Estimate relative volatilities and identify energy-efficient configurations for multicomponent separations.
In the past three decades, commercial process simulators, which employ detailed process models, have developed to the point that we implicitly trust their results. Simulation software has become standard in industry and an integral part of the undergraduate chemical engineering curriculum. Modeling and simulation are used for unit operations across chemical plants, including distillation, for which tailored models are often built into software packages for specific applications (e.g., crude distillation). Shortcut methods that do not require detailed process models, however, are still valuable tools for engineers. For example, the Underwood method can be used to calculate the minimum reflux (1) and the Fenske equation to calculate the minimum number of trays (2).
Shortcut methods are particularly useful for conducting an initial screen of available configuration options. It is impractical to use a process simulator to choose from the numerous options for a given multicomponent separation process (3). Thus, to select a configuration, industrial designers often rely on heuristics and past experience, which do not reliably identify the best configurations. The shortcut methods provide a simple but more thorough exploration of options. For example, these methods have been incorporated into optimization formulations that systematically comb through possible distillation configurations and identify attractive options (4–6).
One of the biggest computational challenges in distillation is the complexity of vapor-liquid equilibrium (VLE) equations, which are interconnected and derived from standard thermodynamic equations of state. Shortcut methods typically assume that the relative volatilities are constant to simplify these equations.
Relative volatility is a measure of the distribution of components between the liquid and vapor phases of a mixture at equilibrium. It is an indicator of the ease with which components can be separated by distillation. Mathematically, the overall relative volatility αi of component i with respect to the heaviest component n in an n-component mixture is:
where x is the liquid mole fraction and y is the vapor mole fraction of components in a mixture at equilibrium. Relative volatility can also be expressed as the ratio of component equilibrium constants, K.
Equation 1 can be written for all components based on the property that mole fractions sum to 1:
When relative volatilities are constant, Eq. 2 fixes the vapor composition of any component in equilibrium to a given liquid composition. As a result, we refer to Eq. 2 as the simplified vapor-liquid equilibrium. In reality, however, relative volatility varies with changes in composition, temperature, and/or pressure for multicomponent mixtures.
While various rules of thumb have been used to calculate a single set of relative volatilities (2, 7), this article proposes a systematic method for estimating these constants. A separation case study demonstrates this method and confirms that the results compare favorably with those of a detailed model...
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