Znd. Eng. Chem. Res. 1994,33, 814-820
814
Calorimetric Investigation of an Exothermic Reaction: Kinetic and Heat Flow Modeling Ralph
N.Landau;*+ Donna G. Blackmond,' and Hsien-Hsin Tung*
Merck Manufacturing Division and Merck Research Laboratories, Merck & Company, Inc., P.O. Box 2000, Rahway, New Jersey 07065-0900
Utilizing an automated laboratory reaction calorimeter, an energetic reaction was investigated to determine feasible pilot plant operating conditions. The calorimetric data led to kinetic parameters and a predictive heat flow model which allowed simulations of the required pilot plant jacket temperature profiles. On the basis of these profiles, several feasible and safe operating conditions were determined. This study demonstrates the power of calorimetry as it relates to process design and scale-up of batch and semibatch processes. Introduction
R
Pharmaceutical reactions are often accompanied by significant heat release and must therefore be thoroughly understood to manage them successfullyon a factory scale. The heat losses often attendant to laboratory-scale apparatus make it difficult or impossible to quantify the rate of heat release associated with the chemistry being carried out therein. The advent of computer-controlled, laboratory-scale calorimeters has provided a tool to elucidate heat flows accurately to about 0.1 W/L with a high degree of reproducibility [ l - 4 ] . Combining the calorimetricdata thus obtained with kinetic analysisallows for the construction of predictive heat flow models which can be applied to vessels of any volume. The work discussed herein focuses on the development of a heat flow model and subsequent simulations of large-scaleplant vessels ultimately leading to achievable, safe operating conditions. Figure 1 shows the desired chemical reaction which involves the attack of a cyclic sulfite by sodium cyanide in the presence of catalyst and solvent to yield the hydroxynitrile. This step produces an intermediate which ultimately leads to a drug currently under investigation in these laboratories. The proposed plant procedure suggests charging all components at ambient conditions followed by a ramp at 1.5 "C/min from 20 to 90 "C where the reaction is carried out to completion. In our laboratory study heat effects were investigated at temperatures up to 110 "C. Experimental Section The equipment utilized in this study was Mettler's RC1 Reaction Calorimeter 151 outfitted with an MKOl batch reactor. All components were charged to the reactor at ambient conditions followed by a reactor temperature ramp to 90 "C at 1.5 "C/min. After 15 min at 90 "C, the temperature was ramped at 1.5 "C/min to 100 "C. Finally, after 15 min at 100 "C, the temperature was ramped at 1.5 "C/min to 110 "C. The reactor temperature was held at 110 "C until all thermal activity had ceased. A stirring rate of 200 rpm was employed throughout the experiment. These conditions were employed to provide kinetic parameters in the vicinityof the proposed pilot plant operating conditions. Calibrations to determine the heat capacity
* To whom correspondence should be addressed. t Merck Manufacturing Division. 1 Merck
Research Laboratories.
0888-5885/94/2633-0814$04.50/0
A I I
0 ,
o,
R +
NaCN
I
Solvent, Catalyst
HO
S
II
CN
0
Figure 1. Desired chemistry which involves the attack of a cyclic sulfite by sodium cyanide in the presence of catalyst and solvent to yield the desired hydroxynitrile. Reactor
----
Pmbe"0n" I
Time Figure 2. Temperature profiles for the jacket and reactor contents during a typical calibration experiment.
and heat-transfer coefficient were performed prior to and after the reaction period. Calorimetric Procedure The reaction calorimeter analyzes the raw data (temperatures and masses) by the heat flow technique. Therefore, an energy balance is performed with the limits at the reactor outer surface. At any given moment in time, for a batch process, the instantaneous heat flow due to reaction, qr, is given by eq 1, where U is the heat-transfer qr = UA(Tr - Tj)
+ mC,(dTr/dt)
(1)
coefficient, A is the wetted area, Tr is the reactor temperature, Tj is the jacket temperature, m is the mass of the reactor contents, and C, is the heat capacity of the reactor contents. A calibration experiment imposing known qr values on the system is used to solve for the unknown quantities U and C,. Figure 2 shows the temperature profiles for the jacket and reactor contents during a typical calibration experiment. There are two distinct parts to the calibration because eq 1has two unknowns. The first part of the experiment involves a short temperature ramp effected by ramping the jacket temperature. During this period, qr is equal to 0 since there is no heat flow. The second portion of the calibration involvesthe action of a precision heating probe (23.5 W in this case). The calorimeter is instructed to 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 4, 1994 815 120 110
1-
I
Table 1. Calorimeter Evaluated Parameters heat-transfer wffX area at t = 0 (UA)o heattransfer coeff x area at t = if ( U A k heat cnpacity (at t = 0)( C d heat capacity (at t = if) (Cd m a of MKOl contents total heat released adiabatic temp rise (AT,)
.. --
I
0
5h
100
150
2.17 WIK 2.72 WIK 1400 J/(kg K) 1750 J/(kg K) 0.120 kg 22.0 kJ 109 ' C
1.25 Exp-mt.1
Cddul.*d
2ba
'lime I Minutes Figure 3. Temperature profiles measured by the automated calorimeter during the heatup and isothermal period(s).
3
0
do
60
l h e AfterStanof Isolhemul Period/ Mum
Figures. Kineticanalyaisofthe heatflowdataobtainedduringthe three isothermal reaction periods.
0
50
lbo
1M
2w
lime / h&utes
Figure 4. Baseline and reaction heat flows calculated during the heat-up and isothermal period(s).
maintain the desired isothermal temperature (using the jacket to remove the heat flow); thus dT,/dt is equal to 0 and q, is equal to 23.5 W. Hence, from these two experiments, the heat-transfer coefficient and the heat capacity may be determined. Normally, this procedure is carried out before initiating reactions and after reaction iscompletetoaccount forchangesin thesepropertieswith extent of reaction. Using these two calibration endpoints, C, and UA at (e = 0 ) and C , and UA at (e = ef), the data analysis allows for several methods of varying (linearly, proportional to heat flow, and others) these properties over the course of the experiment. This is necessary since they generally change during reactions, and eq 1 works best when the most accurate values for U and C, are employed. Results Reactor and jacket temperatures were collected continuously and the instantaneous heat flow was calculated over the course of the experiment. Figure 3 depicts the temperature profiles measured by the calorimeter during the temperature ramp and isothermal periods. Ascan beseen, thereactoreasily maintained thedesired temperature profile, this being due primarily to its significant heat-transfer coefficient and relatively high surfaceareatoreactorcontents massratio. Figure4shows the baseline and reaction heat flows calculated using eq 1 during the temperature ramp and isothermal periods. Equation 2 relates the total heat evolved, AHnet,to the instantaneous heat flow. The total heatevolved was found
to be 22.8 kJ (eq 2), or 190 kJ/kg of material charged to the reactor. In this case, C, and UA were varied in proportion to the fractional heat evolved. Table 1 lists
other significant information calculated from the experiment. The final entry in Table 1,the adiabatic temperature rise, is the theoretical (AT, = AHneJrnCp)temperature rise which could manifest itself if cooling capabilities were lost. The value reported herein, 109 "C, serves as an indicator of the significant exothermic potential of this reaction. A detailed discussion of these calculations is available in the literature [61. Scrutiny of Figures 3 and 4 reveals that the three peaks in heat flow (58.5, 78.0, and 96.6 min) correspond to the exact times at which the reactor temperature reached the threeisothermalstages (90,100,and llO'C, respectively). The subsequent decay in heat evolution in the isothermal period following each of these peaks is directly due to the concentration dependence of the rate expression. From the energy balance, it can be seen that the heat flow can be viewed as the product of the reaction rate, dC/dt, the specific heat of reaction, AH-. and the volume, V, for a simple reaction, as shown in eq 3. The implication of eq (3) 3 for this experiment is that three isothermal kinetic experiments are embedded in these data. The decay in heat flow during each isothermal period is proportional to the expected decay in reaction rate, dC/dt, during that time. A pseudo-first-order model for reaction is given in eq 4, where Co and qa correspond to the concentration
dC/dt = -kC- ln(C/Co) = -kt
-
In(qJq,J = -kt
(4)
and heat flow values at the beginning of an isothermal period. The relationship depicted in eq 4 allows for conversion of the heat flow data obtained with the calorimeter into kinetic information as pseudo-first-order rate constants. Figure 5 shows the results of such an analysis whichappear tofita pseudefirst-order rate model well. Table 2 lists the significant statistical parameters obtained during the regression analysis. For predictive purposes, it would be useful to be able to model the rate constants' variation with temperature. Equation 5 is the well-known Arrheniusexpression, where (5)
816 Ind. Eng. Chem. Rea., Vol. 33, No. 4,1994
Table 2. Kinetic Regression Analysis Results T ('C) k (min-1) stand. error (min-9 correln coeff (9) 90
0.0016
100
0.0328
110
0.0737
0.951 0.998 0.987
O.ooo4 O.ooo4 O.ooO8
-25
0ExperinenW -Arrhdus
-3
-5
am
0
am5
a m
a m
0.Mu)
1fl' (OK)
Figure 6. Arrheniw plot of the ratc constants obtained from the three isothermal reaction periods.
Table 3. Arrhenius Remnsiion Analysis Results param
E. Ao
value 31 kcaVmol 6.0 x 10" min-L
'lkrl
Figure 7. Fractional heat evolutionealeulatadwith eq 6 during the heatupand isothermalperiod(s).The AFHEpericdsshoamindieate the fractional amount of heat r e l e d during the isothermal periods at 90 and 100 'C.
stand. error 5 kcaVmol 2 x 10" min-1
k is the rate constant, A0 is the preexponential factor, E. is the activation energy, R is the gas law constant, and T is the temperature. Figure 6 depicts the fit of the rate constants given in Table 2 to the Arrhenius expression (In k vs lln. The Arrhenius expression fits the data reasonably well (9 = 0.978),although only three points were available for the regression. Table 3 lists the significant statistical parameters. The use of only three isothermal estimates of the rate constant to determine Arrhenius parameters would seem insufficient. However, it is the purpose of this study to predict the global heat evolution rate (not the individual species concentration profiles) in order to carry out the reaction safely on a larger scale. Therefore, slight deviations from linearity (as seen in Figure 6) are acceptable. For the current objective, a polynomial could be used to describe the rate constants' variation with temperature; however, the more familiar Arrhenius expression was used. The heat flow modeling section will show that the slight deviations from linearity have little or no impact on the predictions. It should be clear from the procedure discussed previously that an elegant, however simple, approach for the determination of pseudo-first-order (or other orders via insertion into eq 4) rate constants is possible. Proceeding with this analysisrequires thatthe chemical pathways do not vary significantly over the temperature range. This assumption is valid providing that ultimate temperatures do not exceed the maximum observation of 110 "C. Equation 6 relates the fractional heat evolution, FHE, to the instantaneous heat flow, qr. The only difference
between the two integrands is the upper limit of integration, and by this definition, FHE always varies between 0 and 1. Due to the relationships elucidated in eqs 3,4, and 6 the fractional heat evolution, FHE, may be loosely (in the case of incomplete reactions) or precisely (in the case of complete single reactions) related to the extent of reaction,or conversion. Figure 7 shows theFHEcalculated
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