Efficiency in bubble cap distillation columns

Chemical Engineering Science, 1966, Vol. 21, pp. 833-835. Pergamon Press Ltd., Oxford. Printed in Great Britain.

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Efficiency in bubble cap distillation columns

(Received 22 April SEVERALinvestigations have shown that the performance of a distillation column appears to be a function of composition [1, 2]. This variation in performance has been observed for many different systems and column types, and the reason would appear to be one which is general to the process of rectification rather than specific to any given circumstances. This communication is concerned with the variation in performanee for bubble cap columns. The description of mass transfer on a bubble cap plate must necessarily be considerably simplified due to the complex fluid dynamics of such a device. If one assumes plug flow of vapour and a liquid which is well mixed vertically, then for an area of the tray where the liquid composition is uniform the basic rate equations can be integrated to give [3]

(

kgaPYG

In I

Further, unless there is a large separation and a marked curvature on the equilibrium line, the mean value of ~ may be taken as the value at y = yl and we have simply that

Eog

1

y2--yz) ~1

Eog)

(I)

If we assume that Ng m a y be regarded as constant for any particular plate, we m a y write

-- ln ( l -- Eoa) = ~--~ayfY2 ~ dy yz Yt -- Y y, _ y

~

G 1 (4)

~[~1/2)I= (Ng S c l / 2 ) I I

(2) of

In order to compute Eog from Eq. (3) we require the value ku]kx = ft. The work of A~rDREWS [4] suggests that the

~00 90

•-- Acetone water

o 0

80

o o

o

0

0

O0 0

oo O

o

70

Fitted theoretical

60 t,l

50 40

Total reflux F Factor 0-57

30 20 I0 0

T io

I 20

30

(3)

It must be emphasised that mg is the slope of the chord joining the points xj, y~ and x, y* and not the slope of the equilibrium curve at x, y*, the value frequently used. The use of this equation requires expressions for Ng and NL and the two models chosen for the gas and liquid phases which form the basis of the A.I.Ch.E. design report [3] are in fact completely different. Equation (4) is in itself nothing more than an algebraic transformation of the integrated rate equations based on one model of mass transfer, in this case the gas phase, using over-all driving forces. It is not justifiable to define two different models for the individual phases and then compound them by use of Eq. (4). If we assume that, for a given tray design, F factor and liquid rate, Ngoc Sc -z/~ [3] we can compute both the variation in Ng as a function of composition and also predict from one system to another, viz. : (Ng

where

1

~wo'~--= lv~ + mg Z ~

y*

--In (I --

= I - exp ( - - N g ~ = u l )

In systems in which liquid phase resistance is present Gerster recommends the use of the familiar equation

or in the usual nomenclature

Nog =

1966)

40

50

60

Mean liquid composition,

Fzo. 1

833

I

70 m01e %

t

80

1

90

ioo

Shorter Communications I00 Acetone benzene 90 --

o

~o~o %

oo

o

m 0

7C-6C--

J

o

o

o

~'r.~o = 0 . 0 47 Theoretical

5C 40 Total reflux F Factor 0.57

3C 2C IC

1

I0

I

50

20

I

40

~

50

I

60

Meon liquid composition,

I

70

1

80

90

tO0

mole %

F1G. 2

these "fitted" values. Computation of the variation in No and ~ as functions of composition requires a knowledge of the diffusion coefficients, gas density and viscosity, at the corresponding saturation temperatures. The gas phase properties were computed from the pure component properties using the kinetic theory and the liquid diffusion coefficients were experimentally determined values taken from the literature. The computed efficiency curves are shown in Figs. 2 and 3 together with the experimentally measured efficiency values, and it can be seen there is very good agreement between theory and experiment, particularly in that in one case the efficiency falls off markedly below mole fraction 0"2 and in the other case not. We conclude that much of the experimentally observed variation in efficiency for these systems, distilled in bubble cap columns, may be accounted for by a simple model taking into account the presence of liquid film resistance.

correlation for the film coefficients can be reduced to the simple form a = 0"7 ull~S 112

cm2/cm a

ka = 7 uz/4S-1/~Dg 1/~

cm/sec

kr, = 11 uz/as-I/aDL 1/~ cm/sec This is the same dependence of fl on the diffusion coefficients that would be obtained assuming a penetration type mechanism for the mass transfer processes in both phases. Thus we will use Eq, (3) to compute the values of Eoa and we assume that Ng ocSc -112 and kg/k~ oc( Dg/ DL) I/~ with the appropriate transformation from the concentration to mole fraction units. The efficiency results of the N o r t h Carolina State College [5] were used to check this model which is regrettably still inadequate in that it is a highly idealized picture of the plate. The acetone water system was chosen as unknown in the two parameters Ng and fl and the fitted curve and experimental points are shown in Fig. 1. The values of N¢ and fl were then predicted for the other systems from

C. T. EVEgITT H. P. HUTChUSON

Shell Department of Chemical Engineering Cambridge

I00 Ethanol water 90,

o

% o

-

80 -

°o

oo

o;

o

ooo o

7C

/

Oo

Theoretical

6C

~ 5o 4C 3C h

Total reflux F FoctorO'57

/3r--"o =0"1

20-tO-I0

I

I

I

I

i

20

30

40

50

60

Mean liquid composi! on ,

FXG. 3 834

mole %

I

I

;

70

80

90

IO0

Shorter Communications

NOTATION a D E F G K L N P R

S Sc u y ~b

interfacial area diffusion coefficient point efficiency F factor vapour molal flow rate mass transfer coefficient liquid molal flow rate number of transfer units pressure gas constant

slot submergence Schmidt number superficial vapour velocity vapour mole fraction composition function

Superscript *

equilibrium value

Subscripts g i l og

vapour phase interface liquid phase overall vapour phase

I~FERBNCES [1] [2] [3] [4] [5]

HASELDENG. G. and SUTHERLANDJ. P., Int. Syrup. Dist. (Brighton) 1960 Inst. Chem. Engrs London. SAWITOWSKIH. and SMrm W., Ind. Engng Chem. 1959 51 915. GERSTERJ. A. et aL, Bubble Tray Design Manual, Am. I. Ch. E. 1958. ANDPmWSS. P. S., Alta Technologie Chemica, Proeessi di Seambia Academica Nationale dei Lincei, Rome 1961. Tray Efficiencies in Distillation Columns, Am. I. Ch.E., Final Report, Carolina State College, New York 1958.

Chemical Engineering Science, 1966, Vol. 21, pp. 835-836. Pergamon Press Ltd., Oxford. Printed in Great Britain.

X-ray investigations of flowing powders (Received 6 April 1966) DURING THE course of investigations into the flow of granular materials from bunkers (with special reference to handling wet coal), it seemed possible that additional information could be obtained by taking X-ray radiographs. It was expected that gradations in powder density would show and be related to varying pressures in the powder and it was also expected that strains and velocities could be shown up using small markers. Both these effects have been found. In addition, it was discovered that very distinct and discontinuous internal surfaces of low powder density showed up in X-radiographs of static powder left in a container after flow had taken place. These surfaces are reported here and their significance is discussed. The apparatus comprised an X-ray machine which directed 95 kV X-rays at material in a hopper placed 10 ft away, the front face of which was normal to the X-ray direction. The X-ray sensitive film was placed close to the rear face of the hopper and received varying amounts of irradiation depending upon the density of the material in the hopper. The hoppers were mostly constructed of perspex, though occasionally the front and rear surfaces were of glass. The thickness of the hopper in the direction of the X-rays was 6in., and the sloping walls were variable in angle to the vertical from 5°to 90 ° with a slit to form the bottom exit for material flow of about lin. width. A constant head was maintained in this main hopper by using a subsidiary hopper. Material was removed from under the bunker by a belt conveyor moving towards one side. Rough walled hoppers were made by lining the sloping walls with sandpaper.

It was found that a granular material rather than a spheri cal powder gave greater contrast in the density patterns. The material mostly used was Lustrex Polystyrene type X866 crystals, supplied by Monsanto Chemicals Limited. This had been sieved to pass between 1/32in. sieve and a No. 36 (0"017 in.) sieve. After filling the hopper with the polystyrene material, each was emptied until at least the total volume of the hopper had flowed under conditions of constant head. Flow was then stopped and still X-ray photographs were taken. Figures 1 and 2 show typical results for a 15° hopper with smooth and rough sides respectively. In all cases a number of lines indicating surfaces of low powder density were revealed. It seemed a reasonable assumption that these were surfaces of slip, and visual observation of flow confirmed that slip occurred along lines of similar shape. Cine-film of the emptying suggests that shear occurs at any moment only over a few of the many slip surfaces subsequently visible in the radiograph. It looks probable that these surfaces move down with the powder at least for some distance, and the radiograph reveals all the surfaces over which shear has occurred during some previous period. Further evidence in support of the suggestion that these are slip surfaces is provided by comparing their shape with shapes predicted for slip lines for the failure of a plastic material in the shape of a wedge. Computed solutions have been given for this by, for example, JENIKE[1 ], and the boundary conditions can be deduced from the properties of the powder at the surfaces of the retaining walls. The computed

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