  The formulation of a model for the evolution of the flow of a solid-liquid
mixture (coal-water) in a horizontal pipeline with partial phase separation is
the aim of this work. Problems of instabilities due to complex eigenvalues,
observed in previous models, seem to be completely solved in the present model,
in which we give the genesis of the different terms written in the equations,
coming from the natural definition of mass and momentum balance, and the
consequent proof of well-posedness of the obtained PDE system with
boundary-Cauchy data.
  The model describes a three-layer flow. Most of the material is carried by
the upper layer, while the bottom layer consists of an immobile sediment. The
intermediate layer grows to a maximum thickness and has the role of regulating
the mass exchange between the extreme layers.
  In the last section we present some simulations for a particular choice of
flow regime, and boundary-Cauchy data, that were suggested by experimental
results provided by Snamprogetti (Fano, Italy).
