So far, critical production rates have been discussed. Many times the critical rates are too low, and for economic reasons, a well is frequently produced at rates above critical rate. This results in production of water, as well as oil. Sobocinski and Cornelius ^[8] and Bournazel and Jeanson ^[9] have reported (laboratory) experimental results on water breakthrough time; i.e., they measured the time it takes for a water cone to break through in a vertical well at a given total production rate. (Reference 8 has also reported a numerical solution to verify the laboratory results.) In their experiments, they found that the lower the vertical dimensionless cone height (defined in Table 8-2), the faster the water breakthrough. Their procedures and results are summarized in Table 8-2.

TABLE 8-2: VERTICAL WELL BREAKTHROUGH TIME CORRELATIONS

Sobocinski and Cornelius Method [8] Dimensionless cone height is given by where k h = horizontal permeability, md ? o = oil viscosity, cp B o = oil formation volume factor, RB/STB q o = oil production rate, STB/day ? w = water density, gm/cc ? o = oil density, gm/cc h ? = perforated interval, ft and dimensionless breakthrough time, (t D) BT SC is given by where t BT = breakthrough time, days ? = porosity, fraction k v = vertical permeability, md M = water-oil mobility ratio ??= ? o(k w)