A non-uniform complex fracture network structure formed by fracturing is considered with introducing the fractal theory and combining the stress sensitivity of fracture system to demonstrate the change of fluid flow capacity, and a production prediction model for three-zone compound seepage flow in fractured horizontal wells in low permeability reservoirs is established successfully in this paper. Laplace transform, perturbation theory, and numerical inversion are applied to obtain the analytical solution of the proposed production model, and the productivity formulas for single well under two situations of uniform and non-uniform distribution of fractures in horizontal wells are derived. The reliability of the production prediction model is verified with the real production data and basic parameters of a fractured horizontal well in Bohai oilfield, and the effects of related influential parameters on production of horizontal well are analyzed. The research results show that smaller the stress sensitivity coefficient and threshold pressure gradient results in larger the oil production. Larger the fractal dimension contributes to larger the horizontal well production. Additionally, the oil production increases with the increase of the number of fractures and fracture half-length, but the growth rate slows down, which means these parameters have optimal values.

We investigate the non-isothermal non-Newtonian filling process according to the phase field method in three dimensions. The moving interface between the Newtonian and non-Newtonian fluid is captured by the Cahn-Hilliard equation. Based on phase field parameters, the governing equations of the flow field could be written in a unified form. After that, the Navier-Stokes equations are split into several sub-equations and the FEM and SUPG will be used to handle the appropriate equations. The variation of the viscosity of the polymer melt is described via the Cross-WLF model. The thin wall rectangular cavities with and without obstacles are considered to illustrate the convergence, robustness and accuracy of the numerical algorithm. The influences of the inlet velocity and the size of the injection gate on the filling process are analyzed. The numerical results agree well with the experimental data and also exhibit good mass conservation properties.

The complicated gas entrapment problem in polymer filling process is studied. The moving melt interface is captured with a level set method. An XPP (eXtended Pom-Pom) constitutive model is utilized for the description of viscoelastic fluid. The governing equations of flow field are solved with a coupled continuous and discontinuous Galerkin method. The XPP constitutive equation, level set and its re-initialization equations are solved with an implicit discontinuous Galerkin method. Good agreement between experimental and numerical results illustrates validity of the combined algorithm. Influence of injection velocity and gate size on gas entrapment in a cavity with irregular insert was investigated. Entrapped gas is easier to appear as the injection velocity is higher and the gate size is smaller.