An Advanced Method for the Estimation of Reaction Stoichiometry and Rates from ARC Data

Effective design of emergency relief systems requires accurate modeling. In particular, the PVT relation of such systems is fundamental and unique. This relation must be accurately represented during direct scale-up or computerized simulation. Variables which can significantly alter the PVT behavior of a system should be quantified, and included in the design. 

The pressure/temperature (PT) relation is a function of thermal inertia, liquid fill level (vessel void fraction), composition and chemical identity (vapor-liquid equilibrium, liquid/vapor density, heat of formation, etc). For a specified relief device set pressure, there is a unique corresponding system temperature. For reactive systems, this temperature corresponds to a reaction rate. Small errors in estimating this temperature can lead to inadequate sizing and potential catastrophic vessel failure.

Estimation of fluid flow rates and their associated energy depletion rates is a strong function of chemical identity. Often, simple reaction models are used which ignore this fact. If the reaction model only fits the observed constant PVT relation and PT time histories, it will yield inaccurate predictions. The model may assume, for example, that the reaction products are made of a heavy and a light component. It may also specify a heat of reaction independently. However, these assumptions are often thermodynamically inconsistent and do not guarantee a unique solution, i.e. the chemical identities of the products are not unique. As a result, the estimated flow rates are often in error.

This paper presents a method that guarantees a thermodynamically consistent and unique solution. The method requires that the reaction stoichiometries and chemical identities of the products are thermochemically favorable. This is done by performing a constrained multiphase simultaneous physical and chemical equilibrium calculation. The calculation is performed at constant volume for a proposed stoichiometry and product list. These constraints are imposed as additional atom matrix constraints for the Gibbs free energy minimization; they reduce the search space for rate-limiting reaction steps.

This method yields a reaction stoichiometry that is used as input to a computer program. The program simulates the Accelerating Rate Calorimeter (ARC) test, in order to establish reaction rates— including pre-exponential factors, reaction orders, and activation energies.

We illustrate the use of this method in two cases. Both cases use closed volume data to find reaction stoichiometry and kinetic information. The first case considers the decomposition of di-t-butyl peroxide; the second looks at the esterification of methanol and acetic acid.

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