With principle of conformal transformation and mirror reflection, a mathematical model of flow field in a mixed injection production well pattern was established. Five point horizontal well and vertical well pattern are used for an example. Mathematical expressions of potential function and stream function are derived. Distribution maps of potential line and flow line in a mixed injection production well network with five point method are obtained. Influence of key parameters on internal flow field distribution of mixed injection production well network is analyzed. It shows that at both ends of horizontal well flow lines are relatively dense, and liquid producing capacity at both ends is stronger. The longer the horizontal section, the greater the discharge area of flow line control. As horizontal well is 45 degree angle with vertical wells connection line, displacement effect of horizontal well is relatively good. As horizontal well is perpendicular to direction of main permeability, streamlines are concentrated to production well. Linear displacement is formed and the displacement effect is good. As horizontal well is off center position greater, streamline distribution density differentiation is more obvious.

In productivity evaluation of infill horizontal well interference of oil or water wells are taken into account in a vertical and horizontal well mixed well pattern.With mirror-image method and source-sink theory,a semi-analytical model of productivity evaluation for infill horizontal well in random mixed pattern was built,in which interference of wells and pressure drop caused by wal friction and fluid acceleration were taken into account.It is suitable for infill horizontal well productivity calculation in arbitrary well pattern.

We establish a 2D diffusion mathematic model considering transverse diffusion and feature of channeling reservoir.With Laplace transform an analytical model is solved.A solution with small slug is found.With general-purpose finite element software in a geometrical model numerical solution is solved.2D concentration profile is ploted.It is shown that larger Peclet number leads to higher peak concentration and later break through time.With combination of analytic solution and numerical solution,it is helpful in understanding the essential of mass transfer diffusion.