mws_che_sle_txt_ludecomp_examples

mws_che_sle_txt_ludecomp_examples - Chapter 04.07 LU...

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04.07.1 Chapter 04.07 LU Decomposition – More Examples Chemical Engineering Example 1 A liquid-liquid extraction process conducted in the Electrochemical Materials Laboratory involved the extraction of nickel from the aqueous phase into an organic phase. A typical set of experimental data from the laboratory is given below. Ni aqueous phase, ( ) l g a 2 2.5 3 Ni organic phase, ( ) l g g 8.57 10 12 Assuming g is the amount of Ni in the organic phase and a is the amount of Ni in the aqueous phase, the quadratic interpolant that estimates g is given by 3 2 , 3 2 2 1 + + = a x a x a x g The solution for the unknowns 1 x , 2 x , and 3 x is given by = 12 10 57 . 8 1 3 9 1 5 . 2 25 . 6 1 2 4 3 2 1 x x x Find the values of 1 x , 2 x , and 3 x using LU decomposition. Estimate the amount of nickel in the organic phase when l g 3 . 2 is in the aqueous phase using quadratic interpolation. Solution [ ] [ ][ ] = = 33 23 22 13 12 11 32 31 21 0 0 0 1 0 1 0 0 1 u u u u u u U L A
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mws_che_sle_txt_ludecomp_examples - Chapter 04.07 LU...

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