On the measurement of transport parameters of porous solids in permeation and Wicke–Kallenbach cells

• We derive optimal conditions for the permeation and Wicke–Kallenbach cells.
• Large pressure variations are necessary for estimation of the transport parameters.
• The outlet mole fractions must be close to the middle of their admissible intervals.
• A pore network model helps us specify the limits of continuum mass transport models.
• Biased transport parameters counterbalance the deficiency of the continuum models.

We present sensitivity analysis of gas transport problems related to experimental setups that are routinely used for determination of effective transport parameters of macroporous solids. The relevance of large total pressure variations to reliable estimation of the effective transport parameters is emphasized in two experimental setups, particularly quasistationary permeation and classical Wicke–Kallenbach cells. It is shown that variations of other system parameters, such as temperature, number of gases or inlet flow rates cannot resemble the efficiency of total pressure changes in estimating the parameters. For the classical Wicke–Kallenbach cell and binary mixtures, it was found that there are narrow intervals of outlet mole fractions in which the related boundary-value problem exhibits the maximum sensitivity to modifications of the transport parameters, i.e. there are the optimal conditions for regression analysis. The rule of adjusting the optimal conditions is simple: the outlet mole fractions, which can easily be controlled by setting the inlet flow rates, must be close to the middle of their admissible intervals. Pore network modelling supported these results and helped us reveal a source of systematic deviations between the effective transport parameters obtained either from permeation experiments or from diffusion experiments. Specifically, the overall network flow rate resulting from non-linear functional relationships between fluxes and driving forces on the pore scale and from the law of mass conservation in network nodes does not exactly conform to the similar flow rate based on the effective parameters if the total pressure span is large. Consequently, biased values of the effective transport parameters counterbalance the deficiency of the associated models.