Safer Scale-Up of Batch and Semi-Batch Reactions; Part 2 - Quantification of the Desired Reaction

Donald J. Knoechel, Ph.D., Senior Consulting Engineer, Fauske & Associates, LLC

This is the second of four articles Fauske & Associates, LLC will be publishing on the topic of safer scale-up for batch and semi-batch reactions. The first article discussed desktop reviews and preliminary hazard analysis: Safer Scale-Up of Batch and Semi Batch Reactions; Part 1. This second article addresses characterizing the desired reaction and its implications on scale-up.

Two of the four reasons for thermal runaways mentioned in the first article are related to the behavior of the desired reaction:

1. Insufficient understanding of the process chemistry and the energy/kinetics for the desired reactions

2. Improper design of the heat transfer capacity required at the plant level

The first reason directly so. The second reason, indirectly, as it is the mismanagement of the desired reaction heat with scale up that leads to the runaway. In fact, in the Process Equipment section of the OSHA Process Safety Management 1910.119 rule, an energy balance is required.

While this clause is focused on the plant equipment and its heat transfer capabilities to handle the process, an energy balance cannot be written without knowledge of the heat of reaction and the rate of heat generation from that process chemistry.

Stoessel’s Criticality Classes¹ serves as a universal guideline for the safe process scale up of exothermic reactions. In this approach, the Maximum Temperature of the Synthetic Reaction (MTSR) is one of the critical attributes to be determined. The MTSR is simply the process temperature plus the adiabatic temperature rise (ΔT_ad) due to the desired reaction heat, the latter of the two occurring in a loss of cooling scenario simulated by adiabatic conditions.

These two examples point to knowledge of the heat of reaction and reaction rate as critical parameters for safe process scale up. Previous FAI newsletter articles have elaborated on theoretical heat of reaction (THOR) calculation and reaction calorimetry (RC) as ways to calculate or measure the heat of reaction, respectively. While the former is sufficient to calculate a MTSR (given a heat capacity for the reaction mass), experimental data of conversion versus time for the process chemistry or assumptions of reaction time would be needed to create a heat rate of reaction for an energy balance. RC provides a solution whereby both the heat of reaction and heat rate are derived from the same experiment.

Theoretical Heat of Reaction (THOR)

The paper by Weisenburger et. al.² presents a very comprehensive study on theoretical heat of reaction estimation versus measurement and outlines when calculations can be used and how.  Most notably for any heat of reaction estimation to be sound, values for the enthalpy of formations of the species involved or representative model compounds in the appropriate physical state must be available or reasonably estimated. Of course, a balanced chemical equation representing the process reaction of concern must be known as well. When compiled, the pertinent heats of formation are combined according to equation 1   

ΔH_rx = Σ νΔH_f products – Σ νΔH_f reactants   (1)

where ν is the stoichiometric coefficient for the individual reactant or product in the balanced chemical equation.

Heats of formation can come from the literature whether they are for actual or model compounds. The more complex the molecule, however, the more unlikely a value for its heat of formation will be found. Rather, this is where model compounds can be effective surrogates for the actual compound. A model compound distills the more complex structure down to just its reacting moiety.

With an estimated heat of reaction in hand,  a calculation of the adiabatic temperature rise for a loss of cooling scenario is possible given a process recipe using actual or approximated heat capacities for the reaction mass components.

But not every type of process chemistry lends itself to THOR. In addition, simultaneous heats due to mixing, dissolution, complexation, crystallization, or other physical effects can complicate the calculation to the point of the estimate not being accurate. In these cases, reaction calorimetry is the preferred technique for heat of reaction determination.  

Reaction Calorimetry (RC)

Reaction calorimeters come in many flavors: heat flow, heat flux, or power compensation. Regardless of the underlying calorimetric principle, the common deliverable from RC is a heat flow profile. That is the heat rate presented in watts or normalized by reaction mass as watts/kg versus process time during which either some reagent addition was performed to initiate reaction under isothermal conditions or during a temperature ramp or both. The area under the heat flow profile calculates the total heat from which a heat of reaction is determined by normalizing the total  heat to reaction mass or mole of limiting reagent. The total heat divided by the thermal mass (mass times heat capacity) affords the adiabatic temperature rise (from which the MTSR is calculated).

The shape of the heat flow profile gives information on the kinetics of the reaction. For semi batch processes where there is a reagent addition, the degree of reagent accumulation is an important concept easily illustrated by the RC heat flow profile. If the reagent reacts nearly instantaneously as it is added, the process is said to be addition limited. The heat rate profile will resemble a square wave with the heat rate level realized dictated by the rate of addition. The heat rate will fall off quickly after the addition is ended. If the reaction is slower than the rate of reagent addition, unreacted reagent will accumulate. In this case the heat flow profile steadily rises during the addition most times but not always peaking at the end of the addition. After the addition has ended, the heat rate decays slowly. In a loss of cooling scenario assuming the addition is stopped when the deviation occurs, the accumulated heat is still available to cause a temperature rise, possibly initiating a thermal runaway.

The reaction calorimeters in the FAI toolbox are the Mettler-Toledo RC1 (heat flow), ChemiSens CPA202 (heat flux), and the Thermal Hazards Technology μRC (heat flux).

Gas Generation From the Intended Chemistry

Many process chemistries intentionally generate non-condensable gases. Reductions utilizing hydrides (sodium borohydride, lithium aluminum hydride, diisobutyl aluminum hydride, sodium triacetoxyborohydride, for example) can generate hydrogen when the reagent encounters acidic protons on the substrate or during a post reaction quench to kill excess reagent. Butyl lithium and some Grignard reagents can evolve low molecular weight hydrocarbons which may or may not be soluble in the reaction mass. Any reaction involving carbonate or bicarbonate can generate carbon dioxide.

Often, determining the amount of gas generated from these types of chemistries is simply an exercise in stoichiometry given a balanced chemical equation. This is an extension of the THOR approach. While the total moles of gas estimate can be fairly accurate, the rate at which it comes off is often in question. A reaction calorimeter fitted with a vent line bubble column, mass flowmeter, wet test meter or scrubber on a balance can be used to follow gas generation from the reactor as well as heat flow.  

Simplified Energy Balance

The culmination of the quantification of the desired reaction is the heat rate scale–up calculation whereby a simplified energy balance can be written to demonstrate that the process equipment has adequate cooling capacity (or not) to handle the process chemistry at scale.

The same equations used in the heat flow balance from the Mettler-Toledo RC1 reaction calorimeter used to distill the experimental data down to a heat flow profile can be used to perform a simple heat rate scale up calculation for the plant. The terms in said heat balance are:

Heat Input (from additions to reactor) - Q_in = m_addCp_add(T_r- T_add)/t_add

Heat Generation (from reactions) - Q_gen = (ΔH_rx)(moles of limiting reagent or kg of reaction mass)/t_rx

Heat Removal (from jacket, condenser, heat exchanger, etc.) - Q_out = - UA (T_r – T_j)

Heat Accumulation (temperature change of reaction mass)  - Q_accum = -m_rCp_r(T_f- T_i)/t_T

Where m_add is the mass of the added stream, Cp_add is the heat capacity of the added stream, T_r is the reaction temperature, T_add is the temperature of the added stream, t_add is the addition time, ΔH_rx is the heat of reaction per moles limiting reagent of kg reaction mass (from either THOR or RC), t_rx is the reaction time, U is the heat transfer coefficient, A is the heat transfer area, T_j is the jacket temperature, m_r is the reaction mass, Cp_r is the reaction mass heat capacity, and in the case of a nonisothermal process, T_f is the final temperature, T_i is the initial temperature, and t_T is the time of the reaction mass temperature change. We note in the accumulation term that the time derivative of the reaction temperature (dT_r/dt) is approximated by the linearized difference between the initial reaction mass temperature T_i and the final reaction mass temperature T_f over time t_T.

The energy balance is given by: Input + Generation = Removal + Accumulation

The various temperature terms can be input as desired values. The heat capacity terms are common outputs of reaction calorimetry experiments though many pure component heat capacities, especially solvents, are known³. If not, generalized values of 2000 J/kg-K for an organic component and 1000 J/kg-K for an inorganic component are commonly used. The most elusive term needed in the simplified energy balance is the heat transfer coefficient. For jacketed vessels, values for U depend on the material of construction and jacket utilities though approximate values may be available from the vessel manufacturer (Pfaudler or DeDietrich for instance). The area of heat transfer, A, is easily calculated from the vessel dimensions available from the same source for a given size vessel versus fill volume.

In the absence of an estimate for UA, it can always be derived from a cooling curve of a known heat capacity substance at a specific fill volume and agitation rate in the actual vessel over the temperature range of interest. With no reaction or addition, the simplified energy balance above collapses to just the heat removal and accumulation terms such that U*A = -mCp(dT_r/dt)/(T_r - T_j). For vessels with multiple temperature probes, an average of baffle and bottom valve temperatures can be used for T_r (and dT_r/dt). For the jacket temperature, an average of the inlet and outlet jacket temperature can be used for T_j. For the known Cp substance, either a constant value for Cp (i.e. @ 25°C) or the temperature dependent equation (from DIPPR database³ for example) may be used.

So with ΔH_rx, UA and Cp in hand, the simplified energy balance can be used to predict if there is enough cooling capacity at scale. The easiest version of the energy balance is to assume isothermal conditions are held such that the accumulation term is zero. Then for semi batch processes, given the temperature of the added stream, the addition time, and an assumed reaction time, the jacket service temperature necessary to maintain a desired reaction mass temperature can be calculated. Alternatively, given the temperature of the added stream, an assumed reaction time, and the available jacket service temperature, the minimum addition time necessary to maintain a desired reaction mass temperature can be calculated.  

The biggest assumption in the simplified approach assumes approximate addition limited heat evolution behavior (say reagent accumulation < 15%). In this way, the heat of reaction is averaged over the time of addition unless specific knowledge of accumulation of reaction energy is noted. For cases where accumulation is greater than 15%, separate calculations of the handling of peak heat load during the addition and post addition reaction times can be performed. For large volume additions, an average value of A or UA (in the case of known UA vs. volume) is calculated from the actual volume range involved.

There are always many process situations where one or many of the above assumptions are invalid. However, recall that the main purpose of the simplified energy balance is to demonstrate the capability of the intended equipment and utilities to handle the desired process energy. The simplified format easily does this the majority of the time. If the outcome suggests a challenge, the energy balance gives valuable insight into what may be needed to safely execute the process under modified conditions (lower T_j, longer T_add, or additional heat transfer area [side loop heat exchanger], for instance). For the cases where a longer Tadd is needed, it is important to have  laboratory confirmation that the longer addition time does not introduce new impurities or other undesired process behavior before carrying out the process at scale.   

Characterizing the Undesired Reaction with Adiabatic Calorimetry

Knowing the plant equipment can handle the process under desired conditions is not the end of the story. Protecting the plant equipment in the case of process deviations (loss of cooling, all in additions, fire, etc.) requires characterization of the undesired process behavior and relief vent sizing. Adiabatic temperature rise projections from THOR and RC are limited to just the energy due to the desired reaction. These do not represent the entire runaway scenario but only a minimum possible value. Under actual adiabatic conditions, further reactions may be initiated (with their own heat of reaction) when the actual rise in temperature is experienced which may contribute to a further increase in temperature (and pressure) until all reacting/decomposing components are consumed. Adiabatic calorimetry is required to explore the realm of process upset. The overlap between adiabatic calorimetry and reaction calorimetry lies in the fact that the adiabatic experiment often but not exclusively has the desired reaction as the trigger for runaway. Similarly, if there is off-gassing, quantification of the evolved gas rate is required to ensure the process vent capacity is adequate.

Therefore, the third article in this series will deal with how to characterize the undesired reaction behavior with adiabatic calorimetry and use the subsequent temperature rate and pressure rate data for proper relief valve sizing to keep the plant equipment intact even in the event of a runaway.

Part 3 is out now! 

References

1. Stoessel, F., " Thermal Safety of Chemical Processes: Risk Assessment and Process Design," Wiley-VCH, 2008.
2. Weisenburger et. al., "Determination of Reaction Heat: A Comparison of Measurement and Estimation Techniques," Organic Process Research and Development, 2007, 11, 1112-1125.
3. The DIPPR Information and Data Evaluation Manager for the Design Institute for Physical Properties, V 9.0.1, Database Date 2015, Brigham Young University.

#process chemistry #reaction calorimetry #chemical process #scale-up