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373153 Generalization of the Mist-Onset “Tangency Condition” for Multi-Component Vapor Mixtures Near Cool Surfaces

Anticipating condensation conditions within thermal boundary layers is important in many industrial applications involving condensable flows in contact with cooler solid surfaces. This is particularly relevant in energy recovery applications dealing with trace but potentially corrosive components often found in combustion products, such as acid mists (sulfuric-, nitric-, etc.). In the absence of appreciable nucleation barriers, rigorous prediction of such condensation conditions can be based on vapor-liquid equilibrium (VLE-) conditions, usually involving the solution of a set of transcendental equations for the condensate composition and temperature, for a given vapor composition at constant pressure. However, in most applications the presence of large spatial gradients of temperature and composition introduce the need to also consider transport-based (including Soret-) “shifts” to the former (otherwise) thermodynamic problem.

To predict acid-mist onset conditions in a simple and efficient way, a well-known procedure is the “tangency condition”, first proposed and exploited by Johnstone et al. (1950) for the case of a unary condensate. This incipient supersaturation condition, usually imposed at the gas/solid interface, was recently generalized to the case of a binary condensate by Rosner and Arias-Zugasti (2012), in an analysis which also accounted for Soret modifications to the condensable vapor composition (and hence dew point) near the condenser surface. The binary generalization exploited the usual disparity (p(H2O)>>pi) in condensable vapor partial pressures, and was also based on the use of an empirical correlation (Verhoff and Banchero (1974)) for the saturation temperature as a function of the acid vapor compositions. This enabled a simple result, avoiding a detailed description of the (binary) condensate composition, as well as avoiding the need for information on the activity coefficients for the (usual) case of highly non-ideal condensates. On the other hand, use of the Verhoff-Banchero empirical correlation for the saturation temperature (involving powers of the logarithm of the participating partial vapor pressures), inevitably limits the domain of applicability of that model.

In the present work the now-familiar tangency condition for mist onset near a cooler solid surface is further generalized to the frequently encountered case of a multi-component mixture of condensibles dilute in a “non-condensible” carrier gas. This generalization employs VLE conditions for a multicomponent vapor mixture in equilibrium with the corresponding multi-component condensate. Compared to the classical unary tangency condition for mist onset [Johnstone et al. (1950)], or the binary, semi-empirical generalization of Rosner and Arias-Zugasti (2012), the present theoretical model involves knowledge of the composition of the condensate and the participating component activity coefficients, and does not invoke empirical correlations for the saturation temperature. As a consequence, this generalized tangency condition can be used to predict local supersaturation conditions within such thermal boundary layers provided activity coefficients of the liquid condensate components are known or estimable (for instance via UNIQUAC or UNIFAC models). Conversely, this generalization could be used to infer the behavior of the activity coefficients of highly non-ideal mixtures of practical interest based on careful mist-onset (or deposition rate) observations. Illustrative calculations are discussed for a binary aqueous acid combination of current practical interest.

**References**

Johnstone, H.F., Kelley, M.D., McKinley, D.L., 1950. Fog formation in cooler-condensers. *Ind.** Eng. Chem* 42,2298–2302.

Rosner, D.E., Arias-Zugasti, M., 2012. Estimating transport-shifted acid dew-point surface temperatures and conditions for the avoidance of acid mists in energy recovery operations. *Chem. Eng. Sci. *75, 243–249

Verhoff, F.H., Banchero, J.T., 1974. Predicting dew points of flue gases. *Chem. Eng. Prog*. 70, 71-72.

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