  We consider the finite volume approximation of a reaction-diffusion system
with fast reversible reaction. We deduce from a priori estimates that the
approximate solution converges to the weak solution of the reaction-diffusion
problem and satisfies estimates which do not depend on the chemical kinetics
factor. It follows that the solution converges to the solution of a nonlinear
diffusion problem, as the size of the volume elements and the time steps
converge to zero while the kinetic rate tends to infinity.
