Ind. Eng. Chem. Res. 1996, 35, 3653-3664
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A Geometric Design Method for Side-Stream Distillation Columns† Raymond E. Rooks, Michael F. Malone,* and Michael F. Doherty Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-3110
A side-stream distillation column may replace two simple columns for some applications, sometimes at considerable savings in energy and investment. This paper describes a geometric method for the design of side-stream columns; the method provides rapid estimates of equipment size and utility requirements. Unlike previous approaches, the geometric method is applicable to nonideal and azeotropic mixtures. Several example problems for both ideal and nonideal mixtures, including azeotropic mixtures containing distillation boundaries, are given. We make use of the fact that azeotropes or pure components whose classification in the residue curve map is a saddle can be removed as side-stream products. Significant process simplifications are found among some alternatives in example problems, leading to flow sheets with fewer units and a substantial savings in vapor rate. Introduction and Background Side-stream columns (Figure 1) offer an alternative to sequences of simpler two-product columns. Intuitively, the side stream should contain primarily middleboiling components from a multicomponent mixture. Side streams may be useful when the middle boilers are trace components or even the main product, as in a pasteurization column where the lighter trace components leave overhead. The control of a side-stream column may also need study, but that is not the topic of this paper. Instead, we consider a more primitive question, namely, “which side-stream columns offer a significant economic advantage”, e.g., large enough to justify the control study. Design methods for side-stream columns separating mixtures with vapor-liquid equilibrium (VLE) characterized by a constant volatility model are available for both single-feed (Glinos and Malone, 1985a) and doublefeed (Nikolaides and Malone, 1987) configurations. These design methods were developed for “sharp splits” where the major products are essentially free of at least one of the components in the feed. The question of feasibility for side-stream columns has not been addressed in any detail, probably because the behavior of ideal mixtures is intuitive, i.e., intermediate-boiling components will appear in the side stream, while the lightest and heaviest components concentrate as distillate and bottoms, respectively. Criteria for use of side streams for the separation of mixtures that do not exhibit azeotropes were first developed by Tedder and Rudd in 1978. They analyzed several column configurations, including side-stream columns, and developed criteria for their use in terms of an ease of separation index (ESI), which is a ratio of the relative volatilities (presumably constant or average) of the various components. The results suggest taking a vapor as a side-stream product if the side stream is below the feed and a liquid side-stream product if the side stream is above the feed. An important result from earlier studies is that columns can be designed to make very high-purity sidestream products, although a larger number of two* To whom correspondence should be addressed. Phone: 413-545-0838. Fax: 413-545-1133. Email: mmalone@ ecs.umass.edu. † Parts of this work were presented at the AIChE Annual Meeting, Miami Beach, FL, Nov 1995, Paper 189a.
S0888-5885(96)00036-X CCC: $12.00
Figure 1. Columns with a side stream above the feed or below the feed.
product columns will frequently be more economical, except for certain ranges of feed composition and/or volatilities (Glinos and Malone, 1985a). This is because the attainment of a high-purity side stream may require large reflux ratios and a large number of stages, resulting in distillate or bottoms products that have much higher purities than required. Therefore, sidestream columns will often be advantageous when there is not a high-purity requirement on the side stream or for cases where the distillate or bottoms purity requirements are quite high. However, if there is a sufficient difference in boiling points between components, it can be economical to achieve a side stream with a high purity of the intermediate component. The geometric approach described in this paper does address the feasibility question because intuition is often lacking for nonideal mixtures. For nonideal mixtures, especially those that exhibit azeotropes, there are no simple methods that can be used to design sidestream columns. A common approach is to use repeated simulation, e.g., by estimating the side-stream location and flow rate, and then attempting to converge on a solution. Even when this approach is successful, it can be a time-consuming method which gives little insight. For two-product columns, more efficient and robust geometric design methods are available for both ideal and nonideal mixtures. For example, a “boundary value design procedure” (BVDP) for ternary mixtures was © 1996 American Chemical Society
3654 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
diagram. For side-stream columns, the analogous mass balances are
D+B+M)F
(3)
zDD + zBB + zMM ) zFF
(4)
which requires that the product compositions form a triangle with the feed composition as the “center of mass”, as shown in Figure 2. Once the compositions of the product streams are known, it is possible to calculate the (normalized) flows of all the product streams. The energy balance for an adiabatic column can be written as
FhF ) [(VU)htV - (LU)htL] + [(LL)hbL - (VL)hbV] + MhM (5)
Figure 2. Mass balance constraints for bottoms compositions in a side-stream column. The feed composition must occur inside the triangle formed from the product compositions. The hatched region denotes the possible values of the bottoms composition when the distillate and side-stream compositions are fixed.
described by Levy et al. (1985). This approach can be used to calculate flows and the equipment sizes directly from the product specifications for homogeneous mixtures. Furthermore, it provides a representation of infeasible solutions so that some insight is available even when desired specifications cannot be met. These geometric ideas have been generalized to provide minimum reflux (Julka and Doherty, 1990) and design methods (Julka and Doherty, 1993) for mixtures with more than three components. The purpose of this paper is to develop a geometric method for the design of side-stream columns. We restrict the model development here to mixtures containing three components. In the next section, we develop a model for single-feed side-stream columns. Next, the design procedure is outlined and some examples are presented for both single- and double-feed columns. A procedure to calculate the minimum reflux for side-stream columns is developed in the next section. Finally, we present several alternatives for the separation of a four-component mixture in which side-stream columns can be used to reduce costs.
Model Development The steady-state overall and component mass balances for a two-product column are
D+B)F
(1)
and
where h is the molar enthalpy, the subscripts V and L indicate vapor and liquid, and t and b denote the top and bottom stages of the column. The feed quality q is the dimensionless enthalpy of the feed, measured in latent heat units relative to a saturated liquid; i.e., hf ≡ (1 - q)λF, where λF is the heat of vaporization at the feed composition. For constant molar flows and saturated liquid products, the energy balance (eq 5) takes the simpler form
1 - q ) VU - VL which can also be written as
1 - q ) (r + 1)D - sB
(7)
in which r and s are the reflux and reboil ratios, respectively. We will consider cases where the feed composition, temperature, and column pressure (and thus q) are known. For the geometric design method, it is convenient to choose product compositions and a side-stream flow so that the mass balances in eqs 3 and 4 are satisfied and then use eq 7 to relate s and r. It is straightforward to relax the constant molar flow assumption, and it is used here only to illustrate the principles of the design method. We also take the products to be saturated liquids so that zD and zB in the balances above will be replaced by xD and xB in most of what follows. It is also easy and useful to consider a vapor side stream, which we will do in some of the later examples. Along with the overall and component mass balances and energy balances (eqs 3, 4, and 7), we require expressions for the stage-to-stage variations of compositions and, implicitly through the VLE, the boiling temperatures. To preserve similarity with the twoproduct column, we use the conventional form for the operating relationships in the rectifying (top) and stripping (bottom) sections as follows. For the rectifying profile, numbering down the column, r ) yj+1
zDD + zBB ) zFF
(6)
LU r D x + x VU j VU D
j ) 1, ..., NU
(8)
(2)
The geometric interpretation of eqs 1 and 2 for ternary mixtures is simply the requirement that the feed and product compositions be collinear on a composition
xr1 ) g(xD) where g(xD) is the composition of the liquid in equilibrium with a vapor of composition xD (g is the dew-point
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3655
function). For the stripping profile, numbering up the column, s xj+1 )
VL s B y + x LL j LL B
j ) 1, ..., NL
(9)
ys1 ) f(xB) where f(xB) is the composition of the vapor in equilibrium with the liquid bottoms product (f is the bubblepoint function). In the boundary value design procedure for simple columns, the rectifying profile and the stripping profile are found beginning from initial conditions given by the desired product compositions and then solving eqs 8 and 9, respectively, along with the vapor-liquid equilibrium relationships from one stage to the next within the column until the final “pinch” or fixed point on each profile is reached. If the profiles intersect one another, the design is feasible and this geometric approach can be developed to give both exact and approximate procedures to find minimum reflux and designs. For mixtures with constant volatility, the results for minimum reflux are exactly equivalent to Underwood’s method (Underwood, 1946, 1948), but the geometric approach is more general because nonideal mixtures can also be treated. For side-stream columns, however, we need a modified approach. It is well-known from studies of ideal mixtures that there is a maximum side-stream purity of middle boiler that can be achieved without excessive cost (Glinos and Malone, 1988). (Actually, any purity of the side stream can be achieved in an ideal mixture, but high purities are often impractical because excessive stages and/or vapor boilup will be needed.) The generalization of a middle-boiling component in a nonideal mixture is any azeotrope or pure component whose classification is a saddle in the residue curve map. Thus, we expect that some saddles are feasible targets for the side-stream compositions. In mixtures with distillation boundaries, the candidates are saddles in the same distillation region as the distillate and bottoms compositions. Within a given region or for mixtures without distillation boundaries, the particular saddle(s) that is a potential side-stream product(s) depends upon the feed composition. (In the regions containing only one saddle, the choice is unequivocal, but there are many mixtures that have two saddles in the same region, and a decision is needed for these cases.) We discuss this point in more detail using the examples below. We may attempt to place the side stream at any stage on either the rectifying (upper side-stream) or stripping (lower side-stream) profiles. This sets the composition of the side stream, xM, which is also the initial condition for the middle-section profile. It is convenient to describe the profile in the middle section by one of two different but equivalent forms of the mass balance, depending on the location of the side stream. For example, in a middle section, numbering down the column, we can write
yj+1 )
LM M D x + x + x VM j VM M VM D
j ) 1, ..., NM
(10)
x1 ) xM and there is a similar expression for the calculation of x if we number up the column.
Once we have chosen the side-stream location (and thereby its composition), we must also specify its flow in order to complete a design. Although it provides no guarantee that the desired compositions can be met, it is necessary that the side-stream flow and composition must at least satisfy the mass balances in eqs 3 and 4. For instance, for a column with the side stream above the feed (an “upper side-stream column”), if the feed has been specified, the distillate composition, the sidestream location, and the overall mass balances demand that the bottoms composition be placed in the shaded region shown in Figure 2, perhaps at point B as shown in the figure. After we have selected all of the compositions, we can calculate the flows. A similar picture can be developed for lower side-stream columns, where it is more “natural” to select the bottoms composition and then seek bounds on the distillate composition. We must specify internal flows to calculate profiles within the column, and it is also necessary to relate the flows in each of the sections to one another. We will require the following balances in the degree of freedom analysis in the following section:
M ) LU - LM VM ) VU VU ) LU + D LL ) VL + B
(11)
Degrees of Freedom and Specifications For a single-feed, two-product column, there are 4 degrees of freedom remaining after specifying the column pressure, along with the flow rate, composition, and enthalpy of the feed (Fidkowski et al., 1991). In the BVDP, we usually choose to specify two purities in one product stream and a third purity in the other product, along with either the reboil ratio or the reflux ratio. With this information, the stage-to-stage composition profiles can be found to determine if there is a feasible solution for the specified variables. For side-stream columns, there are independent equations from the overall (eq 3, 1 equation) and component (eq 4, c - 1 equations) mass balances, the mass balances between column sections (eq 11, 4 equations), and the overall energy balance (eq 6, 1 equation). In addition, a feasible column must have two profiles (the middle and stripping profile for a side stream above the feed or the middle and rectifying profile for a side stream below the feed) that have the same composition at the feed stage (c - 1 equations). The remaining pair of profiles (rectifying and middle, or stripping and middle) will automatically have the same composition at the side-stream stage (c - 1 equations). This is a total of 3(c - 1) + 6 equations. The unknown variables are xM, xB, xD, NT, NB, NM, D/F, M/F, B/F, LM/F, VM/F, VU/F, LU/F, VL/F, and LL/F. This is a total of 3(c - 1) + 12 variables, leaving 6 degrees of freedom (DOF). It is convenient to specify some of the variables involving the internal flows in terms of either the reflux ratio, r ≡ LU/D, or the reboil ratio, s ≡ VL/B. For an upper side stream, we first choose xD and r (3 DOF), and this allows a calculation of the rectifying profile. Next, we choose a side-stream stage number, NT, on the rectifying profile, and this 4th DOF determines xM. The final 2 DOF can be specified by choice of either xB or
3656 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 Table 1. Design Algorithm for an Upper Side-Stream Column 1. Specify the column pressure, feed rate (F), feed composition (zF), and enthalpy (q) 2. Choose the distillate composition, xD (2 DOF) 3. Choose a reflux ratio, r (1 DOF) 4. Solve for the rectifying profile (eq 8 and VLE) 5. Choose a side-stream location (NT) on the rectifying profile (1 DOF) 6. Choose the bottoms composition, xB (2 DOF) 7. Solve for the flows of the distillate, bottoms, and side stream (eqs 3, 4) 8. Solve for the middle profile (eq 10 and VLE) 9. Solve for the stripping profile (eq 9 and VLE) 10. If intersection of middle and stripping profiles, stop. Otherwise, go to 11. 11. Adjust r or another specification, and repeat from step 2.
D/F and M/F; the value of xB must fulfill mass balance constraints, as shown in Figure 2. Alternatively, 1 mole fraction in the bottoms product can be chosen, along with either the normalized distillate or side-stream flow. A similar analysis for the lower side-stream column leads to a specification of xB and s, then NB, followed by either xD or B/F and M/F. Design Procedure The basic algorithm is similar for both the upper and lower side-stream columns, and we will describe only the case for an upper side-stream column (Table 1). We will specify the distillate and bottoms composition. We will also pick a side-stream location and the reflux ratio or reboil ratio, depending on whether the side stream is above or below the feed, respectively. Note that the feed stage is at the intersection of the middle profile and the stripping profile. The choice of whether to specify a value of r or s depends on the side-stream location. For instance, if the side stream is above the feed, then r is a natural specification since we calculate the rectifying profile in order to choose the side-stream location. Alternatively, if the column has a lower side stream, it is more natural to specify the reboil ratio. However, there are also cases where the side stream is located above the feed but where the reboil ratio is a more convenient specification. For example, if a pasteurization section is contemplated in order to remove a small amount of light boilers from the mixture, while producing a main product that is the middle boiler as the side stream, we may want to compare the results to a two-product column doing the indirect split. An iterative procedure may be needed for this case. Feasibility Side-stream columns have a larger range of feasible product compositions than two-product columns. The side-stream composition is limited to a subset of compositions on the rectifying or stripping profiles, which are approximately constrained by the singular points in the residue curve map at total reflux. This map is a picture of all the feasible solutions to
dx ) x - y(x) dξ
(12)
and is commonly used to display the limits imposed by phase equilibrium in nonideal mixtures. The solutions of eq 12 are residue curves and analogues for column profiles at total reflux. The singular points of eq 12 are pure components and azeotropes, and a linear stability
Figure 3. Residue curve map for R13 ) 9, R23 ) 2.
analysis at these points can yield only three results: two negative eigenvalues (a “stable node”sanalogous to a high boiler), two positive eigenvalues (an “unstable node”sanalogous to a low boiler), or eigenvalues of mixed sign (a “saddle”sanalogous to a middle boiler). The residue curve map for a constant volatility mixture is shown in Figure 3. The residue curves begin at the lightest component and move toward the middleboiling component before reaching the heaviest component. If we pick a residue curve close enough to the hypotenuse and near the lightest component, the curve will pass close to the pure intermediate component and this saddle is, thus, a target for the side-stream composition. Since the rectifying profile has the same behavior as the residue curve at high reflux, we can obtain a highpurity intermediate product, at the expense of the energy required to provide a high vapor flow. The energy costs, the column diameter, and heat-exchanger areas scale with reflux (vapor rate). Consequently, side streams are not practical to provide high-purity intermediate products in many cases. Also, in order to obtain a side-stream target purity, we may need to overpurify the distillate, i.e., begin a rectifying profile very close to the hypotenuse. This geometric approach to feasibility can be extended easily to nonideal mixtures and to mixtures with azeotropes and distillation boundaries. For mixtures with distillation boundaries, such as acetone, isopropyl alcohol, and water, there is more than one stable node (Figure 4). This mixture has two distillation regions; the upper region has the vertices at isopropyl alcohol (stable node), acetone (unstable node), and the isopropyl alcohol-water azeotrope (saddle). The lower region has vertices at water (stable node), acetone (unstable node), and the isopropyl alcohol-water azeotrope (saddle). Using the same logic as used for constant volatility mixtures, we see that if the distillate is in either region, we may obtain a composition close to the binary azeotrope as a side stream. Designs for Single-Feed Columns Ideal Systems. The simplest vapor-liquid model used in distillation is the constant volatility model. As
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3657
Figure 4. Residue curve map for acetone, isopropyl alcohol, and water.
discussed above, it is possible to obtain nearly pure components in each product with sufficient energy and stages. Whether it is economical to do this or not depends on the feed and product compositions and the relative volatilities. The residue curve map for this mixture (Figure 3) shows two nodes and one saddle, where the relative volatilities are R13 ) 9 and R23 ) 2. The feed composition is balanced (zF ) 0.3, 0.3, 0.4). We can split this mixture into nearly pure products (99% pure) using 2 columns in the direct sequence with 28 stages in the first column and 24 stages in the second column. We choose to design the columns at a reflux ratio 40% above the minimum reflux, although this could also be optimized. We need criteria for evaluating the costs of each column for comparison of alternatives to this simple
sequence. However, a detailed economic analysis can be time-consuming, yet still uncertain, and a simpler method is often adequate for conceptual design. For example, it has been demonstrated that the total vapor rate is a good indicator for comparing designs (Glinos and Malone, 1985b) provided that the vapor boilup for all the streams can be provided with utilities at a similar cost. The total vapor rate per mole of feed for the direct sequence in this example is ∑V/F ) 1.8, and 53 theoretical stages are required. We can compare this with the side-stream column (Figure 5), where the same product purities are achieved at a much larger value of V/F ) 9.23, although with 36 stages. While the number of stages is lower for the side-stream column, the column diameter is larger than for the first column in the direct sequence, due to the large vapor flow rate. In addition, the reboiler will be larger and the operating costs will be much larger for the side-stream column. For this particular case, a side-stream column is not likely to be cost-effective. If the relative volatility of the lightest component is larger, and if the lightest component is present only in small amounts, the results can be quite different. For instance, consider the case of R13 ) 18, R23 ) 3, and a feed composition (zF ) 0.05, 0.45, 0.5). The direct sequence has ∑V/F ) 1.3 and a total of 41 stages for the specification of 99% purity of the key component in each product stream. We find ∑V/F ) 2.0 and a total of 33 stages, for the indirect sequence. The side-stream column has a total of 33 stages, which compares favorably to the direct sequence. Since we have specified a high-purity product, we have a high reflux ratio of 22 (on account of a small distillate flow rate), even though the relative volatility for the lightest component is high. Although the reflux ratio is high, the reflux flow is not so large and the vapor rate for the side-stream column, V/F ) 1.1, is lower than either the direct or indirect sequences. The side-stream
Figure 5. Liquid composition profile for separation of a constant relative volatility mixture (R13 ) 9, R23 ) 2) using a side-stream column. The open circles form the stripping profile, the filled squares form the middle profile, and the open diamonds form the rectifying profile.
3658 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
Figure 6. Direct sequence and liquid composition profiles for the first column to obtain pure acetone. Note that the column profile in the triangle corresponds to the first column in the sequence. The open circles form the stripping liquid profile, and the open diamonds form the rectifying profile. Table 2. Summary of Design Specifications and Resultsa reflux ratio z1,F z2,F z3,F x1,D x2,D x3,D x1,B x2,B x3,B x1,M or y1,M x2,M or y2,M x3,M or y3,M total stages side-stream stage q V/F
Figure 5
Figure 6
Figure 7
Figure 8
3.0 0.3 0.3 0.4 0.99 0.01 1.0 × 10-10 1.0 × 10-10 0.01 0.99 0.0094 0.9905 2.014 × 10-5 36 26 1.0 9.307
3.0 0.63 0.07 0.3 0.99 0.0001 0.0099 1.0 × 10-5 0.1923 0.8077 n/a n/a n/a 33 n/a 1.0 2.545
2.874 0.63 0.07 0.3 0.99 0.0001 0.0099 1.0 × 10-10 0.01 0.999 0.0009 0.6539 0.3452 40 8 1.0 2.572
10.86 0.4 0.55 0.05 0.9933 0.0007 0.006 1.0 × 10-20 1.0 1.0 × 10-5 0.0004 0.761 0.2386 52 30 1.0 4.974
a The specifications appear in italics. Note that the mole fractions are in order of increasing boiling points for the components they represent.
column will be cheaper since there is a single shell instead of two and two heat exchangers instead of four. Nonideal Mixtures An isopropyl alcohol, acetone, and water mixture is produced in the manufacture of acetone from isopropyl alcohol using an azeotropic feed of isopropyl alcohol and water. The vapor-liquid equilibrium for this mixture can be described by the Wilson model (Gnehling et al., 1978, 1981, 1988). There is a low-boiling azeotrope between isopropyl alcohol and water, and the residue curve map (Figure 4) shows a distillation boundary from the azeotrope to pure acetone. The feed composition to the reactor is near the isopropyl alcohol/water azetrope. The resulting composition of the reactor exit stream is in the lower distillation region and is fed to the separation system. With this feed, a direct sequence (Figure 6) can produce nearly pure acetone, nearly pure water, and a product with a composition near the azeotrope for recycle to the reactor. This sequence has a total of 40 stages and ∑V/F
) 2.7. The results for the first column in the sequence are summarized in Table 2. A side-stream column (Figure 7) with a vapor side stream can yield better results than the direct sequence for this feed. It has 40 stages and a nearly identical vapor flow rate V/F ) 2.6 and is an attractive alternative that can be used to replace the two columns of the direct sequence. A different case arises for this same mixture if the feed composition contains a small amount of water (e.g., zF ) 0.4, 0.55, and 0.05, the mole fractions being in order of acetone, isopropyl alcohol, and water) and we wish to recover pure acetone and isopropyl alcohol for which a direct split would be feasible. This sequence has a total of 63 stages and ∑V/F ) 5.9. The second column in the sequence has a bottoms product of isopropyl alcohol and a distillate near the azeotrope. Alternatively, a side stream (Figure 8) near the azeotrope composition allows us to obtain pure isopropyl alcohol and pure acetone as bottoms and distillate products, respectively, from a single column. The total number of stages is 52, and the vapor flow rate V/F ) 5.0. This
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3659
Figure 7. Side-stream column and liquid composition profile for the production of acetone. The open circles form the stripping profile, the filled squares form the middle profile, and the open diamonds form the rectifying profile.
Figure 8. Side-stream column liquid composition profile to obtain pure acetone and isopropyl alcohol. The open circles form the stripping profile, the filled squares form the middle profile, and the open diamonds form the rectifying profile.
alternative has fewer total stages, a lower vapor rate, fewer columns, and fewer heat exchangers than the direct sequence, and therefore, it will be less expensive. As stated above, this technique can be used without the assumption of constant molar flows. The results of a profile calculation including an energy balance and enthalpy changes were compared to a simulation done with HYSYS software, version 1.0. The results are in good agreement, as shown in Table 3. The savings for a side-stream column over the direct sequence is very sensitive to the side-stream composi-
tion specification. As the purity of the side stream approaches the binary isopropyl alcohol-water azeotrope (72 mol % isopropyl alcohol), the vapor flow increases in the side-stream column (Figure 9). This is due to the need to overpurify the bottoms product in order to reach a profile that approaches the azeotropic composition in the side stream. If the mole fraction of isopropyl alcohol in side-stream composition is increased, V/F decreases, and the number of stages increases as this composition is approached. The savings in stages and V/F as a function of the side-stream
3660 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 Table 3. Comparison of Non-CMO Profiles and a Simulationa side stream reflux ratio reboil ratio distillate rate bottoms rate z1,F z2,F z3,F x1,D x2,D x3,D x1,B x2,B x3,B y1,M y2,M y3,M total stages feed stage side-stream stage q V/F
direct
design
simulation
design
simulation
13.61 11.5 0.4026 0.394 0.4 0.55 0.05 0.9933 7.0 × 10-4 0.006 1.0 × 10-20 1.0 1.0 × 10-5 3.0 × 10-4 0.7655 0.2341 53 42 30 1.0 4.533
13.61 11.559 0.4026 0.394 0.4 0.55 0.05 0.994 6.323 × 10-4 0.006 1.218 × 10-21 1.0 2.365 × 10-5 4.247 × 10-5 0.765 0.235 53 42 30 1.0 4.6
11.39 6.16 0.403 0.597 0.4 0.55 0.05 0.9933 7.0 × 10-4 0.006 1.0 × 10-9 0.9203 0.0797 n/a n/a n/a 36 25 n/a 1.0 3.679
11.39 6.121 0.403 0.597 0.4 0.55 0.05 0.994 7.211 × 10-4 0.006 1.865 × 10-11 0.920 0.08 n/a n/a n/a 36 25 n/a 1.0 3.7
a The distillate and bottoms rate are normalized by the feed rate. The specifications appear in italics. Note that only the results of the first column in the direct sequence are shown. The binary separation shows similar agreement.
Figure 9. Comparison of the side-stream column to the direct sequence over a range of compositions in the side stream and distillate in the second column of the direct sequence, respectively.
composition is shown in Figure 10. For an equal number of stages (81 mol % isopropyl alcohol in the side stream or distillate), the savings in the vapor rate are nearly 80% for the side-stream column. The ideal sidestream composition is actually an optimization problem which should include the reactor design and energy costs.
Minimum Reflux Minimum reflux calculations for single-feed, twoproduct columns can be performed using geometric methods and with a numerical solution via continuation methods (Fidkowski et al., 1991). These methods apply to both sharp and nonsharp splits, where at least one component is being removed in each exit stream, and involve tracking the fixed points of certain profile equations. For instance, the fixed points (pinches) of
Figure 10. Comparison of the savings of the side-stream column vs the direct sequence over a range of compositions. The compositions are for the side stream and the distillate in the second column of the direct sequence.
the rectifying equation (eq 8) can be found by solving
y(xˆ r) -
LU r D xˆ x )0 VU VU D
(13)
and for the stripping section
xˆ s -
VL B y(xˆ s) - xB ) 0 LL LL
(14)
Side-stream columns exhibit minimum reflux geometries similar to simple columns (Kohler et al., 1994). The minimum reflux ratio is governed by one profile pinching on another, and to a close approximation, pinches are aligned with the feed composition. The
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3661
strategy for solving for the minimum reflux does differ, though, since there is a new section of the column. The middle-profile pinch equation is
y(xˆ ) -
LM M D xˆ x x )0 VM VM M VM D
(15)
The key to calculating the minimum reflux ratio for side-stream columns is to know which pinches to align. We need to know when the profiles will exhibit the “direct” or “indirect” geometries (Figure 11a or b). In order to calculate the minimum reflux for feed and product specifications that follow direct geometry, the stripping node pinch, the feed composition, and the rectifying saddle must be aligned (Figure 11a). Similarly, for the indirect geometry, the middle-section node pinch, the feed composition, and the stripping saddle pinch must all be aligned (Figure 11b). For most cases, there are two notable results. For a column with a side stream above the feed, if the bottoms composition is close to the heavy boiling component or azeotrope, a indirect geometry will normally result. Alternatively, for a column with a side stream below the feed, if the distillate composition is close to the light boiling component or azeotrope, a direct geometry will normally result. An important similarity for both the two-product column and the side-stream column is that two of the profiles pinch at the feed tray (stripping and rectifying, stripping and middle, or rectifying and middle, depending on which geometry controls). Figure 11c shows the “transition” geometry for a upper side-stream column. The line that divides distillate and bottom compositions leading to the direct and indirect geometries is the “transition line”. This is similar to the results of Fidkowski et al. 1993) (Figure 3c) for simple columns. The difference is that the feed, distillate, and bottoms compositions are not collinear, due to the presence of the side stream. If we examine an upper side-stream column at minimum reflux for the transition split, both the middle and stripping profiles pinch at the same point. For the special case of a saturated liquid feed, these pinches will occur at the feed composition xF. The stripping profile depends only on the bottoms composition and the reboil ratio, and for a given bottoms composition, there will be only one reboil ratio that leads to the stripping section pinching at the feed composition. This does not depend on what is happening in the upper column section(s) (i.e., whether or not there is a side stream above the feed). Therefore, the transition line for side-stream columns is identical to the one for simple columns with the following interpretation. The transition line connects the bottom composition, the feed composition, and the average composition of the product streams above the feed (i.e., distillate and side stream) for a side stream above the feed. A similar result is reached for a side stream below the feed. The transition line can be found by computing the solutions to the equation
qxf + (1 - q)yf - zF ) 0
(16)
With this solution, we can then delineate which splits are direct and indirect. This allows the correct criteria to be applied when calculating the minimum reflux ratio.
Figure 11. Upper side-stream column profiles for (a) direct geometry, where the stripping profile pinches on the middle profile; (b) indirect geometry, where the middle profile pinches on the stripping profile; and (c) transition geometry, where the middle profile and the stripping profile pinch at the same point. The transition line is denoted by the dashed line.
In solving for the minimum reflux for a side-stream column, we must perform the following steps: 1. Find the transition line by solving eq 16 with xf and yf related by VLE. 2. If the bottoms composition indicates a direct geometry, use the rectifying saddle, the middle-section
3662 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
purity of isopropyl alcohol in the isopropyl alcohol product stream, and 99% water in the water product stream. The direct sequence has a distillate product from the first column rich in acetone. The bottoms product contains primarily isopropyl alcohol and water and is sent to the second column, where it is split into a distillate with a composition near the azeotrope and a bottoms containing primarily water. The total vapor flow rate (V/(FL + FU)) for this sequence is 2.33, and the total number of stages is 39. The side-stream column has a bottoms product of water, a distillate of acetone, and a side stream near the azeotrope composition. The vapor flow for this column is 2.29, and the total number of stages is 33. Again, because this column can replace a sequence of two columns and has fewer stages, roughly the same vapor flow rate, fewer heat exchangers, and less instrumentation, it will be more economical. Four-Component Example Figure 12. Residue curve map structure of acetaldehyde, methanol, ethanol, and water at 1 atm of pressure. Note that there is a distillation boundary denoted by the hatched region.
node, and the feed composition to determine the fixedpoint “volume” (Fidkowski et al., 1991). 3. If the bottoms composition corresponds to indirect geometry, use the stripping saddle, the middle-section node, and the feed composition to determine the fixedpoint “volume”. 4. The minimum reflux corresponds to a “volume” of zero. A turning point in the volume-reflux graph corresponds to a tangent pinch and is treated the same way as in Fidkowski et al. (1991). Double-Feed Columns The design method for single-feed columns with side streams naturally extends to double-feed columns. As an example, we return to the acetone, isopropyl alcohol, and water system and consider two feeds in the lower distillation region. The lower feed is rich in water (20% acetone, 20% isopropyl alcohol, 60% water), and the upper stream is rich in acetone (80% acetone, 10% isopropyl alcohol, 10% water). We have selected 99% purity of acetone in the acetone product stream, 99%
The ideas presented in this paper can be used to generate process alternatives. Consider a four-component mixture of acetaldehyde, methanol, ethanol, and water with the residue curve map structure shown in Figure 12. This mixture has three azeotropes, all on the acetaldehyde, ethanol, and water face. There is a distillation boundary that separates the tetrahedron into two regions, one rich in water, the other lean in water as shown in the figure. This mixture was discussed in a previous paper (Julka and Doherty, 1993) and the original data appear in d’AÄ vila and Silva (1970). For feed mixtures with a composition on the waterrich side of the distillation boundary, we can perform a direct split in the first column, where acetaldehyde is the distillate and the bottoms product is on the methanol/ ethanol/water face. Still more alternatives may be possible, such as the indirect split, where water is taken out as the bottoms product; that and some of the other alternatives involve crossing distillation boundaries. The first sequence (Figure 13) has five columns. The first column removes nearly all of the acetaldehyde in the distillate, leaving the remaining three components in the bottoms stream. The second column removes nearly all of the methanol in the distillate and sends the bottoms product of ethanol and water to a “precon-
Figure 13. First sequence to separate acetaldehyde, methanol, ethanol, and water. This sequence has a total of 5 columns, 10 heat exchangers, 178 stages, and a normalized vapor flow of 12.19.
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3663 Table 4. Summary of Design Results for the Four-Component Separation Sequences sequence stages shells heat exchangers vapor flows ∑V/F0
first
second
third
178 5 10 12.19
178 4 8 10.12
166 3 6 9.84
Conclusions
Figure 14. Second sequence to separate acetaldehyde, methanol, ethanol, and water. This sequence has a total of 4 columns, 8 heat exchangers, 178 stages, and a normalized vapor flow of 10.12.
Figure 15. Third sequence to separate acetaldehyde, methanol, ethanol, and water. This sequence has a total of 3 columns, 6 heat exchangers, 166 stages, and a normalized vapor flow of 9.84.
centrator” column. This third column concentrates the distillate to a composition near the ethanol/water azeotrope and removes water in the bottoms. The last two columns are an extractive distillation sequence to break the azeotrope using ethylene glycol as an extractive agent. The second sequence (Figure 14) consolidates the second and third columns. A side-stream column can be used to remove methanol as a distillate, water as a bottoms product, and a side-stream product near the ethanol-water azeotrope. The need for a separate preconcentrator column has been eliminated, and the side stream is fed directly to the extractive distillation sequence. The total number of stages needed is the same, but the total vapor flow is reduced by approximately 20% compared to the first alternative. The third sequence (Figure 15) introduces a new extractive distillation configuration. Ethylene glycol has a high volatility relative to with water, which makes that binary mixture easy to separate. If a side-stream vapor is used to recover the water, the entrainer recovery column can be eliminated since the entrainer is in the bottom stream. The water purity in the side stream is 99%, and this is sent to treatment along with the water from the second column. This sequence has three columns, fewer stages, and a lower total vapor flow rate. The three sequences shown above are summarized in Table 4. All of these sequences have identical designs for the first column. The process alternatives lie in using side streams to replace various downstream columns.
This paper has described a method to design sidestream columns. The methods apply to ideal mixtures as well as to mixtures with azeotropes and distillation boundaries. Middle-boiling components and saddle azeotropes are potential side-stream products. Side-stream columns can be economical under certain process conditions and design requirements. Some of the criteria which favor the use of side-stream columns are as follows: 1. There is an imbalanced feed, such as very little of a middle-boiling component. 2. The sidestream can be taken with flexible purity requirements, such as side streams going to waste treatment, recycle, and as azeotropic feeds to other columns. The best composition of the side stream should then be computed through a optimization over the entire system. Such an optimization could be an important application of the methods displayed here. An additional advantage of a side stream is that it provides an exit point for middle-boiling trace components. For some designs, side-stream columns can lead to lower capital and operating costs. The inclusion of sidestream designs expands the tools available so that better systems can be achieved. Acknowledgment We are grateful for financial support provided by the University of Massachusetts Center for Process Design and Control. We also thank Hyprotech for use of the simulator software HYSYS. Nomenclature c ) number of pure components in the mixture B ) bottoms flow rate D ) distillate flow rate F ) flow of overall feed f(x) ) vapor composition at the bubble point of a liquid with composition x g(y) ) liquid composition at the dew point of a vapor with composition y h ) molar enthalpy L ) liquid stream or flow rate M ) side-stream flow rate N ) number of stages P ) column pressure q ) dimensionless enthalpy of the feed (feed quality) r ) reflux ratio s ) reboil ratio V ) vapor stream or vapor flow rate x ) vector of liquid mole fractions y ) vector of vapor mole fractions z ) vector of mole fractions Greek Symbols Rij ) relative volatility of component i with respect to component j
3664 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 λF ) latent heat of vaporization of the feed ξ ) warped time Superscripts ˆ ) fixed point b ) bottom tray f ) feed tray r ) rectifying section s ) stripping section t ) top tray Subscripts B ) bottoms D ) distillate F ) feed L ) lower section of column M ) middle section of column U ) upper section of column
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Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1981; Vol. I/1a. Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1981; Vol. I/1b. Julka, V.; Doherty, M. F. Geometric Behavior and Minimum Flows for Nonideal Multicomponent Distillation. Chem. Eng. Sci. 1990, 45, 1801-1822. Julka, V.; Doherty, M. F. Geometric Nonlinear Analysis of Multicomponent Nonideal Distillation: A Simple Computer-Aided Design Procedure. Chem. Eng. Sci. 1993, 48, 1367-1391. Kohler, J.; Kuen, T.; Blass, E. Minimum Energy Demand for Distillations with Distributed Components and Side-Product Withdrawls. Chem. Eng. Sci. 1994, 49, 3325-3330. Levy, S. G.; Van Dongen, D. B.; Doherty, M. F. Design and Synthesis of Homogenous Azoetropic Distillations. 2. Minimum Reflux Calculations for Nonideal and Azeotropic Columns. Ind. Eng. Chem. Fundam. 1985, 24, 463-474. Nikolaides, I. P.; Malone, M. F. Approximate Design of MultipleFeed/Side-Stream Distillation Systems. Ind. Eng. Chem. Res. 1987, 26, 1839-1845. Tedder, D. W.; Rudd, D. F. Parametric Studies in Industrial Distillation: Part 1. Design Comparisons. AIChE J. 1978, 24, 303-315. Underwood, A. J. V. Fractional Distillation of Multi-component MixturessCalculation of Minimum Reflux Ratio. J. Inst. Petrol. 1946, 32, 614-626. Underwood, A. J. V. Fractional Distillation of Multi-component Mixtures. Chem. Eng. Prog. 1948, 44, 603-614.
Received for review January 26, 1996 Revised manuscript received July 8, 1996 Accepted July 9, 1996X IE960036T
X Abstract published in Advance ACS Abstracts, October 1, 1996.
