  Motivated by a problem in heterogeneous catalysis, we study a model for
irreversible first-order reactions in which gas transport occurs only by
diffusion, and reaction occurs only at a small number of well-localized sites.
The main problem is to determine fractional conversion in terms of the
diffusion coefficient and geometric properties of the reactor. We formulate an
appropriate stochastic model for this problem, and then show that, when the
domain is composed of a network of thin tubes, reasonably explicit formulas can
be obtained.
