Abstract: A three-dimensional,three-phase,eight-component mathematical model based on the component model and the black oil model is presented. The model considers main factors,such as gravity,capillary force,compressibility of fluid and rock etc.An improved IMPES (implicit pressure, explicit saturation) method is applied in which the phase pressure is calculated implicity and the phase saturation is calculated with high order accuracy.Based on this mathematical model,a numerical simulator is developed for the profile controlling and flooding with weak gel.

Key words: weak gel, profile controlling and flooding, mathematical model, component model, method with high order accuracy