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.