# 27 IChemE IMPROVED ADIABATIC CALORIMETRY IN THE PHI-TEC APPARATUS USING AUTOMATED ON-LINE HEAT LOSS COMPENSATION B Kubascikova, D.G. Tee and S.P. Waldram HEL Ltd, 5 Moxon Street, Barnet, Hertfordshire, EN5 5TS, UK; e-mail: dtee@helgroup.com Low phi-factor adiabatic calorimetry has now found worldwide acceptance as a vital tool for reaction hazard identification and risk assessment in the chemical industry. Its primary use is to mimic the runaway reaction behaviour that could occur as the result of maloperations (particularly loss of cooling) on the industrial plant scale and to generate the data necessary for the safe design of such plant. A specific application includes reactor relief line sizing. This type of instrument is also widely used as a thermal screening device to estimate accurately the onset temperature of exothermic activity in a chemical species or sample mixture. Due to the nature of runaway reactions, very high temperatures and pressures may be developed during experiments and as a consequence even equipment that is described as adiabatic will undoubtedly suffer from some heat losses. These losses may appear small in well designed apparatus but nonetheless are significant and can lead to an overestimation of safe operating temperatures, an underestimation of the temperatures and pressures that may be developed during runaway reactions and an associated underestimation of the total enthalpy release. Several instruments try to compensate for heat losses with a variety of hardware and software based methods. The problem is always that under-compensation still leads to apparent endotherms and over-compensation generates a temperature increase that accelerates or drives the reaction in an artificial manner. For these reasons precise heat loss compensation can often be both difficult and time-consuming to achieve not only because of the widely varying physical properties of the samples being tested but also because it must be effective with the many different types of test cell or sample container that can be used. This paper describes the new automated online heat loss compensation method that has been recently implemented with the PHI-TEC calorimeter: an on-line calibration procedure is employed to counteract precisely the effect of heat losses. This permits the user to obtain high quality data under extreme conditions whilst still being able to work flexibly with a variety of test cells and with materials of grossly different physical properties. The paper is illustrated with a range of experimental data. KEYWORDS: adiabatic, calorimetry, PHI-TEC, exotherm, track, heat loss, compensation BACKGROUND Adiabatic calorimetry can provide data for process development but its main use is to quantify the thermal runaway potential of a chemical reaction process. Upset conditions such as loss of cooling, inadvertent heating, mischarging, etc. can lead to runaway reactions. On full scale plant, with little natural convective cooling, these runaways can occur under near adiabatic conditions. The PHI-TEC is a bench-scale adiabatic calorimeter, developed by HEL, see Figure 1. At the heart of the calorimeter is a sample container, or test cell, which is surrounded by three metal guard heaters: these are top, bottom and circumferential units. The sample temperature is measured by a K type thermocouple in the test cell. When the sample undergoes exothermic reaction leading to a rise in its temperature the guard heaters are independently controlled to match the surrounding temperature to that of the sample. Heat losses are thereby reduced to a minimum and as a consequence the sample is maintained in an adiabatic environment. The PHI-TEC guard heaters can track temperatures at up to 2 8C min 21. The sample test cell and guard heaters sit within the main PHI-TEC pressure chamber; see reference 1 for a more detailed description. On large-scale plant the thermal mass of the reactants is typically much larger than the thermal mass of the reactor containing them. Consequently the phi-factor, as defined below, in large scale plant is often close to 1.. Phi factor ¼ f ¼ thermal mass of sample and container thermal mass of sample ¼ 1 þ (MC p) c (MC p ) s (1) where M is the mass and C p the specific heat, subscript c refers to the sample container and subscript s to the sample material. By using thin walled test cells, which result in a low thermal mass of the cell relative to that of the test sample, PHI-TEC is able to achieve low phi-factor values, e.g. down to 1.2 for aqueous systems or 1.4 for organic samples. A disadvantage of using thin walled test cells is that they can withstand differential pressures of just a few bar. In order to prevent the test cell from rupturing when the sample pressure rises, pressure compensation is employed and nitrogen is admitted to the PHI-TEC pressure 1
# 27 IChemE Figure 1. Schematic of the PHI-TEC II adiabatic calorimeter chamber around the calorimeter assembly, see Figure 1. As the reaction proceeds the rate of this pressurisation is controlled so that only a small pressure differential is allowed to develop across the test cell wall. The pressure compensation system will track the sample pressure at up to bar min 21. A consequence of these design features is that it is possible to test exothermic runaway reactions under essentially adiabatic conditions and to apply results from PHI- TEC directly to large-scale equipment. Hence extrapolation of test data is not required. In the simplest type of test the sample is heated rapidly to a user-defined temperature using a heater wrapped around the test cell. The sample is then either allowed to self-heat or an additional component of the reaction recipe is injected or sucked into the test cell prior to the exotherm developing. Any exotherm will proceed to completion adiabatically with the guard heaters tracking the sample temperature. Exothermic runaway reactions that generate vapour or non-condensible gas can create pressures that lead to rupture of the test cell with possible consequent damage to the calorimeter assembly. With non-condensible gas generation the test cell can be left open to a large pressure containment vessel (either the main pressure chamber or a secondary pressure vessel connected to the test cell via the feed line): an initial nitrogen pad pressure in this larger vessel is used to suppress vaporisation of the test sample. In other tests where the onset temperature of exothermic activity is to be determined. The sample is raised to a user-defined start temperature using an electric heater wrapped around the test cell. The temperature is then allowed to settle and stabilise during the wait period before entering the search period. At the end of the search period, a linear regression is made through the sample temperature data. If the slope of this line has a value in excess of the detection threshold, defined when setting up the experiment, then an exotherm is judged to have occurred and it is tracked adiabatically to completion. If no exotherm is detected, the sample temperature is raised step wise using the test cell heater and the process repeated. The size of the step in temperature is user defined and is typically in the range of 18C to258c. This process is repeated until an exotherm is detected or a maximum temperature, specified at the start of the experiment, has been reached. HEAT LOSSES Although accurate temperature control of the test cell and the surrounding environment is maintained by the guard heaters, small heat losses from the test cell can occur. These heat losses from the system can compromise the adiabatic nature of the system and are produced primarily in three ways: Radiation: In general the PHI-TEC equipment is used within a temperature range for which heat transfer losses due to radiation are smaller than those attributable to conduction and convection. For this reason radiative heat losses are ignored. Conduction: Heat losses via conduction occur primarily along the feed line connecting the cell to the PHI- TEC vessel. For heat transfer by conduction Fourier s law is the fundamental equation. The temperature difference between the cell and the sample is considered as the unique variable for the conductive term. Convection: Heat losses may occur through convection within the PHI-TEC vessel. Convection may be described by the Nusselt equation and this predicts that convective heat losses are proportional to the density of the heat transfer medium and the temperature difference. The density of the gas is directly related to the pressure of the gas within the main containment vessel. The other terms of the equation may be considered as essentially remaining 2
# 27 IChemE constant. Forced convection may occur when the pressure compensation system is running. However, for the majority of the time it will be natural convection that is prevalent and this is the condition assumed by the Heat Loss Compensation software. Sample Reflux: Vapour entering the feed pipe may condense within the cooler sections of the feed line resulting in a net heat loss from the system. If these condensed vapours return to the bulk sample mass they may re-boil and effectively set up a slow but steady reflux cycle. It is difficult to apply a mathematical model to correlate these heat losses. Reflux can be minimised by the use of test cells with small diameter feed lines (e.g. 1/16 ). Compensation for Heat Losses A common method to counteract the effect of heat losses is to compensate for them by increasing the temperature of the guard heaters to a value slightly above that of the sample. This creates a small heat input into the cell which must be such as to balance exactly the heat losses. This requires a careful calibration of the apparatus considering both the temperature and pressure effects. Should the system be under-compensated then heat losses will still be present and the sensitivity of the apparatus will be reduced. Should the system be over-compensated then false exothermic activity may be detected. The mathematical model used as the general description for heat losses (convection and conduction) is of the form described below (2): Correction / a(p 2 (T T )) b þ c(t T ) (2) Where a, b and c are constants. P is the pressure in the PHI-TEC vessel, T is the sample temperature and T the ambient temperature. For natural convection b is taken as.7. Traditionally the values of a and c were determined for each piece of apparatus and type of cell by performing a lengthy heat loss compensation calibration test. In this, the sample and guard heaters are raised to a selected temperature at a given pressure. The pressure and guard heater temperature are then held constant and the sample allowed to reach thermal equilibrium. The measured temperature offset between the guard heaters and the sample is recorded and the sample and guard heaters are then set to a new temperature and pressure. This process is repeated to build up a data set of offset corrections as a function of both pressure and temperature. These data were then fitted to an equation of the following form (3): Correction ¼ Q (a(p 2 (T T )) b þ c(t T )) þ d (3) a is known as the convection factor and c is known as the conduction factor. Q is a user defined variable known as the quality factor. It is a simple correction that can be applied to the fit: for example in cases where the fit is expected to result in over compensation under certain conditions entering a quality factor of Q, 1 will reduce the temperature advance of the guard heaters. d is a user-defined offset, which is explained in more detail later. The range and specific values of the temperatures and pressures employed in these experiments are defined using experimental design techniques. After performing a calibration and modifying the factors in the control loops it is important to verify that the system is working properly. Performing a heat-wait-search on an inert material is recommended: obviously this should not lead to any observed exotherms. If an exotherm is detected then the heat loss compensation software is over-compensating and either the detection threshold in the heat-wait-search procedure must be increased or the heat loss compensation calibration is re-evaluated. Q can also be decreased. If heat losses are experienced then the system is under compensating and the heat loss compensation calibration needs to be re-evaluated. 3 25 8 2 15 exotherm onset at 124.5 C 6 4 2 5 4 2 3 Sample (Left) Sample Pressure (bar) (Right) Guard Heater (Left) typical data without adequate heat loss compensation Figure 2. 2% di-tert butyl peroxide in toluene 3
# 27 IChemE 3 25 2 15 exotherm onset at 16.4 C 8 6 4 2 5 2 3 4 5 6 7 8 9 Sample (Left) Sample Pressure (bar) (Right) Guard Heater (Left) data with on-line heat loss compensation calibration Figure 3. 2% di-tert butyl peroxide in toluene In practice however it is often difficult to obtain a single set of parameters that adequately describe the heat losses over very wide temperature and pressure ranges, i.e. the parameters may be good for most of the operating range but may over compensate under some conditions whilst under compensating under other conditions. In these cases often a compromise must be made and most users prefer to suffer under compensation and consequential heat losses rather than risk detecting false exotherms. Typical data is shown in figure 2. The ability to predict adequately the heat loss compensation parameters is further complicated by changing conditions within the apparatus, e.g. warming of the main pressure chamber and thus an increase in T. Different materials of construction of the test cells have also been noted to affect the parameters as have different physical properties of the sample. Warming from the power required for direct mixing in the test cell may be a factor that changes significantly with sample temperature. ON-LINE CALIBRATIONS The new methodology uses the existing heat loss compensation expression. However rather than pre-determining best fit parameters for each type of test cell it uses an unchanging set of typical values but alters the expression by adjusting T using measured data from an on-line calibration. This is done in practice by first adjusting the sample temperature to an initial calibration temperature. This temperature must be low enough such that the sample is thermally stable but ideally close to the start temperature for the test. The test first enters the calibration phase during which the sample temperature is maintained at a constant value by adjusting the guard heater temperature. Sufficient time should be allowed such that both the sample and guard heater temperatures are permitted to stabilize fully and reach constant values. The offset or difference between the sample and guard heater temperatures is then measured and substituted into the heat loss compensation expression which is then solved iteratively to determine 25 24 23 22 21 8 6 4 2 2 48 5 52 54 56 58 6 Sample Sample Pressure (bar) Guard Heater data with on-line heat loss compensation calibration Figure 4. 2% di-tert butyl peroxide in toluene (Expanded detail from Figure 3) 4
# 27 IChemE the best value of T for fitting the calibration data. The sample is then heated further to the start temperature of the test and the test is followed as normal. In heat-wait-search type procedures this calibration process is repeated each time an exotherm has not been detected during the search phase of the test and before heating to the next step temperature. Special consideration is also given to the case where exothermic activity may be occurring but at a low level beneath the detection threshold. In such cases the calibration would tend to underestimate the required offset to counteract normal heat losses i.e. it would reduce the required offset to balance the effect of the weak exothermic activity. This affect may be cumulative on subsequent steps and would clearly reduce the sensitivity of the apparatus. Thus in such cases if, during a calibration step the measured offset is smaller than for the previous temperature step the expression is not re-calculated and T remains unchanged. In all test procedures the initial calibration should be sufficiently long to allow true stability of the system even following rapid heating of the sample: a typical calibration time might be 4 6 minutes. In the heat-wait search tests the sample and guard heater temperatures are typically near steady following the adjust and search phases and clearly the system may be expected to reach stable conditions earlier. For this reason there is an option to make these second and subsequent calibration steps significantly shorter i.e. perhaps 1 15 minutes. If an exotherm is detected the software forces the test to repeat the longer calibration procedure when a period of adiabatic tracking expires and before continuing with the heat-wait-search. These features are illustrated in figures 3 and 4. This procedure has been found to improve the performance of the PHI-TEC by improving the adiabaticity of the apparatus and increasing the sensitivity hence leading to earlier onset detection. It also corrects for the random differences between the type K thermocouple characteristics in particular test cells, the heating effects from any stirring system and under certain conditions for refluxing effects. In certain circumstances it is not always possible to perform an initial calibration during a single test e.g. when testing a sample taken from a part reacted batch. In such circumstances it is possible within the software to skip the calibration and either to use default heat loss compensation parameters or those determined from a previous calibration run. The software can also cope with occasions when an apparent negative offset is measured e.g. due to normal differences in the readings from different type K thermocouples particularly when operating near to ambient temperatures and when heat losses are small. In this case the d factor is used. The value d is large enough such that when it is added to the measured offset a positive value results. This value is substituted into the heat loss compensation expression such that it can be solved and T evaluated. During the remainder of the test the required offset is calculated at any temperature and pressure using the determined T however the d value is subtracted from this calculated offset before it is applied to define the guard heater temperature set points. REFERENCE 1. Singh, J., 1993, Reliable scale-up of thermal hazards data using the PHI-TEC II calorimeter, Thermochemica Acta 226: 211 22. 5