Answer to Question #213326 in Chemical Engineering for Roszzy

Question

In slurry reactor pure reactant gas is bubbled thought liquid containing suspended catalyst particle.let us view these kinetics in terms of the film theory as shown below in fig p17.3.thus,to reach the surface of the solid the reactant which enter the liquid must diffuse through the liquid film into the main body of liquid and then through the film surrounding the catalyst particle.at the surface of the particle reactant yield product according to first order kinetics.derive an expression for the rate of reaction in terms of these resistance

Answer 1

We have a diffusion of reactant A from the gas phase to the liquid phase at the interface, diffusion of A from the bulk of the liquid into the catalyst's surface, and finally, the surface reaction of the catalyst.  

For interface between gas bubbles and liquid. From the figure we can see that the concentration decreases linearly, rate of diffusion = r

$r=\frac{-1}{v}\frac{dN}{dt}=k_{Ae}a_i(C_{Ai}-C_{Al})$

$k_{Al} =$ gas-liquid mass transfer coefficient

$a_{i}=$ area of gas liquid interface per volumeof reactor (v)

At the catalyst , we have a surface reaction

$r=\frac{-1}{v}\frac{dN}{dt}=k_1C_{As}a_s$

Total $r=\frac{-1}{v}\frac{dN}{dt}=\frac{1}{\frac{1}{k_{Ai}a_i}+\frac{1}{k_{Ai}a_s}+\frac{1}{k_i}}$