Multiple steady states in a catalyst

The adiabatic catalyst problem arises in the field of chemical engineering. If chemical reaction kinetics within a solid catalyst body are influenced by mass transfer multiple steady states are possible for a certain range of the governing parameters: arrhenius number, prater number and thiele modulus. This is a common example arising in the education of undergraduate chemical engineering students.

The program computes eta vs. thiele plots. Eta (catalyst efficiency) represents the ratio of the mean actual rate in the catalyst to such a value of the rate which is subject to conditions at the outer catalyst surface.
Eta is, therefore, a measure for the efficiency of a catalyst for a given set of the dimensionless parameters prater and arrhenius numbers. The dimensionless thiele number represents the ratio of chemical reaction rate to mass transport kinetics.
Large thiele numbers (>>1) indicate mass transfer limited macrokinetics. For highly exothermic (large positive prater number) and heat sensitive (large arrhenius number) reactions eta can strongly exceed 100% due to the formation of a hot spot in the catalyst core. For a certain range of thiele numbers multiple steady states may be observed.
In order to fully explore the region of multiplicity each point in the
plot is computed by performing up to 4 attempts on the boundary value problem varying the initial guess for the concentration profile inside the catalyst matrix.

Start at etavsthiele.m