  In this paper we discuss some features of the BCRE model. We show that this
model can be understood as a mapping from a two-dimensional to a
one-dimensional problem, if some conditions are satisfied. We propose some
modifications that (a) guarantee mass conservation in the model (what is not
assured in its original form) and (b) correct undesired behaviors that appear
when there are irregularities in the surface of the static phase.
  We also show that a similar model can be deduced both from the principle of
mass conservation (first equation) and a simple thermodynamic model (from which
the exchange equation can be obtained). Finally, we solve the model
numerically, using different velocity profiles and studying the influence of
the different parameters present in this model.
