We present a tractable nonlinear programming (NLP) formulation
that models a given multi-component distillation configuration and
searches for its global minimum heat duty. The novelty in the current
model is that it can explore feasible heat integrations with a pre-specified
desired minimum approach temperature between various condensers and
reboilers while simultaneously optimizing the operating conditions
within the configuration. We do not use cumbersome thermodynamic models
for the equilibrium temperature calculation of a saturated multicomponent
mixture. Instead, we propose a modified version of the well-known
Antoine equation that reduces the calculation of the temperature at
a given pressure to a simple function of component mole fractions
and relative volatilities while retaining the fidelity of more complex
models. We explore possible heat integrations by creating a heat exchange
network between column condensers, reboilers, and side draw product
locations. Considering these integrations along with the heat duty
minimization is essential because it is often possible to alter the
operating conditions of the columns and reduce energy consumption
by admitting more heat integration possibilities. Finally, we demonstrate
the power of our framework in identifying optimal configurations that
yield large energy savings for several four- and five-component zeotropic
distillation systems.
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