Cover Story
Part 1.
DISTILLATION:
Revisiting Some
Rules of Thumb
C. M. Lek
Singapore Armed Forces
G. P. Rangaiah and K. Hidajat
National University of Singapore
istillation is the most common
unit operation for separating
liquid mixtures into valuable
and/or high purity products. It
is also one of the most energyintensive operations. Hence, optimization of distillation-column design and
operation should get high priority.
Numerous distillation heuristics
(rules of thumb) for quick optimization have emerged over the years. For
instance, heuristics on optimal reflux
ratio as a certain multiple of the minimum reflux ratio have been widely
used as quick tools to estimate optimum reflux ratio.
However, changes over time in the
relative cost of equipment and energy
(which affects operating cost) can affect the validity of such rules of
thumb. Meanwhile, it has now become
more feasible to assess their validity,
as today’s availability of commercial
simulators and high-speed computers
allows rigorous and thus more-accurate distillation calculations be carried out with relative ease.
This article assesses the validity of
optimal-reflux-ratio and other heuristics in light of recent cost data, by considering seven binary and six multicomponent
systems.
Distillation
columns for each of the 13 have been
designed and optimized by both shortcut (heuristics-based) calculations
and rigorous simulations. In addition
to the reassessment, a key observa-
D
50
Heuristics regarding optimal reflux ratio and number
of stages, as well as the selection of the feed stage,
get some reassessment here, consistent with
changes in the relative costs of equipment and energy
tion emerges: that the cost of a column
designed by shortcut calculations can
be reduced substantially by optimizing the location of the feed stage.
Laying the groundwork
The reflux ratio is a key variable, affecting both the capital cost and the
operating cost of a column. As the reflux increases, the number of stages
and the column height both decrease
but the flowrates in the column and,
consequently, its diameter increase.
Despite that diameter increase, the
capital cost of the column generally
decreases as the reflux increases, because the savings in tower height
more than offset the cost of the increase in diameter. However this is
not the case at very high reflux ratios.
And as alternatives having successively higher reflux ratios are compared with each other, there is a particular, high ratio at which the capital
cost of the column begins to rise again
[7]. In addition, the capital as well as
the operating costs for the reboiler
and condenser will rise in proportion
to the vapor rate in the column.
Column optimization, therefore, reflects a balance between (1) the capital cost, which decreases (to a certain
point, as just discussed) as reflux increases, and (2) the operating cost,
which increases as the reflux increases. The total cost is minimum at
an intermediate reflux ratio.
CHEMICAL ENGINEERING WWW.CHE.COM SEPTEMBER 2004
Generally speaking, the number of
theoretical stages at the optimal reflux
has been stated as being on the order
of twice the minimum number of theoretical plates (corresponding to total
reflux), and the optimal reflux ratio,
Ropt, as being in the range of 1.1 to 1.5
times the minimum reflux ratio, Rmin
[1]. A study described in this magazine
over 30 years ago [19] evaluated a
large number of cases, mainly via
shortcut methods, and stated that Ropt
lies between 1.1 and 1.6 times Rmin,
the lower value being favored by high
relative volatilities. Conversely, relative volatilities closer to unity and
sharper separations were said to require higher values of Ropt/Rmin within
the above range. Since then, many articles and books have recommended
estimates of Ropt/Rmin for various situations, as summarized in Table 1. The
range of recommended Ropt/Rmin values in the open literature is 1.05 to 1.6,
with the lower value for systems involving refrigerants and the higher
value for systems using cooling water.
Despite the diversity in ranges in
Table 1, the use of a rule-of-thumb on
optimal reflux ratio as a certain multiple of the minimum reflux ratio has
been widespread and, indeed, has
proved beneficial over recent decades
as a quick method to estimate optimum reflux ratio. But as mentioned
earlier, the relative costs of equipment
and energy (which affects utilities)
Example
No.*
1
2
3
4
5
6
7
Components
Benzene
Toluene
i-Butane
n-Butane
Propylene
Propane
Acetone
Water
n-Hexane
p-Xylene
Methanol
1,4-Dioxane
Methanol
Water
TABLE 2. DETAILS OF BINARY EXAMPLES
Feed Mole
Feed
Column
Fraction
Conditions
Pressure
0.45
700 lb-mol /h,
Pcond : 0.98 atm
0.55
1 atm , sat. liq.
Preb : 1 atm
0.233
30,000 bbl/d,
Pcond : 42 psia
0.767
50 psia, sat. liq.
(refrigerant)
Preb : 50 psia
0.5045
84.2 m3/d,
Pcond : 1.798 MPa
0.4955
1.86 MPa, sat. liq.
Preb : 1.86 MPa
0.5
500 lb-mol /h,
Pcond : 0.98 atm
0.5
1 atm, 55% vap
Preb : 1 atm
0.55
200 kmol/h,
Pcond : 0.98 atm
0.45
1 atm, 50% vap
Preb : 1 atm
0.54
10,000 lb/h,
Pcond : 0.98 atm
0.46
1 atm, sat. liq.
Preb : 1 atm
0.7
12,000 lb/h,
Pcond : 0.98 atm
0.3
1 atm, sat. liq.
Preb : 1 atm
Product Purity
Specifications (mole%)
Top : 92% Benzene
Btm : 95% Toluene
Top : 91.7% i-Butane
Btm : 90% n-Butane
Top : 96.2% Propylene
Btm : 91.1% Propane
Top : 91% Acetone
Btm : 97.8% Water
Top : 95% n-Hexane
Btm : 97% p-Xylene
Top : 99% Methanol
Btm : 98% Dioxane
Top : 99% Methanol
Btm : 99% Water
*Sources for Examples: 1 and 2 from Peters and Timmerhaus (1991); 3 and 4 from King (1980); 5 to 7 from Doherty and Malone (2000).
Items in italics indicate unavailable specifications, or ones modified to allow column optimization by varying the reflux ratio.
Thermodynamic package used: Peng-Robinson for Eamples 1, 2, 3 and 5; and NRTL for Examples 4, 6 and 7.
Cooling water for cold utility unless stated otherwise.
Pcond = pressure at condenser; Preb = pressure at reboiler
have been changing, particularly during the latter years of that time period.
Furthermore, some of the early studies on optimal reflux ratio were based
on shortcut calculation methods or
graphical correlations, whereas today,
rigorous calculations (with more-accurate results) can be made with ease.
Such calculations can assess the
suitability of the heuristics on optimum reflux ratio with current cost
data and, if necessary, update those
heuristics. Furthermore, it is possible
to determine whether, and how, the
capabilities of commercial simulators
for rigorous distillation simulation
can also be used for optimizing reflux
ratio. Both of these questions are addressed in what follows, by considering industrially relevant applications
that involve both binary and multicomponent mixtures. Along the way,
we also scrutinize the validity of some
other heuristics for distillation-column design.
Equations and data for sizing and
costing of columns, including reboilers
and condensers, are taken from the
open literature. This study is limited
to simple (but not necessarily binary)
columns, each with a single feed
stream and two product streams.
Examples and procedures
The 13 distillation examples also come
from the open literature, for the most
part. Seven examples have two com-
TABLE 1. RECOMMENDED VALUES FOR THE
OPTIMUM-TO-MINIMUM REFLUX RATIO IN THE LITERATURE
Reference
Van Winkle and Todd,
1971 [19]
Brian,1972 [1]
Frank,1977 [4]
Zdonik,1977 [21]
King,1980 [7]; Walas, 1987 [20]
Thompson,1980 [15]
Perry, others, 1997 [13]
McCormick and Roche,
1979 [9]
McCormick and Roche,
1997 [10]
Peters, others, 2003 [12]
Ropt/Rmin
1.1 to 1.6
1.1 to 1.5
1.05 to 1.1
1.1 to 1.2
1.2 to 1.3
1.25
1.1 to 1.2
1.2
1.2 to 1.3
1.1 to 1.5
1.1 to 1.2
1.2 to 1.4
1.05 to 1.10
1.10 to 1.20
1.2 to 1.5
1.4 to 1.5
1.05 to 1.2
Remarks
Lower values for high relative
volatilities
Low-level refrig. (< -150°F)
High-level refrig.
Water- and air-cooled condensers
Generally accepted
With increased energy costs
Common fractionators
Petroleum-distillation columns
Refrig. is involved
Cooling-tower water used in condensers
Low-level refrig. (-300 to -150°F)
High-level refrig. (-150 to 50°F)
Cooling water
Air cooling
1.2 to 1.25
ponents (Table 2); the others involve
multiple components (Table 3). Besides showing the components, Tables
2 and 3 specify feed conditions, column pressure and product specifications for each system. In a few cases,
the specifications were either unavailable in the original references or were
modified to suit the needs of this study
(for instance, the reflux ratio should
not have a specified value).
The selected examples cover a wide
range of design and operating conditions. Some operate at high pressures,
others at atmospheric pressure. A few
require a refrigerant as the cold utility. The number of stages for the examples ranges from 9 (short columns)
to more than 100 (tall columns).
Steady state simulation and design
of column for each example is done
using HYSYS, the simulation system
CHEMICAL ENGINEERING WWW.CHE.COM SEPTEMBER 2004
51
Example
No.*
Components
8
Nitrogen
CO2
Methane
Ethane
Propane
i-Butane
n-Butane
Propylene Oxide
Propylene Glycol
Water
Propene
Propane
1-Butene
n-Butane
n-Pentane
Acetone
Methanol
Ethanol
Water
1-Butanol
Propylene
Propane
1,3-Butadiene
n-Butane
n-Pentane
Ethane
Propylene
Propane
Propadiene
n-Butane
9
10
11
12
13
TABLE 3. DETAILS OF MULTICOMPONENT EXAMPLES
Feed
Feed
Column
Mole
Conditions
Pressure
Fraction
0.0020
140.85 kmol/h,
Pcond : 1,378 kPa
0.0046
4,000 kPa,
(refrigerant)
0.2412
sat. liq.
partial condenser
0.2576
(vapor distillate)
0.2561
Preb : 1,413 kPa
0.1219
0.1166
0.0129
618.5 kmol/h,
Pcond : 103 kPa
0.2296
120 kPa, sat. liq.
Preb : 117 kPa
0.7575
0.2158
1,000 lb-mol/h,
Pcond : 97 psia
0.1817
100 psia,
(refrigerant)
0.2010
sat. liq.
Preb : 100 psia
0.2312
0.1703
0.20
1,000 kmol/h,
Pcond : 0.98 atm
0.20
101.3 kPa,
Preb : 1 atm
0.20
sat. liq.
0.20
0.20
0.0005
538 m.t./d,
Pcond : 431.5 kPa
0.0002
6.29 atm,
Preb : 470.7 kPa
0.3060
sat. liq.
0.4160
0.2773
0.0005
15m.t./h,
Pcond : 1,380 kPa
0.9500
1,457.4 kPa,
Preb : 1,450 kPa
0.0450
sat. liq.
0.0030
0.0015
Product Purity
Specifications
(Mole %)
Top : 0.6% n-Butane
Btm : 2% Propane
Top : 2 X 10-5 %
Propylene Glycol
Btm : 0.5% Water
Top : 4.74% 1-Butene
Btm : 2.54% Propane
Top : 2% Ethanol
Btm : 2% Methanol
Top : 1% n-pentane
Btm : 1% n-butane
Top : 2% Propane
Btm : 50% Propene
*Sources of Examples: 8 and 9 from HYSYS Documentation; 10 from Van Winkle and Todd (1971);
11 from Ishii and Otto (2001); 12 and 13 from typical petrochemical industries.
Items in italics indicate unavailable specifications, or ones modified to allow column optimization by varying the reflux ratio.
Thermodynamic package used: Peng-Robinson for Examples 8, 10, 12 and 13; UNIQUAC for Example 9; and NRTL for Example 11.
Cooling water for cold utility unless stated otherwise.
Pcond = pressure at condenser; Preb = pressure at reboiler
readily available to the authors. For
predicting the mixture properties, an
appropriate thermodynamic model
(fluid package) is selected for each example based on the recommendations
given in the HYSYS documentation,
and then verified by comparing its
predictions with the experimental
vapor-liquid equilibrium (VLE) data
in Reference [5]. Footnotes to Tables 2
and 3 spell out the thermodynamic
models thus selected.
For each example, the shortcut column in HYSYS is first used to estimate Rmin, and the number of theoretical stages and the feed stage location
for the chosen reflux ratio. These values then serve as the basis for rigorous simulation of the column with reboiler and either total or partial
condenser (the latter is the choice
when the feed contains non-condensable components). To satisfy the product specifications of each example in
Tables 2 and 3, HYSYS adjusts the reflux ratio and other quantities suitably. Thus, the reflux ratio obtained
by rigorous simulation is slightly dif52
ferent from that obtained earlier by
shortcut calculations.
After each rigorous simulation, the
column, condenser and reboiler are
sized, and their combined cost is estimated for optimization. The sizing
pertains to the height and diameter of
the distillation column and the design
of the condenser and reboiler. The column diameter depends mainly on the
velocity of the vapor stream within
the column: to avoid excessive liquid
entrainment or a high pressure drop,
the maximum gas velocity, Vmax, is
calculated in meters per second by the
following equation [14]:
Vmax = [-0.171S2 + 0.27S - 0.047]
3 [(rliq - rvap)/rvap]1/2
where S is tray spacing in meters and
rliq and rvap are the liquid and vapor
density, respectively.
In our examples, the vapor velocity
used for actual design is typically 80%
of Vmax. Because columns are customarily fabricated in increments of 0.5 ft
in diameter, D, the diameters calculated are rounded up to the nearest
CHEMICAL ENGINEERING WWW.CHE.COM SEPTEMBER 2004
half foot. This practice results in a
lower vapor velocity and, hence, a
more conservative estimate.
Tray spacing, S depends on the column diameter, and is at least 0.5 m
for the sake of cleaning the trays [16].
Our designs take into account recommendations [18] that the tray spacing
should be 0.5 m for columns with diameters up to 1 m, and that for wider
columns, spacing should be a function
of column diameter:
S = 0.5D0.3
The column height, H, is determined by multiplying the number of
real trays by S and adding an extra
space of 1.5 to 3 m (5 to 10 ft) both at
the top of the tower for vapor-liquid
disengagement and at the bottom for a
liquid sump [3]. An overall efficiency
of 70% is used to calculate number of
real trays from the number of ideal
trays in the simulation.
The heat transfer areas of the condensers is estimated assuming an
overall heat transfer coefficient of 510
W/(m2)(K) [13]. For the reboilers, a
TABLE 4. SELECTED RESULTS FROM RIGOROUS SIMULATION AND OPTIMIZATION OF ALL 13 EXAMPLES
Example Number of
Feed
Annualized Operating
Total
Ropt
Rmin@
Ropt/Rmin
Nmin@
Stages*
Stage#
Capital
Cost,
Cost,
Cost, $/yr
$/yr
$/yr
1
21
10
57,741
364,533
422,274
1.362
1.261
1.08
5.3
2
65
34
316,353
10,752,075 11,068,428
10.36
10.00
1.04
13.3
3
102
72
199,542
197,489
397,031
18.63
15.08
1.24
47.7
4
9
8
31,145
59,013
90,158
0.365
0.348
1.05
1.7
5
9
5
29,018
94,197
123,215
0.540
0.381
1.42
2.2
6
23
21
46,517
110,516
157,034
1.135
0.764
1.49
6.1
7
23
19
57,188
296,692
353,880
0.798
0.484
1.65
6.1
8
25
11
54,695
170,794
225,489
0.491
0.441
1.11
8.7
9
21
18
77,954
795,940
873,900
0.080
0.050
1.60
5.3
10
18
8
55,025
902,703
957,729
0.961
0.778
1.24
3.9
11
48
19
194,885
1,343,503
1,538,388
2.019
1.730
1.17
10.0
12
25
13
75,286
428,830
504,117
0.771
0.727
1.06
8.0
13
105
42
452,312
1,617,538
2,069,850
6.081
5.215
1.17
37.0
* Excluding reboiler and condenser.
# Counted from the top with condenser as zero.
@ Minimum reflux ratio and minimum number of stages (excluding reboiler and condenser) obtained from shortcut calculations.
Cost totals may not agree with cost components due to rounding.
conservative heat flux of 35,490 W/m2,
suggested by Reference [3], is used to
estimate the required areas.
Estimates of the costs
Fixed capital is the capital needed for
the plant to be ready for startup, and
it represents the capital cost of all
equipment, including installation and
auxiliaries, that are needed for the
complete process operation. Baremodule cost equations, expressed as a
function of characteristic size of
equipment by Reference [17], are
used for estimating the capital cost of
the columns, condensers and reboilers. However, these correlations are
in many cases applicable for certain
size ranges only. In examples where
the size of the equipment exceeds the
upper limit, then the usage of the
minimum number of multiple units of
that upper-limit size within the applicable range is assumed, for a conservative estimate.
As the cost data are historical and
subject to inflation, the Chemical Engineering Plant Cost Index (CEPCI) is
used to update capital and operating
costs to January 2002 (CEPCI =
390.3). Annualized capital costs are
found using an annualization factor of
15% to account for depreciation, interest and maintenance associated with
the equipment.
The operating cost for distillation
columns consists mainly of utility costs
for heating in the reboiler and cooling
in the condenser. In the examples, utility costs are estimated using cost equations given in Reference [18], which
contain two separately escalating components. One is due to materials and
labor, which inflates at a rate typified
by the CEPCI, and the other is energy
(fuel) cost, which escalates at a different rate. In this study, fuel price is
taken to be $2.516/GJ based on a typical price of $0.40/gal for residual fuel oil
in January 2002 (from http://www.
eia.doe.gov/oil_gas/petroleum/data_
publications/petroleum_marketing_
monthly/pmm.html) with a heating
value of 42 GJ/m3 [18]. All other cost
data are also in U.S. dollars, and the
column is assumed to operate for 8,500
hours per year (97% onstream time).
Varying the reflux ratio
We wish to find the reflux ratio that is
optimal while continuing to meet the
given product specifications, but the
only way to do so in the rigorous simulation is by changing number of stages
and feed stage. It was found that these
two quantities could not be used as decision variables in the built-in optimizer of HYSYS. Following a suggestion from Hyprotech’s support group,
Visual Basic programs were developed for optimizing the column by
varying the number of stages and/or
the location of the feed stage (in larger
steps initially over a wider range, and
then in single steps over a shorter
range). The steps in the Visual Basic
Program are as follows:
1. Select total number of stages, Nt,
and the feed stage, Nf
2. Transfer Nt and Nf to HYSYS, and
instruct HYSYS to perform a rigorous simulation
3. Collect column data (for example,
temperatures, flowrates, exchanger
duties) in Excel
4. Based on those data, find the size
and the cost the column, reboiler
and condenser in Excel
5. Sort the costing results for the user
to identify the optimal point.
What was found
The results of minimizing the total
cost of each column by varying both
the number of stages and feed stage
are summarized in Table 4. In this
table and Table 5, the number of
stages excludes the reboiler and the
condenser; they and the feed stage
refer to theoretical or equilibrium
stages. The feed stage is counted from
the column top, with the condenser
counted as zero.
Values of Ropt/Rmin for many of the
examples fall within the range of 1.05
to 1.6 as suggested in the literature
(Table 1); the exceptions are Examples 2 and 7 with Ropt/Rmin equaling
1.04 and 1.65 respectively.
Examples 1, 4 to 10, and 12 require
short towers with 9 to 25 theoretical
stages, which results in low capital
cost. Example 2 entails a very high operating cost, as the separation requires a refrigerant and very large exchanger duties; also, the tall column
and multiple heat exchangers for the
large feedrate of 30,000 bbl/day mean
a high capital cost.
Example 3 involves the difficult separation of propylene and propane, thus
requiring a tower of over 100 ideal
stage and hence incurring a large capi-
CHEMICAL ENGINEERING WWW.CHE.COM SEPTEMBER 2004
53
Cover Story
TABLE 5. RESULTS BY SHORTCUT CALCULATIONS WITH ROPT/RMIN = 1.2,
tal cost. As for Example 10, alFOLLOWED BY RIGOROUS SIMULATION AND FEED-STAGE OPTIMIZATION
though the column is short, a large
feed rate of 1,000 mol/h and a sepaExample Results for Ropt/Rmin = 1.2
Results for Ropt/Rmin = 1.2
after feed stage optimization
ration requiring a refrigerant result
Number of
Feed
% Increase
Feed
% Increase
Ropt/Rmin
in a high operating cost. Examples
stages
stage in total cost Stage
in total cost
11 and 13 process large quantities
1
15
7
3.1
7
3.1
1.19
of feed; accordingly, the bulk of the
2
29
20
11.4
20
11.4
1.18
total cost lies in the operating cost.
The optimal number of stages is
3
97
58
3.5
68
1.1
1.29
expected to be close to twice the
4
8
3
71.5
7
1.8
1.10
minimum number of stages [12].
5
9
4
0.1
5
0
1.42
However, the results in Table 4
6
18
10
19.8
16
1.7
1.70
(Column 2 and last column) show
7
18
8
16.1
14
1.7
1.80
that this heuristic is generally not
8
25
14
3.1
11
0
1.11
valid.
9
25
25
29.0
22
0.2
1.40
To test the validity of the heuris10
12
6
4.2
5
3.6
1.34
tic saying that Ropt/Rmin equals 1.1
11
25
13
15.0
11
12.2
1.45
to 1.6, the column for each example
12
22
10
0.9
11
0.4
1.09
is first designed in accordance with
13
78
42
12.1
28
4.1
1.27
successive shortcut column calculations to estimate the number of
Note: % increase in total cost is from the minimum total cost shown in Table 4.
stages and the feed stage assuming
that Ropt/Rmin equals 1.1 to 1.6 in in- that the feed stage from the shortcut feed stage optimization via minimizing
crements of 0.1; these estimates are calculations
(for
instance,
for the reflux ratio. This equivalence is to
followed by a rigorous simulation and Ropt/Rmin equaling 1.2 in Table 5) is be expected, as the total cost is often
cost estimation. For each case, percent very different from the feed stage in dominated by operating cost when the
increase in total cost from the mini- Table 4, even if the total number of total number of stages is fixed.
mum total cost in Table 4 is calculated. stages is comparable.
After the feed stage optimization,
In fact, Reference [7] points out that the feed-stage location, the Ropt/Rmin
Results from this extensive study
show that the variation in percent in- the guideline for optimal feed stage is value and the percent increase in total
crease in total cost depends on the ex- that the ratio of key-component mole cost for Examples 1, 2, 5, 10 and 12
ample; it is within 11% in five exam- fractions in the liquid on the feed are comparable to those with the feed
ples (1, 5, 8, 10 and 12), but is stage should be close to the corre- stage determined by the shortcut calsponding ratio in the liquid part of the culations. On the other hand, the total
significantly more in other examples.
A reasonable value for Ropt/Rmin feed. The key-ratio plot in Figure 1 for cost decreases dramatically in Examwithin 1.1 to 1.6 is 1.2. Results for this Example 4 indicates that the feed- ples 4, 6, 7, 9 and 13. In the other
particular case (Columns 2 to 4 in stage location should be closer to the three examples (Nos. 3, 8 and 11), too,
Table 5) show that the increase in reboiler. The feed stage in the opti- the total cost decreases, by about 3
total cost is in the range of 0.1% to mized design is consistent with the percentage points.
about 70%, and the average increase heuristic given in Reference [7].
Thus, after the feed stage optimizaA recent reference [8] states that the tion to minimize the reflux ratio, the
is about 14% for all 13 examples.
Thus, although the heuristic on optimal feed location for a specified increase in total cost (from the miniRopt/Rmin equaling 1.1 to 1.6 seems to total number of stages and separation mum total cost shown in Table 4) is
be valid in five out of the 13 examples minimizes the reflux ratio (and there- less than 4.1% for all examples except
tested, these results nevertheless show fore the reboiler and condenser duties). Nos. 2 and 11. The optimal total numthe potential for reducing the total col- In accordance with this guideline, the ber of stages and reflux ratio for these
umn cost by further optimization.
feed stage for the case of Ropt/Rmin two examples (Table 4) are different
equaling 1.2 in Table 5 is optimized by from those for Ropt/Rmin equaling 1.2
Revelations about the feed stage varying the feed stage in the rigorous (in Table 5).
In addition to the above findings, a simulation and finding the reflux ratio
In other words, column design by
closer analysis of the results for vari- to achieve the desired separation. shortcut calculations can be improved
ous Ropt/Rmin values indicated that These optimized results after feed significantly by changing the feed
the feed stage given by shortcut col- stage optimization are shown in the stage to minimize reflux ratio for the
umn calculations can be inappropri- last three columns of Table 5.
same total number of stages found for
ate. The most extreme case is ExamA separate exercise was carried out Ropt/Rmin equaling 1.2. This change
ple 4, for which increase in the total to optimize the feed stage by minimiz- can be carried out easily with the aid
cost ranged from 70 to 260% with ing total cost for the case of Ropt/Rmin of a simulator, because it does not inRopt/Rmin in the range 1.1 to 1.6. One equaling 1.2 for all examples. These re- volve sizing and cost estimation of the
can see from the optimized results sults are identical to those obtained by column, condenser and reboiler.
54
CHEMICAL ENGINEERING WWW.CHE.COM SEPTEMBER 2004
Authors
FIGURE 1.This plot, relevant to Example 4, relates the column stage number with the
key ratio for the liquid at that stage, for both shortcut and optimized design
Summarizing the conclusions
Column optimization through rigorous simulation, sizing and costing
commonly gives an Ropt/Rmin value in
the range of 1.1 to 1.6. Also, the
heuristic that the optimal number of
stages is twice the minimum number
is generally not valid.
Shortcut (as opposed to rigorous)
calculations using the heuristic,
Ropt/Rmin = 1.1 to 1.6, produce
columns whose total cost is generally
more than the minimum. For the specific case of Ropt/Rmin equaling 1.2, the
total cost of a column by shortcut calculations (followed by rigorous simulation, sizing and costing) is on aver-
age 14% higher than the minimum attainable by rigorous simulation and
optimization. However, the design in
this case can often be improved substantially by optimizing the feed stage
(for a specified number of stages and
separation), and the total cost of a column can be reduced to within 4% of
the minimum.
In a few cases, potential exists for
further cost reduction by varying both
the number of stages and feed stage,
and simulating the column rigorously.
These findings are applicable to simple columns with a single feed stream
n
and two product streams only.
Edited by Nicholas P. Chopey
C.M. Lek is currently an Engineering Officer in the Singapore Armed Forces. Mr.
Lek received his bachelor’s
degree in chemical engineering from the National University of Singapore in 2003 with
second class honors (Upper
Division). The work reflected
in this article began as his senior-year research project,
and continued after completion of that project. Mr. Lek has a particular interest in software development.
G.P. Rangaiah is an Associate Professor in the Dept. of
Chemical and Biomolecular
Engineering, National University of Singapore (Singapore 119260; Phone: [65]
6874-2187; email: RangaiahGP@nus.edu.sg).
He
worked for Engineers India
Ltd. (New Delhi) for two
years, and has been lecturing
at the National University of
Singapore since 1982. His research interests are
in process control, modeling and optimization.
He has supervised nine research fellows/assistants and more than 20 postgraduate theses, has
published about 70 papers in international journals, and has presented nearly 50 papers in conferences. He received his baccalaureate, masters
and doctorate degrees in chemical engineering
from India’s Andhra University, IIT Kanpur and
Monash University, respectively.
Kus Hidajat is an Associate
Professor in the Dept. of
Chemical and Biomolecular
Engineering, National University of Singapore (email:
chehidak@nus.edu.sg).
He
has been lecturing at the National University of Singapore since 1983. His research
interests are in simulatedmoving-bed adsorptive separation processes with or without reaction, plus modeling and optimization,
and catalytic membranes. He has supervised
four research fellows/assistants and 26 postgraduate theses, has published about 65 papers
in international journals, and has presented
about 40 papers in conferences. He received his
baccalaureate and doctorate degrees in chemical
engineering in the U.K., from the University of
Manchester Institute of Science and Technology
(UMIST) and the University of Cambridge, respectively.
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