  In this work we derive a posteriori error estimates for the
convection-diffusion-reaction equation coupled with the Darcy-Forchheimer
problem by a nonlinear external source depending on the concentration of the
fluid. We introduce the variational formulation associated to the problem, and
discretize it by using the finite element method. We prove optimal a posteriori
errors with two types of calculable error indicators. The first one is linked
to the linearization and the second one to the discretization. Then we find
upper and lower error bounds under additional regularity assumptions on the
exact solutions. Finally, numerical computations are performed to show the
effectiveness of the obtained error indicators.
