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Reaction Kinetics & Chemical Reaction Models

3. Quantum-Rice-Ramsperger-Kassel (QRRK) Treatment of Energy Transfer Limited Reactions

Only a brief introduction will be given here to the QRRK treatment of unimolecular and bimolecular reactions.  References will be provided for the reader to become more acquainted with this theory as well as software available to carry out the computations needed under the theory.

The Lindemann Theory deviates somehow form the experimentally determined behavior of unimolecular reaction (see Figure 1).  The reason for this can be explained by discussing what is presented illustrated in Figure 2.  The molecule A is activated to A* but in the QRRK treatment, the rate coefficient k_rxn(E) depends on the excess energy of the activated molecule over the ground state.  As the figure shows, QRRK treats the molecular energy as being quantized.  A full discussion of this problem can be found in Westmoreland et al. (1986).

In a similar manner, for bimolecular reactions (Westmoreland,et al., 1986), the process is depicted in Figure 3.  As with unimolecular reactions, the reaction leads to an activated molecule A*.  The fate of this molecule depends on its excess energy.  The rate coefficient k₂(E) for the decomposition to products P + P’ depends on excess energy over the ground state.  The energy is considered as being quantized.  More complex schemes involving izomerization of the activated molecule can be found in Kazakov et al. (1994).

Software for the mathematical treatment of chemically activated reactions can be found, see for example Dean, Bozzelli, and Ritter (1991) for an introduction to the CHEMACT program and Dean and Westmoreland (1987) for additional information.  The reader is referred to these references for a more thorough discussion of chemical activation.

4. Computer Software for Chemical Reactor Engineering

Chemical Kinetics

References were given above for programs that are available to estimate chemically activated reaction.  However, very often no information is available for the activation energy of chemical reactions, or properties of the transition state to be able to estimate rate coefficients according to TST.   Computer software is now available that can be used to make estimates of such parameters.  The software uses the methods of quantum chemistry, a discussion of these methods is beyond the scope of this manuscript, and the reader is referred to Gargurevich (1997), Pople (1970), and Murrell (1972) for a thorough discussion of the theory upon which these programs are based.

The software that the author is most familiar with is the Molecular Orbital Package (MOPAC) developed through the Quantum Chemistry Program Exchange at Indiana University.  MOPAC is based on semi-empirical methods that use experimental data to arrive at solutions of the equations derived from quantum chemistry.  Other properties can be calculated using MOPAC such as the heat of formation of chemical species if needed.

Computer software is also available that use ab initio methods, i.e., the equations derived from quantum chemistry are solved using strict theoretical calculations.  These require more computer memory and speed than the semi-empirical methods.

A list of computer software can be found in www.chemistry-software.com/software_guide/modeling_index.htm.

As it was stated above, a major problem in studying reactions by any current theoretical models is the lack of experimental data for properties of the transition state.  Calculations of these properties then have not been tested, and the performance of the method used for such calculations is safer, the better the performance of the method in question in all areas where it can be tested.

Chemical Reactor Design

The reactor simulator that the author is most familiar with is the CHEMKIN package developed by Sandia National Laboratories (R. J. Kee, F. M. Rupley, and J. A. Miller, Sandia National Laboratories Report, SAND89-8003, 1989).  CHEMKIN uses different modules in order to carry out the necessary simulation of plug flow reactors, or combustion phenomena for example.  These modules are as follows: (1) chemical species and their thermodynamic properties,  (2) the elementary reactions composing the complex mechanism, and the reaction rate constants for each reaction, (3) transport properties of each chemical species (this is necessary for the treatment of combustion phenomena).  The modules interface with each other to numerically solve the problem at hand.  This software was used extensively by the author to simulate combustion phenomena (Gargurevich, 1997).

There are other process simulators available that also can be used for the simulation of chemical reactors.  The most commonly used are software from Aspen Technology Inc.( Cambridge, Mass.), Simulation Sciences Inc. (Brea, Calif.), Hyprotech ( Calgary, Alberta) , and Chemstations Inc. (Houston, Texas) (“Simulators seek a broader community  of users”, Chemical & Engineering News, March 27, 1995).  The author is not familiar with the use of these simulators in the design of chemical reactors except for PRO II 5.5 (Simulations Science) for other applications.  PRO II has a plug flow reactor unit operation plus others which allow the user to specify the reactions and the rate coefficients for each reaction.

 LEAST COMPLEX

Chemical Rate Limited

(1)   Simple Kinetic Theory of bimolecular reactions: reaction rate coefficient equals the collision frequency.

(2) Modified Kinetic Theory: reaction rate coefficient equals, collision frequency x activation energy factor x steric factor

(3)   a. Transition State Theory (TST): unimolecular/bimolecular reactions.  Rate coefficient includes an activation energy factor, and an entropy factor to account for steric effect.

      b. Lindemann theory of unimolecular reactions.

Energy Transfer Limited

(4)   Quantum mechanical treatment of thermal activation, and unimolecular/bimolecular chemical activation.  Rate coefficients depend on the internal energy of molecular species.

Most Complex