A kind of structure model for double porosity medium systems and its application

摘要

This paper studies problems of modeling and simulation for infinite dimensional systems. In the early 1960s, Barenblatt and the others proposed well-known permeable models through double porous media. It is an essential hypothesis for their theory that every point belongs to both the fracture system and the pore system in a domain. However, in real gas or oil reservoirs, distribution of fractures and pores is so heterogeneous that the ideal "duality" does not exist anywhere and the double porosity structure disappears locally, i.e. double porosity structure or single porosity structure may occur alternatively. Based upon the facts, we derive and ad hoc function expressed by integration, set up a block structure model as well as its approximate semi-discrete form for the variable structure system, and prove uniqueness and existence of the solutions. Applying this model to the identification problem for the fracture-pore domain we get a feasible method to determine the position of fracture system and pore system and take a practical example to verify the usefulness of the structure model for a gas reservoir.