(117e) The Unexpected Weirdness of Rate-Based Simulation of Some High-Pressure Column Operations

Diffusion is the process by which molecules randomly move towards a phase interface. For the most part, molecules move from a region of high concentration to one with low concentration. It has long been known that diffusion in multicomponent systems is complicated and, in fact, molecules can diffuse from low concentration to high.

One way to model multicomponent diffusion is with a version of Fick’s law: (J) = - [D] d(c)/dz where [D] is a matrix of multicomponent diffusion coefficients. [D] is the product of two other matrices, one of which involves partial derivatives of the fugacity or activity coefficients.

Thermodynamics requires that that the matrix [D] be positive definite and it is usually the case that all of the elements on the main diagonal of [D] have a positive value (this is not a requirement of positive definiteness). Ten years ago, Wambui-Mutoru and Firoozabadi showed that CO2-rich and N2-rich hydrocarbon systems could have main diagonal elements of [D] that are negative.

Using rate-based column simulations, we have found that these negative main diffusion coefficients readily occur in some high-pressure distillation operations. Our purpose in this paper is to investigate the thermodynamics of these processes in more detail, to identify the circumstances in which negative main diffusion coefficients can occur and to explore the consequences for the design and operation of columns in which this phenomenon is predicted to occur.