Analysis of gas transport in laminated semi-infinite solid: Novel method for complete membrane characterization during highly transient state

Gas transport in a two-layer membrane system, subjected to a step increase in feed pressure, is modeled under highly transient state in which the Layer 2 behaves as a semi-infinite solid. The system of governing partial deferential equations is solved using Laplace transforms, and the solution is used to obtain the expression for the pressure decay in the upstream volume. Accordingly, the pressure decay at short and long times is directly proportional to the square root of time, where the early and late slopes are dependent on the properties (i.e., diffusivity and solubility) of the materials of Layer 1 and Layer 2, respectively. Knowing the properties of the material of Layer 2, the material of Layer 1 can be fully characterized based on the early slope and the rate at which this early slope changes once the penetrant enters Layer 2. Since the thickness of Layer 1 in the two-layer system can be orders of magnitude smaller than that of a stand-alone membrane, the approach presented in this paper may allow characterizing barrier materials, which otherwise could not be characterized in a reasonable timeframe by traditional integral, permeation and sorption techniques. In addition, the new method may be used for characterization of the selective layer in thin film composite membranes.