A system of nonlinear differential and algebraic equations governing diffusion and reaction is used to simulate a Film-Theory model of absorption of carbon dioxide and hydrogen sulfide in a tertiary-amine scrubber. Solutions to this system of equations are developed by applying various linearization methods.
First, the corresponding system of partial differential equations, with both spatial and temporal derivatives - i.e. which govern nonsteady-state behavior - is approximated with a finite-difference scheme, the results of which converge to a steady state (thereby providing what is believed to an exact “numerical solution”). However, its computation times make it unwieldy for optimization purposes.
Second, the method of van Krevelen and Hoftijzer (VKH) is applied to the ordinary differential equations (ODEs) and coupled algebraic equations governing steady-state behavior, and shown to provide reliable results over widely ranging conditions. However, the insertion of concentrations of nonvolatile reactants in the rate equation, whereby the VKH method linearizes the ODEs, is potentially problematic when applied to cases with higher pressures of hydrogen sulfide; in such cases, absorption rates based on the VKH lose accuracy when compared with those calculated using numerical methods. With that caveat, the VKH method is used to explore the role of the tertiary amine's pKa in optimizing selectivity for hydrogen sulfide.
Third, a regular perturbation method is applied to the steady-state problem. The resulting power series solution [with the Hatta number (a ratio of characteristic diffusion and reaction times) as the expansion parameter], truncated after the first order term, places an upper bound on the Hatta number range over which the zero-order solution may be considered valid. Inclusion of second order and third order terms does little to expand the range of accuracy.
Explicit solutions are also derived for the limiting cases of purely physical absorption (no reaction) and local reaction equilibrium. All models are applied over a range of conditions to calculate the enhancement factors by which chemical reactions multiply absorption rates, and in so doing, infer the approximate solutions' regimes of accuracy.
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|Advisor:||Meldon, Jerry H.|
|Commitee:||Borgers, Christoph, Mess, Derek|
|Department:||Chemical and Biological Engineering|
|School Location:||United States -- Massachusetts|
|Source:||MAI 56/01M(E), Masters Abstracts International|
|Subjects:||Applied Mathematics, Chemical engineering|
|Keywords:||Gas sweetening, Reactive absorption, Regular perturbation, Selective hydrogen sulfide absorption, Two-film theory, Van krevelen - hoftijzer linearization|
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