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Calculation of simultaneous catalytic reaction rates represents a system of nonlinear differential equations with two boundaries; additionally, nonlinear algebraic equations are added if external mass and energy resistances are significant. For highly exothermic reactions and some reaction networks, numerical solution with typical shooting methods encounters difficulties to find good initial guesses since the equation system becomes very rigid. A Numerical Homotopy Continuation approach is proposed in which the particle size is progressively increased until the specified dimensions; shooting variables corresponding at the center of the particle are used as nearby solutions which allows to trace and update the initial guesses.

Homotopy Continuation Method to Evaluate Catalytic Rates for Highly Exothermic Reaction Systems