Finite Element Simulation of Deep‐Well Wet‐Oxidation Reactor
Publication: Journal of Engineering Mechanics
Volume 116, Issue 8
Abstract
A finite element model is developed for the numerical simulation of a deep‐well wet‐oxidation reactor. The temperature distribution in the well‐earth system is investigated. The governing equations involved in the analysis are the conductive heat equation for the earth, and an energy balance equation describing convective heat transfer and reaction in the reactor tubes. The two equation sets are coupled by the continuity of the temperature and heat flux at the interface between the earth and the reactor tubes. Proper scaling is carried out for the dimensionless forms of these equations. A Galerkin finite element formulation is used for the spatial discretization of the heat equation in the earth. A Petrov‐Galerkin finite element formulation is employed for the convection‐reaction equation in the reactor tubes. The resultant set of ordinary differential equations is solved by a predictor/multi‐corrector algorithm. A numerical test is performed for a model deep‐well reactor. Compared to our previously published work, this formulation is more accurate and consumes less CPU time. It can be used in the design of a deep‐well reactor for oxidation of aqueous sludge. It can also be employed to test control strategies for the operating reactor system.
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References
1.
Brooks, A. N., and Hughes, T. J. R. (1982). “Streamline upwind/Petrov‐Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier‐Stokes equations.” Computer Methods in Appl. Mech. and Engrg., 32(Sept.), 199–259.
2.
Gelus, E., Deans, H. A., and Tezduyar, T. E. (1988). “Finite element analysis of the start‐up dynamics of a deep‐well oxidation process.” Presented at Solid Waste Mgmt. Options for Texas Conf., Austin, Tex., May.
3.
Hughes, T. J. R. (1987a). “Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier‐Stokes equations.” Finite Elements in Fluids, 7, R. H. Gallagher, R. Glowinski, P. M. Gresho, J. T. Oden, and O. C. Zienkiewicz, eds., John Wiley and Sons, New York, N.Y., 273–287.
4.
Hughes, T. J. R. (1987b). The finite element method. Prentice‐Hall, Englewood Cliffs, N.J.
5.
Smith, J. M., and Raptis, T. J. (1986). “Supercritical deep well wet oxidation of liquid organic wastes.” Int. Symp. on Subsurface Injection of Liquid Wastes, National Water Well Association, Mar.
6.
Tezduyar, T. E., and Ganjoo, D. K. (1986). “Petrov‐Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: Application to transient convection‐diffusion problems.” Computer Methods in Appl. Mech. and Engrg., 59(Nov.), 47–71.
7.
Tezduyar, T. E., and Park, Y. J. (1986). “Discontinuity‐capturing finite element formulations for nonlinear convection‐diffusion‐reaction equations.” Computer Methods in Appl. Mech. and Engrg., 59(Dec.), 307–325.
8.
Tezduyar, T. E., Deans, H. A., and Marble, J. (1987). “Finite element/finite difference analysis of a deep‐well oxidation process.” 5th International Conference on Numerical Methods in Thermal Processes, Montreal, Canada, Jun.
9.
Tezduyar, T. E., Glowinski, R., and Liou, J. (1988). “Petrov‐Galerkin methods on multi‐connected domains for the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations.” Int. J. Numerical Methods in Fluids, 8(Oct.), 1269–1290.
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Copyright © 1990 ASCE.
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Published online: Aug 1, 1990
Published in print: Aug 1990
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