Assignment 2 Solutions 2009

We have 2n equatio ns the degrees of freedo m at this

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Unformatted text preview: so consider the velocit y u to be a variable as the throughput for the chromatography co lumn 0 may change. Also, k a , j , k d , j , q , j , e , e t , D L m This yields 5N+4 variables. We have 2N equatio ns. The degrees of freedo m at this point are: F = (5 + 4 - 2 N = 3 + 4 N ) N Can we come up with more relationships? Fo llowing assumpt ions are appropriate: · Void fract ions ( e , e t ) are constant. · Maximum adsorbate concentration q , j is a constant. m This yie lds N + 2 addit ional relat ionships. The adsorption and desorption rate constants can vary with t ime during the chromatographic process. They can also be related to the intrinsic adsorption/desorption rate constants (Lin et al., Ind. & Eng. Chem. Research, 1998). We will assume that they can be expressed as: k d , j = f ( d , j , q m , j , c , i ,.....) k 0 k a , j = f ( a , j , q , j , c , i ,.....) k m 0 This yields 2N more relationships. Finally, the dispersio n coefficient can be expressed as: d p u 0 = 0.2 + 0 011 e 0 . 48 . R D L In summary, we have F = (3 + 4 - ( N + 2 - 2 N - 1 = 1 N ) ) Thus, the degree of freedo m is one. c. The system is underdetermined because F = 1 > 0 . d. What we, as process control engineers, would do is to use a controller t...
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