ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

Bond-graph description and simulation of membrane processes: Permeation in a compartmental membrane system

Piotr Szczepański, Grażyna Szczepańska, and Romuald Wódzki

Faculty of Chemistry, Nicolaus Copernicus University, Gagarina Str. 7, 87-100 Toruń, Poland

E-mail: piotrs@chem.uni.torun.pl

Abstract: Network and numerical analysis of permeation through a membrane under non-stationary, stationary, and pseudo-stationary conditions is described. A compartmentalized membrane system (feed solution|membrane|stripping solution) was represented by a linear network of capacitances, diffusion, and sorption/desorption graphs. Reticulation degree of diffusion layers sufficient for quantitative modeling of the diffusion through a homogeneous membrane was estimated. It was found that for membranes of the thickness from 0.001 cm to 0.1 cm and the diffusion coefficients from 1 × 10⁻⁷ cm² s⁻¹ to 1 × 10⁻⁵ cm² s⁻¹, the membrane (or other diffusion layer) partition into ten slices leads to simulated time lags and stationary fluxes differing from the theoretical ones by less than 0.5 % and 1 %, respectively. Extended model with two unstirred interfacial layers and the feed and stripping solution of finite volumes was applied to characterize the effects caused by possible membrane heterogeneity.

Keywords: membrane permeation modeling – network analysis – bond-graph method

Full paper is available at www.springerlink.com.

DOI: 10.2478/s11696-012-0204-9

Chemical Papers 66 (11) 999–1009 (2012)