Second-Order Reaction with Diffusion in a Liquid Film
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Gas absorption is often enhanced by a chemical reaction. For instance, acid gases ( and ) are usually eliminated from natural gas by absorption using ethanolamine () as a basic solvent.
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Contributed by: Housam Binousand Brian G. Higgins (July 2013)
Open content licensed under CC BY-NC-SA
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In the discrete Chebyshev–Gauss–Lobatto case, the interior points are given by . These points are the extrema of the Chebyshev polynomials of the first kind, .
The Chebyshev derivative matrix at the quadrature points is an matrix given by
, , for , and for and ,
where for and .
The matrix is then used as follows: and , where is a vector formed by evaluating at , , and and are the approximations of and at the .
References
[1] P. Moin, Fundamentals of Engineering Numerical Analysis, Cambridge, UK: Cambridge University Press, 2001.
[2] L. N. Trefethen, Spectral Methods in MATLAB, Philadelphia: SIAM, 2000.
[3] M. B. Cutlip and M. Shacham, Problem Solving in Chemical Engineering with Numerical Methods, Upper Saddle River, NJ: Prentice Hall, 1999.
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