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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



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

DOI: 10.2478/s11696-012-0204-9


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

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