Article pubs.acs.org/IECR
Improved Rectifying Columns Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100, United States ABSTRACT: Standard rectifying columns have a single vapor feed. The two-enthalpy feed rectifier condenses a portion of this vapor feed to produce a liquid feed of the same composition. With the same total amount of cooling, the two-enthalpy feed rectifier has a smaller diameter but requires more stages than standard rectifiers. Detailed Aspen Plus simulations for 10 mol % argon−90% oxygen producing a 98% argon distillate at an external reflux ratio ∼1.2 times the minimum show the column volume could be reduced by 12.1% or energy could be reduced by 8.3% compared to the case with a standard rectifier. Savings are lower when simulations are operated closer to the minimum reflux ratio. The feed condensation temperature is 2.2 K higher than the condensation of distillate. Reducing the amount of feed condensed gives the new rectifier design excellent turn-down properties with less energy required per mole of distillate. Methanol−water and a ternary hydrocarbon mixture had larger savings than argon−oxygen.
1. INTRODUCTION AND LITERATURE REVIEW Because the cost of separations is typically in the range from 40 to 70% of the operating and the capital expenses of chemical plants,1 development of separation processes is a critical part of process development. Distillation is the venerable work horse of the process industries. Although Keller2 showed that a reasonable rule of thumb is that one-half to two-thirds of the yearly cost is operating and one-third to one-half is capital, there has been considerably more research on reducing the energy cost of distillation than on reducing the capital cost. Wankat and Kessler3 introduced the use of two-enthalpy feed (part of the feed is vapor and part is liquid with both parts at the same composition) for binary and multicomponent flash columns, stripping columns, and complete distillation columns. Rectifying columns were mentioned, but the analysis was not developed. The focus of their paper was more effective use of waste heat. Soave and Feliu4 independently developed the idea of two-enthalpy feed using the hot bottoms product to heat a portion of a liquid feed. With two-enthalpy feed, the reboiler energy requirements could be reduced without increasing the cooling required in the condenser. Beneke et al.5 developed an alternate method of distributing the feed to multiple locations that did not require changing the enthalpy of the feed. However, their method is not applicable to binary systems or to sharp separations. The volume of complete distillation columns that have a significantly larger calculated diameter in one section of the column can often be reduced by reducing the vapor velocity in the section with the larger calculated diameter. For vapor feeds the molar vapor velocity V in the rectifying section can be reduced by adding an intermediate condenser, using twoenthalpy feed, or conditioning the feed (partially or totally condensing the entire feed stream).6 Vapor flow rate in the stripping section can be reduced by adding an intermediate reboiler, using two-enthalpy feed, or conditioning the feed.7 Intermediate condensers, intermediate reboilers, and twoenthalpy feed systems can be designed to require the same amount of energy as the standard column, but the number of equilibrium stages required increases. Capital cost savings occur © 2013 American Chemical Society
when the reduction in column area is greater than the increase in column height. To obtain significant reductions in cost, a standard column needs to have significantly different calculated diameters in different sections.6,7 With vapor feeds the calculated diameter in the rectifying section is usually larger than in the stripping section. Rectifying columns (no reboiler and no stripping section) are an interesting special case because they always have a vapor feed. Figure 1A illustrates a two-enthalpy feed rectifying column which can be compared to the standard rectifying column in Figure 1B. The research questions posed in this paper are 1. Under what conditions will rectifying column costs be reduced if two-enthalpy feed is employed? 2. Under what conditions will rectifying energy use be reduced if two-enthalpy feed is employed? 3. What other advantages does the two-enthalpy feed rectifier have compared to standard rectifiers? 4. Does the two-enthalpy feed method work for strippers? To explore these questions, I first present a qualitative analysis and then the results of detailed Aspen Plus simulations.
2. QUALITATIVE ANALYSIS OF TWO-ENTHALPY FEED RECTIFIER For a qualitative feel for the two-enthalpy feed rectifier, assume the simplest possible case: binary separation with constant molar overflow (CMO), total condensation of the portion of the feed that is condensed, a vapor that is an ideal gas, same pressure in the two rectifiers, negligible pressure drop in the column, and constant relative volatility. These assumptions are invoked only to simplify the analysis. The simulations shown later use more rigorous VLE correlations, do not assume CMO, and include ternary separation. Special Issue: Massimo Morbidelli Festschrift Received: Revised: Accepted: Published: 9158
August 19, 2013 November 7, 2013 November 11, 2013 November 11, 2013 dx.doi.org/10.1021/ie4027204 | Ind. Eng. Chem. Res. 2014, 53, 9158−9168
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Figure 2. McCabe−Thiele diagram showing operating lines for a standard rectifier and for a two-enthalpy feed rectifier.
z − xB D = F xD − xB
V̅ = V = (1 − fL )F
L = FV − D = (1 − fL )F − D
and
L̅ = L + FL = (1 − fL )F − D + fL F = F − D
2.1. Identical Product Purities. If we specify that F, z, xD, and xB are constant, the external mass balances in eq 2 show that bottoms B and distillate D molar flow rates are the same for the standard rectifier and the two-enthalpy feed rectifier. Alternatively, if we specify constant F, z, xD and distillate recovery D/F, the external mass balances show that B, D, and xB are the same for the standard rectifier and the two-enthalpy feed rectifier. Because compositions and pressures are the same in the two rectifiers, the temperatures and enthalpies of the product streams are the same. Then, energy balances around each rectifier show that
Figure 1. (A) Two-enthalpy feed rectifying column. (B) Standard rectifying column. Stage numbers follow Aspen Plus numbering convention.
Q c,total,2F = Q c,feed,2F + Q cond,2F = Q c,standard
The McCabe−Thiele diagram for the simplified system is shown in Figure 2. The constant relative volatility VLE equation is y=
αx 1 + (α − 1)x
(2)
(3a)
Note that with equal purities in the distillate and bottoms the energy use is the same without requiring CMO to be valid. This equation is also valid if we compare standard and two-enthalpy rectifiers with partial condensers. With a total condenser and CMO
(1)
Q c,standard = −λF
The mole fractions of the more volatile component (MVC) in the feed, distillate, and bottoms are z, xD, and xB, respectively. The operating line for the standard rectifying column is the straight line from point (y = z, x = xB) to point (y = xD, x = xD). The operating lines for the two-enthalpy feed system intersect at the vertical saturated liquid feed line at y = yI. Define f L as the fraction of the feed that is condensed in the feed condenser, f L = FL/F (the standard rectifier has f L = 0). Then molar vapor feed is FV = (1 − f L)F, and with external mass balances and CMO we can determine the vapor and liquid velocities.
Q c,feed,2F = −λfL F
Q cond,2F = −λ(1 − fL )F
(3b)
where λ is the latent heat of vaporization, which is constant when CMO is valid. With constant λ adding the two-enthalpy feed condenser duty to the condenser duty in the column gives eq 3a. With a partial condenser and CMO Q c,standard = −λ(F − D)
Q c ,feed,2F = −λfL F
Q cond,2F = −λ[(1 − fL )F − D] 9159
(3c)
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With constant λ, adding the two-enthalpy feed condenser duty to the partial condenser gives eq 3a. The slopes of the operating lines are L̅ 1 − D/F L D/F = =1− V̅ 2F 1 − fL V 2F 1 − fL x −z L D =1− = D V standard F xD − xB
1 − D/Fmax y* − z L̅ = = Vmax z − x* 1 − fLmax ̅ fLmax = 1 −
and
(4a, b, c)
(5a,b,c)
where x* is the mole fraction at the pinch point [x value in equilibrium with y = z from eq 1]. Because the distillate and bottoms flow rates are identical for the standard and two-enthalpy feed systems (constant xD, xB, z, and F), Dmax and Bmin are the same for the two systems. If CMO is valid, the ratio L̅ Dmin ,2F
⎛B ⎞ Bmin L = = ⎜ min ⎟ = Dmax ,2F ⎝ Dmax ⎠ Dmin ,standard standard
(6a)
L̅ L̅ L L =M× = =M× Dmin ,standard D 2F Dmin ,2F D standard
(6e,f)
Nreal = Nequil /EO
(7a)
h = Nreal × (tray spacing) + disengagement heights
(7b)
hpacking = Nequil × HETP (6b)
(7c)
hcolumn = hpacking + disengagement heights
From F = L + D and F = L̅ + D we find
⎛ L̅min ⎞ 1 −1 ⎜ ⎟ = (Dmax /F ) ⎝ Dmax ⎠2F
( VL )max
If the feed stage for the liquid in the two-enthalpy feed rectifier has a markedly different efficiency than the other stages, eq 7b can be adjusted to include this difference. In a packed column, Nequil and the HETP can be used to determine the height of packing and of the column.
Because L̅ = L + FL, the ratio L̅ /(Dmin,2F) is the effective minimum reflux ratio for the two-feed (2F) system. Operation will typically be at a multiplier M times (L/D)min,standard
⎛ Lmin ⎞ 1 = −1 ⎜ ⎟ (Dmax /F ) ⎝ Dmax ⎠standard
1 − D/Fmax
where L̅ and V̅ are from eq 2 and y* is the y value in equilibrium with x = z from eq 1. To explore the effect of the feed composition in the twoenthalpy feed rectifier, compare f Lmax values (determined at the pinch points where the feed lines intersect the equilibrium curve) for systems with α = 2.0 with low (z = 0.1) and high (z = 0.8) mole fractions of the MVC in the feed when a pure product (xD ∼ 1) is desired. When z = 0.1, eq 1 gives x* = xB = 0.0526 and eq 5a) gives D/(Fmax) = (z − xB)/(xD − xB) = 0.05003. Because from eq 1 y* = 0.1818, the maximum slope of the bottom operating line in the two-enthalpy feed rectifier is L̅ /(V̅ max) = (y* − z)/(z − x*) = 1.726. Equation 6f gives f Lmax = 0.450. If we repeat the two-enthalpy feed rectifier calculation for z = 0.8, we obtain x* = xB = 0.6667, y* = 0.8888, D/Fmax = 0.4, L̅ /(V̅ max) = 0.6667, and f Lmax = 0.100. The maximum amount of feed that can be condensed is considerably less when there is a high concentration of the MVC in the feed than when there is a low concentration of MVC in the feed. Thus, because vapor flow rate cannot be reduced by much for feeds with high MVC concentrations, we would expect much less potential for reducing the area and lowering capital costs. For the systems studied, the conclusion is the two-enthalpy feed rectifier is more likely to be less expensive than a standard rectifier when there is a low fraction of MVC in the feed. The height h of a tray column is determined from the number of real stages, which can be determined from the number of equilibrium stages Nequil and the overall efficiency, EO.
Equation 4c is based on Vstandard = F. Because D/F is constant for constant values of feed, distillate, and bottoms mole fractions, the slope of the top operating line, L/(V2F), decreases as f L increases. Thus, as the fraction of feed f L that is condensed increases, the operating lines become closer to the equilibrium curve (Figure 2). Although for reasons of clarity stages are not shown in Figure 2, they can easily be stepped off. For identical separations and feed rates the two-enthalpy feed rectifier will require more stages than the standard rectifier. The highest value of D/F is obtained when xB is as small a possible, which occurs at the pinch point with the vapor feed line. Then for the standard rectifier (V = F), x −z x −z L = D = D Vmin xD − xB x D − x* Dmax L z − x* = 1 − min = F V x D − x* x −z L /Vmin L = = D Dmin 1 − L /Vmin z − x*
and
+ feed section (in 2F) height
and
(7d)
Costs for packing and columns can be estimated on the basis of the packing volume and the column volume.7 packing capital cost = Cpack(packing volume)np
(6c,d)
Complete distillation columns are typically designed with multiplier M in the range from 1.05 to 1.25. The results shown later indicate that the multiplier should probably be lower for rectifiers. For the two-enthalpy feed system the maximum value of L̅/V̅ occurs when the operating line is pinched simultaneously at both feed lines. Then,
= Cpack(hpacking × area)np
(7e)
column capital cost = Ccol(column volume)nc = Ccol(hcolumn × area)nc 9160
(7f)
dx.doi.org/10.1021/ie4027204 | Ind. Eng. Chem. Res. 2014, 53, 9158−9168
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For large columns the packing cost per cubic meter becomes constant (exponent np = 1.0) and I estimated the exponent for the column shell as nc = 0.85 from the graph of column costs.8 If the height of the column increases less than the area decreases, the packing and column capital costs will decrease. Costs for trays depend on the type of tray, the number of trays, and the tray area. trays capital cost = f (N )C tray(column area)nt
area =
For large diameter columns with a large number of trays nt = 1.0 and f(N) = N. If the number of stages N increases less than the area decreases, the tray capital cost will decrease. Although column diameters and cross-sectional areas are easily calculated with commercial simulators, it will be worthwhile to consider a simplified analysis. On the basis of Fair’s method of calculating column diameters,9,10 the operating velocity uop is a fraction (frac) of the flooding velocity uflood,
(Csb)2F,top > (Csb)standard > (Csb)2F,bottom
V2F,top = V2F,bottom = (1 − fL )F < Vstandard = F
where the flooding velocity is calculated from the following, (8b)
For
(area)2F ∼ (1 − fL )(area)standard
log10 Csb = − 0.94506 − 0.70234 log10 Flv − 0.22618 (log10 Flv)2 0.5
0.5 L MWL ⎛ ρV ⎞ ⎜⎜ ⎟⎟ = V MWV ⎝ ρL ⎠
(8d)
where WL and WV are the mass flow rates of liquid and vapor, MW is the molecular weight, and ρ is the mass density. Then, area = (V )(MWV )/(3600uopρV η)
(8e)
where η is the fraction of column cross sectional area available for vapor flow. These equations can be simplified for the special case of an ideal gas at pressure p and temperature T with negligible pressure drop in the column, ρV =
pMWV RT
and
ρL ≫ ρV
and
p = constant (9a)
The flow parameter in eq 5d becomes 0.5 WL ⎛ ρV ⎞ ⎜ ⎟ Flv = ⎜ ⎟ WV ⎝ ρL ⎠ 0.5 L MWL ⎛ ρV ⎞ = ⎜⎜ ⎟⎟ V MWV ⎝ ρL ⎠
⎛ ⎞0.5 p L ⎟⎟ = MWL⎜⎜ V ⎝ RTMWVρL ⎠
(10b)
(11)
From eqs 7e, 7f, and 7g capital cost depends on area, column height, and the number of stages or packing height. Thus, the two-enthalpy feed rectifier will reduce the capital cost if the area decreases more than hcolumn and either N or hpacking increase. 2.2. Reducing Energy Use. Three approaches have been identified that might be applicable to reduce the energy requirements. First, Soave and Feliu4 reduced energy use by using the bottoms to heat a portion of a liquid feed. The analogous operation for the two-enthalpy feed rectifier with a partial condenser is to use a portion of the vapor distillate to condense part of the vapor feed. Although in theory this will work, the fraction of liquid produced will be quite small because D/F is usually small and CP,VΔT ≪ λ. Second, in the previous section I showed that in many cases the two-enthalpy feed rectifier can reduce the volume and cost of the column compared to a standard rectifier when both systems have identical purities and D/F. We can trade capital savings to cause energy savings by decreasing the column diameter and simultaneously increasing the number of stages to keep the total volume constant. With constant xD (or yD with a partial condenser), increasing the number of stages in the twoenthalpy feed rectifier will allow operation at a lower effective reflux ratio, which lowers the value of xB and increases D/F. With a partial condenser, eq 3c shows this automatically reduces Qcond,2F if f L is constant. For a total condenser with constant f L , Q cond,2F is constant but Q cond,2F /D, the condensation energy per kilomole of product, is reduced. In some cases it is possible to achieve modest reductions in column cost and energy use simultaneously. Third, when the column is operated at lower than designed feed rates, the fraction of feed that is liquid f L is reduced and eventually set to zero. With less or no liquid feed, the column is overdesigned in the sense that it has too many stages for the design D/F value. The result will be higher purity than required if the reflux ratio is unchanged. The alternative is to reduce the
(8c)
The flow parameter W ⎛ρ ⎞ Flv = L ⎜⎜ V ⎟⎟ WV ⎝ ρL ⎠
(10a)
Everything else being equal, the change in Csb reduces the diameter in the top section of the two-enthalpy feed rectifier and increases the diameter in the bottom section. However, in all of the simulations discussed later, the change in vapor flow rate was the dominant effect and the cross-sectional areas observed were approximately
0.2
Csb is determined from a graph or from an equation. example, with 0.6096 m (24 in.) tray spacing10
(9c)
With the assumptions made, the vapor flow rate is constant throughout each column section, and
(8a)
10
(pρL )0.5
From eq 9c the column area appears to be directly proportional to the vapor flow rate. Because the vapor flow rate in the 2F rectifier is (1 − f L)F instead of F, the area should be reduced by (1 − f L). However, Csb is different in the different rectifiers. The two-enthalpy feed rectifier has a lower L/V in the top of the column and a higher L/V in the bottom of the column than a standard rectifier. Csb increases as L/V decreases, until Csb reaches an asymptotic value at low values of FLV.9,10 Thus, for f L > 0,
(7g)
⎛σ ⎞ u flood = Csb⎜ ⎟ [(ρL − ρV )/ρV ]0.5 ⎝ 20 ⎠
0.2
( 20σ )
η(frac)Csb
8
uop = (frac)u flood
V (RTMWV )0.5
(9b)
In addition, the variation of the surface tension σ can often be ignored and an average value can be used. Then, 9161
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Table 1. Results of Rectifier Simulations for Argon−Oxygen Separation with Aspen Plusa feed stage
D, kmol/h
Qc,feed,2F kJ/s
Qc,standard or Qcond,2F kJ/s
feed rate, kmol/h
N
fL
1000 1000 1000 1000 1000 830.8 830.8 1000 1000 726 1000 800
36 36 38 39 39 39 39 43 43 43 47 47
0 0 0.134 0.169 0.169 0 0 0.274 0.274 0 0.326 0.157
A1d-td
674.5
47
0
0.994
18.73
0.0744
0
−1225
A1 d-td-En
674.5
47
0
0.980
22.01
0.0703
0
−1220
A1-base†-retrofit
1377.4
43
0.274
0.980
38.22
0.0749
A1a-En A1b-En A1c-En A1d-En
1000 1000 1000 1000
41 43 49 52
0.134 0.169 0.274 0.326
A2-base A2a A2b A2c A2d A2e A2a-EN A2b-EN A2c-EN
1000 1000 1000 1000 1000 1000 1000 1000 1000
38 40 41 42 43 44 42 44 45
0 0.103 0.132 0.160 0.185 0.205 0.103 0.132 0.160
A3-base A3a A3b A3c A3a-EN A3b-EN A3c-td
1000 1000 1000 1000 1000 1000 840
41 44 45 47 45 46 47
0 0.100 0.125 0.160 0.100 0.125 0
840
47
0
1000 1000 1000
47 49 50
run A1-base A1-base† A1a A1b A1b† A1b-td A1b-td-En A1c A1c† A1c-td A1d A1d-td-p
A3c-td-EN
A4-base A4-a A4-b
yD,MVC
xB,MVC
Base 1: D/F = 0.02775, which is L/D = 1.196 × (L/D)CMO,min 0.980 27.75 0.0749 0 −1817 0.980 27.75 0.0749 0 −1817 35 0.980 27.75 0.0749 −227.6 −1589 36 0.980 27.75 0.0749 −316 −1501 36 0.980 27.75 0.0749 −316 −1501 0.986 23.06 0.0747 0 −1509 0.980 25.48 0.0722 0 −1505 39 0.980 27.75 0.0749 −511.3 −1306 39 0.980 27.75 0.0749 −511.3 −1306 0.991 20.16 0.0746 0 −1319 40 0.980 27.75 0.0749 −607.4 −1209 40 0.991 22.21 0.0745 −235.1 −1218
39
−704.2
−1798
36 0.98 30.00 0.0728 −227.6 −1585 37 0.980 30.20 0.0726 −315.3 −1497 40 0.980 29.77 0.0730 −511.3 −1302 42 0.980 28.81 0.0739 −608.3 −1206 Base 2: D/F = 0.0299, which is L/D = 1.107 × (L/D)CMO,min 0.980 29.9 0.0729 0 −1813 36 0.980 29.9 0.0729 −174.9 −1638 36 0.980 29.9 0.0729 −246.3 −1567 37 0.980 29.9 0.0729 −298.5 −1514 37 0.980 29.9 0.0729 −345.2 −1468 38 0.980 29.9 0.0729 −382.5 −1430 36 0.980 30.85 0.0720 −192.2 −1619 37 0.980 31.18 0.0717 −246.3 −1564 37 0.980 31.07 0.0718 −298.5 −1512 Base 3: D/F = 0.03165, which is L/D = 1.044 × (L/D)CMO,min 0.980 31.65 0.0712 0 −1810 37 0.980 31.65 0.0712 −169.8 −1640 37 0.980 31.65 0.0712 −208.9 −1601 38 0.980 31.65 0.0712 −271.7 −1538 37 0.980 31.87 0.0710 −169.8 −1640 37 0.980 31.78 0.0711 −233.2 −1576.3 0.989 26.586 0.0709 0 −1520 0.980
27.42
0.0703
0
−1518.8
Base 4: D/F = 0.032637, which is L/D = 29.64,or L/D = 1.012 × (L/D)CMO,min 0 0.980 32.637 0.0703 0 −1808.1 0.0425 36 0.980 32.637 0.0703 −79.3 −1728.7 0.060 36 0.980 32.637 0.0703 −112.0 −1696
max diam, m
max area, m2
vol, m3 ( vol/vol base)
1.562 1.92 44.4 1.945 2.97 34.4 1.463 1.68 41.0 (0.923) 1.423 1.59 39.7 (0.895) 1.772 2.46 30.8 (0.896) same as A1b, operates 80.11% flood 1.423 1.59 39.7 1.346 1.42 39.0 (0.88)b 1.67 2.20 30.2 (0.88)† same as A1c, operates 78.12% flood 1.308 1.34 40.0 (0.90) same as A1d, 76.84% to 73.90% flood same as A1d, 76.98% to 73.71% flood same as A1d, 76.85% to 73.67% flood same as A1-base†, need alternative to sieve trays. 1.462 1.68 44.0 1.422 1.59 43.6 1.346 1.42 44.3 1.308 1.34 44.2 1.561 1.486 1.454 1.430 1.409 1.395 1.486 1.454 1.430
1.92 1.73 1.66 1.61 1.56 1.53 1.73 1.66 1.61
46.7 44.4 (0.95) 43.5 43.1 42.8 (0.92)b 42.9 46.4 46.5 46.1
1.561 1.91 50.1 1.488 1.74 48.8 (0.97) 1.471 1.70 48.7 (0.97)b 1.442 1.63 48.8 (0.97) 1.488 1.74 49.9 1.471 1.70 49.7 same column A3c QC/D same as A3-base same column A3c QC/D 3.1% less A3-base 1.561 1.527 1.513
1.91 1.83 1.80
57.2 56.9 (1.0)b 57.0
a
The feed is 10 mol % argon. VLE uses the Peng−Robinson correlation. Fresh feed rate = 1000 kmol/h, except where listed otherwise. N and feed stage are reported in Aspen Plus notation. The error tolerance for Aspen Plus runs is 1.0 × 10−6. Except for turn-down (td) runs, operation is at 80% flood using the Fair correlation for diameters.9 p = 1.0 atm. Partial condenser. The spacing between trays is 0.6096 m except for runs marked with † where the spacing is 0.3048 m. The space for two trays is added to the height for disengagement. bThe lowest column volume for given feed with tray spacing = 0.6096 m.
reflux ratio, which increases D/F and reduces Qc,total,2F/D. This alternative is explored further in section 3.3.
including estimation of the diameter required. The systems studied were argon−oxygen, methanol−water, and light hydrocarbons. The rectifier calculations were first done for the standard rectifier (base case) by adjusting the number of stages and the distillate flow rate to match the target for the distillate mole fraction. For the constant purity runs there are
3. DETAILED SIMULATIONS FOR RECTIFIERS 3.1. Identical Product Purity Simulations. The commercial Aspen Plus simulator was used to do detailed simulations 9162
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Base case 1 designs were done with both a 0.6096 m (24 in.) (run A1-base) and a 0.3048 m (12 in.) (run A1-base†) tray spacing. As expected, the smaller tray spacing resulted in a shorter-fatter design with lower tower volume. The twoenthalpy feed rectifier with N = 39 (Aspen notation) was designed with both tray spacings (runs A1a and A1a†). As expected, the lower tray spacing again produced a lower column volume; however, the ratios (volume A1a)/(volume A1-base) = 0.895 and ratio (volume A1a†)/(volume A1-base†) = 0.896 are essentially identical. This comparison was repeated for runs A1b and A1b† and both ratios were 0.88. Thus, volume ratios could be compared even though the tray spacing differed. The two-enthalpy feed rectifier with N = 43 (run A1b), had the maximum reduction in the column volume (12.1%) with 27.4% of the vapor feed condensed and fed as liquid. Volume was decreased despite having more stages because the maximum diameter decreased from 1.562 m for the standard design to 1.346 m in the two-enthalpy feed rectifier. In addition to reducing the column volume or energy requirements (explored in section 3.3), the two-enthalpy feed rectifier can have two additional advantages compared to the standard rectifier design. The temperature of the top condenser in run R1-base for the argon−oxygen separation in the standard rectifier is 87.3 K. In run A1b the top condenser is at the same temperature, but only 71.9% of the cooling load is done at this temperature. The remaining 28.1% of the cooling is used to condense the feed, which condenses at 89.5 K. Doing a portion of the condensation at a higher temperature, can be an advantage particularly in refrigerated systems. The third advantage is two-enthalpy feed rectifiers have excellent turn-down properties (separation obtained varies little for feed rates below the design value). This is illustrated in Table 1 for argon−oxygen separation. Runs A1b-td (td = turndown), A1c-td, A1d-td, and A1d-td-p (td-p is for partial turndown) explore turn-down by assuming that the original twoenthalpy feed design was A1b, A1c, or A1d, respectively. All original designs were designed for a total feed rate of 1000 kmol/h. If a lower feed rate is required, this can be accommodated up to a point by reducing the liquid flow rate. Runs A1b-td, A1c-td, and A1d-td had the fresh feed rate set at the vapor feed rate, FF = (1 − f L)F, from runs A1b, A1c, and A1d, respectively. The cooling in the condensers was set so that Qc/(fresh feed rate) is the same as in A1-base. These three turn-down runs operate with no liquid feed. Note that, when operated in the columns designed for the two-enthalpy feed rectifiers, the Aspen tray rating program shows that all turneddown columns are operating at a maximum percentage of flood that is not far from the 80% design factor; thus, we would expect the stage efficiencies will be close to the design stage efficiencies. In addition, although now operating in the same mode as a standard rectifier, the two-enthalpy feed rectifiers were designed with more stages than the standard rectifier. As a result, the distillate product is purer than in the designs operating at design flow rates. Reducing the reflux rate (increasing D/F) to reduce energy use during turn-down operation is explored in section 3.3. Reductions in feed rate to values less than reported in Table 1 for the td runs will reduce the vapor velocity and the stage efficiency will depend on the performance characteristics of the tray. Run A1d-td-p explores the case where the desired feed rate (arbitrarily chosen as 800 kmol/h) is between the feed rates for runs A1d and A1d-td. Initial operating conditions can be obtained by operating this column at the same vapor flow rate
several methods to design the two-enthalpy feed rectifier. Perhaps the easiest is to first specify the distillate rate. Initial values for the fraction of the feed condensed f L, number of stages N, and liquid feed stage were selected and the simulation was run to obtain the distillate mole fraction. The optimum feed stage for the condensed liquid was determined as the feed location that maximized the distillate mole fraction of the MVC. Fortunately, the optimum feed locations varied in a predictable fashion. Once a reasonable number of stages was determined, the value of f L was adjusted until the exact (to 10−4 mole fraction or closer) target value for the distillate mole fraction was obtained. This approach was fairly fast, but Qtotal,2F did not always exactly match Qc,standard and xB sometimes varied slightly from run to run. A more exact match of energies and xB values was obtained by setting the condenser energy in the column specifications. An initial value for the fraction of the feed condensed f L was selected and the simulation was run to obtain the value of Qc,feed,2F from the simulation of the feed condenser. Because total energy use in the standard and two-enthalpy feed rectifiers must be the same for equal purities, Q cond,2F = Q c,standard − Q c,feed,2F
(12)
Qcond,2F was used as the operating specification for the twoenthalpy feed rectifier simulation. Each new value of f L required a calculation of Qc,feed,2F and Qcond,2F. The largest column diameter and cross-sectional area of the column were obtained from Aspen Plus. The column volumes were calculated with a height determined from eqs 7a and 7b with an arbitrary overall efficiency of 1.0 (equilibrium stages), an arbitrary tray spacing of either 0.6096 or 0.3048 m, and extra height for disengagement equal to twice the tray spacing. h = (Nreal + 2) × (tray spacing)
(13)
The volumes reported do not correspond to a specific real system. However, the simulations for the argon−oxygen system (Table 1) and the ternary system (Table 3) show that the ratio (volume 2F rectifier)/(volume standard rectifier) is insensitive to plate spacing. Thus, this ratio allows comparison of the standard and two-enthalpy feed rectifiers. Argon is usually produced in an air separation unit (ASU) by first removing the nitrogen and then sending the resulting argon−oxygen mixture from the low pressure column to a rectifying column.11 Argon is the MVC and is produced as the distillate product. The bottoms are typically returned to the low pressure main column. Oxygen is usually the principal product of an ASU, and argon product rates are highly correlated with oxygen demand. Because oxygen demand is cyclic, the argon column often has to operate at feed rates lower than the design feed rate. For the purpose of this study the focus was on the use of a two-enthalpy feed system and the argon−oxygen column was equipped with trays and a partial condenser. In practice, a low pressure drop structured packing would probably be used to produce a 98% distillate product from the 10 mol % argon− 90% oxygen feed.10 Table 1 shows three base case designs. The different base cases have different values of M, the multiplier times the minimum reflux ratio calculated assuming CMO is valid. On the basis of CMO, a value of (L/D)min,CMO = 29.3 was calculated. A nominal value of M was chosen and the appropriate number of stages for the base case design was determined. Then M was varied until the desired purities were obtained. For example, in base case 1 the initial value of M was 1.20, and the final value was 1.196. 9163
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Table 2. Results of Rectifier Simulations for Methanol−Water Separation with Aspen Plusa feed stage
yd,MVC
0 0.385 0.457 0.505 0.538 0.565 0 0.507 0.385
8 8 8 9 9 11 9 8
0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
10 12 14 16
0 0.325 0.442 0.502
8 8 9
0.999 0.999 0.999 0.999
1000 1000 1000 1000
10 12 14 16
0 0.240 0.340 0.394
8 9 10
0.999 0.999 0.999 0.999
M60-base M60a M60b
1000 1000 1000
10 12 14
0 0.160 0.235
8 10
0.999 0.999 0.999
M2-base M2a M2b M2c M2c-En M2c-Vol-VEn
1000 1000 1000 1000 1000 1000
10 12 14 16 34 30
0 0.528 0.625 0.671 0.671 0.671
9 9 10 11 9
0.999 0.999 0.999 0.999 0.999 0.999
run
F
N
fL
M10-base M10a M10b M10c M10d M10e M10-95V-base M10-95Va M10a-En
1000 1000 1000 1000 1000 1000 1000 1000 1000
10 12 13 14 15 16 11 17 17
M20-base M20a M20b M20c
1000 1000 1000 1000
M40-base M40a M40b M40c
D, kmol/h M10. Feed 69.94 69.94 69.94 69.93 69.95 69.92 69.92 69.92 71.54 M20. Feed 141.35 141.35 141.35 141.37 M40. Feed 284.4 284.4 284.4 284.4 M60. Feed 425.1 425.1 425.1 M2. Feed 13.0 13.0 13.0 13.0 14.175 14.06
XB,MVC
Qc,feed,2F, kJ/s
10 mol % Methanol 0.0324 0 0.0324 −4326 0.0324 −5135 0.0324 −5674 0.0324 −6045 0.0324 −6348 0.0324 0 0.0324 −5410 0.0307 −4326 20 mol % Methanol 0.0685 0 0.0685 −3614 0.0685 −4915 0.0684 −5582 40 mol % Methanol 0.1619 0 0.1619 −2604 0.1619 −3690 0.1619 −4276 60 mol % Methanol 0.3050 0 0.3050 −1687 0.3050 −2477 2 mol % Methanol 0.00711 0 0.00710 −5976 0.00711 −7074 0.00710 −7594 0.00592 −7594 0.00604 −7594
Vol, m3 (vol/vol base)
Qc,standard or Qcond,2F, kJ/s
max diam, m
max area, m2
−10534 −6208 −5399 −4860 −4489 −4186 −9968 −4558 −6192
2.484 1.959 1.822 1.737 1.667 1.625 2.421 1.689 1.941
4.85 2.96 2.61 2.37 2.21 2.07 4.60 2.24 2.96
35.5 25.8 24.1 23.1 22.9 22.7 36.5 25.9 34.3
−9711 −6097 −4796 −4129
2.457 2.006 1.817 1.711
4.74 3.16 2.59 2.30
34.67 27.0 (0.78) 25.3 (0.73) 25.2 (0.73)b
−8046 −5441 −4356 −3770
2.397 2.070 1.917 1.829
4.51 3.37 2.89 2.63
32.99 28.8 (0.87) 28.2 (0.85)b 28.9 (0.87)
−6374 −4687 −3896
2.327 2.112 2.002
4.25 3.50 3.15
31.1 29.9 (0.96)b 30.7 (0.99)
−11186 −5210 −4113 −3592 −3580 −3581
2.505 1.719 1.531 1.434 1.433 1.434
4.93 2.32 1.84 1.62 1.61 1.61
36.1 19.8 18.0 17.8 35.4 31.5
(0.71) (0.68) (0.65) (0.65) (0.64)b (0.71)
(0.55) (0.50) (0.49)b (0.98) (0.87)
a
VLE used the NRTL correlation. Fresh feed rate = 1000 kmol/h, except where listed otherwise. The feed is saturated vapor except feeds labeled 95 V are 95% vapor and 5% liquid. N and feed stage are reported in Aspen Plus notation. The error tolerance for Aspen Plus runs is 1.0 × 10−6. Except for turn-down (td) runs, operation is at 80% flood using the Fair correlation for diameters.9 p = 1.0 atm. Partial condenser. The spacing between trays is 0.6096 m. The space for two trays is added to the height for disengagement . bThe lowest column volume for given feed with tray spacing = 0.6096 m.
as run A1d, which was 1000(1 − f L) = 1000 (1 − 0.326) = 674 kmol/h. Because for run A1d-td-p we want a total feed rate of 800 and the vapor flow rate is 674, FL = 800 − 674 = 126 kmol/h of feed is condensed in the feed condenser. The energy required to condense this amount of feed Qc,feed,2F is determined from the Aspen Plus heater block. The total amount of energy per kmol/h of feed was set equal to the amount used in the standard rectifier, run A1-base. This allows calculation of Qc,total,2F and the energy available in the column condenser, Qcond,2F = Qc,total,2F − Qc,feed,2F. As expected, the values of f L, yAr,D, D, and xAr,B for run A1d-td-p are between the values obtained for runs A1d and A1d-td. The two-enthalpy feed rectifier operated successfully with larger fractions of the feed condensed for the easier methanol− water separation (Table 2). The operating point that minimized the column volume for the 10% and 20% methanol feeds occurred when more than 50% of the feed was condensed. In agreement with the qualitative analysis, increasing the feed concentration of MVC reduced the amount of feed that could be condensed and there was less reduction in column volume. For a 10 mol % methanol feed, the run with the largest decrease in column volume (M10e) resulted in a 36% decrease in column volume compared to that with a standard rectifier
whereas for a 60 mol % methanol feed, (M60a) reduced the volume compared to that with a standard rectifier by only 4%. The turn-down ratios based on setting f L = 0 are also larger at lower concentrations of methanol in the feed, although the turn-down ratios are significant even for a 40% methanol feed (runs M40b and M40c). The feed does not have to be a saturated vapor. Superheated vapors and two-phase feeds with a small amount of liquid can also be processed in the two-enthalpy feed rectifier. With a twophase mixture the entire feed is split into two parts. One part is condensed and the other part can be fed as the vapor feed. Run M10-95V-base (Table 2) is a repeat of run M10-base but with a feed that is 95% vapor. Run M10-95Va simulated the same feed in a two-enthalpy feed rectifier. Comparing these two runs to M10-base and M10c, respectively, the separation of the partially liquid feed required more stages but less energy. The twoenthalpy feed rectifier required more stages but was a smaller diameter and smaller total volume than run M10-95V-base. If the feed is all liquid, part of it would have to be vaporized to use a two-enthalpy feed rectifier and all of the feed would be vaporized for a normal rectifier. A regular column with a condenser and reboiler uses significantly less energy for a 10% methanol liquid feed (simulations not shown). Two-phase 9164
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Table 3. Results of Rectifier Simulations for Ternary Hydrocarbon Separation with Aspen Plusa run
N
fL
T-base T-base† Ta Tb Tb† Tc Td
10 10 12 14 14 15 16
0 0 0.373 0.500 0.500 0.541 0.567
feed stage
yd,MVC
D, kmol/h
XB,MVC
Qc,feed,2F, kJ/s
Qc,standard or Qcond,2F, kJ/s
max diam, m
max area, m2
vol, m3 (vol/vol base)
7 8 8 8 8
0.995 0.995 0.995 0.995 0.995 0.995 0.995
76.45 76.45 76.45 76.45 76.45 76.43 76.45
0.0259 0.0259 0.0259 0.0259 0.0259 0.0259 0.0259
0 0 −2965 −3974 −3974 −4300 −4507
−7288 −7288 −4323 −3313 −3313 −2988 −2781
3.250 4.046 2.691 2.464 3.054 2.384 2.332
8.29 12.9 5.69 4.77 7.33 4.46 4.27
60.6 47.2† 48.6 (0.80) 46.5 (0.77) 35.7 (0.76)† 46.2 (0.76)b 46.9 (0.77)
a Ternary consists of n-C4, n-C5, n-C6. The feed is 10 mol % n-C4 and 60 mol % n-C5. Fresh feed rate = 1000 kmol/h. Feeds are saturated vapor. N and feed stage are reported in Aspen Plus notation. VLE uses the Peng−Robinson correlation. Error tolerance for Aspen Plus runs is 1.0 × 10−6. Except for turn-down (td) runs, operation is at 80% flood using the Fair correlation for diameters.9 p = 1.0 atm. Partial condenser. The spacing between trays is 0.6096 m except for runs marked with † where spacing is 0.3048 m. The space for two trays is added to the height for disengagement. bThe lowest column volume for given feed with tray spacing = 0.6096 m.
3.2. Retrofitting Rectifying Columns to Two-Enthalpy Feed Configuration with Identical Purities. Retrofitting to increase the column throughput is of considerable interest. In this case the column dimensions are fixed and we need to add a feed stage and in most cases additional stages. This will require retraying the column or use of a more efficient packing. As a case study, assume that we wish to increase the capacity of existing rectifying column A1-base†, and that by suitable modifications of the internals we can increase the number of equilibrium stages to 43 with a feed stage located at stage 39. Thus, the column has the stages of the column in run A1b†, but the dimensions of A1-base†. The column condenser has the capacity of the condenser in A1-base†. How much increase in feed capacity can we obtain? A reasonable first design can be obtained by setting f L = 0.274 (the value in run A1b†) and then requiring that the vapor flow rate FV = Fretrofit(1 − f L) = FA1base† = 1000 kmol/h. Solving for the new total feed rate we obtain Fretrofit = 1377.4 kmol/h. With the same argon purity yD,Ar = 0.980, we can find the distillate flow rate from the ratio Dretrofit/Fretrofit = (D/F)R1base† = 27.75/1000, which gives Dretrofit = 38.22 kmol/h. Using the dimensions of A1-base† with these values for f L, Fretrofit, and Dretrofit in Aspen Plus the results shown in Table 1 for run A1base†-retrofit are obtained. The column condenser needs to remove slightly less energy than in run A1-base†. A new feed condenser capable of condensing 377.4 kmol/h of feed (QF,cond = −704.2 kJ/s) will be required. If the new trays have the same hydraulic characteristics of sieve trays, with a new tray spacing of 0.2574 m, the Aspen Plus tray rating utility shows a maximum percentage of flood of 87.4% at tray 39 (the feed stage). The lowest percent flooding is 82.1% at the tray above the feed stage. The largest (downcomer backup)/(tray spacing) = 0.575. Thus, the column should operate but might be cranky. A better solution is to use trays or packing with better hydraulic characteristics than sieve trays. For example, according to the Aspen Plus tray rating utility Glitsch Ballast trays with valve type V-1 and a tray spacing of 0.2574 m will have a maximum of 75.5% flood on tray 2 and a maximum ratio downcomer backup to tray spacing of 0.55 on tray 39. Thus, if the additional seven equilibrium stages can be added to the base rectifier, the capacity can be increased by 37.7%. 3.3. Reducing Energy Use. Argon−oxygen simulations will be used to illustrate reduction in energy. By fixing the diameter at the reduced size determined for the two-enthalpy feed rectifier and increasing the number of stages, we can increase D/F and reduce Qc,total,2F/D by trading capital cost savings for energy savings with constant distillate product
feeds that are mostly liquid should probably also be sent to a regular column. The 2 mol % methanol feed runs are of interest for a number of reasons. Remarkably, it is possible to condense more than two-thirds of the feed and the column volume can be reduced by more than 50% (run M2c). Feed concentrations this low are often considered to be too low for distillation because the column volume and the amount of cooling required per kilogram of product are quite high. Keller12 recommends considering adsorption instead of distillation for dilute feeds ( 0 saves energy, but less energy than operation with f L = 0 (simulations not shown).
diameters for the standard stripper varied from 2.80 m at the top to 2.92 m at the bottom. Because the results for the standard pentane−hexane strippers show very little change in diameter, there is not much room for improvement. The best results for the two-enthalpy feed stripper for pentane−hexane separation (run S1a) showed a 1.7% reduction in the column volume by vaporizing 10% of the feed. In a complete distillation column the acetic acid−water system can show a 2-fold increase in diameter at the bottom of the column compared to at the top.7 The base case for the standard rectifier with a 10 mol % acetic acid feed had calculated column diameters of 1.78 and 3.12 m at the top and bottom, respectively. The corresponding calculated column diameters for the 25% acetic acid feed were 1.84 and 2.96 m. Thus, for the acetic acid−water separation there is some room for improvement. The best volume reduction result obtained for the two-enthalpy stripper was run S4c with a 2.7% reduction in column volume for a 25% acetic acid feed with 13.5% of the feed vaporized. This stripper can be operated for increased turn-down with f v = 0 and the fresh feed rate reduced from 1000 to 865 kmol/h. The two-enthalpy feed stripper may be useful in special circumstances, but in general it appears much less useful than the two-enthalpy feed rectifier.
4. STRIPPING COLUMNS Because the two-enthalpy feed method can be useful for complete columns with the largest diameter at the bottom of the column,7 it is reasonable to ask, is the two-enthalpy feed method useful for stripping columns? In a stripping column the liquid feed is sent to the top stage. The two-enthalpy feed stripper would take a fraction f V of the feed, vaporize it, and feed it lower in the column than the liquid feed. External mass and energy balances show that for identical feed rates and feed and product mole fractions (z, xB, and yD) the product flow rates B and D are the same for two-enthalpy feed and standard strippers, and the total heating duties are identical, Qreboiler,standard = Q2F,total = Qheat feed,2F + Qreboiler,2F. Because the temperature required to vaporize the feed is less than the reboiler temperature, it may be possible to use a less expensive energy source for feed vaporization. In the top of the stripper V = D; thus, because the D values are the same, the maximum V values are the same in the two designs. However, the vapor velocity is smaller at the bottom of the stripper for the twoenthalpy feed design. Unlike the two-enthalpy feed rectifier, for the two-enthalpy feed stripper to have a lower column volume, there has to be a significant diameter increase at the bottom of the standard stripper caused by variables other than vapor velocity. Many separations such as the distillation of light hydrocarbons and the separation of acetic acid and water require a larger diameter at the bottom of a complete column than at the top.6 The results of the Aspen Plus stripper simulations are shown in Table 4. For the 90 mol % n-pentane and 10 mol % n-hexane feed, the calculated diameters for the standard stripper varied from 3.11 m at the top to 3.19 m at the bottom. For a 50 mol % n-pentane and 50 mol % n-hexane feed, the calculated
5. DISCUSSION Ternary rectifier runs T-base and Tb were repeated to check the assumption that the ratio (volume 2F rectifier)/(volume standard rectifier) was insensitive to plate spacing. Runs Tbase† and Tb† were identical to runs T-base and Tb except the plate spacing was 0.3048 m (12 in.). This change does not affect the separation, but it changes the column dimensions significantly. The results in Table 3 (tray spacing of 0.3048 m is marked with †) show a significant reduction in volume of run T-base† compared to T-base and of Tb† compared to Tb. However, the ratio (volume Tb†)/(volume T-base†) = 0.76 is very close to the ratio (volume Tb)/(volume T-base) = 0.77. These results validate the assumption made earlier that these ratios would be close when columns with different tray spacings were compared. 9167
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(5) Beneke, D.; Hildebrandt, D.; Glasser, D. Feed Distribution in Distillation: Assessing Benefits and Limits with Column Profile Maps and Rigorous Process Simulation. AIChE J. 2013, 59, 1668. (6) Wankat, P. C. Balancing Diameters of Distillation Column with Vapor Feeds. Ind. Eng. Chem. Res. 2007, 46, 8813. (7) Wankat, P. C. Reducing Diameters of Distillation Column with Largest Calculated Diameter at the Bottom. Ind. Eng. Chem. Res. 2007, 46, 9223. (8) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaeiwitz, J. A.; Bhattacharyya, D. Analysis, Synthesis, and Design of Chemical Processes, 4th ed.; Prentice-Hall: Upper Saddle River, NJ, 2012; pp 962−963. (9) Fair, J. R. Gas Absorption and Gas-Liquid System Design. In Perry’s Chemical Engineers’ Handbook, 7th ed.; Perry, R. H., Green, D. W., Eds.; McGraw-Hill: New York, 1997; pp 13−23 to 13−38. (10) Wankat, P. C. Separation Process Engineering. Includes Mass Transfer Analysis, 3rd ed.; Prentice-Hall: Upper Saddle River, NJ, 2012. (11) McGuinness, R. M.; Kleinberg, W. T. Oxygen Production. In Oxygen-Enhanced Combustion, 2nd ed.; Baukal, C. E., Jr., Ed.; CRC Press: Boca Raton, FL, 2013; Chapter 3. (12) Keller, G. E., II. Adsorption, Gas Absorption, and Liquid-Liquid Extraction: Selecting a Process and Conserving Energy; Manual 9 in Industrial Energy Conservation; The MIT Press: Cambridge, MA, 1982.
In effect, the two-enthalpy feed rectifier partially decouples the vapor flow rate from the amount of feed input into the column. Starting with f L = 0, the number of stages required initially increases slowly while the calculated column area decreases linearly as f L is increased. Because keeping xD and D/ F constant makes Qc,total,2F constant, as f L increased, Qcond,2F decreased linearly, the internal reflux ratio (L/V)2F decreased following eq 4b, the column area decreases almost linearly, and the number of stages increased nonlinearly. In the three systems studied the column volume first decreased and eventually increased as f L increased. The Csb term in eq 9c has a small effect on the change in column area. If the required column area is larger at the bottom of the column than at the top (e.g., argon−oxygen and light hydrocarbons), this Csb effect causes the calculated area of the two-enthalpy feed rectifier to be slightly larger than the area predicted by eq 11. For example, eq 11 predicts that the area of run A1c in Table 1 is (1 − 0.274) (1.92) = 1.39 m2, but the detailed simulation gives an area of 1.42 m2. If the required column area is larger at the top of the column than at the bottom (e.g., methanol−water), the Csb effect in the top section reduces the required area compared to the prediction of eq 11. For example, eq 11 predicts the area of run M10e (Table 2) is (1 − 0.565)(4.85) = 2.11 m2, but the detailed simulations calculated 2.07 m2. The optimum operating conditions depend upon which of the advantages of the two-enthalpy feed rectifier are most important for a given separation. Usually, capital cost will be lowest at or near the minimum column volume. However, the column diameter continues to decrease as f L is increased past the point of minimum volume. If this further reduction in diameter allows shipping a shop fabricated column instead of requiring field fabrication, a design that allows shipping might be optimum. Operating costs are expected to be a higher percentage of annual costs than capital charges when refrigeration is required for the condenser. In this case the higher operating temperature of the feed condenser might be valuable, leading the designer to design at a higher value of feed fraction condensed than the value of f L that minimized column volume. If flexibility in turn-down of the feed flow rate is valuable, the designer might again opt for a higher f L value.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Parts of these results were presented orally at CHEMPOR 2011, Lisbon, Portugal, September 5−7, 2011.
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REFERENCES
(1) Humphrey, J. L.; Keller, G. E., II. Separation Process Technology, McGraw-Hill: New York, 1987. (2) Keller, G. E. Separations: New Directions for an Old Field; AIChE Monograph Series; AIChE: New York, 1987; Vol. 83, p 17. (3) Wankat, P. C.; Kessler, D. P. Two-Feed Distillation: Same Composition Feeds with Different Enthalpies. Ind. Eng. Chem. Res. 1993, 32, 3061. (4) Soave, G.; Feliu, J. A. Saving Energy in Distillation Towers by Feed Splitting. Appl. Therm. Engr. 2002, 22, 889. 9168
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