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CXd = coefficient of fluid stream deflection at lower surfaceof distributora = coefficient of fluid stream deflection at bed upperboundary6 6 = thickness of distribu tor= local mean voidage = unperturbed voidage6 = voidage perturbation6d = local mean voidage in porous distributor= ratio of support pressure drop to that across bed inynperturbed stateb = critical wavelengthA,-- = bulk viscosity of particle phase in unperturbed s tat ef = shear viscosity of fluidizing fluid

PO = shear viscosity of particle phase in unperturbed

= coefficient of resistance for bed support

statep = ratio of fluid density t o solid dens ity@ = density of fluidizing fluidp s = density of solid materialSymbols with and without circumflex denote correspond-ing dimensional and dimensionless variables, respectively.Li terature Ci tedAnderson, T. 6 Jackson, R. Ind . fn g. Chem. Fundam..8 528 1967).Beavers, 0 S. Joseph, D. D.. J. FluMMech. 30, 197 1967).Clift. R. Grace, J. R.. Weber, M. E. lnd Eng. Chem. Fundam. 13, 45 1974).Medlin, J., Wong, K W. , Jackson, R. Ind. f n g . Chem. Fundam. 13, 247Saffman. P.G. Stud. Appl. Math. 50 93 1971).1974).

Receiued fo r reoiew December2,1974Accepted May 19,1975

Steady-State Energy Conservation Aspects of Distillation ColumnControl System Design

William L. LuybenDepartment of Chemical Engineering Lehigh University Bethlehem Pennsylvania 18015

Energy consum ption in distillation column op eration is minimized by controlling compos itions at both ends of th ecolumn. This dual composit ion control can how ever present dynamic stabil ity and interact ion problems. Thisstudy points out that the energy savings may often not be worth the increased cost and com plexity of instru-mentat ion. Simple stable alternat ive control schemes where ref lux-to-feed rate or steam-to-feed rate rat iosare maintained and ov erfract ionat ion is deliberately used som etimes con sum e very litt le additional energ y.Steady-state calculations are emp loyed to evaluate the incent ive or lack of incentive for dual comp ositioncontrol.

IntroductionRecent rapid increases in fuel costs have stimulated ex-tensive redesign of many processes. These design changesnormally involve increasing capital investment in order toreduce energy operating costs. Since distillation columnsare often major energy consumers in plants , the process de-sign, operating strategies, and control systems of distilla-tion columns are being intensively studied. Th e old brute-force, energy-inefficient control strategies are being reev-aluated.For a simple two-product distillation column, energyconsumption is minimized when both products are held at

specified purities. Controlling only one product composi-tion and using excess reflux or vapor boilup to guaranteetha t the other product is always at or above its desired pu-rity resul ts in more energy consumption.Therefore, from a steady-state energy consumptionstandpoint, it is desirable simultaneously to control bothproduct compositions in a distillation column. This iscalled dual composition,control. Figure illustrates atypical control system.However, dual composition control can lead to dynamiccontrol problems. Interaction between the two compositioncontrol loops can result in closed-loop stab ility difficulties.Instrumenta tion complexity and cost increase if interactioncompensators (decouplers) are required. Engineering costsare also significantly increased if dynamic simulation stud -

ies, detailed control system design, and/or plant tests arerequired.It is important to note also th at dual composition controlis not needed in order to minimize energy consumptionwhen feed rate changes occur. Throughput disturbancescan be simply handled by ratioing reflux or heat input tofeed r ate while controlling one product composition.Feed composition variations are the principal distur-bances that require a dual composition control system inorder t o minimize energy consumption. Therefore the ene r-gy savings of dual composition control must come primarilyfrom achieving the minimum vapor boil-up/feed ratio(V/F s feed composition disturbances are encountered.Steady-State Calculations

To quantitatively determine the economic incentive fordual composition control, a series of s teady-stat e distilla-tion calculations should be made to compute VlF ratios forvarious control systems over a suitable range of feed com-positions. The three alternative control systems or operat-ing strategies are constant reflux operation, constant-heat-input operation, or constant-product-composition opera-tion. Th e last will yield th e lowest VlF ratios, but t he firsttwo cases mu st be calculated to see if the incentive for dualcomposition control is significant enough to justify poten-tial dynamic problems and increased instrumentationcosts.Ind. Eng. Chem. Fundam. Vol. 14, No. 4. 1975 321

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l D

1.0

1 6

i t t V/FAV

xo

1.4

Figure 1. Typica l dual composit ion control system.

V / F A v

a = 2 N = 2 3 N I t

1.2

3

1.0

1.4

1.2

1.0 R/F\I

0 3 0.4 0 8 0 0 0 7X FFigure 2. Energy requ iremen ts for three differ ent control systems.

1 ) Constant Product Composition Case. Calculatethe vapor boilup V and reflux R required to achieve thespecified product purities X D nd X s feed compositionXF varies over a typical operating range experienced in theplant. These calculations are performed for a fixed column,i.e., one with a fixed number of total trays NT and a con-

a = 2 N = 4 6 N = 21I C O N S T A N T X /X = 0 999/0 001

t

-R / F1.2

1.1 L0 B 0.4 0 6 0.6 0. T

Figure 3. Energy requirem ents for three different control systems.X F

stant feed plate location NF.The top curves in Figure 2give the V I F and R IF ratios required to maintain X D andX t 0.95 and 0.05, respectively, for a 23-tray column fedon the 11 th tray in a system having a constant relative vol-atility of 2. The maximum V l F ratio 1.505) occurs in thiscase at t he top of the X F ange studied.2 ) Constant Vapor Boilup Case. Fix the vapor boilupat the maximum value calculated for any of th e cases in 1)above, and hold one product composition constant (eitherXD r X B by manipulating reflux. Since excess vapor boil-up is being used, th e composition of the uncontrolled prod-uct will always be better than specification purity. Themiddle curves in Figure 2 show how the R IF ratio changesfor this fixed V l F operation. At a feed composition of 0.50the V I F ratio is 0.094 higher using a fixed V IF ratio thanusing dual composition control. This represents a 6.7 in-crease in energy consumption at this feed composition.Less energy will be wasted at higher feed compositions, andmore a t lower feed compositions.3 ) Constant Reflux Case. Fix the reflux rate at themaximum value calculated for any of the cases in 1)above,and hold one product composition constant by manipulat-ing vapor boil-up. Since excess reflux is used, the uncon-trolled product purity will always exceed specification. Thebottom curves in Figure 2 show how the VlF ratio changesfor this fixed R IF case. At X F = 0.50 the VlF ratio is only0.0074 higher (0.5 ) than the minimum dual-compositioncase. Thus for this particular column, a constant reflux-to-feed control system will be very nearly as energy-efficientas dual composition control (if X F = 0.50 is the averagefeed composition tha t the column operates with).

322 Ind. Eng. Chem., Fundam., Vol. 14, No. 4, 1975

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a 2 X, ~ 0 . 9 5 X, = 0 05 N 19

V / F

0.4 0.6 0 EX ?Figure 6. VIF ratios for various feed trays.

a = 2 X 0 999 X = 0 001 N 641

V/

X D / X B = 0 . 99 / 0 . 01301 0 0 0

0 0 00 0 0 0 0

o o a

I x , / x , = o . ~ ~ / o . o I a a I aa x

0.2 0.4 0.1) 0 8X F

Figure 8. Optimum feed t ray locat ion.

1.0

1.6

V/1.4

1 2

11

0 .999/0.001I

2 0.4 0 6 0.1X F

0 8 0 8 Figure 9. VIF ratios for a f ixed feed t ray and for the opt imumfeed tray a t each feed composition.0 . 2 0.4

X FFigure 7. VIF ratios for various feed trays.

tha t the feed tray should be moved u p the column as thefeed composition becomes lighter. This is probably a resultth at most engineers would intuitively feel is a general one.some fixed location, can be quite significant (see Figure 9).The column and system considered in Figure 6 showed324 Ind. Eng. Chem. Fundam. Vol. 14, No. 4 1975

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Figure 7 illustrates a different system in which just th e re-verse is true.In this high purity case the optimum feed tray location isseen to move down the column as X F ncreases. Figure 8shows how th e optimum feed plate varies with feed compo-sition for several values of product purities and relativevolatilities. High-purity columns require a decrease in feedtray location as feed composition increases. Although thisresult may be unexpected, i t is easily understood by consid-ering what happens on a simple McCabe-Thiele diagramfor high-purity products. As feed composition increases,the difference between the slopes of the equilibrium linenear the X = 1 point a nd th e rectifying operating line de-creases. More trays are required in the rectifying sectioneven though the difference in composition between X F ndX D ecreases. The reverse is true in the str ipping section asX F ncreases, so fewer trays a re needed below the feed tray.NomenclatureB = bottoms flow rateCC = composition controller

D = distillate rateF = feedrateLC = level controllerPC = pressure controllerNT = total number of theoretical trays in the columnNF = number of trays in the stripping section (feed trayNFOPt = optimum feed trayR = reflux rateV = vapor boil-up rateX composi tion of bot toms (mole fraction more-vola-X D = composition of distillate product (mole fractionX F = feed composition (mole fraction more-volatile corn-a = relative volatilityAV = difference in V / F ratio between a given system andthe minimum V / F ratio attainable with dual compositioncontrol

number)

tile component)more-volatile component)ponent)

Receiued for reuiew ecember 30, 1974Accept ed June 27,1975

On the Estimation of Thermal Conductivity of Organic Vapors. Datafor Some Freons

A . Burl DonaldsonSandia Laboratories Albuquerque New Mexico 87115

This paper describes and presents the results of analytical and experimental studies performed to determinethe thermal conductivity of organic vapors. In the analysis data collected in an experimental study of five com-mercial Freons C-318 22 114 12 and 13B1 are analyzed to establish a mathematical model for predictingthe thermal conductivity of organic vapors in general. The model utilizes a sequence of previously publishedproperty relations to estimate the thermal conductivity from the molecular structure and the normal boilingpoint. For both the analysis and the experiment the pressure is atmospheric and the temperature range is 3OCto 78OC.

IntroductionThe purpose of this study was to determine if gases oflow thermal conductivity, comparable to xenon, exist. Apurely experimental investigation would eventually yieldthe desired information; however, an analytic study wouldidentify those parameters which affect the thermal conduc-tivity of a gas and thereby would minimize the number ofcandidates for experimental determination. Numerous th e-

oretical studies of the thermal conductivity of gases havebeen reported in th e literature (Reid and Sherwood, 1966);however, application of the methods used in those studiesto gases in general requires a knowledge of propertieswhich are not always available. Therefore, in the analysisdescribed in this paper, a sequence of empirical and theo-retical relationships is used which will allow the estimationof thermal conductivity of an organic vapor by knowingonly its molecular structure and normal boiling point, twofactors which ar e generally available for an identified gas.Substantial experimental investigations on the thermalconductivity of Freons have been reported in th e literature.Tsederberg (1965) and Touloukian et al. (1970) have com-piled the results of several studies on common Freons and

Mas il an d Sonet (1961) give dat a for several of t he lesscommon Freons.Theory

On the basis of theoretical arguments and mean valuesfor the Buckingham and Lennard-Jones potentials, Hirsch-felder (1957) proposed an improvement to the usual Euck-en relationship for the t hermal conductivity of a polyatom-ic gas A 0.115 0.354 ?Rwhere A is the thermal conductivity of a polyatomic gas, Ais the thermal conductivity assuming an equivalent rigidsphere gas, C is the constant pressure specific heat, and Ris the gas constant. Instead of the usual form of the Chap-man-Enskog equation (Hirschfelder et al., 1954) for thethermal conductivity of a rigid sphere gas, a form suggestedby Bromley and Wilke (1951) will be used

where t / k is an interaction parameter, M is molecularInd. Eng. Chem. Fundam. Vol. 14 No. 4, 1975 325