By: Donald J. Knoechel, Ph.D., Senior Consulting Engineer, Fauske & Associates, LLC
In this article, we discuss adapting the Mettler-Toledo RC1 Reaction Calorimeter for operation at atmospheric reflux. This type of work has been covered in detail before for an RC1 [1-2]. Recently, a simplified method  has been proposed for use in an OptiMax and EasyMax. Normally, in heat flow calorimetry the dominant term in the heat balance is the heat flow term whereby the heat entering or leaving the jacket is given by UA(Tr-Tj), where U in the heat transfer coefficient, A the area of heat transfer and Tr and Tj are the temperature of the reactor and the jacket, respectively. Calibration for U is done before and after the reaction by providing a known amount of heat via an immersed heater probe and measuring the response of the reactor and jacket temperatures (conventional heat flow) or continuously via a programmed oscillating heat input (RTCal™ technology).
Under reflux conditions, the heat flow (out) is pushed from the reactor jacket up into the condenser by operating the reactor jacket with a constant fixed Tr – Tj (Tj > Tr) to provide the driving force for boiling. At steady state refluxing conditions, the heat flow is then tracked by the change in the temperature of the outgoing condenser cooling fluid (Tout) from the temperature of the incoming fluid (Tin) provided the flow of the condenser fluid is constant. The proportionality constant multiplying (Tout – Tin) is not UA but dm/dt x Cp where dm/dt is the mass flow rate of the condenser fluid and Cp its heat capacity. A “factor" representing this multiplier can be calibrated for by the same routine used for heat flow through the jacket. In the reflux case, the calibration heater is turned on for a set amount of time and its wattage signal is integrated and divided by the integral of the (Tout – Tin) response during the same time period under baseline refluxing conditions. The reflux heat term can then be constructed as follows:
Qreflux = ΔTreflux • factor = (Tout – Tin) • factor with factor = ∫ Qcal / ∫ ΔTreflux
Calibrations are done before and after the reaction. In order for this simplified approach to work, reflux must be maintained over the course of the reaction to ensure that the heat flow occurs in the condenser only. Otherwise, the heat flow will move down into the lid and associated fittings where temperature measurements and thus heat flow is not tracked and the ability to do calorimetry is blinded until reflux has fully subsided and the heat flow fully returns back in and out of the reactor jacket.
Normally, the complete heat balance for the RC1 is given by:
Qreaction = Qflow + Qaccum + Qdos + Qloss + Qreflux - Qcal
Where Qflow is the reactor jacket heat, Qaccum accounts for temperature changes in the reaction mass, Qdos for the sensible heat of added streams, Qloss for heat losses to ambient temperature, Qreflux as defined above and Qcal is the calibration heat. In the simplified method, the heat balance collapses to just the Qreflux and Qdos.
In our AP01-0.5-3w ambient pressure glass reactor with the Cov-PTFE-00-0.5 glass-impregnated Teflon™ cover, the normal 5-watt calibration heater does not generate enough power to effect a large enough change in reflux at the condenser to accurately determine the factor. Consequently, for reflux operations, a 25-watt calibration probe is used. A custom skinny reflux condenser was fabricated by Meints Glassblowing, LLC. This condenser requires no offset adapter and fits directly into the M24 19/26 lid adapter in either the angled or vertical port clear of the stirrer bearing. The condenser and set-up are shown in Figure A.
Figure A: Left – the FAI/Meints Skinny Reflux Condenser for RC1 Right – Insulated and Mounted on the 500 ml Reactor
The condenser fluid inlet feeds an internal large bore central cooling tube with a continuous bulbous-type shape for extra heat transfer surface. The central cooling tube connects to an outer cooling jacket that travels back up the length of the condenser to the outlet. Fittings on the inlet and outlet provide attachment points for auxiliary Pt100 temperature sensors (normally designated T1 and T2) held in place via GL-14 gasketed screw cap fittings to measure Tin and Tout, respectively. A VWR recirculating chiller provides a steady flow of stable temperature condenser heat transfer fluid (50:50 ethylene glycol:water).
The User Defined Trend feature in the RC1 iControl software is used to define a ΔT signal for the condenser that is T2 – T1 (Tout – Tin).
In this demonstration, we explore the neutralization of methanolic sodium methoxide by acetic acid producing sodium acetate and methanol. In practice, reacting 25% wt. sodium methoxide in methanol with one mole equivalent of acetic acid produces a very thick slurry as by-product sodium acetate is not very soluble in methanol. Even with 10% starting methoxide concentration, the sodium acetate slowly precipitates after reaction. However, adding one mole equivalent of water solubilizes the sodium acetate maintaining a homogeneous solution before and after reaction.
The choice of this reaction system was by design to provide an addition limited reaction (acid-base chemistry). Theoretical Heat of Reaction (THOR) estimation (subject featured in FAI's Summer 2016 Process Safety News) calculates a heat of reaction of -27.85 kJ/mol based on a heat of formation for dilute sodium methoxide in methanol (60 parts methoxide, 2.73 wt%). This estimated heat was used to calculate an addition time that would produce roughly a 25 W heat flow such that the heat flow from the reaction would be of order as the calibration heat.
Figure B shows the conventional heat flow calorimetry (subreflux) experiment performed at 55°C starting with ~10% sodium methoxide in methanol adding one equivalent of 1:1 (mole) acetic acid:water over 10 minutes.
The heat flow signal was integrated with a linear baseline to yield -14,696 J. Normalizing the measured heat by the moles of acetic acid added results in a measured heat of reaction of -29.39 kJ/mol. This value is a little greater than the estimated heat of reaction but is easily explained by a higher starting concentration of methoxide (10%) used versus the theoretical value available for the estimate (2.73%).
To give an appreciation for the complexity of an experiment at reflux, Figure C shows the entire sequence including heat up, two-fold calibration before, addition/ reaction and two-fold calibration after. The two-fold calibration (at two different Tr-Tj values at reflux) before and after the reaction are necessary to determine a UA at reflux and the heat loss term  in case the Qflow and Qloss terms are important in the overall heat balance.
The RC1 experiment was initially started at 25°C and the reactor heated to 55°C in Tr mode. A QuickCal was run at 55°C to establish UA and Cp for the reaction mass. From 55°C, the reactor was then heated in distillation mode with |Tr-Tj| = 10°C and jacket endpoint of 90°C. Of course, the jacket never reaches 90°C as the boiling point of the starting 10% sodium methoxide in methanol is 69.3°C. It is noted at the 70 minute mark as the boiling temperature is reached, the T2-T1 signal (dark green) begins to rise as the solvent vapor reaches the condenser. Also shown is a 25 point average of T2-T1 (gray) which smooths the noisy condenser ΔT signal. At the 95 minute mark, the 25W calibration heater (yellow) is activated for 15 minutes and the T2-T1 signal responds accordingly. The ratio of the two integrands provide the factor for quantifying Reflux Heat. After the first calibration at reflux, the |Tr-Tj| is increased to 15°C and a second calibration is performed. At the 185 minute mark, 39.4 g of 1:1 (mole) acetic acid:water was added in 10 minutes (magenta).
The light green curve (Tdos2) shows the dosing temperature of the added stream that is used to calculate the Qdos for the heat balance. Over the course of the addition/reaction, the reactor temperature/boiling point (light blue) decreases to 67.4°C and there is a corresponding shift in the T2-T1 baseline. As the |Tr-Tj| is fixed at 15°C, the jacket temperature also decreases accordingly. However, down in the reactor, as the area of heat transfer increases due to the added aqueous acid, even though Tr-Tj is held constant and there is likely little change in the heat transfer coefficient, the heat flow into the reactor does increase slightly, hence the shift in baseline T2–T1 at the condenser. The two-fold post reaction calibrations at with |Tr-Tj| = 15°C and |Tr-Tj| = 10°C are consecutively performed followed by a final cooling to sub reflux conditions at 55°C and a final QuickCal.
Figure D shows the calorimetry at reflux experiment plot and the different calculated contributions to the heat balance.
Qreflux (purple) is based on the 25 point average T2-T1 signal and the Factor (before and after at |Tr-Tj|= 15°C) interpolated across the reaction proportional to the change in reactor temperature. The green curve is Qdos given by the mass flow rate (slope of the magenta line) times 2.568 J/g°C, the heat capacity of 1:1 (mole) acetic acid:water times (Tr-Tdos2). Because the boiling point changed, Qaccum (gray curve) is calculated by dTr/dt times the reaction mass times the heat capacity of the reaction mass. The heat capacities determined in the QuickCals at 55°C were extrapolated to the reflux temperature based on the Cp(T) for methanol. Qloss (dark blue) and the Qflow (dark red) are calculated from UA at reflux and Qloss derived from the set of two-fold calibrations at reflux. The Simple Heat (bright green) is Qreflux + Qdos. The yellow curve is the Simple Heat + Qaccum. The Total Heat (red), is the sum of the Qreflux + Qdos + Qaccum + Qflow + Qloss.
Table 1 shows the results of integrating the various signals and heat balances over the reaction period with a baseline proportional to reactor temperature.
As the boiling point decreased during the reflux experiment, the Simple Heat (Qreflux + Qdos) analysis overestimates the heat and adding in the accumulation term is required to achieve a heat of reaction in better agreement with the sub-reflux experiment. Accounting for all terms (Total Heat) arrives at a similar heat of reaction. Looking back at Figure D, the role of including the Qloss and Qflow terms adjusts the baseline to near zero and corrects for the baseline shift due to the change in boiling point. Note from Table 1, however, neither term contributes much to the overall integral.
The system demonstrated here was an addition limited reaction (acid-base chemistry) and the addition rate was adjusted to achieve a heat flow similar to the calibration heat of 25 W to optimize the calorimetry in the determination of the reflux factor. As such, the system was ideal and “tunable.” Mildly exothermic or endothermic processes or even moderately energetic but slow reactions may be more difficult to quantify accurately as lower heat flow signals could begin to approach the level of the noise (+2W).
Reflux or not, if you have a process and require information on the heat of reaction or heat rate, contact testing lab that has a full suite of reaction calorimeters that can be used to gather the necessary data for your process. Please contact Don Knoechel at firstname.lastname@example.org or 630-887-5251 to discuss your process or scale-up concerns. www.fauske.com
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