multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
multivariate production systems optimization - Stanford University
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5.2.6 Modify the Vapor and Liquid Compositions<br />
For the purposes of this study, a successive substitution scheme was used to estimate new<br />
equilibrium ratios for successive iterations. The fugacity coefficient is defined as<br />
It follows that<br />
V<br />
φi = fi V<br />
L<br />
φi = fi L<br />
59<br />
Yi P (5.34)<br />
L<br />
L<br />
φi fi Yi =<br />
V V Xi<br />
φi<br />
fi<br />
Yi P (5.35)<br />
At equilibrium, the partial fugacities are equal. The equation simplifies to<br />
L<br />
φi<br />
V<br />
φi<br />
= Yi<br />
Xi<br />
(5.37)<br />
(5.36)<br />
which is simply the definition of the equilibrium ratio. Therefore, we can used the fugacity<br />
coefficients determined in the current unsuccessful iteration to estimate new K-values.<br />
k i k+1 = fi L<br />
fi V k i k<br />
The new K-values are used to restart the procedure.<br />
(5.38)
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