In order to accurately describe the change law and influencing factors of reservoir seepage flow near injection wells in low permeability reservoirs, a well test analysis method for composite reservoir with dynamic non-Darcy effect outside injection wells was constructed. Firstly, Darcy flow is considered as the inner seepage mode, and non-Darcy flow as the outer seepage mode composed of starting pressure gradient effect and dynamic permeability effect. Secondly, numerical method is used for discrete solution to calculate the bottom-hole pressure of the injection well, and then the typical curve of bottom-hole pressure response is drawn. Typical curves are divided into 5 flow sections: wellbore storage section, transition section, inner radial flow section, outer low seepage flow section and boundary reflection section. Finally, sensitivity analysis of starting pressure gradient and dynamic permeability parameters is carried out, and pressure response of different seepage laws is compared. Taking an injection well in Changqing Oilfield as an example, the well test results show that the permeability around the injection well is larger, and the outer zone is affected by the combination of starting pressure gradient and dynamic permeability, and there is a starting pressure gradient in the outer area, and the permeability is smaller, which is consistent with the field practice. This method is a relatively general numerical pressure calculation method, among which the conventional injection well composite well test analysis method and low permeability reservoir single zone test analysis method are special cases of this method.

A Darcy-Brinkman-Forchheimer model based lattice Boltzmann method is conducted to the simnlation of double-diffusive natural convection in an inclined square porous enclosure. Effects of porosity (0.2≤ε≤0.9), Rayleigh number (10³≤Ra≤10⁶), buoyancy ratio (-4≤Br≤2) and inclination angle (0°≤γ≤80°) on the local and total entropy generation are systematically investigated. It shows that as ε and Ra increased, peaks of local entropy generation due to heat transfer, fluid friction and mass transfer grow higher and the contribution of fluid friction to total entropy generation increased prominently. In addition, the clear fluid term has more influence on fluid friction entropy generation. Br=-1 is a critical value for the change of local entropy generation distribution. At the same time, the total entropy generation tends to zero. With the increase of inclination angle, the high entropy generation region of local fluid friction entropy generation moves clockwise. The maximum entropy caused by clear fluid term and Darcy dissipation term appears at 40° and 60°, respectively.

The numerical simulation of oil (gas) reservoirs can be described by two-phase penetration dynamic equations, which are high-dimensional, non-linear, singular and time-dependent partial differential equations, subjected to some appropriate initial and boundary conditions.The partial differential equations are discretized by differencing schemes (such as Fully Implicit method, 1MPES,etc.)and produce different non-linear algebraic systems.To solve a non-linear system Newton's method is the most popular method. But it requires calculation of a Jacobi matrix and solving a linear system in each iteration.These will consume huge computing CPU time.For saving the CPU time we have modified the Newton's method with Samanskii's idea and controled the number of iterations in solving the linear systems. The programming is quite simple. We tested our algorithm in a set of ideal data.The results are as accurate as those obtained from the Newton's method and the efficiency is better.