Effect of geometrical parameters on conversion in

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Department of Chemical Engineering ... C φ. = -(1). PDF created with FinePrint pdfFactory trial version www.pdffactory.com .... V = volume of column, cm3.
Effect of geometrical parameters on conversion in sieve tray column as reactor from RTD studies By Dhaval Mehta, J.L.Purohit*, Dr.N.S.Jayakumar Department of Chemical Engineering D D Institute of Technology (Deemed University) College Road, Nadiad-387 001 [email protected]

Abstract An industrial chemical reactor is a complex device in which heat transfer, mass transfer and momentum transfer may occur with chemical reaction and it must be safe & controllable. Mixing characteristics, flow pattern, RTD and efficient utilization of the available geometry of reactor play very important role in industrial application. In the present experimental study, residence time distribution data were collected in sieve tray column. The effect of different geometrical parameters such as tray spacing, no. of trays, column diameter, sieve diameter, on conversion is studied. The relation between them in the form of dimensionless ratios also found out and optimized for desired conversion. The relation,  D C = 0 .04335  Co  uL t

   

0 .354

 Ls  d  h

   

0 .177

 dt  d  h

   

0 .076

 d t / Ls   D / uL  t

   

0 .342

is found to be in satisfactory argument with experimental results. Introduction Sieve tray geometry has been used in various mass transfer operations and also as reactor in a few applications like in urea manufacturing, in hydrogenation of nitrobenzene to produce toluene. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution and efficient utilization of the surface of porous catalysts also arise. One of these factors or can dominate a particular process by several of them; for example, a reactor may on occasion be predominantly a heat exchanger or a mass transfer device. A successful commercial unit is an economic balance of all these factors. The general characteristics of the main type of reactors- batch and continuous are quite clear. Batch processes are suited to small production rates, to long reaction times or to reactions where they may have superior selectivity, as in some polymerizations. They are conducted in tanks with

stirring of the contents by internal impellers, gas bubbles or pump around. Large daily production rates are mostly conducted in continuous equipment, either in a series of stirred tanks or in units in which some degree of plug flow is attained. Using the dimensional analysis technique, the rational relationship between the various geometrical parameters such as tray spacing, sieve diameter, tower diameter etc. and the dispersion number and velocity of the fluid through the sieve tray tower, is obtained. Dimensional Analysis Dimensional analysis allows one to reduce the number of variables that must be considered to model experiments or correlate data. Conversion (Xa) in form of concentration can be expressed in terms of various other parameters or variables by way of functional relationship by this method. Variables affecting the final concentration can be listed in table 1. Table 1 Variable Symbol Unit Dimensional (CGS) Formula Rate constant K sec-1 T Dispersion D cm2/se L2/T coefficient c Length of Lt cm L tower Tray spacing Ls cm L Diameter dt cm L of tower Diameter dh cm L of holes Velocity U cm/sec L/T Initial Co gm/cm M/L3 3 concentration Concentration C gm/cm M/L3 3 at Time t C = φ ( k , D , L t , L s , d t , d h , u , C o ) -(1)

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F = (C , k , D , L t , L s , d t , d h ,u , C o ) = 0

-(2)

Applying dimensional analysis, equation (2) may be written as π = C a , k b , D n , Lt f , Ls g , d t e , d h m , u h , C o i = 0 -------(3) So, from dimensional analysis,  dt   Ls   D   d / Ls  C =  t  φ 3  φ 2  φ 1  C o d h  d h   uL t   D / uL t 

-------(4) Experimentation Residence time distribution (RTD) for waterNaOH system has obtained in sieve tower with varying dimensions. Water has been used as main fluid because it is the cheapest chemical available. NaOH is used as tracer as it can be easily detected using HCl for titration. Water is entered from the bottom of the column and samples are collected from the top. NaOH is injected near the input of water to the system in the form of pulse input. After steady state obtained and the level in the water tank is maintained, the flow rate of water through the tower is measured. To get idea about the residence time of the tracer inside the tower, a dummy tracer, KMnO4 is injected as pulse input and time is noted for the tracer to come out of the reactor completely. Actual tracer, NaOH is injected and samples are collected at regular intervals. The samples are titrated against HCl and concentration of NaOH is obtained. From the experimental results, conversion is calculated. For various dimensions, respective dimensionless terms are calculated and corresponding conversions are tabulated. From this data, relationship between various geometrical parameters and conversion is obtained. Empirical Relation Following dimensionless groups are involved in the present work. 1. Amount of reactant remained in the reactor = C =1-x Co

2. 3. 4. 5.

D = x1 uL t L s = x2 dh d t =x3 dh d t / L s =x4 D / uL t

The above groups are related in the form of dimensionless formula as,  d / Ls C = t C o  D / uL t

  D φ 1    uL t

  Ls φ 2   dh

  dt  φ 3    dh 

---------(5) Assuming polynomial correlation amongst them, 1− x =

C = n ( x1 ) a ( x 2 ) b ( x 3 ) c ( x 4 ) d Co

---------(6) log( 1 − x ) = log n + a log x1 + b log x 2 + c log x 3 + d log x 4 X = N + aX 1 + bX 2 + cX 3 + dX 4 where , log( 1 − x ) = X , log n = N , log x1 = X 1, log x 2 = X 2 , log x 3 = X 3 , log x 4 = X 4

Optimization Values of N, a, b, c, d and n are obtained by applying the linear programming technique to the above problem, which are given below. N = -1.36298, a = 0.3543, b = 0.177, c = 0.0763, d= 0.3415, n = 0.04335 Putting the values in equation (6)  D C = 0 .04335  Co  uL t

   

0 .354

 Ls  d  h

   

0 .177

 dt  d  h

   

0 .076

 d t / Ls   D / uL  t

   

0 .342

--------(7) Discussion & Discussion Equation (7) gives empirical relation between conversion and various geometrical & reaction parameters. Conversion is increases with column diameter and dispersion coefficient. It decreases with hole diameter, tray spacing and length of tower and velocity of reacting fluid. From above variation, it can be inferred that the behavior of the reactor tends to back mix reactor as tray spacing is increased i.e. the number of trays are decreased. Individual tray represents BMR so as the number of trays are increased, BMRs in series are increased and it tends to plug flow and conversion increases. As the velocity of the fluid increases, the flow rate is increased, which causes the behavior to move towards BMR. At low flow rates, the reactor behaves as plug flow reactor. From the comparison of conversions obtained from experimental result and equation, maximum deviation is ±5%, which is in the acceptable range. The equation obtained is derived using the results form experimentation, where the flow rates are varied from 10 cm3/sec to 150 cm3/sec. So the equation can be applicable for acceptable range of flowrates.

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Table 2 Experimental and Predicted Results. Sr. No. D d /L t

uL t

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Ls dh

s

D / uLt

0.33 0.19 0.28 0.38 0.21 0.137 0.314 0.17 0.088 0.18 0.513 0.25 0.31 0.26 0.257 0.512 0.40 0.43 0.47

0.758 0.877 1.78 1.97 4.76 0.5 0.75 5.88 0.5 0.75 0.975 1.33 1.613 2.56 1.297 1.3 0.83 1.163 1.418

Conversion

dt dh

4.0 6.0 60.96 40.64 30.48 152.4 101.6 76.2 38.1 25.4 25.4 60.96 40.64 30.48 38.1 19.05 152.4 101.6 76.2

1.0 1.0 30.48 30.48 30.48 76.2 76.2 76.2 19.05 19.05 12.7 20.32 20.32 20.32 12.7 12.7 50.8 50.8 50.8

Experimental

Predicted

0.994 0.924 0.916 0.876 0.84 0.8 0.863 0.84 0.935 0.958 0.953 0.926 0.834 0.9 0.822 0.757 0.796 0.787 0.814

0.969 0.973 0.865 0.852 0.863 0.878 0.829 0.806 0.941 0.921 0.896 0.893 0.884 0.885 0.912 0.893 0.83 0.82 0.812

Experimental & Predicted Conversion 1.2

1

Conversion

0.8 Experimental

0.6

Predicted

0.4

0.2

0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Figure 1

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17

18

19

Nomenclature: C = Concentration at any time t, moles/liter C0 = Initial concentration, moles/liter dt = Column diameter, cm dh = Hole diameter of sieve tray, cm D = Dispersion coefficient, cm2/sec k = First order rate constant, sec-1 Ls = Tray spacing, cm Lt = Length of column, cm u = Velocity of the reacting fluid, cm/sec V = volume of column, cm3 x = % Conversion n, a, b, c, d = Constants References: 1. Bamford, C. H. and Tipper, C. F. H., Comprehensive Chemical Kinetics, 1, 343 (1969). 2. Curl, R. L. and McMillin, M. L., Accuracies in Residence Time

3.

4.

5.

6. 7. 8. 9.

Measurement, AIChE J., 12, 819 (1966). Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall India, (1992). Hill, C. G., An Introduction to Chemical Engineering Kinetics and Reactor Design Wiley, New York (1977). Jenson, V. G. and Harris, T. R., Mathematical Methods in Chemical Engineering, (1963). Levenspiel, O., Chemical Reaction Engineering, Wiley, New York (1967). Perry R. H. and Green, D. W., Perry’s Chemical Engineers’ Handbook, (1997) Richardson, J. F. and Coulson, J. M., Chemical Engineering, Vol.1, () Shah, Y. T., Gas-Liquid-Solid Reactor Design Series, 327, pp. 58-62, (1979).

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