(145f) Relaxing the Constant Relative Volatilities and Constant Molar Overflow Assumptions in Distillation While Retaining Their Benefits

In the previous century, shortcut models for evaluating distillation (such as the McCabe-Thiele method, the Fenske method, and the Underwood method) were commonly used due to the ease and simplicity of calculations by hand they provided. With the outstanding rise in computational processing power and the development of process simulation software, distillation columns can now be evaluated with a click of a button and, most importantly, with higher fidelity thermodynamic models. This may give the impression that such shortcut models currently serve a role only in the classroom and for toying with perfectly ideal systems in the realms of academics. Yet despite the advances in computational performance, evaluating a multicomponent distillation configuration separating four or more components with multiple columns, sloppy splits, and thermal couplings is not straightforward. Furthermore, the process engineer may want to know which among the numerous different configurations (which number to 6,128 for five-component separations) is best for their separation, and how much benefit they might expect compared to their current choice. Including optimization for each configuration, this endeavor quickly becomes unwieldy.

Shortcut models that capture essential physics adequately offer a solution to this dilemma. By optimizing such a shortcut model formulation for each configuration, the process engineer can screen the vast search space to quickly identify a handful of attractive configurations, and subsequently determine their precise benefits using a detailed simulation. But while shortcut models offer computational simplicity, they have been censured for being at the cost of real mixture behavior. The two most commonly criticized aspects of the traditional shortcut models is their usage of the constant relative volatilities (CRV) and the constant molar overflow (CMO) assumptions. CRV assumes that component relative volatilities (parameters which describe vapor-liquid equilibrium) are the same throughout a configuration. CMO assumes that the molar flowrates of vapor and liquid traffic are the same on every stage in a column section, with the underlying assumption being that the different components have the same latent heats of vaporization. Clearly, these two assumptions do not strictly hold up in the real world.

In this talk, we present simple methods to relax the CRV and CMO assumptions, to account for the real-world physics they appear to ignore, but without compromising on the simplicity they offer. For CRV, we use the well-established idea of parameter estimation to fit α in the CRV equation to VLE data, treating it as a surrogate model for the true VLE [1,2]. This allows a single choice of relative volatility values to capture the wide variations in a distillation configuration. For CMO, we employ a variable transformation to generate latent-heat variables corresponding to every molar variable [3­–6]. For example, heat duty is the latent-heat analog of vapor duty. Then, by simply replacing each molar variable in a CMO model by its latent-heat analog, we obtain a new model which now accounts for the different latent heats of vaporization, and thereby varying molar traffic within a column. Most importantly, the final model after applying these two methods is mathematically equivalent to the original CMO and CRV model. Thus, the relaxed model accounts for the missing physics of the traditional model while retaining its computational benefits.

Using these relaxation methods, we have built a formulation to optimize multicomponent distillation configurations. On a four-component mixture of paraffins, we will demonstrate that these methods allow our formulation to correctly predict the ranklist of configurations compared to a sensitivity analysis in Aspen Plus. We then identify a heat-integrated energy-efficient configuration for a five-component separation of aromatics, among the 6,128 possible. Thus, we can now identify energy-efficient configurations while accounting for varying relative volatilities and the different latent heats of components.

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