Abstract: Horizontal well technology is an effective one of increasing production. A horizontal well can bring out three-dimensional flow in the direction of normal of developing and revolving spheroids-conjugate equal-pressure spheroids and hyperboloid streamline bunches whose focal points are the two ends of the well when it works. A mathematical model of oil and water two phase fluid non-darcy flow in the direction of normal of the spheroids with starting pressure gradient (spg) taken into account, which is a nonlinear equation with a moving boundary,is established according to concepts of revolving spheroids and equivalent developing cylinders. Characteristic linear and finite difference solutions to the model are derived respectively and water saturation distribution curves are presented. And the law of the moving boundary is found. Results show good agreement between the characteristic linear and finite difference solution.
Influence of spg and injection rate on water cut and its derivative, saturation distribution and the laws is discussed respectively. The paper provides numerical simulation of water flood development to low permeability oil fields in the case of horizontal wells with theoretical basis. The mathematical model is also fit for water flood development of bingham viscous oil fields in the
case of horizontal wells.

Key words: horizontal well, oils water boundary, threephase flow, finite difference method