  We are motivated to model a heat transfer to a multiple layer regime and
their optimization for heat energy resources. Such a problem can be modeled by
a porous media with different phases (liquid and solid).
  The idea arose of a geothermal energy reservoir which can be used by cities,
e.g. Berlin.
  While hot ground areas are covered to most high populated cites, the energy
resources are important and a shift to use such resources are enormous.
  We design a model of the heat transport via the flow of water through the
heterogeneous layer of the underlying earth sediments.
  We discuss a multiple layer model, based on mobile and immobile zones.
  Such numerical simulations help to economize on expensive physical
experiments and obtain control mechanisms for the delicate heating process.
