(399c) Building Kinetic Models for the Liquid Phase: Hydrocarbon Autoxidation

We present new methods for automatically generating and solving detailed kinetic models for liquid phase reactive systems, including solvation thermodynamics and diffusion kinetics. We further apply these methods to the autoxidation of a diesel fuel surrogate.

Kinetic models for gas-phase reacting systems, such as atmospheric chemistry and combustion, often contain thousands of species and reactions. Researchers in these fields have developed a number of tools to help them generate, manage, and solve these detailed models. Many reacting systems of interest to chemical engineers, however, occur in the liquid phase. Liquid phase kinetic models of similar complexity, and the tools required to work with them, have yet to be developed. To begin, we have modified our Reaction Mechanism Generator (RMG) software enabling it to estimate the thermodynamics of solvation for reacting species using Abraham's model (a Linear Solvation Energy Relationship) with parameters from a group contribution method formulated by Platts et al. (1999). This allows RMG to automatically generate kinetic models with solvation-corrected thermochemistry for reactions in solution. Secondly, we have developed a kinetic model solver that incorporates diffusion limited reaction rates, estimating species diffusivities using the Stokes-Einstein Relation, so that detailed kinetic models can be easily used in simulations of liquid phase systems. Finally, we demonstrate the use of these tools to investigate the liquid phase autoxidation of a mixture of hydrocarbons representing diesel fuel.

Automatic kinetic model generation with RMG

RMG is an automatic reaction mechanism generator (Song et al., 2003; Van Geem et al., 2006; http://rmg.sourceforge.net). Molecules are represented as graphs, with atoms as nodes and bonds as edges connecting the nodes. Standard graph-theory methods are used to identify equivalent graphs and ensure uniqueness. RMG uses ?reaction families? to generate all the possible reactions that a species can undergo in the presence of the other species in the chemical mechanism. Every reaction family represents a particular type of elementary chemical reaction, such as bond-breaking, or radical addition to a double bond. Each reaction family has a recipe for mutating the graph, and a library of rate expressions for different reacting sites. Because the model can contain thousands of species and rates, the estimation of thermochemical and kinetic parameters must be very fast. As with most mechanism generating tools, RMG uses a database of known values wherever possible to find thermochemical data for species, but usually it estimates parameters using a group contribution method. The functional groups are recognized using a graph-theory matching algorithm. A similar method is used to estimate the rate coefficients for the reactions. RMG uses a rate-based termination criterion; the reaction network is expanded until the rates of all reactions going to species not included in the network fall below a certain threshold.

For liquid phase simulations the estimated thermochemistry of a species must be modified to take into account its solvation. We use Abraham's model, which, given a set of five molecular descriptors for a solute, can estimate the partition coefficient of the solute between different phases for which solvent descriptors are also known. The Gibbs free energy change of solvation can be estimated from the partition coefficient with appropriate assumptions about the reference states, and can be split into enthalpic and entropic contributions using analyses from scaled particle theory, so all that remains is to estimate the five molecular descriptors of each solute species in the kinetic model. We do this using the group contribution method of Platts et al. (1999). These modified solution phase thermochemical data are then used when evaluating reaction rate and equilibrium constants.

Solving detailed kinetic models in the solution phase

Simulating a reacting chemical system with a detailed kinetic model requires solving a list of ordinary differential equations (ODEs) ? one for each species concentration. The terms in these ODEs represent the chemical reactions that create or consume the species, and their magnitudes depend on species concentrations and reaction rate coefficients. For reverse reactions these rate coefficients are calculated using the equilibrium constant, which is in turn dependent on the thermochemistry of the reacting species. Although any ODE solver can be used to integrate the ODEs, the complexity is in managing and correctly evaluating all of the terms in the equations. Software to take care of these details and simplify running kinetic simulations in the gas phase has been around for decades (Chemkin, Cantera) but reactions in solution require additional considerations.

Reaction rate coefficients in gas phase kinetic simulations are usually represented by modified Arrhenius expressions (r = A Tⁿ exp(-E_a/RT)). )). In solution, however, the rate is also a function of (and is often limited by) the rate of diffusion of the reacting species towards each other. We estimate species diffusivities using the Stokes-Einstein relation. For this we need the diameter of each species, which we estimate using the UNIFAC group contribution scheme, and the viscosity of the solvent.

Modeling surrogate diesel fuel autoxidation

The tools described above were used to investigate the autoxidation of a diesel fuel surrogate exposed to air and heated. The kinetic model is dominated by the most reactive of the surrogate components: n-decylbenzene.

We hope that these new, free, tools for generating and using detailed kinetic models of reacting systems in solution will be of general interest to a wide audience and will find a variety of uses in the chemical engineering community.

References

J.A. Platts, D. Butina, M.H. Abraham, A Hersey (1999) Estimation of Molecular Linear Free Energy Relation Descriptors Using a Group Contribution Approach. J. Chem. Inf. Comput. Sci., 39 (5), 835?845. doi:10.1021/ci980339t

J. Song, S. Raman, J. Yu, C.D. Wijaya, G. Stephanopoulos, W.H. Green (2003). RMG: the next generation of automatic chemical reaction mechanism generator. Proceedings AIChE Annual Meeting. San Francisco, CA, USA.

K.M. Van Geem, M.-F. Reyniers, G.B. Marin, J. Song, W.H. Green and D.M. Matheu (2006). Automatic reaction network generation using RMG for steam cracking of n-hexane. AIChE J., 52, 718?730. doi:10.1002/aic.10655

RMG Website and Open Source project homepage: http://rmg.sourceforge.net/