4. Conclusions
In the paper a new, simple and very fast method for numerical solution
of mass and heat transfer in catalyst pellet, for problems in which dead
zone could develop was presented. The CPU time needed for calculation
the dead zone position takes fraction of second, and calculation the
dependency between effectiveness factor \(\eta\) versus \(\Phi\) takes
only several seconds. It was proven that the double precision in
representation of the real number in most compilers cannot be sufficient
for obtaining correct solution when Thiele modulus \(\Phi\) is greater
than about 10, despite the fact that numerical solution converges.
The OCFE method proved to be robust and efficient method for solving
models of packed bed reactor in which dead zone could develop.
The agreement between numerical solutions and known analytical solutions
for catalyst pellet or reactor was excellent.