Can a nonlinearity be neglected? An example

We report the difference in the solution of two tubular reactor PDE models in which the continuity (mass) balance: (1) includes only the reactant partial pressure, as reported in the literature, and (2) a revised continuity balance that includes reactant molar density (i.e., a nonlinear function of reactant partial pressure and temperature) throughout all of the PDE derivatives. We found, somewhat surprisingly, that the numerical solutions for the two models are in close agreement, and we therefore examine the conditions for which the apparent strong and pervasive nonlinearity in the second model appears to have little effect on the solution. The solutions to the two PDE models were computed by the numerical method of lines (MOL), and we therefore comment on the tests performed to ensure convergence of the MOL solutions.