10.1021/es202359j.s001
David M. Lorenzetti
David M.
Lorenzetti
Michael D. Sohn
Michael D.
Sohn
Numerical Solution of the Polanyi-DR Isotherm in Linear Driving Force Models
American Chemical Society
2016
sorption relations
concentration
isotherm
model complexity
method
Numerical Solution
transport rate
microporous materials
2016-02-22 12:53:12
Journal contribution
https://acs.figshare.com/articles/journal_contribution/Numerical_Solution_of_the_Polanyi_DR_Isotherm_in_Linear_Driving_Force_Models/2577769
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 simulatione.g., of whole-building pollutant transportit 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.