  The transport and chemical reactions of solutes are modelled as a cellular
automaton in which molecules of different species perform a random walk on a
regular lattice and react according to a local probabilistic rule. The model
describes advection and diffusion in a simple way, and as no restriction is
placed on the number of particles at a lattice site, it is also able to
describe a wide variety of chemical reactions. Assuming molecular chaos and a
smooth density function, we obtain the standard reaction-transport equations in
the continuum limit. Simulations on one- and two-dimensional lattices show that
the discrete model can be used to approximate the solutions of the continuum
equations. We discuss discrepancies which arise from correlations between
molecules and how these disappear as the continuum limit is approached. Of
particular interest are simulations displaying long-time behaviour which
depends on long-wavelength statistical fluctuations not accounted for by the
standard equations. The model is applied to the reactions $a + b
\rightleftharpoons c$ and $a + b \rightarrow c$ with homogeneous and
inhomogeneous initial conditions as well as to systems subject to autocatalytic
reactions and displaying spontaneous formation of spatial concentration
patterns.
