Tower optimization reflux ratio

Fractionating towers optimal reflux ratio, heat exchange, and so forth... 

Martin and coworkers described an application of optimization to an existing tower separating propane and propylene. The lighter component (propylene) is more valuable than propane. For example, propylene and propane in the overhead product were both valued at 0.20/lb (a small amount of propane was allowable in the overhead), but propane in the bottoms was worth 0.12/lb and propylene 0.09/lb. The overhead stream had to be at least 95 percent propylene. Based on the data in Table E12.4A, we will determine the optimum reflux ratio for this column using derivations provided by McAvoy (personal communication, 1985). He employed correlations for column performance (operating equations) developed by Eduljee (1975). 

Similar kinds of constraints involve the reflux ratio in distillation, which must exceed the minimum value for the required separation. If the distillation tower pressure is adjusted, the minimum reflux ratio will change and the actual ratio must be maintained above the minimum value. Even when optimization is not performed, the decision variable values must be selected to avoid violating the inequality constraints. In some cases, the violations can be detected when examining the simulation results. In other cases, the imit subroutines are unable to solve the equations as, for example, when the reflux ratio is adjusted to a value below the minimum value for a specified split of the key components. 

Here, the equality constraints are augmented by the tear equations, h[x = 0, which must be satisfied as well at the minimum of/[i. For this and similar flowsheets, the decision variables include the residence times in the reactors, the reflux ratio of the distillation tower, and the purge/recycle ratio. In one-dimensional space (i.e., with one decision variable), as d varies, the objective function can be displayed as shown in Figure 18.10a. Clearly, the optimizer seeks to locate the minimum efficiently, a task that is complicated when multiple minima exist and it is desired to locate the global minimum. 

The shortcut column performs Fenske-Underwood shortcut calculations for simple refluxed towers. The Fenske minimum number of trays and the Underwood minimum reflux are calculated. A specified reflux ratio can then be used to calculate the vapor and liquid traffic rates in the enriching and stripping sections, the condenser duty and reboiler duty, the number of ideal trays, and the optimal feed location. The shortcut column is only an estimate of the column performance and is restricted to simple refluxed columns. For more realistic results, the rigorous column operation should be used. This operation can provide initial estimates for most simple columns. 

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