By Nitin H. Kolhapure* and Rodney O. Fox, Department of Chemical Engineering, Iowa State University, Ames, IA *Presently at DuPont Engineering Technology, Wilmington, DE

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With the ever-increasing availability of high-performance computing tools, CFD is becoming a significant technology, though still not dominant, for reactor design in the chemical process industry. CFD is emerging as a design tool for the development of new processes and optimization of existing ones at a fraction of the cost and time of traditional experimental and pilot-plant approaches. At Iowa State, the ability of CFD to simulate turbulent reacting flows in processes involving fast, mixing-sensitive reactions has been investigated. These flows are characterized by interactions between large and small chemical and mixing time scales that play a significant role in determining reactant consumption (yield), product quality (selectivity), and reactor stability. Traditional reactor models based on idealized flow assume perfect micromixing and fail to account for such interactions.

To improve upon these models, a comprehensive CFD algorithm that links FLUENT with a sub-grid-scale multienvironment micromixing (MEM) model and detailed low-density polyethylene (LDPE) chemistry has been developed for plant-scale tubular reactors. In LDPE reactors, a small amount of initiator is injected into a preheated monomer flow to start a complex series of reactions that produce polymers of varying length (molecular weight). These reactors are extremely sensitive to local mixing conditions due to stiff and highly exothermic kinetics and hence, they serve as an excellent test case for commercial reactors where control of the reaction conditions and optimization of the reactor performance (i.e., reactor stability, initiator efficiency, polymer molecular weight distribution) are desired.

The mean mass fractions for initiator (top, 0 to 1.15x10-3), monomer (middle, 0.95 to 1), and temperature (bottom, 250 to 307°C) inside a tubular reactor (d = 3.8 cm, L = 10 m)

The injection region (0 to 0.2 m) is zoomed in to highlight the non-uniform initiator distribution, which caused a loss of 64% initiator compared to plug-flow conditions

An interactive interface was created for the project using user-defined functions (UDFs) in FLUENT. C routines for the MEM model and FORTRAN routines for a customized in-situ adaptive tabulation (ISAT)¹ algorithm for the LDPE chemistry were compiled and linked to FLUENT. The continuity equation, the k-e model, the MEM model, and the chemistry were solved sequentially at each grid point in a 2D axisymmetric computational domain. An unsteady coupled implicit solver was chosen to limit the effects of truncation errors on the solution. The UDF interface updated the mixing and chemical source terms at each time step as per the formulation in the MEM model and the ISAT algorithm. The interface also provided an ability to account for the inter-dependence of the kinetic, physical, and thermodynamic properties of the polymer reaction mixture. ISAT enabled the inclusion of a total of 16 species and offered ten-fold computational gains by replacing the conventional direct integration with a less expensive multi-linear interpolation. It proved to be a powerful technique to include chemistry calculations in CFD without restricting the degrees of freedom of the chemical composition vector. More details of the CFD algorithm with the UDF interface and the MEM model can be found elsewhere.^2,3

The effect of micromixing is shown through local temperature fluctuations in the reacting environment (top, 250 to 329°C) and higher polydispersity (molecular weight distribution) (bottom, 0 to 7.15)

The CFD results demonstrated the capabilities of the algorithm to capture the strong coupling between micromixing and complex chemistry and predict the complete reacting flow information, including species and temperature distributions close to physical reality. The flow information at the micro-scale provided important insights into the occurrence of small-scale temperature fluctuations (hot spots), deterioration of polymer quality, and loss of initiator under extreme operating and mixing conditions. The influence of feed temperature, initiator concentration, and degree of premixing on steady-state reactor performance was helpful in making wiser, more well-informed operational decisions. By replacing pilot-plant tests, CFD offered a low-cost alternative to explore a variety of design options for optimizing initiator consumption while controlling the product quality and reactor safety. Though validation of such a CFD approach against key experimental data remains an integral and essential part of the design procedure, it opens greater opportunities for the development of safe and efficient chemical processes at reduced costs and time. The study has brought turbulent reacting flow simulation for singlephase finite-rate chemistry closer to realistic chemical process engineering applications.

References

1 Pope S.B., "Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation." Combustion Theory and Modeling, 1:41-63, 1997.

2 Fox R.O., "Computational methods for turbulent reacting flows in the chemical process industry." Revue de l'Institut Français du Pétrole, 51:215-243, 1996.

3 Kolhapure N.H. and Fox R.O., "CFD in polymer reaction engineering: Combining polymerization chemistry and detailed flow models." DECHEMA Monogr., 137:247-271, 2001.

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