Francesco Scura

Sieverts law empirical exponent for Pd-based membranes: critical analysis in pure H2 permeation.

In this paper, the physical meaning of the Sieverts-type driving force exponent n is analyzed for hydrogen permeation through Pd-based membranes by considering a complex model involving several elementary permeation steps (adsorption on the membrane surface on the feed side, desorption from the surface on the permeate side, diffusion through the metal lattice, and the two transition phenomena surface-to-bulk and bulk-to-surface). First, the characteristic driving force of each step is evaluated, showing that adsorption and desorption singularly considered and the adsorption and desorption considered at the same time are characterized by driving forces depending on the ratio of feed and permeate hydrogen pressure. On the contrary, the diffusion step is found to present a driving force that is composed of two terms, one which corresponds to the original Sieverts law (with an exponent of 0.5) and the other which is the product of the pressure difference and a temperature-dependent factor. Then, the characteristic n is evaluated by applying the multistep model to two different membranes from the literature in several cases, (a) considering each permeation step as the only limiting one and (b) considering the overall effect of all steps. The results of the analysis show that for a low temperature and thin membrane thickness, the effect of the surface phenomena is, in general, a decrease of the overall exponent n toward values lower than 0.5, even though, under particular operating conditions, the n theoretical value of the surface phenomena is equal to unity. At a higher temperature and thickness (diffusion-controlled permeation), n tends to 0.5, even though the rapidity of this tendency depends strictly on the membrane diffusional parameters. In this frame, the expression developed for the diffusion step provides a theoretical reason why n values higher than 0.5 are found even for thick membranes and high temperature, where diffusion is the only rate-determining step.

Mathematical Modeling of Pd‐Alloy Membrane Reactors

Publisher Summary This chapter discusses mathematical modeling of Pd–alloy membrane reactors. In these systems, reaction and separation are performed in the same vessel. A permselective membrane, dividing the reactor into a reaction volume (where the reaction happens) and a permeate side allows the selective removal of products from the reaction volume under the effect of a driving force that is a function of the species partial pressures on the reaction and permeate sides. It can be created by means of an inert sweep gas in the permeate compartment (nitrogen, helium, and water), or with the application of a pressure difference between the retentate and the permeate compartments or by their combination. The removal of a product from the reaction volume allows the thermodynamic equilibrium limit of a traditional reactor (TR) to be exceeded, obtaining higher conversion in analogous-operating conditions. This allows the membrane reactors (MRs) to achieve—for endothermic reactions—the same conversion as that attained in a TR but at significantly lower temperatures. The simulations of MRs behavior are useful to predict and analyze the effect of some parameters on the performance of a Pd–alloy MR.

Coupling Newton‐Raphson and Bisection Solving Methods to Simulate Hydrogen Permeation through Pd‐based Membranes with Inhibition by CO and Concentration Polarization

In this work, hydrogen permeation through Pd‐based membranes is modeled and simulated taking into account the presence of both concentration polarization and inhibition by CO. Hydrogen permeation is described as a series of several elementary steps, which are numerically solved by means of a method combining a Newton‐Raphson and bisection routines. The results are expressed in terms of maps of the permeation reduction coefficient (PRC), which is a coefficient taking into account the permeance reduction due to polarization and inhibition. This model can be very useful to improve the design of the Pd‐based membrane separation modules, being able to be fully integrated as a separated numerical routine in CFD commercial software.

Modelling and Simulation of Catalytic Membrane Reactors

Membrane reactors and catalytic membranes were modeled taking into account the separation provided by the membranes. One-dimensional (1D) mathematical models were presented for tubular reactors with cylindrical symmetry and first- or second-order differential equations were considered depending on the importance of the axial diffusion. The permeation through the membrane was described by the specific transport model. The models presented include both mass and energy balances because the simulation discussed is related to energy-intensive reactions. Simulations for reactions producing hydrogen, such as methane steam reforming and water gas shift, were discussed. When the reaction takes place inside the membrane pores or on its surface, the mathematical modeling has to consider the orthogonal direction as the main one to the membrane surface. Therefore, 1D second-order models and related simulations are presented. The models presented are relative to enzymatic reactions characterized by low kinetics and low reaction heat. This means that the energy balance is useless.