3
z
degree of polymerization of free radicals concentration of polymer of chain length j , moles/ liter 2-transform #ofthe polymer chain length distribution, moles/liter volume rate of production of species s, moles (liter)-l (minute) -:‘ concentration of free radical of length i, moles/liter Z-transform of the free radical chain length distribution, mole!r/liter species s time, minutes frequency of the oscillation, radiansjminute input oscillatory function (sinusoidal in this case) any dependent variable dispersion defined by. Equation 71 . 2-transform variable
GREEKLETTERS dimensionless constant, kldl, dimensionless constant, kz8M, dimensionless constant, k&4, fractional amplitude of input oscillation dimensionless constant dimensionless constant average residence time of material in vessel, minutes dimensionles!r time dimensionless kth moment of free radicals average fractional deviation from steady-state value of kth moment of distribution of free radical chain length kth moment of distribution of polymer chain length, moles/liter
pkrn
=
Yk
=
vkrn
= =
Ck
=
3k
=
’
=
kth moment of distribution of polymer chain length a t steady state, moles/liter kth moment of distribution of free radical chain length, moles/liter kth moment of distribution of free radical chain length a t steady state, moles/liter dimensionless constant, kld dimensionless kth moment of distribution of polymer chain length defined by Equation 22 average fractional deviation from steady-state value of kth moment of distribution of polymer chain length notation to designate perturbed variables
literature Cited
Abraham, W. H., Ind. Eng. Chem. Fundamentals 2, 221 (1963). Bamford, C., Barb, W., Jenkins, A., Onyon, P., “Kinetics of Vinyl pp. 71, 219, ButterPolymerization by Radical Mechanisms,” worths, London, 1958. Denbigh, K. G., Trans. Faradav Sod. 43. 648 11947). Douglas,’ J. M.; IND.ENG. CHEM.PROCESS DESIGNDEVELOP. 6, 43 (1967). Douglas, J. M., Rippin, D. W. T., Chem. Eng.Sci. 21, 305 (1966). Horn, F. J. M., Lin, R. C., IND.ENG.CHEM.PROCESS DESIGN DEVELOP. 6, 21 (1967). Kilkson, H., Ind. Eng. Chem. Fundamentals 3, 281 (1964). Kruissink, Ch. A., Van der Want, G. M., Staverman, A . J., J . f % l p ~ eSci. r 30,67 (1958). Miyake, A., Stockmayer, W. H., Makromol. Chem. 88, 90 (1965). Saidel, G. M., Katz, S., A.Z.CI2.E. J . 13, 319 (1967). Zeman, R. J., Amundson, N. R., A.Z.Ch.E. J . 9,297 (1963).
__
RECEIVED for review October 30, 1967 ACCEPTED March 27, 1968
CHEMICAL REACTORS Intuence of Packing on Effective Reactor Volume A L B E R T R. SHUKI,’ T H O M A S E. CORRIGAN,2 A N D M I C H A E L J. Ohio Staie University, Columbus, Ohio
DEAN2
When an ernpty vessel with a low ratio of length to diameter is used as a continuous flow chemical reactor, the flow pattern involves a considerable amount of backmixing. The empty vessel may behave as the perfect mixer or the mixer with d e a d space. Putting a tower packing in such a vessel will have a twofold effect: the effective volume will b e lessened, and the amount of backmixing will be reduced. The net effect depends upon packing characteristics, packing size, and void volume. The flow pattern will depend upon the packing characteristics and can b e evaluated in terms of the axial dispersion model or the series of tanks model. This paper evaluates the two effects of adding packing for various types of packings.
a packing material to a n empty unstirred vessel of low ratio of length to diameter will considerably reduce the backmixing when the vessel is used as a continuous flow reactor (Bauer and Corrigan, 1967). The increase in capacity due to the lessened backmixing is counterbalanced by the decrease in active volume due to the space occupied by the packing. Whether the net effect of adding packing is to increase or decrease the reactor capacity depends upon the nature of the ADDING
Present address, Standard Oil Co., Cleveland, Ohio. Present address, Mobil Chemical Co., Edison, N. J.
packing, the length to diameter ratio of the vessel, the degree of conversion, and the kinetics of the reaction. The purpose of this paper is to evaluate this effect for various types of packing a t low LID ratios and at various degrees of conversion, Since unstirred vessels with low length to diameter ratios can behave as perfect mixers with up to 18y0dead space, depending upon flow patterns (Sonawala, 1966), the perfect mixer was chosen as the criterion for the vessel with no packing. The vessel with packing was represented by the axial dispersion model. Values of (D/uL) were determined from the packing characteristics and the length to diameter ratio of the bed (Leva, 1951 ; Levenspiel, 1962). VOL 7
NO. 3
JULY 1968
433
Table 1.
k0 n 1 2 3 4
Effect of Packing on Conversion at L/D of 0.5 Conversion. 9% 3-inch 2-inch ceramic metal 3-inch Raschig Raschig spheres, rings, rings, 347, free 74% free 92% free space, space, space, h’o D/uL = D/uL = D/uL = 0.0354 packing 0.247 0.720 n n 0 0 56.0 27.1 49.8 58.9 82.8 44.5 72.5 66.7 92.2 57.3 84.1 75.0 96.4 65.9 90.4 80.0
Packing Data
The three packings investigated were spheres, stoneware Raschig, and metal Raschig rings. The important factors considered were the equivalent sphere diameter, the per cent free space, the length to diameter ratio, and the axial dispersion number for the packing. Wall effects are neglected, since the packing is less than one tenth the reactor diameter. T h e evaluation is made based upon first-order irreversible reactions. The vessel without packing was evaluated as a continuous stirred tank reactor and with packing as the axial dispersion model. The model with open-open boundary conditions was used. The equation for these boundary conditions is: In (1
- x)
=
(h)
(1
- 2/1+4ab)
(11
Results and Conclusions
Reactors with L I D ratios of 0.5 were evaluated, using the axial dispersion model. Values of (D/uL) were estimated using the generalized value of ( D &,) = 2.0 (Levenspiel, 1962, page 275). Mean axial velocities were restricted to values which gave Reynolds numbers between 0.1 and 100.
434
I & E C PROCESS DESIGN AND DEVELOPMENT
T h e results for 3-inch spheres, 2-inch metal Raschig, and 3-inch ceramic rings are shown in Table I. I t can be seen that the effect of spheres is negative-that is, the spheres occupy so much volume that any improvement in flow characteristics is more than nullified. Both the metal and ceramic Raschig rings increase the reactor capacity, since the reduced backmixing more than compensates for the space occupied by the packing. For the spheres, the void volume is only 34% and the value of D/uL is 0.247 at an L / D ratio of 0.5. The best results were obtained for 2-inch metal Raschig rings with 92% void volume and a D/uL value of 0.0354 a t an L I D ratio of 0.5. The criteria of the effectiveness of a packing are: high void volume, small packing size (low dp/L), and low value of (DIeud,). There is a lower limit to packing size, or practical considerations such as pressure drop will come into effect. I t can be concluded that some packings will increase reactor capacity. Nomenclature a
= dispersion number, D/uL
b = D = D = dp =
L = u =
e = x =
nominal dimensionless first-order holding time, eke dispersion coefficient diameter of vessel nominal equivalent packing diameter reactor length velocity void fraction conversion
literature Cited
Bauer, J. L., Corrigan, T. E., Chem. Eng. 74,111 (1967). Leva, Max, “Tower Packings and Packed Tower Design,” United States Stoneware Co., Akron, Ohio, 1951. Levenspiel. Octave. “Chemical Reaction Engineering,” Wiley, .. New’York, 1962. ’ Sonawala, S. K., “Kinetic Study of Second-Order Chemical Reaction in Steadv and Transient Tank Flow Svstem,” Ph.D. dissertation, Ohio ’State University, 1966. RECEIVED for review October 16, 1967 ACCEPTEDFebruary 14, 1968
