], and all costs are estimated in 2011 US dollars. A three-year payback period is used. -

Vessel and column shells (IX)

At the end of 2011, the Marshall & Swift equipment cost index (M&S) had a value of 1536.5. Both D (diameter) and H (height) are expressed in meters. The cost factor (F c) takes into account the material (Fm) and pressure (Fp) as follows: (X) ,

P in bar

(XI)

For a shell material in stainless steel, Fm = 3.67.

-

Column packing

The specified cost for the packing is 2,800 $/m3.

-

Heat exchangers

(XII) The heat exchange area (A) is given in m² for a size of 20 < A < 500 m² per shell. The cost factor is defined as follows: (XIII) where Fm, Fd, and Fp are the correction factors for material, design type, and design pressure, respectively. For shell and tubes in stainless steel, Fm = 3.75. For a kettle reboiler, Fd = 1.35. For a condenser with a floating head, Fd = 1.00. For a design pressure of less than 10 bar, Fp = 0.

-

Utilities cost

The cost of the vapor stream is fixed at 0.396 $/kmol, and the cost of the cooling water is fixed at 0.00126 $/kmol.

28

APPENDIX D: Detailed results Table 9. Results of the two shortcut methods for the ideal mixture of ethanol, n-propanol, and n-butanol M1

Production zone method

Case 01

rmin

D

F1

3.6958

26.32

S1

xD

xW

FUG shortcut NET Rect.

Total

0.9500*

0.0271

12

15

rmin

D

3.8848

25.13

xD

xW

NET Rect.

Total

0.9950

0.0267

15

17

smin

W

0.0499

0.0229

Strip.

Feed tray

D

0.9261*

W

0.0048

0.0385

Strip.

Feed tray

0.2405

73.68

0.0001

0.9500*

2

13

W

0.9999*

74.87

0.0002

0.9349

1

16

Case 02

rmin

D

xD

xW

NET

rmin

D

xD

xW

NET

F1

1.2513

26.32

1.3402

25.10

q=0

S1

Rect.

Total

0.9500*

0.0271

12

23

Rect.

Total

0.9959

0.0267

14

16

smin

W

0.0499

0.0229

Strip.

Feed tray

D

0.9260*

W

0.0040

0.0387

Strip.

Feed tray

0.8040

73.68

0.0001

0.9500*

10

13

W

0.9999*

74.90

0.0001

0.9346

1

15

Case 03

rmin

D

xD

xW

NET

rmin

D

xD

xW

NET

F2

5.5922

19.70

5.4824

19.54

q=1

S2

Rect.

Total

0.9900*

0.0062

12

16

Rect.

Total

0.9983

0.0062

16

19

smin

W

0.0099

0.0038

Strip.

Feed tray

D

0.9752*

W

0.0015

0.0058

Strip.

Feed tray

0.3718

80.30

0.0001

0.9900*

3

13

W

0.9999*

80.46

0.0002

0.9880

2

17

Case 04

rmin

D

xD

xW

NET

rmin

D

xD

xW

NET

F2

1.5290

19.70

1.4833

19.68

q=0

S2

Rect.

Total

0.9900*

0.0057

8

17

Rect.

Total

0.9931

0.0057

14

19

smin

W

0.0080

0.0043

Strip.

Feed tray

D

0.9771

W

0.0047

0.0051

Strip.

Feed tray

0.6219

80.30

0.0020

0.9900*

8

9

W

0.9995

80.32

0.0022

0.9892

4

15

Case 05

rmin

D

xD

xW

NET

rmin

D

xD

xW

NET

F3

1.9488

618.00

1.8921

61.80

q=1

S3

Rect.

Total

0.0647

0.0000

6

22

Rect.

Total

0.0647

0.0000

6

21

smin

W

0.9000*

0.0100

Strip.

Feed tray

D

0.9932*

W

0.9000

0.0099

Strip.

Feed tray

2.1525

38.20

0.0353

0.9900*

15

7

W

0.9455*

38.20

0.0353

0.9901

14

7

Case 06

rmin

D

xD

xW

NET

rmin

D

xD

xW

NET

F3

1.2210

61.80

1.1881

61.85

q=0

S3 q=1

Rect.

Total

0.0647

0.0000

7

23

Rect.

Total

0.0647

0.0000

8

22

smin

W

0.9000*

0.0100

Strip.

Feed tray

D

0.9932*

W

0.8993

0.0100

Strip.

Feed tray

3.5721

38.20

0.0353

0.9900*

15

8

W

0.9455*

38.15

0.0361

0.9900

13

9

* Recovery ratios are identical for each method and are use as data. They were transformed into purity specifications for the PZ method that requires composition specifications.

29

Table 10. Simulation results of both shortcut methods for the ideal mixture of ethanol, npropanol, and n-butanol M1

Simulation initialized with PZ results

Case 01

QB (MW)

D

F1

1.74

26.32

S1 q=0

0.0264

W

0.0479

0.0236

73.68

0.0001

0.9500

xD

xW

QB (MW)

D

F1

2.89

26.32

S1

0.9545

0.0255

W

0.0456

0.0244

73.68

0.0000

0.9501

xD

xW

Case 03

QB (MW)

D

F2

2.12

19.70

S2 q=0

0.9780

0.0091

W

0.0183

0.0017

80.30

0.0037

0.9891

xD

xW

Case 04

QB (MW)

D

F2

2.48

19.74

S2 q=1

0.9842

0.0071

W

0.0086

0.0041

80.26

0.0072

0.9888

xD

xW

Case 05

QB (MW)

D

F3

4.90

61.80

S3 q=0

Relative gap purity

recovery

0.21%

0.21%

0.00%

Relative gap purity

recovery

0.47%

0.48%

0.01%

purity

recovery

−1.21%

−1.22%

purity

recovery

−0.59%

−0.58%

recovery

0.0000

W

0.8974

0.0142

−0.29%

−0.29%

38.20

0.0379

0.9858

−0.42%

−0.43%

xD

xW

QB (MW)

D

F3

6.71

61.80

S3

Relative gap purity

25.13

recovery

0.0647

0.0000

W

0.9020

0.0068

0.22%

0.22%

38.20

0.0333

0.9932

0.32%

0.32%

xD

xW

0.9564

0.0396

W

0.0436

0.0255

74.87

0.0000

0.9350

QB (MW)

D

xD

xW

2.89

25.20 0.8514

0.0751

W

0.0565

0.0211

74.80

0.0921

0.9038

QB (MW)

D

xD

xW

1.99

19.54 0.9613

0.0151

W

0.0186

0.0017

80.46

0.0202

0.9832

QB (MW)

D

xD

xW

2.45

19.52 0.9238

0.0227

W

0.0117

0.0034

80.48

0.0645

0.9740

QB (MW)

D

xD

xW

4.70

61.80

−0.12%

Relative gap purity

1.70

−0.08%

Relative gap

−0.12%

D

0.01%

Relative gap

−0.09%

QB (MW)

0.00%

0.0647

Case 06

q=1

xW

0.9520

Case 02

q=1

xD

Simulation initialized with FUG shortcut results Relative gap Purity

recovery

−3.88%

−3.88%

0.01%

0.01%

Relative gap Purity

recovery

−14.51%

14.19%

−3.30%

−3.41%

Relative gap Purity

recovery

−3.71%

3.69%

−0.48%

0.48%

Relative gap Purity

recovery

−6.98%

7.44%

−1.54%

−1.42%

Relative gap Purity

recovery

0.0647

0.0000

W

0.8990

0.0053

−0.11%

−0.11%

38.20

0.0363

0.9947

0.46%

0.47%

QB (MW)

D

xD

xW

6.64

61.85

Relative gap Purity

recovery

0.0647

0.0000

W

0.9027

0.0055

0.38%

0.38%

38.15

0.0325

0.9947

0.47%

0.34%

30

Table 11. Results of the two shortcut methods for the non-ideal mixture of acetone, water, and acetic acid M2

Production zone method

Case 07

rmin

D

F1

2.8941

26.37

S1

xD

FUG shortcut

xW

NET

rmin

D

Rect.

Total

3.1197

25.63

0.9500*

0.0265

5

7

xD

xW

NET Rect.

Total

0.9774

0.0262

8

10

smin

W

0.0481

0.0235

Strip.

Feed tray

D

0.9278*

W

0.0206

0.0332

Strip.

Feed tray

0.0364

73.63

0.0019

0.9500*

1

6

W

0.9993*

74.37

0.0020

0.9406

1

9

Case 08

rmin

D

xD

xW

NET

rmin

D

xD

xW

F1

0.7145

26.32

Rect.

Total

0.3787

0.20

q=0

S1

0.9500*

0.0271

12

23

NET Rect.

Total

0.9923

0.0267

14

16

smin

W

0.0499

0.0229

Strip.

Feed tray

D

0.9260*

W

0.0076

0.0376

Strip.

Feed tray

0.6124

73.68

0.0001

0.9500*

10

13

W

0.9999*

74.80

0.0001

0.9358

1

15

Case 09

rmin

D

xD

xW

NET

rmin

D

xD

xW

F2

4.9050

19.70

Rect.

Total

4.4523

19.52

q=1

S2

0.9900*

0.0062

5

19

NET Rect.

Total

0.9993

0.0062

10

12

smin

W

0.0099

0.0038

Strip.

Feed tray

D

0.9755*

W

0.0006

0.0061

Strip.

Feed tray

0.2033

80.30

0.0001

0.9900*

13

6

W

0.9999*

80.48

0.0002

0.9878

1

11

Case 10

rmin

D

xD

xW

NET

rmin

D

xD

xW

F2

1.9359

19.70

Rect.

Total

0.4715

19.52

q=0

S2

0.9900*

0.0062

7

9

NET Rect.

Total

0.9993

0.0062

13

15

smin

W

0.0099

0.0038

Strip.

Feed tray

D

0.9755*

W

0.0006

0.0061

Strip.

Feed tray

0.7202

80.30

0.0001

0.9900*

1

8

W

0.9999*

48.56

0.0002

0.9878

1

14

Case 11

rmin

D

xD

xW

NET

rmin

D

xD

xW

F3

3.3362

61.80

Rect.

Total

1.7625

61.80

q=1

S3

0.0647

0.0000

17

23

NET Rect.

Total

0.0647

0.0000

7

21

smin

W

0.9000*

0.0100

Strip.

Feed tray

D

0.9932*

W

0.9000

0.0099

Strip.

Feed tray

0.4555

38.20

0.0353

0.9900*

5

18

W

0.9455*

38.20

0.0353

0.9901

13

8

Case 12

rmin

D

xD

xW

NET

rmin

D

xD

xW

F3

3.0377

61.80

Rect.

Total

1.0487

61.85

q=0

S3 q=1

0.0647

0.0000

18

24

NET Rect.

Total

0.0647

0.0000

8

22

smin

W

0.9000*

0.0100

Strip.

Feed tray

D

0.9932*

W

0.8993

0.0100

Strip.

Feed tray

0.6668

38.20

0.0353

0.9900*

5

19

W

0.9455*

38.15

0.0361

0.9900

13

9

* Recovery ratios are identical for each method and are use as data. They were transformed into purity specifications for the PZ

method that requires composition specifications.

31

Table 12. Simulation results of both shortcut methods for the non-ideal mixture of acetone, water, and acetic acid M2

Simulation initialized with PZ results

Case 07

QB (MW)

D

F1

10.00

26.3700

S1 q=0

0.0223

W

0.0376

0.0273

73.6300

0.0008

0.9504

xD

xW

QB (MW)

D

F1

17.30

26.3200

S1

0.9724

0.0191

W

0.0276

0.0309

73.6800

0.0000

0.9501

xD

xW

Case 09

QB (MW)

D

F2

16.90

19.7000

S2 q=0

0.9783

0.0091

W

0.0216

0.0009

80.3000

0.0001

0.9900

xD

xW

Case 10

QB (MW)

D

F2

22.30

19.7000

S2 q=1

0.9873

0.0068

W

0.0124

0.0032

80.3000

0.0002

0.9900

xD

xW

Case 11

QB (MW)

D

F3

78.80

61.8000

S3 q=0

purity

recovery

1.22%

1.22%

0.04%

Relative gap purity

recovery

2.36%

2.37%

0.01%

Relative gap purity

recovery

−1.18%

−1.22%

0.00%

Relative gap purity

recovery

−0.27%

−0.30%

0.00%

Relative gap purity

recovery

0.0119

−0.13%

−0.13%

38.2000

0.0365

0.9881

−0.19%

−0.20%

xD

xW

10.70

61.8000

S3

25.6300

Relative gap purity

recovery

0.0647

0.0000

W

0.8984

0.0125

−0.18%

−0.18%

38.2000

0.0369

0.9875

−0.25%

−0.26%

xD

Relative gap

xW

0.9856

0.0234

W

0.0144

0.0354

74.3700

0.0000

0.9413

QB (MW)

D

xD

xW

1.30

25.2000 0.8519

0.0740

W

0.0781

0.0138

74.8000

0.0701

0.9122

QB (MW)

D

xD

xW

1.32

19.9200 0.9953

0.0071

W

0.0047

0.0051

80.0800

0.0000

0.9878

QB (MW)

D

xD

xW

1.07

19.5200 0.7849

0.0581

W

0.0169

0.0021

80.4800

0.1982

0.9398

QB (MW)

D

xD

xW

4.68

61.8000

0.00%

0.8988

F3

1.12

0.01%

W

D

D

0.01%

0.0000

QB (MW)

QB (MW)

0.04%

0.0647

Case 12

q=1

Relative gap

xW

0.9616

Case 08

q=1

xD

Simulation initialized with FUG shortcut results

Purity

recovery

3.74%

0.84%

−0.92%

0.07%

Relative gap Purity

recovery

−10.33%

−14.14%

−3.98%

−2.51%

Relative gap Purity

recovery

0.53%

1.62%

−0.22%

−0.49%

Relative gap Purity

recovery

−20.72%

−21.47%

−5.08%

−4.86%

Relative gap Purity

recovery

0.0647

0.0000

W

0.8135

0.1499

−9.61%

−9.61%

38.2000

0.1218

0.8501

−14.13%

−14.13%

QB (MW)

D

xD

xW

59.10

61.8500

Relative gap purity

recovery

0.0647

0.0000

W

0.7996

0.1716

−11.16%

−11.08%

38.1500

0.1357

0.8284

−16.32%

−16.43%

32

Table 13. Results of the two shortcut methods for the azeotropic mixture of acetone, isopropanol, and water M3

Production zone method

Case 13

rmin

D

F1

0.9834

52.52

S4

xD

FUG shortcut

xW

NET

rmin

D

Rect.

Total

1.1702

52.83

0.9500*

0.0023

15

29

xD

xW

NET Rect.

Total

0.9444

0.0022

3

12

smin

W

0.0121

0.0077

Strip.

Feed tray

D

0.9979*

W

0.0178

0.0013

Strip.

Feed tray

0.0876

47.48

0.0379

0.9900*

13

16

W

0.9593*

47.17

0.0378

0.9965

8

4

Case 14

rmin

D

xD

xW

NET

rmin

D

xD

xW

F1

0.8340

52.63

Rect.

Total

0.2181

53.10

q=0

S4

0.9500*

0.0001

15

22

NET Rect.

Total

0.9416

0.0000

2

20

smin

W

0.0101

0.0990

Strip.

Feed tray

D

0.9999*

W

0.0188

0.0001

Strip.

Feed tray

2.0373

47.37

0.0399

0.9900*

6

16

W

0.9571*

46.90

0.0396

0.9999

17

3

Case 15

rmin

D

xD

xW

NET

rmin

D

xD

xW

F2

1.2482

62.57

Rect.

Total

1.3582

58.66

q=1

S5

0.9500*

0.0149

11

17

NET Rect.

Total

0.9975

0.0361

27

30

smin

W

0.0231

0.9500*

Strip.

Feed tray

D

0.9752*

W

0.0000

0.8950

Strip.

Feed tray

1.0867

37.43

0.0269

0.0351

5

12

W

0.9999*

41.34

0.0025

0.0690

2

28

Case 16

rmin

D

xD

xW

NET

rmin

D

xD

xW

F2

0.8710

62.98

Rect.

Total

0.8369

63.91

q=0

S5

0.9500*

0.0046

9

19

NET Rect.

Total

0.9361

0.0047

6

20

smin

W

0.0291

0.9500*

Strip.

Feed tray

D

0.9972*

W

0.0286

0.9746

Strip.

Feed tray

3.1829

37.02

0.0209

0.0454

9

10

W

0.9505*

36.09

0.0352

0.0207

13

7

Case 17

rmin

D

xD

xW

NET

rmin

D

xD

xW

F3

1.5884

60.33

Rect.

Total

1.6529

60.30

q=1

S6

0.9900*

0.0069

18

24

NET Rect.

Total

0.9905

0.0069

12

23

smin

W

0.0038

0.9900*

Strip.

Feed tray

D

0.9954*

W

0.0038

0.9892

Strip.

Feed tray

0.5995

39.67

0.0062

0.0031

5

19

W

0.9943*

39.70

0.0057

0.0039

10

13

Case 18

rmin

D

xD

xW

NET

rmin

D

xD

xW

F3

1.1659

60.45

Rect.

Total

0.9857

60.58

q=0

S6 q=1

0.9900*

0.0038

17

29

NET Rect.

Total

0.9879

0.0039

11

25

smin

W

0.0058

0.9900*

Strip.

Feed tray

D

0.9974*

W

0.0057

0.9933

Strip.

Feed tray

3.1704

39.55

0.0042

0.0062

11

18

W

0.9913*

39.42

0.0064

0.0028

13

12

* Recovery ratios are identical for each method and are use as data. They were transformed into purity specifications for the PZ method that requires composition specifications.

33

Table 14. Simulation results of both shortcut methods for the azeotropic mixture of acetone, isopropanol, and water M3

Simulation initialized with PZ results

Case 13

QB (MW)

D

F1

3.71

52.52

S4 q=0

xD

xW

0.9302

0.0242

W

0.0180

0.0012

47.48

0.0519

0.9748

xD

xW

Case 14

QB (MW)

D

F1

3.41

52.63

S4

Relative gap purity

recovery

−2.09%

−2.09%

−1.54%

0.0000

QB (MW)

D

4.22

52.83

recovery

xD

xW

0.9004

0.0515

W

0.0096

0.1041

47.17

0.0899

0.9381

QB (MW)

D

xD

xW

21.50

53.10

−1.54%

Relative gap purity

0.9500

Simulation initialized with FUG shortcut results

0.00%

0.8698

0.0813

W

0.0060

0.0145

46.90

0.1242

0.9042

QB (MW)

D

xD

xW

1.50

58.66

Relative gap purity

recovery

−5.22%

−4.66%

−5.25%

−5.87%

Relative gap purity

recovery

−8.44%

−7.61%

−8.67%

−9.58%

0.01% q=1

W

0.0088

0.0114

47.37

0.0412

0.9886

xD

xW

Case 15

QB (MW)

D

F2

1.42

62.57

recovery 0.27%

W

0.0360

0.9283

−2.28%

−6.08%

37.43

0.0263

0.0361

xD

xW

D

F2

4.15

62.98

Relative gap purity

recovery

0.9447

0.0135

−0.55%

−0.56%

W

0.0353

0.9393

−1.12%

−1.12%

37.02

0.1993

0.0471

xD

xW

S5

Case 17

QB (MW)

D

F3

2.14

60.33

Relative gap purity

recovery

0.9879

0.0101

−0.21%

−0.21%

W

0.0063

0.9861

−0.40%

−0.40%

39.67

0.0058

0.0038

xD

xW

S6

Case 18

QB (MW)

D

F3

4.62

60.45

Relative gap purity

recovery

0.9881

0.0068

−0.19%

−0.19%

W

0.0080

0.9866

−0.35%

−0.35%

39.55

0.0039

0.0066

S6 q=1

purity −1.30%

QB (MW)

q=0

Relative gap

0.0356

Case 16

q=1

−0.14%

0.9377

S5 q=0

−0.14%

Relative gap purity

recovery

0.9519

0.1007

0.20%

−4.57%

W

0.0178

0.8697

−8.45%

−2.82%

41.34

0.0303

0.0296

QB (MW)

D

xD

xW

4.15

63.01

Relative gap purity

recovery

0.9298

0.0160

−2.13%

−2.08%

W

0.0508

0.9353

−1.55%

−4.02%

36.09

0.0194

0.0487

QB (MW)

D

xD

xW

2.29

60.30

Relative gap purity

recovery

0.9857

0.0142

−0.44%

−0.48%

W

0.0116

0.9795

−1.07%

−0.99%

39.70

0.0041

0.0063

QB (MW)

D

xD

xW

4.23

60.58

Relative gap purity

recovery

0.9706

0.0304

−1.96%

−1.74%

W

0.0256

0.9626

−2.76%

−3.09%

39.42

0.0037

0.0069

34

Highlights -

A non-ideal shortcut method for distillation design is proposed The method uses production segment rather than completely specified product The method is a better initialization for rigorous simulations than FUG shortcut Purity and recovery rate are closer to the specifications The method leads to a more efficient design in terms of energy as well as economic

35