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Ind. Eng. Chem. Res. 2010, 49, 350–358
Extended Ponchon-Savarit Method for Graphically Analyzing and Designing Internally Heat-Integrated Distillation Columns Tsung-Jen Ho,†,‡ Chi-Tsung Huang,*,§ Liang-Sun Lee,*,† and Chi-Tsung Chen† Department of Chemical and Materials Engineering, National Central UniVersity, Chung-li 32001, Taiwan, and Department of Chemical Engineering, Tunghai UniVersity, Taichung 40704, Taiwan
The heat-integrated distillation column, generally called HIDiC, applies the principle of internal heat integration between the rectifying section and the stripping section of a distillation column by increasing the temperature of the rectifying section with a compressor. In this work, a theoretical stage-to-stage study of a HIDiC based on the Ponchon-Savarit method is performed. Several HIDiC design variables, such as the number of theoretical stages, reboiler (or preheater) duty, minimum overall internal heat-transfer rate, and configuration, can easily be interpreted in the Ponchon-Savarit (Hxy) diagram. Such an approach brings new insights into and better understanding of the features of HIDiC. A preliminary (or shortcut) HIDiC design procedure using Hxy diagrams is also proposed. The obvious advantages are that the proposed method allows the direct design of a HIDiC and avoids trial-and-error design using a commercial simulator. In addition, the proposed graphical method can foresee possible pinch points before requiring use of a rigorous simulator. Furthermore, the proposed graphical estimation of internal stages of a HIDiC is applied to a binary methanol-water system and compared to the rigorous simulation results obtained using Aspen Plus. Moreover, the McCabe-Thiele diagram of the HIDiC is also drawn using the extended Ponchon-Savarit method and presented in this study. Introduction Distillation is still one of the most popular methods of separation in the chemical and petrochemical industries. However, this process is also energy-intensive, and thus, since the 1950s, many techniques have been proposed to reduce the energy consumption of distillation columns. An efficient way of saving energy is to use an internally heat-integrated distillation column (HIDiC). A HIDiC can be considered as one kind of heat-pump-assisted distillation column. Many authors have done theoretical and experimental studies on this type of column since 1985. Nakaiwa et al.1 recently published a detailed review about the relevant research including thermodynamic analysis, practical process design, and operation. They1 also pointed out that experiment-based development of HIDiC configurations is very expensive. Moreover, publications that discuss the design fundamentals of HIDiCs from basic principles unfortunately still seem to be relatively scarce in the literature. Despite the widespread availability of computer facilities and software for the design and calculation of distillation processes, traditional graphical methods,2 such as McCabe-Thiele and Ponchon-Savarit diagrams, although not very popular, have still been used continually. Graphical methods seem tedious and time-consuming, but they are useful for obtaining quick preliminary design scopes. Another advantage of graphical methods is that they allow the interrelationships of several process variables to be easily understood, visualized, and grasped. Recently, Huang et al.3 proposed a heuristic synthesis method for HIDiCs using McCabe-Thiele diagrams, which normally utilized only material balances and equilibrium relationships to approximate the separation in a distillation column. The Ponchon-Savarit method, which includes the * To whom correspondence should be addressed. E-mail: huangct@ thu.edu.tw (C.-T.H.),
[email protected] (L.-S.L.). † National Central University. ‡ Present address: Pilot Process and Applications of Chemical Engineering and Technology Division, Industrial Technology Research Institute, Hsinchu, Taiwan. § Tunghai University.
energy balance, is considered to be more rigorous than the McCabe-Thiele method. Furthermore, a HIDiC is a heatintegrated column, and thus, under normal circumstances, the energy-balance relationship cannot be neglected during the preliminary design. Thus, the Ponchon-Savarit method seems to be more suitable than the McCabe-Thiele method for HIDiC design. Although the Ponchon-Savarit method has almost been left out of most unit-operation textbooks and is rarely discussed in the classroom, several new design methods based on this technique for separation processes have recently been proposed. These include employing the geometrical concepts of the Ponchon-Savarit method in quaternary liquid-liquid extraction,4 ternary distillation,5 and reactive distillation.6,7 The authors of those works have emphasized that graphical methods can delve into the fundamental aspects of separations. In addition, Lee et al.6 studied reactive distillation and stated that the pinch point of the reaction zone can be found by a graphical method. Furthermore, several computer programs for the traditional Ponchon-Savarit method have been developed during the past 2 decades. A Fortran source program for Ponchon-Savarit calculations is available in Luyben and Wenzel.8 Farag and Karri9 developed a computer simulator for the analysis and design of binary distillation columns including the modified Ponchon-Savarit method.10 Salem and Fekri11 proposed a rigorous Ponchon-Savarit computational algorithm using the UNIQUAC activity coefficient equation to estimate equilibrium and enthalpy data. Moreover, industrial applications of the Ponchon-Savarit method with a commercial process simulator for multicomponent and multiple-feed distillation columns can be found in Campagne.12,13 He12,13 stated that, by translating the multicomponent output from a simulator into pseudobinary data, the Ponchon-Savarit method can be an invaluable tool when used interactively with a process simulator. Campagne12,13 also claimed that the pseudobinary Ponchon-Savarit technique can handle any nonreactive component mixture, including highly nonideal separations, such as homogeneous or heterogeneous azeotropic distillations.
10.1021/ie9005468 CCC: $40.75 2010 American Chemical Society Published on Web 11/18/2009
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basis, as illustrated in Figure 1. Assumptions are imposed including steady-state operation, negligible heat losses from the HIDiC to the surrounding environment, and equal numbers of stages in the rectifying and stripping sections, as shown in Figure 1. The last assumption is for easier consideration and can be relaxed for a real column. Rectifying Section. The essential design equations are derived based on material and energy balances around the dotted-line envelope of the rectifying section in Figure 1 as follows Total mass balance
Vn - Ln+1 ) VD
(1)
Mass balance for the light component Vnyn - Ln+1xn+1 ) VDyD
(2)
Total energy (enthalpy) balance Figure 1. Conceptual configuration of a HIDiC.
To provide further considerations of this subject, one of the purposes of the present work is to show that all relevant equations of the HIDiC can be incorporated into the PonchonSavarit construction to yield more general diagrams. Several HIDiC design variables, such as the number of theoretical stages, minimum overall internal heat transfer, configuration, reboiler (or preheater) duty, and compressor shaft work, can easily be interpreted in terms of enthalpy-concentration diagrams (abbreviated as Hxy diagrams). The Hxy diagram, therefore, will bring new insights into and a better understanding of the features of HIDiC designs. In this study, a graphical HIDiC design procedure using Hxy diagrams is also proposed; an example applying this proposed HIDiC design procedure to a binary methanol-water system is illustrated and compared to the results obtained from a rigorous simulation using Aspen Plus.14 Furthermore, a McCabe-Thiele diagram of the HIDiC using the extended Ponchon-Savarit method is drawn and also presented. Extension of Ponchon-Savarit Method One deficiency of the conventional distillation column is that it has a reboiler in the bottom to vaporize liquid and also has a condenser in the top to condense vapor. To save energy, the HIDiC in this study does not require any condenser or reflux drum. There are two types of HIDiC configurations to be discussed in this study. One is the HIDiC with a reboiler in the bottom of the stripping section, and the other is that with a preheater for feed flow.1 Huang et al.15 reported economic and controllability analyses for these two HIDiC configurations. On the basis of a control-degree-of-freedom analysis, thermodynamic analysis, and engineering judgment, Ho et al.16 recently considered that the reboiler is a necessary part of a HIDiC. The distillation of a binary mixture in a HIDiC without a condenser is schematically shown in Figure 1. The top product (VD) is vapor, and the bottoms product (LB) is liquid. There are five parts of a HIDiC: the rectifying section, the stripping section, the feed stage, a compressor, and a partial reboiler (or preheater). Trays in the stripping and rectifying sections are assumed to be ideal and are individually numbered from the bottom. There are NR stages in the rectifying section and NS stages in the stripping section. The column pressure of the rectifying section is higher than that of the stripping section because a compressor is purposely employed. Thus, the basic principle of the HIDiC is that heat is transferred from the rectifying section to the stripping section on a stage-to-stage
NR
∑
VnHn - Ln+1hn+1 ) VDHD +
qj
(3)
j)n+1
The variables H and h refer to the vapor and liquid enthalpies, NR qj represents the overall internal respectively. The term ∑j)n+1 heat-transfer rate around the dotted-line envelope of the rectifying section with NR denoted as the top stage. In addition, the internal heat-transfer rate between the corresponding stages in the rectifying section and the stripping section (qj) is qj ) UjAj(TRj - TSj) ) UjAj∆Tj
(4)
where TRj is the temperature of rectifying stage j and TSj is that of the corresponding stage in the stripping section, Uj is the overall heat-transfer coefficient, and Aj is the heat-transfer area. For simplicity, a constant qj is assumed in this study, but this condition can be removed for a more realistic consideration. As in conventional Ponchon-Savarit constructions,2 a pseudoflow rate (∆D), which is the difference between the vapor stream (Vn) and the liquid stream (Ln+1) passing each other in the rectifying section of the column, is employed in this study. Equations 1-3 then become Vn - Ln+1 ) ∆D
(5)
Vnyn - Ln+1xn+1 ) ∆DyD
(6)
(
NR
VnHn - Ln+1hn+1 ) ∆D HD +
∑
qj
j)n+1
VD
)
(7)
From the graphical mixing rule,2 the above equations tell us that the coordinates of this ∆D stream will lie on a straight line joining the points Vn (yn, Hn) and Ln+1 (xn+1, hn+1)in an Hxy diagram. Thus, the ∆D point can be used to estimate component NR qj, which varies with and energy balances. In addition, ∑j)n+1 stage location, is a varying quantity. Unlike the conventional Ponchon-Savarit method,2 the ∆D value of a HIDiC, however, is not a fixed point, but a moving point. Thus, beginning at the top stage of the rectifying section, one can use the moving ∆D point to construct operating lines and phase equilibrium tie lines in a distillation column. Now, let n ) NR - 1 in eq 7. Then, one has the energy balance of the top stage of the rectifying section (NR) as
(
VNR-1HNR-1 - LNRhNR ) VD HD +
qNR VD
)
(8)
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Lm+1xm+1 - Vmym ) ∆BxB
(
m
Lm+1hm+1 - VmHm ) ∆B hB -
QR LB
∑q
j
j)1
LB
)
(14)
(15)
As shown in Figure 1, the vapor V0 is usually considered to be in equilibrium with the liquid product LB in the reboiler. The temperature of the liquid product (LB) is assumed to be its bubble point. Also, no internal heat transfer between the reboiler and the rectifying section is assumed in this study. Thus, point V0 can easily be found from the equilibrium line of an Hxy diagram as shown in Figure 2. As for the rectifying section, m qj) in eq 15 is a the overall internal heat-transfer rate (∑j)1 varying quantity. Thus, the ∆B value in the stripping section is also a moving point in an Hxy diagram observable from eqs 13-15. For stage 1 (m ) 1), eq 15 becomes Figure 2. Extended Ponchon-Savarit method for a HIDiC.
The vapor product from the top stage is VD (yD, HD), which is in phase equilibrium with liquid LNR. Thus, VNR-1 is obtained from the operating line, and then LNR-1 is obtained from the equilibrium line, as shown in Figure 2. If n ) NR - 2 (two stages from the top) in eq 7, one has
VNR-2HNR-2 - LNR-1hNR-1
(
qNR qNR-1 ) VD HD + + VD VD
)
(9)
Lm+1 - Vm ) LB
(10)
Mass balance for the light component Lm+1xm+1 - Vmym ) LBxB
(11)
Total energy balance m
Lm+1hm+1 - VmHm ) LBhB - QR -
∑q
j
(12)
j)1
As for the rectifying section, a difference quantity, ∆B, which relates to all pairs of passing streams in the stripping section, is defined. Again, the heat-transfer rate (qj) between the corresponding stages in the two sections is also considered to be a constant. Equations 10-12 then become Lm+1 - Vm ) ∆B
(13)
QR q1 LB LB
)
(16)
where q1 is the heat transfer from the rectifying section to the bottom stage of the stripping section. Similarly, for stage 2 (m ) 2), one has
(
L3h3 - V2H2 ) ∆B hB -
Similarly, one can obtain VNR-2 and LNR-2 by the graphical method in the Hxy diagram shown in Figure 2. It is obvious that the ∆D point is moving up vertically. One can continuously calculate the equilibrium stages of the rectifying section until an equilibrium line reaches the feed stage, which is called “topdown calculations” in this study. Stripping Section. The equations for the total and lightcomponent mass balances and for the energy balance around the dotted-line envelope of the stripping section including a reboiler with duty QR shown in Figure 1 are given as Total mass balance
(
L2h2 - V1H1 ) ∆B hB -
QR q1 q2 LB LB LB
)
(17)
Therefore, beginning from the reboiler, one can use the varying ∆B value to construct operating lines and vapor-liquid equilibrium lines. The ∆B point is moving down vertically, as shown in Figure 2. One can continuously calculate the equilibrium stages of the stripping section until an equilibrium line reaches the feed stage. This procedure is called the “bottom-up calculations” in this study. Overall Consideration of a HIDiC. The overall material balances of the whole HIDiC as shown in Figure 1 are F ) L B + VD
(18)
FzF ) LBxB + VDyD
(19)
From the first law of thermodynamics, one has ∆H ) Q + WS, where WS is the shaft work, for open systems with negligible kinetic and potential energies.17 Thus, the energy balance of the whole HIDiC including the compressor shaft work, as shown in Figure 1, can be expressed as
(
FhF ) LB hB -
)
QR + WS + VDHD LB
(20)
Just as in stripping section, eqs 18-20 are represented by straight lines in the Hxy diagram. If the feed condition is a saturated liquid, the vapor product (VD) is at its dew-point temperature, and the liquid product (LB) is at its bubble-point temperature; the drawing of the overall HIDiC in an Hxy diagram is shown in Figure 3. This figure indicates that the total input energy, i.e., QR + WS, can also be estimated from the straight line in an Hxy diagram. For the case of a HIDiC without a reboiler,1 which normally needs a pre-heater with duty QF, the total energy balance then becomes
(
F hF +
)
WS + QF ) LBhB + VDHD F
(21)
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Figure 3. Overall enthalpy balance for a HIDiC with a saturated liquid feed and a reboiler.
353
Figure 5. Relationships between the minimum reflux ratio and the minimum overall internal heat-transfer rate.
proximated shaft work WS of the compressor can be estimated from eq 22, and one can estimate either QR from Figure 3 or QF from Figure 4. Furthermore, the overall internal heat-transfer rate of the whole HIDiC between the rectifying section and the stripping section, QHT, is represented as NS
QHT )
∑q
j
(25)
j)1
Figure 4. Overall enthalpy balance for a HIDiC with a subcooled liquid feed and a preheater.
If the feed is a subcooled liquid, then the material and energy balances of eqs 18, 19, and 21 are also straight lines, as shown in Figure 4. Similarly, the total input energy, that is, the shaft work (WS) and the preheater duty (QF), can be estimated from Figure 4. Here, the ideal compression work for a reversible adiabatic process (also called an isentropic process) can normally be calculated from the equation17 WS )
[( )
γRTIN POUT γ - 1 PIN
(γ-1)/γ
]
- 1 VF
(22)
where VF is the vapor flow leaving from the feed stage, as shown in Figure 1. The coefficient γ is the ratio of specific heats, and γ ) 1.4 was used in this study. Furthermore, the material balances for the rectifying section in Figure 1 are VF - LR1 ) VD
(23)
VFyF - LR1xR1 ) VDyD
(24)
Values of yF and xR1 can normally be estimated from the stageto-stage calculations of a Ponchon-Savarit diagram (shown in the examples). Thus, the values of VF and LR1 can be obtained by solving the simultaneous eqs 23 and 24, because VD and yD are already specified before design. Consequently, the ap-
Minimum Overall Internal Heat-Transfer Rate. In a convectional distillation column design, the minimum external reflux ratio, rmin, is normally required. The value of rmin can be obtained from either the feed pinch or the tangent pinch in a McCabe-Thiele diagram or Ponchon-Savarit diagram. Figure 5 shows a minimum reflux ratio obtained from the feed pinch. If one extends the VLE (vapor-liquid equilibrium) tie lines through the feed point (zF) to intersect with a vertical line through yD, as shown in Figure 5, the highest intersection point (∆min D ) establishes the value rmin of the feed pinch. The minimum reflux ratio in a convectional distillation column, however, is the ratio of the distances a and b (i.e., rmin ) a/b) shown in Figure 5, if the condensate is a saturated liquid. On the other min /VD in the hand, the distance a in Figure 5 is equivalent to QHT HIDiC. Therefore, it can represent the minimum required overall min ) for a HIDiC, as VD is a fixed internal heat-transfer rate (QHT value for process design. It can also be explained that the overall internal heat-transfer rate (QHT) in the HIDiC is equivalent to the external reflux ratio, r, in a convectional column, because the distance b is fixed. In addition, a higher reflux ratio r can normally get more concentrated top product in a convectional distillation column. Thus, one can say that the larger the QHT value, the higher the concentration of the top product produced in a HIDiC. The overall internal heat-transfer rate (QHT) becomes an important purification factor for the HIDiC configuration design. The result from this consideration is the same as in the reports of de Rijke et al.18 and Olujic et al.19 Moreover, the higher pressure of the rectifying section and the lower pressure of the stripping section are normally specified during process design. In addition, the feed stage is located in the stripping section, and the top product is located in the rectifying section. Thus, the point ∆Dmin in Figure 6 should be modified by adding a distance ∆Hcomp, which is the enthalpy difference between the higher and lower pressures on the vertical line of yD. Alternatively, if one uses the distance between points c and d in Figure 6 instead of ∆Hcomp, this is also feasible. Furthermore, if the basic column conditions of a HIDiC are
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Figure 6. Determination of the minimum overall internal heat-transfer rate required for a HIDiC between the rectifying and stripping sections. min selected, then QHT is obtained from Figure 6. If one assumes that ∆T and U are constants during the preliminary HIDiC design, one can roughly estimate the minimum required overall min min min ) using Aoverall ) QHT /U∆T, as the heat-transfer area (Aoverall variations of parameters ∆T and U are normally small.
Preliminary Design Procedures From the above analysis, it is obvious that most of the HIDiC design parameters can be estimated from Hxy diagrams and that two types of HIDiC graphs can feasibly be developed for different energy balances between eqs 20 and 21. If the separation purities (yD and xB), feed composition (zF), and feed property are specified, the preliminary (or so-called shortcut) design procedures for the binary HIDiC are summarized as follows: Step 1. Do the overall mass and component balances for the HIDiC. Step 2. Assign proper pressures, normally setting the stripping-section pressure to be the same as the feed pressure. However, the rectifying-section pressure must be properly assigned. One key point to select a rectifying pressure from an Hxy diagram is that the temperature difference between the dewpoint temperature of the top product (rectifying) and the bubblepoint temperature of the bottoms product (stripping) should be significant, say, larger than 10 °C. This temperature difference will influence the internal heat-transfer rate for the corresponding stages of two sections. Step 3. Draw the overall material and energy balances of the whole column in an Hxy diagram, such as Figure 3 or Figure 4. Then, estimate WS + QR from Figure 3 or WS + QF from min from the equilibrium line of the feed Figure 4. Also, find QHT min value is not stage as shown in Figure 6. Although the QHT directly used in the graphical design, the value provides a min ). reference for selecting qj (or Aoverall Step 4. Assign a proper heat-transfer rate, qj, from the rectifying section to the stripping section. Although several factors including the structure of heat-transfer panels18,19 can affect the value of qj, a constant heat-transfer rate per stage is assumed in this graphical design. Step 5. Simultaneously draw the top-down-calculation lines and the bottom-up-calculation lines of the extended PonchonSavarit diagram as shown in Figure 2. Then, estimate NS, NR, xR1, and yF from this diagram.
Figure 7. Overall enthalpy balance and determination of the minimum overall heat-transfer rate for a HIDiC with a preheater in example 1.
Step 6. Estimate VF by substituting xR1 and yF into eqs 23 and 24. Step 7. Estimate WS by substituting VF into eq 22. Step 8. Estimate QR or QF from the results of steps 3 and 7. Drawing the McCabe-Thiele Diagram Nakaiwa et al.,20 Huang et al.,3 and others have tried directly drawing the McCabe-Thiele diagram of a HIDiC to explore the fundamentals. In fact, their results were not obtained so straightforwardly. The basic assumption of the McCabe-Thiele method for conventional distillation is the constant molar overflow, and either the top or the bottom operating line is therefore fixed. In contrast to the case for a conventional distillation column, the liquid and vapor flow rates on each stage of a HIDiC could be varying through the internal heat transfer. The McCabe-Thiele diagram (xy diagram) of a HIDiC, however, can be plotted based on the essential equations derived in the previous sections for the extended Ponchon-Savarit diagram. From eq 2 for the rectifying section, one has yn )
Ln+1 VDyD x + Vn n+1 Vn
(26)
For the McCabe-Thiele approach, let H∆D be defined as NR
H∆D ) HD +
∑
qj
j)n+1
VD
(27)
Then, substituting eqs 5 and 27 into eq 7, one obtains Rn )
H∆D - Hn Ln+1 ) Vn H∆D - hn+1
(28)
where Rn is the internal reflux ratio for the rectifying section. Furthermore, combining eqs 1, 26, and 28, one has yn ) Rnxn+1 + (1 - Rn)yD
(29)
Equation 29 is actually one of the operating lines of the rectifying section in xy diagram. It should be noted that Rn, Hn, hn+1, and H∆D vary from stage to stage. Thus, the operating lines
Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010
Rm )
h∆B - Hm Lm+1 ) Vm h∆B - hm+1
355
(32)
Combining eqs 10, 30, and 32, the operating lines of the stripping section in the xy diagram can be expressed as ym ) Rmxm+1 + (1 - Rm)xB
As for the rectifying section, the values of Rm, Hm, hm+1, and h∆B vary with stage location and can be obtained from the extended Ponchon-Savarit diagram. On the other hand, the thermal condition of the feed, q, which is the number of moles of saturated liquid formed in the feed stage per mole of feed,2 should normally be specified for a conventional McCabe-Thiele diagram. Notice that the q line is used to draw the operating line in the McCabe-Thiele diagram for the rectifying and stripping sections, and it is normally specified prior to construction of the graph. In a conventional distillation column, the value of q can normally be estimated by dividing the molar enthalpy required to bring the feed to saturated vapor by the molar latent heat of vaporization of the feed.2 A HIDiC with a reboiler is similar to a conventional column, and one can directly obtain the value of the parameter q from the actual feed thermal conditions. The parameter q for a HIDiC with a preheater, however, can be estimated from the line segment cf and the segment ce as shown in Figure 4, that is
Figure 8. Graphical estimation of the internal stages of a HIDiC with a preheater using qj ) 432.3 MJ/h for example 1.
q)
of the McCabe-Thiele diagram of a HIDiC, i.e., eq 29, are also varying with stage location. These variables, however, can easily be obtained from the extended Ponchon-Savarit diagram. Similarly, from eq 11 for the stripping section, one has
To illustrate the proposed HIDiC design procedures, a methanol-water separation is discussed. The general design specifications for this separation are (i) a feed rate (F) of 250 kmol/h, (ii) a stripping pressure of 0.1013 MPa, (iii) a rectifying pressure of 0.2026 MPa, (iv) a feed composition (zF) of 58 mol % methanol, (v) a feed thermal condition of saturated liquid (71.7 °C), (vi) a top product specification (yD) of 90 mol % methanol, and (vii) a bottoms product specification (xB) of 10 mol % methanol. From the overall material balances, one has the top flow rate VD ) 150 kmol/h and the bottoms flow rate LB ) 100 kmol/h. Specific enthalpies and VLE data are obtained
(30)
m
h∆B
∑q
j
j)1
(31)
LB
(34)
Illustrative Examples
Let h∆B be defined as
QR ) hB LB
cf ce
It should be noted that point f in Figure 4 is not the actual feed condition; it is just a thermal balance point in the feed stage. In addition, the value of parameter q is influenced by the preheater duty (QF) and the compressor shaft work (WS), as shown in Figure 4. Furthermore, one can therefore plot the McCabeThiele diagram for a HIDiC, because the top operating line (eq 29), the bottom operating line (eq 33), and the q line (eq 34) are all available.
Figure 9. Conceptual configuration of a HIDiC with a preheater using qj ) 432.3 MJ/h for example 1.
Lm+1 LBxB ym ) x Vm m+1 Vm
(33)
Then, substitute eqs 13 and 31 into eq 15, obtaining the internal reflux ratio (Rm) for the stripping section as Table 1. Simulation Results Obtained Using Aspen Plus for Example 1a
stream ID
temperature (°C) pressure (MPa) vapor fraction flow rate (kmol/h) enthalpy (MJ/h) water (mol frac) methanol (mol frac) a
1
2
3
4
5
6
7
71.7 0.1013 0 250.0 8535 0.4200 0.5800
75.6 0.1013 0.535 250.0 13422 0.4200 0.5800
87.1 0.2026 1 149.6 12802 0.0947 0.9053
88.6 0.1013 0 100.4 1148 0.9044 0.0956
76 0.1013 1 244.7 18970 0.2748 0.7252
123.4 0.2026 1 244.7 19493 0.2748 0.7252
94.4 0.2026 0 95.1 2808 0.5577 0.4423
WS ) ∆H6 - ∆H5 ) 523 MJ/h, qj ) 432.3 MJ/h, QF ) 4891.4 MJ/h.
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Figure 10. McCabe-Thiele diagram of a HIDiC with a preheater using qj ) 432.3 MJ/h for example 1.
Figure 13. Graphical estimation of the internal stages of a HIDiC with a reboiler using qj ) 216.2 MJ/h for example 2.
Figure 14. Conceptual configuration of a HIDiC with a reboiler using qj ) 216.2 MJ/h for example 2. Figure 11. Graphical estimation of the internal stages of a HIDiC with a preheater for a methanol-water system using qj ) 216.2 MJ/h.
Figure 12. Overall enthalpy balance and determination of the minimum overall heat-transfer rate for a HIDiC with a reboiler in example 2.
from the Aspen Plus14 using the Wilson equation to calculate the activity coefficients. The reference state for specific enthalpies is the liquid methanol at 0.1013 MPa and 0 °C.
Example 1: HIDiC with a Preheater. If a HIDiC with a preheater is chosen, the line for the overall balance is drawn in Figure 7. From the VLE line of the feed stage, one finds that the temperature of the feed stage is 76 °C and its thermal quality min ) 3175 MJ/h is estimated from the (q) is 0.412. Also, QHT point ∆Dmin in Figure 7. Then, the heat-transfer rate from the rectifying section to the stripping section, qj ) 432.3 MJ/h, is chosen, and the Ponchon-Savarit diagram is drawn as in Figure 8. One therefore has NS ) 9 and NR ) 10 from Figure 8. A conceptual configuration of this HIDiC is also given in Figure 9. It should be noted that one stage in the rectifying section does not transfer heat to the stripping section as shown in Figure 9; therefore, ∆D on this stage is stationary in Figure 8. The overall internal heat-transfer rate in this case is about QHT ) 3890 MJ/h, which is greater than Qmin HT (3175 MJ/h). In addition, one has xR1 ≈ 0.43 and yF ≈ 0.71 from Figure 8. Substituting xR1 and yF into eqs 23 and 24, one has VF ) 251.79 kmol/h. Then, one estimates WS ) 553.6 MJ/h from eq 22. Moreover, (WS + QF)/F ) 21.78 MJ/kmol is found from Figure 7, and one therefore has QF ) 4891.4 MJ/h. On the other hand, a rigorous Aspen Plus14 simulation was implemented to check the goodness of the proposed graphical method. Based on Figure 9 and the above data (i.e., feed conditions, QF, NS, NR, and qj), the simulation results are reported in Table 1. Furthermore, a McCabe-Thiele diagram of this HIDiC case, which was
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357
a
Table 2. Simulation Results Obtained Using Aspen Plus for Example 2
stream ID
temperature (°C) pressure (MPa) vapor fraction flow rate (kmol/h) enthalpy (MJ/h) water (mol frac) methanol (mol frac) a
1
2
3
4
5
6
71.7 0.1013 0 250.0 8535 0.4200 0.5800
87.7 0.1013 1 151.7 12887 0.1091 0.8909
88.2 0.2026 0 98.3 1155 0.9000 0.1000
71.9 0.1013 1 198.2 16105 0.1802 0.8198
117.5 0.1013 1 198.2 16528 0.4123 0.5877
90.9 0.2026 0 46.5 1696 0.1802 0.8198
WS ) ∆H5 - ∆H4 ) 423 MJ/h, qj ) 216.2 MJ/h, QR ) 5089.8 MJ/h.
Table 3. Comparison between Results from Aspen Plus and the Proposed Method example 1
yD (mol frac) xB (mol frac) VF (kmol/h) WS (MJ/h) QR (MJ/h)
example 2
Aspen Plus
proposed
difference
Aspen Plus
0.9053 0.0956 244.7 523.0
0.9000 0.1000 251.8 553.6
0.59% -4.60% -2.90% -5.85%
0.8909 0.1000 198.2 422.6 5089.8
drawn using the Ponchon-Savarit data in Figures 7 and 8, is shown in Figure 10. Example 2: HIDiC with a Reboiler. In some cases, the drawing of a Ponchon-Savarit diagram for a HIDiC could reach a pinch point and not be able to work further if the heat-transfer rate, qj, is designated too small. Figure 11 shows a failed case if qj ) 216.2 MJ/h is chosen for the previous HIDiC column without a reboiler. This case is equivalent to a reflux ratio smaller than the minimum reflux ratio (rmin) in a conventional distillation; one might also say that it is a pinch-point case. However, if a reboiler is added, the line of overall balances in Figure 12 is drawn using the saturated top vapor and the saturated feed liquid. Then, one obtains WS + QR ) 5421 MJ/h min is 1210 from this line. Moreover, Figure 12 shows that QHT MJ/h, which is less than the value for the HIDiC in the previous min ) 3175 MJ/h). Figure 13 shows the graphical example (QHT result for the same HIDiC (i.e., qj ) 216.2 MJ/h) with a reboiler, and one has NS ) 9 and NR ) 11. The conceptual configuration of the HIDiC with a reboiler is therefore shown in Figure 14. In addition, one has xR1 ≈ 0.61 and yF ≈ 0.82 from Figure 13, and VF ) 207.143 kmol/h is therefore obtained from eqs 23 and 24. Thus, WS ) 454.85 MJ/h is calculated by eq 22, and QR ) 4996.05 MJ/h is estimated. As for example 1, the rigorous Aspen Plus14 simulation results based on Figure 14 using the above data (i.e., feed conditions, NS, NR, and qj) are also included in Table 2. Furthermore, a comparison of the estimated parameters between the Aspen Plus simulation and the proposed graphical method for the above two examples is given in Table 3. Comparison of the data in Table 3 shows that the proposed graphical estimations are reasonably close to the results of the Aspen Plus simulation. Moreover, based on the above examples, it appears that it is easy to encounter the pinch point for a HIDiC, especially for a HIDiC without a reboiler,1 if the heat-transfer rate qj is not properly designed. A rigorous commercial simulator, say Aspen Plus, usually cannot easily detect the pinch point. The proposed graphical method, however, can foresee the possible pinch point before use of the rigorous simulator. In addition, a HIDiC with a reboiler can solve the pinch-point problem easier than one without a reboiler.1 Ho et al.,16 from a process control viewpoint, also considered that a reboiler is a necessary part of a HIDiC. Conclusions An approach for the shortcut design of an internally heatintegrated distillation column (HIDiC) has been proposed in this
proposed 0.9000 0.1000 207.1 454.9 4996.1
difference -1.02% 0.00% -4.49% -7.64% 1.84%
study. This method is based on the graphical concepts of the Ponchon-Savarit method for binary systems. An analysis of the extended Ponchon-Savarit method was provided in this study. Several HIDiC design variables, such as the number of theoretical stages, minimum overall internal heat transfer, reboiler (or preheater) duty, compressor shaft work, and so on, can be directly calculated from the Hxy diagram. This approach will bring new insights into and better understanding of the features of HIDiCs. Also, a preliminary HIDiC design procedure using Hxy diagrams is proposed, and the HIDiC configuration is therefore obtained. An obvious advantage of the suggested design procedure is that it allows for the direct design of HIDiCs and can foresee possible pinch points. Thus, the proposed method can avoid trial-and-error design in using commercial simulators. Furthermore, the proposed method has been applied to a methanol-water system, and it yields good results in comparison to those obtained in a rigorous Aspen Plus14 simulation. Moreover, the technique of drawing the McCabeThiele diagram of a HIDiC, which has never been reported in the literature, has also been presented based on the extended Ponchon-Savarit method proposed in this study. Acknowledgment This work was supported by the Industrial Technology Research Institute, Taiwan, under Grant D24200N410. Literature Cited (1) Nakaiwa, M.; Huang, K.; Endo, A.; Ohmori, T.; Akiya, T.; Takamatsu, T. Internally Heat-Integrated Distillation Columns: A Review. Chem. Eng. Res. Des. 2003, 81, 162. (2) Smith, B. D. Design of Equilibrium Stage Processes; McGraw-Hill: New York, 1963. (3) Huang, K.; Matsuda, K.; Iwakabe, K.; Takamatsu, T.; Nakaiwa, M. Graphical Synthesis of an Internally Heat-Integrated Distillation Column. J. Chem. Eng. Jpn. 2006, 39, 703. (4) Marcilla, A.; Gomez, A.; Reyes, J. A.; Olaya, M. M. New Methods for Quaternary Systems Liquid-Liquid Extraction Tray to Tray Design. Ind. Eng. Chem. Res. 1999, 38, 3083. (5) Reyes, J. A.; Gomez, A.; Marcilla, A. Graphical Concepts to Orient the Minimum Reflux Ratio Calculation on Ternary Mixtures Distillation. Ind. Eng. Chem. Res. 2000, 39, 3912. (6) Lee, J. W.; Hauan, S.; Westerberg, A. W. Graphical Methods for Reaction Distribution in Reactive Distillation Column. AIChE J. 2000, 46, 1218. (7) Daza, O. S.; Perez-Cisneros, E. S.; Bek-Pedersen, E.; Gani, R. Graphical and Stage-to-Stage Methods for Reactive Distillation Column Design. AIChE J. 2003, 49, 2822.
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ReceiVed for reView April 3, 2009 ReVised manuscript receiVed October 2, 2009 Accepted October 15, 2009 IE9005468
