First Principles Based Simulations of Steam Cracking of Ethane/Propane and Ethane/Butane Mixtures

1. Introduction

Design and optimization of industrial steam cracking reactors is focused on maximization of the product yields and the energy efficiency. An adequate kinetic description of the reaction chemistry in combination with an appropriate reactor model is essential for that purpose. This requires on the one hand that the chemistry involved in the steam cracking is modeled accurately at the molecular scale. On the other hand, the proposed reactor model should be of sufficient complexity to allow a proper description of the studied system. Only a fundamental simulation model with a reaction network based on elementary reaction steps, a so called single event microkinetic (SEMK) model, enables accurate and efficient modeling of the numerous reactions taking place in a steam cracking reactor. Even for cracking of light hydrocarbons, the networks describing the radical chemistry of the cracking process can contain up to thousands of reactions and hundreds of species. It is one of the most challenging tasks in reaction engineering to provide these networks with accurate kinetic and thermodynamic data. For steam cracking, the lack of thermodynamic and kinetic parameters for all elementary steps is commonly circumvented by using a combination of parameters originating from various sources such as kinetic databases (e.g. the NIST database), model predictions (e.g. Evans-Polanyi relation, group additivity schemes) and fitting to experimentally observed product yields. However, there is frequently a rather large scatter on the reported kinetic data for a given reaction. Also, the use of rate coefficients that are fitted to the observed product yields can obscure deficiencies in the reaction network. Therefore, in this work, all required thermodynamic and kinetic rate data are consistently obtained using group additive models based on high-accuracy CBS-QB3 quantum chemical calculations.

2. Single event microkinetic model

The SEMK model for steam cracking consists of two parts: 1. the single event reaction network and 2. the reactor model equations and the solver of the resulting set of differential algebraic equations. The reaction network forms the heart of the SEMK model and determining the net reaction rates requires that both the thermochemistry and kinetics for each of the elementary steps in the reaction network are known. Calculating all required parameters by ab initio methods is infeasible due to the large number of reactions. Therefore, a group additive method is applied that links the thermodynamics and kinetics for larger species to high-accuracy ab initio data for smaller species.

The thermochemical values of primary importance for the calculation of equilibrium coefficients and enthalpy balances, are the standard enthalpy of formation D_fH°(298 K), the standard entropy S°(298 K) and the molar heat capacity at constant pressure C_p°(T), for hydrocarbons and hydrocarbon radicals. Thermodynamic data have been calculated using the CBS-QB3 method, involving corrections for all internal rotations. The applied methodology yields very good agreement with experimental data for standard enthalpies of formation (MAD=1.3 kJ mol^-1), entropies (MAD=1.2 J mol^-1 K^-1) and heat capacities (MAD=1.2 J mol^-1 K^-1). [1,2] From these data a set of 95 consistent group additive values (GAVs) was derived for the calculation of the thermochemistry of large hydrocarbons and hydrocarbon radicals, involving 41 GAVs that had not been determined before.

To study the kinetics, the elementary reactions are grouped into reaction families. The 3 studied reaction families that contribute most significantly to the product yields in steam cracking are (i) radical addition to an unsaturated bond and the reverse β scission, (ii) hydrogen abstraction, and (iii) C-C and C-H bond scission and radical recombination reactions. Rate coefficients for the elementary steps have been calculated by extending the group additive method developed by Saeys et al.[3,4] to pre-exponential factors. In the group additive method, the activation energy and the pre-exponential factor are related to the structure of the transition state. The group additive values are determined from kinetic parameters calculated using the CBS-QB3 method taking into account the internal rotation about the forming/breaking bond. Tunneling has also been accounted for when necessary. Out of several ab initio methods, this method gave the best agreement in comparison with experimental rate coefficients for a test set of 49 reactions containing all the reaction families relevant to steam cracking. The CBS-QB3 method with hindered rotation and Eckhart tunneling corrections yielded the lowest mean factor of deviation from the experimental values, smaller than a factor 3 in all cases which is better than many commonly used DFT-based methods.[5,6] Based on the thermodynamic and kinetic data calculated in this work, a reaction network was generated using the rate-based RMG code [7,8].

3. Reactor simulation

The reaction network generated using only the ab initio thermodynamic and kinetic data has already shown to yield excellent results for ethane cracking[9] and enabled, for the first time, to simulate an industrial steam cracker on an entirely ab initio basis without using a single adjustable parameter or experimental value. In this work, simulation results are presented for the co-cracking of ethane, propane and butane in the pilot plant set-up of the Laboratory for Chemical Technology and in an industrial reactor. The pilot plant experiments were performed in a broad range of experimental conditions. Using the first principles based reaction network, the product yields up to benzene could be reproduced within 15% for both pilot plant and industrial reactor.

Acknowledgements

We are grateful for financial support from the Fund for Scientific Research-Flanders (F.W.O.-Vlaanderen) and of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen).

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