Liquid metal flow subject to a uniform magnetic field vertical to streamwise direction confined in a rectangular duct with 45° and 90° sudden expansion, and electrically conducting walls is numerically studied using magnetohydrodynamic (MHD) flow solver developed in OpenFOAM environment. Velocity distribution, induced electric current, pressure gradient and three-dimensional MHD effect are analyzed in detail. It shows that as external magnetic field is parallel to direction of duct expansion, velocity distribution is better in 45° sudden expansion duct than that in 90° expansion duct since there is no vortex at the expansion. With Hartmann number increasing, high velocity jets and intensive induced electric current cause a strong instability at the expansion. Instability grows to upstream of the expansion through induced electric current. As external magnetic field is vertical to expansion direction, induced electric current along streamwise direction is significant. With Hartmann number increasing, MHD pressure drop increases remarkably. Dimensionless pressure drop in fully developed duct is almost the same in different expansion duct as direction of applied magnetic field and Hartmann number are the same.

The Theories and model of well testing analysis for a fractal composite reservoir have been discussed with non-Newtonian power law fluid flow. In order to completely describe the situation of real reservoirs, the fractal composite reservoir is defined as fractal reservoir that consists of many zones with different fluid and different format properties. The initial and three outer boundary conditions such as infinite, finite with constant pressure and closed boundary have been given according to polymer flooding in an oil field. A new effective well radius mathematical model of this fractal composite reservoir is suggested involving the wellborn storage and skin effects. The analytical solutions in Laplace-space for the mathematical model and two special cases of two and three regions are derived by Laplace transformation. The dimensionless wellborn pressure for the modern well test analysis is given by using Stehfest numerical inversion. The well test analysis theories and the pressure behavior of this reservoir are also discussed for the two region model.

Effective well radius combined mathematical models are suggested for non-Newtonian power-law fluids with the low-velocity non-Darcy flow in the fractal reservoir.The formation models consist of internal regions and external regions.Porous medium flow in the fractal network of the internal regions obeys the low-velocity non-Darcy law of the non-Newtonian power-law fluids while the one in the external region obeys the Darcy law of the non-Newtonian power-law fluids.The initial and the three outer boundary conditions of infinite,finite with constant pressure and closed boundary are given according to the polymer flooding in a fractal reservior.Solutions of the well test models in Laplace space are obtained.The relationship between the dimensionless pressure and time is studied by using the Stehfest numerical inversion.The dynamic feature of the pressure and parameter effect are disscussed.This method can be used to predict formation permeability,skin factor and reservoir pressure of non-Newtonian fluids such as the polymer fluid flow and locate the polymer flooding frontier.

Lateral wells increasing, it becomes more and more important to evaluate the pressure performance and formation damage in the heterogeneous reservoirs with lateral drilling. Considering the properties of lateral drilling in the heterogeneous reservoirs, the paper has presented a mathematical model of 3D unsteady flow. Since it is intricate to solve the model by analytical method, the model is solved by boundary element method and regional division technique for the pressure performance of lateral drilling well produced at constant rate or bottom well pressure. By reasonable incorporation of pseudo skin factor, dimensionless damaged radius, dimensionless well storage coefficient, and permeability of damaged region; we can get type curves, which can be used for evaluation of formation damage caused by lateral drilling. The application to well test data of a lateral-drilling well of Liaohe oil field in the East China shows that the model and method are all valid.