Quantitative method of channeling-path by diffusion theory in high permeability reservoir

As high permeability reservoir is interconnected poorly, it is usually thought that there is strong washing action when water fooding. The channeling-path generated from this action looks like spindle in plane and extreme heterogeneity in vertical. Therefore, it results in the current quantitative method and corresponding mathematical model are so complex that they are regularly solved with numerical approach, generally in which includes geological model establishment and discretization in time and space domain, rather than analytical method. Based on the new method proposed in this paper, the 3-D channeling-path physical model of channeling-path in interwell is equivalent with superposition between a horizontal model and vertical model respectively. Consequently, there is a new 3-D mathematical model which is the combination between a horizontal model with equivalent diffusion coeffcient which represents horizontal spindle shape, and a vertical model with dilution coeffcient which represents extreme vertical heterogeneity. Based on the above proper descending dimension simplifcation, the outlet water cut could be solved analytically. The proposed method has applied in channeling-path quantifcation of 3 wells by typical water cut curves characteristics matching. The obtained parameters, including channeling-path thickness ratio, heterogeneity coeffcient and equivalent diffusion coeffcient, reasonable agree with tracer interpretation results. Furthermore, the sensitivity analysis gives physical meaning of equivalent diffusion coeffcient that could characterize the effect of fnger advance in early term and sweep area in late term.