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In class we derived the equation for the effectiveness factor for a porous spherical catalyst pellet and a porous slab. The Levenspiel text derived the
In class we derived the equation for the effectiveness factor for a porous spherical catalyst pellet and a porous slab. The Levenspiel text derived the expression for diffusion and reaction in a single cylindrical pore where the gas enters from one end of the pore. In this problem I want you to derive the expression for the effectiveness factor for a porous cylindrical catalyst pellet where diffusion occurs in the radial direction. Assume that the cylinder ends are impermeable and that the length of the cylinder is much longer than the radius so end effects a Start by using a differential mass balance to derive the differential equation that describes the system. You should also state the boundary conditions for the system hint one of them is that the is finite at the center of the cylinder You may assume that there are no external diffusion limitations b Solve the differential equation to obtain as a function Some information that may be helpful: The differential equation, has the solutions and which are the modified Bessel functions these functions look somewhat like and multiplied by an exponential decay function and that goes to negative infinity at c Using your result form part b derive an equation for the effectiveness factor for this system. Useful formula:
In class we derived the equation for the effectiveness factor for a porous spherical catalyst
pellet and a porous slab. The Levenspiel text derived the expression for diffusion and reaction
in a single cylindrical pore where the gas enters from one end of the pore. In this problem I
want you to derive the expression for the effectiveness factor for a porous cylindrical catalyst
pellet where diffusion occurs in the radial direction. Assume that the cylinder ends are
impermeable and that the length of the cylinder is much longer than the radius so end effects
a Start by using a differential mass balance to derive the differential equation that
describes the system. You should also state the boundary conditions for the system
hint one of them is that the is finite at the center of the cylinder You may assume
that there are no external diffusion limitations
b Solve the differential equation to obtain as a function
Some information that may be helpful:
The differential equation, has the solutions
and which are the modified Bessel functions these functions look somewhat
like and multiplied by an exponential decay function and that goes
to negative infinity at
c Using your result form part b derive an equation for the effectiveness factor for this
system.
Useful formula:
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