ChemicalEngineeringScience, VoI. 5 l, No. I 1, pp. 313 |-3137, 1996 Copyright O 1996 Ehevi¢~ Science Ltd Printed in Great Britain. All rights reserved 0~9-2509/96 $15.00 + 0.00
T E M P E R A T U R E O S C I L L A T I O N C A L O R I M E T R Y IN S T I R R E D T A N K R E A C T O R S
A. TIETZE, I. LUDKE, K.-H. REICHERT (Institut fdr TeclmischeChemie,Sekr. TC 3, TechnischeUniversitatBerlin, StraBedes 17. Juni 135, 10623 Berlin,Germany)
Abstract - Temperature oscillation calorimetry in laboratory scale stirred tank reactors has been applied to the free radical polymerization of acrylic monomers in solution. R has been shown that this method can be used to determine on-line during the reaction the heat transfer value of the reactor and simultaneously the rate of reaction. The information about the heat transfer value is contained in small, forced temperature oscillations. The experimental setup of the calorimeter used is simple and consists only of commercially available components. This new method can also be incorporated into existing laboratory scale stirred tank reactors.
INTRODUCTION The aim of a reaction calorimetric study is the correct evalulation of rate and conversion of a chemical reaction. These quantities are obtained from the chemical heat flow Q chumwhich is calculated from the energy balance of a stirred tank reactor: Cp~ dTR dt - UA(Tj -TR) + Qoh~+ Q,o~ + P , t ~
In case of a constant heat transfer value UA during the reaction the heat transfer value can be determined by calibration before the reaction. However, in case of significant changes of the heat transfer value during the reaction the chemical heat flow can no longer be calculated from eq. (1). A common procedure is to perform a second calibration atter the reaction and estimate the change of the heat transfer value afterwards by linear interpolation between these two values, in the most simple case. This procedure may lead to false results and gives no information about the change of the heat transfer value during the reaction. The problem of a correct calorimetric evaluation despite a changing heat transfer value may be solved with the heat balance calorimetry which makes use of the overall energy balance of jacket and reactor . The disadvantage of the heat balance calorimetry is the complex setup with its need for well trained personnel. In contrast, the temperature oscillation calorimetry requires only a comparably simple setup. Temperature oscillation calorimetry makes only use of the re,actor energy balance and determines already during the reaction the heat transfer value from forced temperature oscillations. This new method in laboratory scale stirred tank reactors  to determine the chemical heat flow simultaneously to a changing heat transfer value requires only the use of a mathematical procedure for evaluation of the measured data and a slightly modified process operation.
SETUP OF THE CALORIMETER The calorimeter used (fig. 1) is built up from commercially available components. The re,action vessel (1) is a jacketed stirred tank reactor (2 1, stainless steel) with a heated lid. The stirrer is a combination of an anchor stirrer and helix stirrer and especially suitable for mixing a viscous reaction mass. A simple 3131
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® Figure 1: Setup of the temperature oscillation calorimeter: (1) stirred tank reactor with heated lid and stirrer, (2) main thermostat for temperature control, (3) thermostat for the lid, (4) data aquisition and control unit thermostat (3) keeps the lid of the reactor on reaction temperature and minimizes the heat losses to the surroundings. The main thermostat (2) controls the jacket temperature and allows to track a desired setpoint of the reactor temperature. The setpoint is passed from the PC via the serial communication port. Since this thermostat contains no tempering bath, which is common to usual thermostats, a very dynamic temperature control is possible. A digitial muitimcter (6 ½ digits) performs the data aquisition (4) of all analog signals and measures the PT100 sensors with a resolution of 1 mK. The digital multimcter communicates via an IEEE-Bns with the PC (486-66DX/2) which processes the data under Windows. The measured variables are the jacket inlet fin) and outlet temperature (Tj2), the reactor temperature (TR), the torque of the stirrer (Md) and the stirrer
speed 0q). CALORIMETRIC EVALUATION The evaluation of the energy balance of a stirred tank reactor (eq. 1) is performed in two steps and has been significantly simplified compared to former works . In thefirst step the heat transfer value UA is calculated from the temperature oscillations. For this, only the oscillating contributions to the energy balance are considered. Those terms which contribute only slightly to the heat oscillations are neglected ( 0 ~ , 0 l~,, P,,r~). This leads to:
Temperature oscillation calorimetry
Cp~ dTg = UA (T, - TR) (2) dt with the oscillat~ parts of the temperatures Tj = 6T~ei®t and Tg =~TR ei(e0t+q~l) . In this notation it is assumed that the temperatures oscillate in the same way as the sinusoidal heat input. Considering the imaginary part and the real part ofeq. (2) an equation for the heat transfer value can be derived:
UA=-°% I. L
The quotient of the temperature amplitudes 6TR and 8% can be directly ealcul~t~ from the oscillating parts of the raeasured temperatures integrating over one period t, of data:
[Jo r f,t. ~ 2
8TR= d(c0t__.____~) TI~ 6Yj
~ ' T 2 d(cot)
The integral heat capacity Cg is given by the sum of the heat capacities of reactants and stirrer. Eq. (3), used here to calculate the heat transfer value, gives the same results but is easier to compute than the equation reported in . The heat transfer value can not only be calculated off-line from eq. (3) but also on-line with a delay of one period. In the second step the reactor energy balance without the oscillating heat contributions is considered and the chemical heat flow Q ~hm is calculated from eq. (1). Although the calorimeter operates under isothermal conditions it is necessary to consider the accumulation term C~ dTR/dt which can be calculated with numerical differentiation. The heat transfer value UA is given by eq. (3). The power input of girting P ~ can be determined from the measured torque and the stirrer speed. The heat loss Q Io~ can be evaluated from the base line difference between reactor and jacket temperature before the reaction. Rate of re,action and conversion are subsequently calculated from the chemical heat flow: Qoh~m r - VR(--AHR)
X = f rVg dt no
PROCESS OPERATION A characteristic feature of the temperature oscillation calorimetry performed in this work is that to the constant setpoint of the reactor temperature a small sinusoidal temperature oscillation is added. The oscillating setpoint forces an oscillating heat input into the heating device of the thermostat. The amplitude of the setpoint has to be chosen large enough at the beginning of the reaction (conditions of good heat transfer) so that the amplitude of the oscillation in the reactor temperature is still measurable (minimum 0.1°C) at the end of the reaction (conditions of poor heat transfer). The period of the oscillation should be chosen as small as possible. Yet, because of the low pass behavior of the reactor and the decreasing comer frequency the period for laboratory reactors is always in the range of minutes. A reasonable period t, for the calorimeter used is 6 rain and the decrease of the amplitude of the reactor temperature oscillation is less than five times of its initial value. An alternative is to start with a small amplitude in the setpoint and to increase the amplitude during the reaction. This procedure leads to disturbances in the heat transfer value which are due to the mathematieal calculation and not to a measured effect in the process. Therefore, this procedure has not been used.
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RESULTS The temperature oscillation calorimetry was applied to the free radical polymerization of an acrylic monomer in water. A characteristic of this reaction is a strong increase of viscosity in the reaction mass: Recipe:
acrylic monomer des'filled water initiator TR N period t~ amplitude of the setpoint oscillation
225 g 1285 g 1.0 g 50°C 160 rpm 6 min 0.9°C
o 48 Tj 47 46 I -50
I 50 time lminl
Figure 2: Temperatures of the reactor (bold line) and the jacket (normal line) during the solution polymerization of an acrylic monomer at 50°C Fig. 2 shows the course of the temperatures in the reactor and jacket. At time t=0 the reaction is started by injecting the initiator solution. The amplitude of the reactor temperature decreases from 0.6°C to 0.2°C during the polymerization. The measured torque (fig. 3) reflects the large increase of viscosity during the solution polymerization (about 3 orders). Fig. 3 shows also the course of the calculated heat transfer value which decreases to 20% of its initial value. The heat transfer value before the reaction is the same as obtained by a calibration measurement (63 W/K). This shows that with the use of the temperature oscillation calorimetry a calibration heater is no longer necessary. The value of the integral heat capacity is 5950 J/K. With the determined heat transfer value the chemical heat flow 0 ~h~ can be calculated from the reactor energy balance. The chemical heat flow leads with eq. (5) to the rate of reaction and conversion (fig. 4). The calorimetrically calculated time course of the conversion agrees well with conversion values obtained from off-line titration measurements (ll).
60 20 50 4o
time [mini Figure 3: Heat transfer value and torque of the stirrer during the solution polymerization of an acrylic monomer at 50°C
0.6 i L.
Rate of reaction and conversion of the solution polymerization of an acrylic monomer at 50°C
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The same reaction has been carried out in semi-batch operation in a l-liter glass reactor with an anchor stirrer using the following recipe: Initial reactor contents:
destilled water initiator acrylic monomer destilled water
400 g 0.5 g 75 g 280 g
The feed rate was 5 g/min over a time period of 71 min; the other reaction conditions remained the same as in the batch experiment. The procedure for the calorimetric evaluation is the same as described above for the batch operation. The only difference is that in the reactor energy balance (eq. 1) the feed stream has to be aegounted for: Qdo~= thcp0(T0 - TR). This leads also to a more complex equation for the calculation of the heat transfer value UA. In the experiment the heat transfer value increases during feeding because of the increasing heat transfer area. In the subsequent batch period UA decreases because of the increasing viscosity. The resulting chemical heat flow and conversion are shown in fig. 5.
0.9 0.8 0.7
. . . . . . simulation
0 0 start of feeding and initiation
end of feeding
Figure 5: Chemical heat flow (measured and simulated) and conversion of the solution polymerization of an acrylic monomer at 50°C in semi-batch operation The conversion calculation is based on the total amount of monomer and is therefore the same in the semibatch and batch period. The chemical heat flow obtained from a simulation shows a time course of the chemical heat flow without inhibition. The underlying mathematical model assumes three reaction steps: initiation, propagation and bimolecular termination. The rate constant of initiation kd = 0.8.10 -s [1/s] is taken from the manufacturer  and the ratio of rate constants k:p/kt = 12.43 [I/mol s] is estimated from batch experiments. The measured chemical heat flow shows a time lag due to inhibition which leads to a larger monomer accumulation during feeding. Therefore, the chemical heat flow in the experiment during the batch period is higher than in the simulation.
Temperature oscillation calorimetry
NOTATION C~ [J/K] c.~
kp kt AHR r no
[l/mol s] [l/mol s] [J/mol] [mol/1 s] [mol] [g/s] [Ncm] [I/s]
integral heat capacity of the reactor specific heat capacity of the feed stream rate constant of initiation rate constant of propagation rate constant of termination enthalpy of reaction rate of reaction mole of monomer at the beginning of the reaction mass flow rate of the feed stream torque of the stirrer stirrer speed chemical heat flow
power input of stirrer time period of oscillation reactor temperature jacket temperature [ Tj = 1 /2 (TjI + Tj2 ) ] oscillating part of the reactor temperature oscillating part of the jacket temperature amplitude of the reactor temperature oscillation amplitude of the jacket temperature oscillation temperature of the feed stream heat transfer value volume of reaction mass conversion phase shift frequency
To UA VR x q~R o
[K] [W/K] [m31
[-1 [rad] [l/s]
convective heat flow of the feed stream
REFERENCES  Schmidt, C.-U., Reichert, K.-H., 1987, Chem.-Ing.-Tech. 59, 739-42  DE-PS 4334828, 1993, Carloff, R., Prol3, A., Reichert, K.-H.  Carloff, R., Profi, A., Reichert, K.-H., 1994, Chem. Eng. Techn. 17, 406-413  Tietze, A., Profi, A., Reichert, K.-H., in Dechema Monographs, Vol. 131, 5th International Workshop on Polymer Reaction Engineering, ed. Reichert, K.-H, Moritz, H.-U., VCH, 673-680  Product information V-50, WAKO Chemicals, Hamburg ACKNOWLEDGEMENT A. Tietze gratefully acknowledges the financial support by the Deutsche Forschtmgsgemeinschai~ through the Graduiertenkolleg "Polymerwerkstoffe" at the TU Berlin.