Oil and gas are the main reserves in the fractures of rocks. Under different pressure conditions, fracture permeability of reservoir rock directly affects the flow of oil and gas, which is an important object of oil and gas exploration and development. The permeability of single fractured rock and double fractured rock under different pressure conditions was studied by using high-precision hydro-mechanics coupled triaxial experimental equipment. The experimental scheme is as follows: (i) permeability test under increasing confining pressure, (ii) permeability test under increasing liquid pressure, (iii) permeability test under cyclic loading and unloading deviatoric stress and (iv) permeability test under synchronously increasing confining pressure and deviatoric stress. Results show that the entire change of permeability is irreversibly reduced. This is due to the presence of residual factors in permeability after the dilation cycle and the recompaction cycle ends. On the basis of the dual medium model of fracture, the permeability model of fractured rock is proposed considering the interaction among fracture system, matrix system and expansion deformation of fracture under external stress. The simulation results of the model are in good agreement with the experimental results. These results can provide an important basis for the prediction of permeability of fractured rock and efficient oil and gas exploitation.
A construction of all homomorphisms of a heterogeneous algebra into an algebra of the same type is presented. A relational structure is assigned to any heterogeneous algebra, and homomorphisms between these relational structures make it possible to construct homomorphisms between heterogeneous algebras. Homomorphisms of relational structures can be constructed using homomorphisms of algebras that are described in [11].