Chapter 14, Problem 14.28P

Ultra-pure hydrogen is required in applications ranging from the manufacturing of semiconductors to powering fuel cells. The crystalline structure of palladium allows only the transfer of atomic hydrogen (H) through its thickness, and therefore palladium membranes are used to filter hydrogen from contaminated streams containing mixtures of hydrogen and other gases. Hydrogen molecules (H₂) are first adsorbed onto the palladium’s surface and are then dissociated into atoms (H), which subsequently diffuse through the metal. The H atoms recombine on the opposite side of the membrane, forming pure H₂. The surface concentration of H takes the form $C_H=K_s{p}_{H_i}^{0.5}$ , where $K_s\approx 1.4$ ${\text{ kmol/m}}^{\text{3}}\cdot {\text{bar}}^{\text{0}\text{.5}}$ is known as Sieivert’s constant. Consider an industrial hydrogen purifier consisting of an array of palladium tubes with one tube end connected to a collector plenum and the other end closed. The tube hank is inserted into a shell. Impure 112 at $H_{2}atT=600K,p=15bars,x_H=0.85$ is introduced into the shell while pure H₂ at p = 6 bars. T = 600 K is extracted through the tubes. Determine the production rate of pure hydrogen (kg/h) for N = 100 tubes which are of inside diameter D _i = 1.6 mm, wall thickness t = 75 $\text{μm}$ , and length L = 80 mm. The mass diffusivity of hydrogen (H) in palladium at 600 K is approximately $D_{AB}=7\times 10m^2/s$ .