Catalyst Pellet Design

When using an expensive material such as zirconium tungstate as a catalyst for an industrial reaction the main goal is to use as little of this material as possible while still being effective in order to control cost. The industrial standard for a pellet coating is between 1-3 micrometers in thickness. The catalyst is typically deposited on a less expensive material such as aluminum oxide (alumina).

The first step in the calculations is to find the volume of the outer and inner sphere as depicted in the figure. We will assume that the outer diameter of the pellet is 1 cm. The layer of catalyst will be 1 micrometer thick. We will calculate volume in cubic meters for simplicity purposes. It is important that all measurements me in meters

Total Volume of the Pellet = V(total) =  (4/3)*PI*((OD/2)^3)

Where OD is the outer pellet diameter (.01m in this case) and PI~3.141592654. V(tot) = 5.24E-7 cum

Inner Volume = V(alumina) = (4/3)*PI*(((OD-2t)/2)^3)

Where t is the thickness of the catalyst layer (10^-6 m in this case). V(alumina) = 5.233E-7cum

Outer Volume = V(catalyst) = V(total)-V(alumina) = 7E-10 cum

 Next we will calculate the mass of alumina and the mass of catalyst in each pellet. Alumina has a density of 1130 kg/cum. Zirconium tungstate has a density of 1600 kg/cum. This is a very simple calculation.

Mass = Volume * Density

M(alumina) = 5.913E-4 kg, M(zirconium tungstate) = 1.12E-6 kg

Total Mass = M(total) = M(alumina) + M(zirconium tungstate)

M(total) = 5.924E-4 kg

Next we will calculate the mass fraction of each substance in the pellet.

MF(alumina) = M(alumina)/M(total)

MF(zirconium tungstate) = M(zirconium tungstate)/M(total)

MF(alumina) = .998, MF(zirconium tungstate) = .002

Finally we will calculate the cost per kg of pellets. The cost of alumina is $0.44/kg. Zirconium tungstate is $1600/kg.

Cost/kg(pellet) = (MF(alumina)*.44)+(MF(zirconium tungstate)*1600)

Our cost per kg of pellets comes out to $3.64/kg.

We will factor in that the maufacturer will seek a profit by making pellets of this composition. We will assume they desire a profit of 15%.

This brings the retail price to $4.19/kg