PROBLEM: An instrument is to be designed to measure the concentration of methane

Question

PROBLEM: An instrument is to be designed to measure the concentration of methane in air. Methane has a lower flammable limit concentration of 5 mole percent in air, and the instrument is to be designed for a known response at steady state when the methane concentration is 25 percent of the lower flammable limit (the LFL for methane is 5.0 mole percent). Methane and oxygen diffuse through a thin porous coating to the catalyst surface, where they react immediately, producing carbon dioxide and water. It has been found that methane must diffuse to the catalyst surface at a rate of o.1 2 grams/hr-cm2 to produce the desired heating rate at the catalyst surface. The porous coating for the catalyst surface has an effective diffusivity 36.5 percent of the molecular diffusivity. The surface temperature of the catalyst reaches 175 °C at steady state and the ambient temperature is 25 °c. How thick should the porous coating be to provide the correct diffusion rate? The reaction at the surface is 1 3 Co2 2 H20

Explanation / Answer

In the above problem main parameter to be evaluated is mass transfer coefficient 'k'. Here we know effective diffusivity as a function of molecular diffusivity.

We know N = k*Ceq g/h.cm^2

k=0.1/Ceq

Ceq = 0.25*0.05 mole/cm^3 =0.0125 mole/cm^3 = 0.0125*16g/cm^3 = 0.2 g/cm^3

Which gives k =0.5 cm/h

Where Sherwood number gives relation between mass transfer coefficient and diffusivity, Sh = kL/D

D = 0.36*(6*10^-6) = 2.16 *10^-6m^2/s = 77.76 cm^2/h

Taking Sh =2

We get thickness of porous coating, L =4*77.76 =311 cm

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