Consider the catalytic reaction process shown in the figure below. The control volume has two catalytic zones:

Question:

Consider the catalytic reaction process shown in the figure below. The control volume has two catalytic zones: a porous catalyst (catalyst I) that fills the control volume, and a nonporous catalyst surface (catalyst II) on the left side of the control volume (x = 0; y = 0 to H). Reactant A diffuses into the porous catalytic material (catalyst I) with effective diffusion coefficient D_Ae, and is converted to product B according to a homogeneous reaction of the form

where k₁ is the first-order reaction rate constant (s^€“1). Reactant A can also diffuse to the nonporous catalyst surface (catalyst II), and is converted to product C according the surface reaction of the form

where k_s is the first-order surface reaction rate constant (cm/s).

The source for reactant A is well-mixed flowing fluid of constant concentration c_A,ˆž. It is reasonable to assume that c_A(x,0) ‰ˆ c_A,ˆž (0 ‰¤ x ‰¤ L). Reactant A is diluted in inert carrier fluid D. Therefore, the control volume contains four species: A, B, C, and inert diluent D. The right side (x = L; y = 0 to H) and top side (x = 0 to L, y = H) of the catalytic zone are impermeable to reactant A, products B and C, and diluent fluid D.

a. It can be assumed that the process is dilute with respect to reactant A. State three additional reasonable assumptions for the mass-transfer processes associated with reactant A, including the source and sink for reactant A, that allow for appropriate simplification of the general differential equation for mass transfer, and Fick€™s flux equation.

b. Develop the differential forms of the general differential equation for mass transfer and Fick€™s flux equation for reactant A within the process. Carefully label the differential volume element. Combine the general differential equation for mass transfer and Fick€™s flux equation to obtain a second-order differential equation in terms of concentration c_A(x,y).

c. Formally specify all relevant boundary conditions on reactant A for a steady-state process.