Numerical Solution of the Polanyi-DR Isotherm in Linear Driving Force Models

2016-02-22T12:53:12Z (GMT) by David M. Lorenzetti Michael D. Sohn
The Polanyi–Dubinin–Radushkevich isotherm has proven useful for modeling the adsorption of volatile organic compounds on microporous materials such as activated carbon. When embedded in a larger dynamic simulatione.g., of whole-building pollutant transportit is important to solve the sorption relations as quickly as possible. This work compares numerical methods for solving the Polanyi-DR model, in cases where transport to the surface is assumed linear in the bulk-to-surface concentration differences. We focus on developing numerically stable algorithms that converge across a wide range of inputs, including zero concentrations, where the isotherm is undefined. We identify several methods, including a modified Newton-Raphson search, that solve the system 3–4 times faster than simple bisection. Finally, we present a rule of thumb for identifying when boundary-layer diffusion limits the transport rate enough to justify reducing the model complexity.