C ov over er Story
Part 1.
DISTILLATION:
Revisiting Some Rules of Thumb C. M. Lek S ing ingapor apore e A rmed Forces Forces
G. P. Rangaiah Rangaiah and K. Hidajat
Heurist ics regarding optimal ref lux rati o and and number of st ages ages,, as as w ell as the selecti se lecti on of of t he feed stage, stage , get some some reasse reassessment ssment here, consistent w it h changess in t he relative costs of equipment and energy change
N ation ational al U niver niversity sity of S ing ingapor apore e
D
istillation is the most common unit operation for separating liquid mixtures into valuable a nd/or high purity products. It is also one of the most energyintensive opera opera tions. Hence, optimiza optimiza tion of distillation-column design and opera ope ra tion should get high priority. Numerous distillation heuristics (rules of thumb) for quick optimization have emerged over the years. For instance, heuristics on optimal reflux ra tio as a ce certa rta in multiple multiple of of the minimum reflux ratio have been widely used as quick tools to estimate optimum r efl eflux ux ra tio. 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. Meanw hile hile,, it ha s now become 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 out w ith relat ive ease. ease. This article assesses the validity of optimal-reflux-ratio and other heuristics in light light of recent cost cost da ta , by conconsidering seven binary and six multicomponent systems. Distillation columns for each of the 13 have been designed an d optimized optimized by both both sh ortcut (heuristics-based) calculations an d rigorous rigorous simulat io ions. ns. In addition to the reassessment, a key observa50
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tion emerges: tha t th e cost cost of a column designed by shortcut calculations can be reduced substantially by optimizing th e locat locat ion of of the feed sta ge.
L aying the groundwo groundwork rk 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 a t very high reflux rat io ios. s. And as alternatives having successively higher reflux ratios are compared with each other, there is a particular ticul ar , high ratio at wh ic ich h the capital cost co st of th e column column begins t o rise aga in [7] . In addition, the capital as well as the operating costs for the reboiler and condenser will rise in proportion to the va po porr ra te in the column. 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 ra tio.
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Generally speaking, the number of theoretical theoretic al st ages a t t he optimal optimal r efl eflux ux ha s been been sta ted as bei being ng on the order of twice the minimum num ber of theotheoretical plates (corresponding to total reflux), and the optimal reflux ratio, 1.1 to 1.5 1.5 R opt , as being in the ra nge of 1.1 times the minimum reflux ratio, R m i n [1 ]. A study desc described ribed in this ma ga zine over 30 years ago [19 ] evaluated a large number of cases, mainly via shortcut shortc ut methods, an d stat ed that R opt lies between 1.1 and 1.6 times R m i n , the lower value being favored by high relative volatilities. Conversely, relative volatilities closer to unity and sharper separations were said to require higher va lues of of R opt /R m i n within the a bo bove ve range. Since Since then, many a rticles and books have recommended estimates of R opt /R m i n for various situa tions, as summa rized in Ta Ta ble 1. 1. The The range of recommended R opt /R m i n values in t he open litera tu re is 1.05 1.05 to 1.6, 1.6, with the lower value for systems involving refrigerants and the higher va lue for for syst ems using cool cooling ing wa ter. Despite the diversity in ranges in Table 1, the use of a rule-of-thumb on optimal op timal reflux ratio as a ce certa rta in 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 ear lie lier, r, th e relat ive costs costs of equipment equipment and energy (which affects utilities)
TABLE 2.
DETAILSOF BINARY EXAMPLES
Ex a m p le N o .*
C o m p o ne n ts
Fe e d M o le Fra c tio n
Fe e d C o nd itio ns
C o lu m n Pre ssu re
Pro d uc t Pu rity Sp e c ific a tio ns (m o le % )
1
Be nze n e To lu e ne
0.4 5 0 .5 5
70 0 lb - m o l / h, 1 atm , sa t. liq .
P cond : 0.98 atm Pre b : 1 a tm
Top : 92% Benzene Btm : 9 5 % To lue ne
2
i- Buta ne n- Bu ta ne
0 .2 33 0.7 67
30 ,00 0 b b l/ d , 50 psia , sat. liq.
P cond : 42 psia ( refrigera nt) P reb : 50 psia
Top : 91.7% i-Buta ne Btm : 90% n-Buta ne
3
Pro p y le ne Pro p a ne
0 .5 04 5 0.4 95 5
84 .2 m 3 / d , 1.86 MPa , sa t. liq .
P cond : 1.798 MPa Pre b : 1 .86 M Pa
Top : 96.2% Prop ylen e Btm : 9 1 .1 % Pro p a ne
4
A c e to ne W a te r
0.5 0.5
50 0 lb - m o l / h, 1 atm , 5 5% va p
P cond : 0.98 atm Pre b : 1 a tm
Top : 91% Ac etone Btm : 9 7 .8 % W a te r
5
n- He xa ne p - X y le n e
0 .5 5 0 .4 5
20 0 k m o l/ h, 1 a tm , 50 % v a p
P cond : 0.98 atm P reb : 1 atm
To p : 9 5 % n - H e x a n e Btm : 97% p-X ylene
6
M e tha no l 1,4 - D io x a ne
0 .5 4 0 .4 6
10 ,00 0 lb / h, 1 a tm , sa t. liq .
P cond : 0.98 atm P reb : 1 a tm
To p : 9 9% M e t h a n o l Btm : 98% Dioxa ne
7
M e tha no l W a te r
0 .7 0.3
12 ,00 0 lb / h, 1 atm , sat. liq.
P cond : 0.98 atm P reb : 1 atm
To p : 9 9% M e t h a n o l Btm : 99% Wa ter
*Sources for E xamples: 1 a nd 2 fr om P eters a nd Timmerhau s (1991); 3 and 4 from King (1980); 5 to 7 from D oherty a nd Malone (2000). I t e m s i n i t a l i c s i n d i c a t e u n a v a i l a b l e sp ec i f i c a t i o n s , o r o n es m o d i f i ed t o a l l o w c o l u m n o p t i m i z a t i o n b y va r y i n g t h e r e f l u x r a t i o .
Thermodyna mic package used: P eng-Robinson for Eam ples 1, 2, 3 an d 5; and NRTL for Exa mples 4, 6 an d 7. Cooling water for cold utility unless stated otherwise. P c o n d = pressure at condenser; P re b = pr essure at reboiler
have been changing, part icularly during the lat ter year s of that time period. Furt hermore, some of the ear ly studies on optimal reflux ratio were based on shortcut calculation methods or graphical correlations, whereas today, rigorous calculations (with more-accura te results) can be ma de 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 wheth er, a nd how, the capabilities of commercial simulators for rigorous distillation simulation can also be used for optimizing reflux ra tio. B oth of these questions a re addressed in wha t follows , by considering industrially relevant applications that involve both binary and multicomponent mixtures. Along the way, we a lso scrutinize the va lidity 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 s t r e a m a n d t w o p r od u ct s t r e a m s .
Examples and procedures The 13 dist illat ion exam ples als o come from the open literature, for the most part . Seven examples ha ve tw o com-
RECOMMENDED VALUESFOR THE OPTIMUM-TO-MINIMUM REFLUX RATIO IN THE LITERATURE TABLE 1.
Reference
Ropt/ Rmin
Remarks
V a n W in k le a n d To d d , 1 9 7 1 [1 9 ]
1 .1 to 1 .6
Bria n,1972 [1 ]
1.1 to 1 .5
Frank,1977 [4 ]
1 .0 5 to 1 .1
Lo w - le v e l re frig . (< - 15 0 °F)
1 .1 to 1 .2
H ig h - le v e l re frig .
1 .2 to 1 .3
W a te r- a n d a ir- c o o le d c o n d e n se rs
Zdo nik,1977 [ 21 ]
1 .25
G e ne ra lly a c c e p te d
1 .1 to 1 .2 King,1980 [7 ]; Wa las, 1987 [20 ]
Lo w e r v a l ue s fo r h ig h re l a t iv e vo la tilitie s
W ith in c re a se d e n e rg y c o sts
1 .2
Thom pson,1980 [1 5 ]
1.2 to 1 .3
C o m m o n fra c tio na to rs
Perry, o thers, 1997 [1 3 ]
1.1 to 1 .5
Pe tro le u m -d istilla tio n c olum ns
1 .1 to 1 .2
Re frig . is in v olv e d
1 .2 to 1 .4
C o o lin g - to w e r w a t e r u se d in c o n densers
M c C o rm ic k a nd Ro c he , 1 9 7 9 [9 ]
1 .05 to 1.10
Lo w -le ve l re frig . (- 30 0 to - 15 0°F)
1 . 1 0 to 1 . 2 0
H ig h - l e v e l re f rig . ( - 1 5 0 t o 5 0 °F)
1.2 to 1.5
C o olin g w a te r
1.4 to 1.5
A ir c o oling
M c C o rm ic k a nd Ro c he , 1 9 9 7 [1 0 ]
1 .0 5 to 1 .2
Peters, othe rs, 200 3 [ 12 ]
1 .2 to 1 .25
ponents (Table 2); the others involve multiple components (Table 3). Besides showing the components, Ta bles 2 and 3 specify feed conditions, column pressure and product specifications for each syst em. In a few cases, the specifications w ere either una vailable in the original references or were modified to suit t he needs of this stu dy (for instance, the reflux ratio should not ha ve a specified value).
The selected exam ples cover a wide range of design and operating conditions. Some operate a t h igh 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 t ha n 100 (ta ll columns). Steady state simulation and design of column for each example is done using HYSYS, the simulation system
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DETAILSOF MULTIC OMPONENTEXAMPLES
TABLE 3.
Example No.*
Components
Feed Mole Fraction
Feed Conditions
Column Pressure
Product Purity Specifications (Mole %)
8
N itro g e n CO2 M e tha ne Etha ne Pro p a ne i- Buta ne n- Buta ne
0 .00 2 0 0 .00 4 6 0 .24 1 2 0 .25 7 6 0 .25 6 1 0 .12 1 9 0 .11 6 6
14 0.8 5 k m o l/ h, 4,0 00 k Pa , sa t. liq .
P cond : 1,3 78 kPa ( refrigera nt) p a rtia l c o nd e nse r (va p o r d istilla te ) P reb : 1,413 kPa
Top : 0.6 % n-Buta ne Btm : 2% Propa ne
9
Pro p y le n e O xid e Pro p y le n e G ly c o l W a te r
0 .01 2 9 0 .22 9 6 0 .75 7 5
61 8.5 k m o l/ h, 12 0 k Pa , sa t. liq .
Pc o n d : 103 kPa Pre b : 117 kPa
Top : 2 X 10 -5 % Propylene Glycol Btm : 0.5% Wa ter
10
Pro p e ne Pro p a ne 1 - Bute ne n- Buta ne n- Pe nta n e
0 .21 5 8 0 .18 1 7 0 .20 1 0 0 .23 1 2 0 .17 0 3
1,0 00 lb - m o l/ h, 10 0 p sia , sa t. liq .
P cond : 97 psia ( refrigera nt) Pre b : 100 p sia
Top : 4.74% 1-Butene Btm : 2.54% Propa ne
11
A c e to ne M e tha no l Etha no l W a te r 1 - Buta n o l
0 .20 0 .20 0 .20 0 .20 0 .20
1,0 00 k m o l/ h, 10 1.3 k Pa , sa t. liq .
P cond : 0.98 a tm Pre b : 1 atm
Top : 2% Etha nol Btm : 2% Metha nol
12
Pro p y le n e Pro p a ne 1 ,3 - Buta d ie ne n- Buta ne n- Pe nta n e
0 .00 0 5 0 .00 0 2 0 .30 6 0 0 .41 6 0 0 .27 7 3
53 8 m .t./ d , 6.2 9 a tm , sa t. liq .
Pc o n d : 4 31 .5 k Pa Pre b : 4 70 .7 k Pa
To p : 1 % n- p e nta ne Btm : 1% n- b uta ne
13
Etha ne Pro p y le ne Pro p a ne Pro p a d ie ne n- Buta ne
0 .00 0 5 0 .95 0 0 0 .04 5 0 0 .00 3 0 0 .00 1 5
15 m .t./ h, 1,457.4 kPa , sa t. liq .
Pc o n d : 1,3 8 0 k Pa Pre b : 1 ,4 5 0 k Pa
To p : 2 % Pro p a ne Btm : 50 % Pro p e ne
*Sources of Exam ples: 8 and 9 from HYS YS D ocumenta tion; 10 from Van Winkle an d Todd (1971); 11 from Ishii a nd Otto (2001); 12 an d 13 from typical petrochemical indus tries. I t e m s i n i t a l i c s i n d i c a t e u n a v a i l a b l e sp ec i f i c a t i o n s , o r o n es m od i f i ed t o a l l o w c ol u m n o p t i m i z a t i o n b y v a r y i n g t h e r e f l u x r a t i o .
Thermodyna mic package used: P eng-Robinson for Exa mples 8, 10, 12 an d 13; UNIQU AC for Exam ple 9; a nd NR TL for E xample 11. Cooling water for cold utility unless stated otherwise. P cond = pressure at condenser; P reb = 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 ]. Footn otes t o Ta bles 2 and 3 spell out the thermodynamic models thus selected. For each example, the shortcut column in HYSYS is first used to estim a t e R m i n , an d the number of theoretica l sta ges and t he feed sta ge location for the chosen reflux ra tio. These va lues 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-condensa ble components). To sa tisfy the product specifications of each example in Ta bles 2 a nd 3, HYSYS a djusts th e reflux ratio and other quantities suitably. Thus, the reflux ratio obtained by rigorous simulation is slightly dif52
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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 a nd diameter of the distillation column a nd t he design of the condens er a nd r eboiler. The column diam eter 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, V m ax , is calculat ed in meters per second by the following equa tion [14 ]: V m ax = [-0.171 S 2 + 0.27S - 0.047] 3
[(rl i q - rva p )/rva p ]1/2
w h e r e S is tray spa cing in meters a nd rl i q a n d rva p a re the liquid and va por density, respectively. In our exa mples, the vapor velocity used for actua l design is typically 80% of V m ax . Because columns are customa rily fa bricat ed in increment s of 0.5 ft in diameter, D , the diameters calculated are rounded up to the nearest
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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 th e sake of cleaning the t ra ys [16 ]. Our designs ta ke into a ccount recommendat ions [18 ] t h a t t h e t r a y s p a ci n g should be 0.5 m for columns with dia meters up to 1 m, a nd tha t for wider columns, spa cing should be a fun ction of column diam eter: S = 0. 5D 0.3
The column height, H , is determined by multiplying the number of r e a l t r a y s b y S a n d a d d i n g a n e x t r a space of 1.5 to 3 m (5 to 10 ft) both at the top of the tower for vapor-liquid disenga gement and a t th e bottom for a liquid sump [3 ] . An overall efficiency of 70%is used to calculate number of real trays from the number of ideal tra ys in the simulat ion. The heat transfer areas of the condensers is estimated assuming an overall hea t t ra nsfer coefficient of 510 W/(m 2)(K) [13 ]. For the reboilers, a
TABLE 4.
SELECTED RESULTS FROM RIGOROUS SIMULATION AND OPTIMIZATION OF ALL13 EXAMPLES Total C ost, $/ yr
Ropt
Rmin@
Ropt/ Rmin
Nmin@
3 64 ,53 3
42 2 ,2 7 4
1 .36 2
1 .26 1
1 .08
5.3
3 16 ,35 3
1 0,7 52 ,07 5
11 ,06 8 ,4 2 8
10 .36
10 .00
1 .04
1 3.3
72
1 99 ,54 2
1 97 ,48 9
39 7 ,0 3 1
18 .63
15 .08
1 .24
4 7.7
9
8
31 ,14 5
59 ,01 3
9 0 ,1 5 8
0 .36 5
0 .34 8
1 .05
1.7
5
9
5
29 ,01 8
94 ,19 7
12 3 ,2 1 5
0 .54 0
0 .38 1
1 .42
2.2
6
23
21
46 ,51 7
1 10 ,51 6
15 7 ,0 3 4
1 .13 5
0 .76 4
1 .49
6.1
7
23
19
57 ,18 8
2 96 ,69 2
35 3 ,8 8 0
0 .79 8
0 .48 4
1 .65
6.1
8
25
11
54 ,69 5
1 70 ,79 4
22 5 ,4 8 9
0 .49 1
0 .44 1
1 .11
8.7
9
21
18
77 ,95 4
7 95 ,94 0
87 3 ,9 0 0
0 .08 0
0 .05 0
1 .60
5.3
10
18
8
55 ,02 5
9 02 ,70 3
95 7 ,7 2 9
0 .96 1
0 .77 8
1 .24
3.9
11
48
19
1 94 ,88 5
1,3 43 ,50 3
1 ,53 8 ,3 8 8
2 .01 9
1 .73 0
1 .17
1 0.0
12
25
13
75 ,28 6
4 28 ,83 0
50 4 ,1 1 7
0 .77 1
0 .72 7
1 .06
8.0
13
10 5
42
4 52 ,31 2
1,6 17 ,53 8
2 ,06 9 ,8 5 0
6 .08 1
5 .21 5
1 .17
3 7.0
Example
Number of Stages*
Feed Stage#
Annualized C apital Cost, $/ yr
1
21
10
57 ,74 1
2
65
34
3
10 2
4
Operating Cost, $/ yr
* Excluding reboiler a nd condenser. # Counted from the top wit h condenser as zero. @ Minimum reflux ra tio and m inimum num ber of stages (excluding reboiler and condenser) obtained from short cut calculations. Cost totals may not agree with cost components due to rounding.
conser va t ive hea t flu x of 35,490 W/m 2, suggested by Reference [3 ] , is used to estimate the required ar eas.
Estimates of the costs Fixed capita l is the capita l needed for t h e p l a n t t o be r e a d y f o r s t a r t u p , a n d it represents the capital cost of all equipment, including insta llation and auxiliaries, that are needed for the complete process operation. Baremodule cost equa tions, expressed a s a function of characteristic size of equipment by Reference [17 ], are used for estima ting t he 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 num ber 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 Chemi cal E n- gineering P lant C ost Index (CE P CI) is used to update capital and operating costs to J an uar y 2002 (CEP CI = 390.3). Annualized capital costs are found using an an nua lizat ion fa ctor of 15%to a ccount for depreciat ion, int erest and maintenance associated with the equipment. The operating cost for distillation columns consists ma inly of utility costs for heating in the reboiler and cooling in the condenser. In th e exa mples, utility costs a re estimated using cost equa tions given in Reference [18 ], which
conta in tw o separa tely escala ting components. One is due to materials and labor, which inflates at a r at e typified by the CEP CI, a nd the other is energy (fuel) cost, w hich esca lat es at a d ifferent rate. In this study, fuel price is ta ken to be $2.516/G J bas ed on a ty pical price of $0.40/ga l for r esidua l fuel oil in J a nua ry 2002 (from ht tp://w w w. eia .doe.gov /oil_ga s/pet roleu m/da ta _ publicat ions/petr oleum_ma rket ing_ month ly/pmm.ht ml) wit h a h eat ing va lue of 42 G J /m 3 [18 ]. All other cost d a t a a r e a l s o i n U . S . d ol la r s , a n d t h e column is a ssumed t o operat e for 8,500 hours per yea r (97%onstrea m time).
Varying the reflux ratio We wish t o find th e reflux ra tio tha t is optimal while continuing to meet the given product specifications, but the only wa y to do so in the rigorous simulation is by changing num ber of sta ges a n d f e e d st a g e . I t w a s f o u n d t h a t t h e s e tw o quan tities could not be used a s 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 va rying t he number of sta ges an d/or th e locat ion of the feed sta ge (in lar ger steps initially over a wider ra nge, and then in single steps over a shorter range). The steps in the Visual Basic P rogram a re as follows: 1. Select total number of stages, N t , an d the feed stage, N f 2. Tra nsfer N t a n d N f t o H Y S Y S , a n d instruct HYSYS to perform a r igorous simulation
3. Collect column da ta (for exam ple, temperatur es, flowrat es, exchanger duties) in E xcel 4. B ased on those data , find the size and the cost the column, reboiler a nd condenser in E xcel 5. Sort th e costing results for the user to identify the optima l 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 sta ges. The feed sta ge is counted from the column top, with the condenser count ed as zero. Values of R opt /R m i n for ma ny 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 R opt /R m i n equaling 1.04 a nd 1.65 respectively. Exa mples 1, 4 to 10, a nd 12 require short towers with 9 to 25 theoretical stages, which results in low capital cost. E xa mple 2 enta ils a very high operating cost, as the separation requires a refrigerant an d very lar ge exchan ger duties; a lso, the ta ll column and multiple heat exchangers for the la rge feedr a te of 30,000 bbl/da y mea n a high capital cost. Example 3 involves the difficult sepa ra tion of propylene an d propa ne, thus requiring a tower of over 100 ideal sta ge and hence incurring a large capi-
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Cover Story TABLE 5. RESULTS BY SHORTCUTCALC ULATIONS WITH ROPT/ RMIN =1.2, tal cost. As for Example 10, alFOLLOWED BY RIGOROUS SIMULATION AND FEED-STAG E OPTIMIZATION though th e column is short, a large feed ra te of 1,000 mol/h a nd a sepaExample Results for Ropt/ Rmin = 1.2 Results for Ropt/ Rmin = 1.2 after feed stage optimization ra tion requiring a refrigera nt result Number of Feed % Increase Feed % Increase Ropt/ Rmin in a high operating cost. Examples stages stage in total c ost Stage in total c ost 11 and 13 process large quantities 1 15 7 3 .1 7 3 .1 1.1 9 of feed; accordingly, the bulk of the 2 29 20 11 .4 20 1 1 .4 1.1 8 total cost lies in the operating cost. The optimal number of stages is 3 97 58 3 .5 68 1 .1 1.2 9 expected to be close to twice the 4 8 3 71 .5 7 1 .8 1.1 0 minimum number of stages [12 ]. 5 9 4 0 .1 5 0 1.4 2 However, the results in Table 4 6 18 10 19 .8 16 1 .7 1.7 0 (Column 2 and last column) show 7 18 8 16 .1 14 1 .7 1.8 0 tha t t his heuristic is genera lly not 8 25 14 3 .1 11 0 1.1 1 valid. 9 25 25 29 .0 22 0 .2 1.4 0 To test th e validity of the heur is10 12 6 4 .2 5 3 .6 1.3 4 tic saying tha t R opt /R m i n equa ls 1.1 11 25 13 15 .0 11 1 2 .2 1.4 5 to 1.6, the column for each exa mple 12 22 10 0 .9 11 0 .4 1.0 9 is first designed in accorda nce with 13 78 42 12 .1 28 4 .1 1.2 7 successive shortcut column calculations to estimate the number of Note: %increase in total cost is from the minimum t otal cost shown in Table 4. sta ges and the feed sta ge assuming t h a t R opt /R m i n equals 1.1 to 1.6 in in- that the feed stage from the shortcut feed sta ge optimizat ion 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 R opt /R m i n equaling 1.2 in Table 5) is be expected, as the total cost is often cost est imat ion. For ea ch 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 tota l number of stag es is fixed. mum t otal cost in Table 4 is calcula ted. sta ges is compar a ble. After the feed stage optimization, Results from this extensive study In fa ct, Reference [7 ] point s out tha t the feed-stage location, the R opt /R m i n show tha t th e variat ion in percent in- th e guideline for optima l feed sta ge is value a nd the percent increase in total crease in tota l cost depends on th e 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 a re compara ble to those with the feed ples (1, 5, 8, 10 and 12), but is stage should be close to the corre- sta ge determined by th e shortcut calsignificantly more in other examples. sponding ra tio in t he liquid par t of the culat ions. On the other ha nd, the total A reasonable value for R opt /R m i n feed. The key-ra tio plot in F igur e 1 for cost decreases dramatically in Examwit hin 1.1 to 1.6 is 1.2. Results for t his 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 th ree exa mples (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 ra nge of 0.1% to mized design is consistent with the percentage points. a bout 70%, an d the a vera ge increase heurist ic given in Reference [7 ]. Thus, a fter t he feed sta ge optimizais a bout 14%for a ll 13 examples. A recent reference [8 ] stat es tha t the tion to minimize the reflux ratio, the Thus, although the heuristic on optimal feed location for a specified increase in total cost (from the minitotal number of stages and separation mum total cost shown in Table 4) is R opt /R m i n equa ling 1.1 to 1.6 seems to be valid in five out of the 13 examples minimizes the reflux ratio (and there- less tha n 4.1%for a ll examples except tested, th ese results nevertheless show fore the reboiler a nd condenser dut ies). Nos. 2 a nd 11. The optimal t ota l numthe potential for reducing t he tota l col- In accordance with this guideline, the ber of sta ges and r eflux ra tio for th ese umn cost by furth er optimizat ion. feed stage for the case of R opt /R m i n two examples (Table 4) are different equa ling 1.2 in Ta ble 5 is optimized by from those for R opt /R m i n equaling 1.2 Revelations about the feed stage varying the feed stage in the rigorous (in Ta ble 5). In addition to the above findings, a simulation and finding the reflux ra tio In other words, column design by closer a na lysis of the r esults for va ri- to achieve the desired separation. shortcut calculations can be improved ou s R opt /R m i n 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 sta ge to minimize reflux ratio for t he umn calculations can be inappropri- las t t hree columns of Ta ble 5. sam e total num ber of sta ges found for ate. The most extreme case is ExamA separate exercise was carried out R opt /R m i n 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 ra nged from 70 to 260% with ing total cost for the case of R opt /R m i n of a simula tor, because it does not inequa ling 1.2 for a ll examples. These re- volve sizing an d cost estima tion of th e R opt /R m i n in th e ra nge 1.1 to 1.6. One can see from the optimized results sults a re identical t o those obta ined by column, condenser a nd r eboiler. 54
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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 a n R opt /R m i n value in the range of 1.1 to 1.6. Also, the heuristic that the optimal number of sta ges is twice the minimum number is generally not va lid. Shortcut (as opposed to rigorous) calculations using the heuristic, R opt /R m i n = 1.1 to 1.6, produce columns whose total cost is generally more than the minimum. For the specific ca se of R opt /R m i n equa ling 1.2, the total cost of a column by shortcut calculations (followed by rigorous simulation, sizing and costing) is on aver-
age 14%higher tha n the minimum at tainable by rigorous simulation and optimization. However, the design in this case can often be improved substa ntia lly by optimizing the feed stage (for a specified number of stages and separ a tion), and t he tota l cost of a column can be reduced to within 4% of the minimum. In a few cases, potential exists for further cost reduction by va rying both the number of stages and feed stage, an d simulat ing th e column rigorously. These findings are applicable to simple columns with a single feed stream an d tw o product st reams only. n Ed it ed by N icholas P. Chopey
C.M. Lek is currently an E ngineering Officer in the Singapore Armed Forces. Mr. Lek received his bachelor’s degree in chemical engineering from the National U niversity of Singa pore in 2003 with second class honors (Upper Division). The work reflected in this a rticle began as h is senior-year research project, and continued after completion of that project. Mr. Lek has a pa rticular interest in software development. G.P. Rangaiah is a n Associate Professor in the Dept. of Chemical and Biomolecular Engineering, National University of Singapore (Singapore 119260; P hone: [65] 6874-2187; email:
[email protected]). He worked for Engineers India Ltd. (New Delhi) for two years, a nd ha s been lecturing at the National University of Singa pore since 1982. His research interests a re in process control, modeling and optimization. He ha s supervised nine resea rch fellows /as sista nts a nd more than 20 postgradua te theses, has published about 70 papers in international journals, a nd ha s presented near ly 50 papers in conferences. He received his baccalau reat e, masters and doctorate degrees in chemical engineering from India’s Andhra University, IIT Kan pur and Monash University, respectively. Kus Hidajat is an Associate Professor in the Dept. of Chemical and Biomolecular Engineering, National University of Singapore (email:
[email protected]). He has been lecturing at th e National University of Singapore since 1983. His resea rch 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/ass ista nts an d 26 postgradua te theses, has published about 65 papers in international journals, and has presented about 40 papers in conferences. He received h is baccalaureate and doctorate degrees in chemical engineering in the U.K ., from the Un iversity of Ma nchester In stitu te of Science and Technology (UMIST) and the University of Cambridge, respectively.
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15. Thompson, R. E ., McCa be-Thiele Methods – Advanced Topics, in “AIChEMI Modular Instruction. Series B, Stagewise and Mass Transfer Operations”, American Institute of Chemical E ngineers, New York, 1980. 16. Treyba l, R. E., “Mas s-Tra nsfer Operations”, 3rd Ed., McGra w-Hill, New York, 1980. 17. Turton, R., “Analysis, Synthesis and Design of Chemical Processes”, Prentice Hall PTR, New J ersey. 1998. 18. Ulrich, G. D., “A Guide to Chemical E ngineering Process Design and Economics”, Wiley, New York, 1984. 19. Van Winkle, M. an d Todd, W. G., Optimu m Fractionation Design by Simple Graphical Methods, Chem. Eng. , p. 136, Sept. 20, 1971. 20. Wala s, S. M., Rules of Thumb, Chem. Eng. , p. 75, Ma r 16, 1987. 21. Zdonik, S. B., Techniques for Sa ving Energy in P rocesses a nd E quipment” Chem. Eng. , p. 99, J uly 4, 1977.
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