Prediction of capillary fluid interfaces during gas or water coning in vertical wells

Gas and water coning significantly reduce oil production while increasing production costs. Simulation and experimental methods, coupled with simple analytical solutions or correlations, are typically used to identify the oil rate that minimizes coning and maximizes recovery. Current analytical solutions, however, are overly simplified in that they assume negligible capillary pressure, which leads to segregated flow. This paper presents new benchmark analytical solutions that relax this assumption and also allow for simultaneous two-phase flow. The new coning solutions apply to vertical wells where in-situ fl uids are in vertical equilibrium. The development identifies the important dimensionless groups that control the effect of coning on oil recovery and illustrates how simultaneous two-phase flow affects capillary fluid levels in the formation. Dimensionless two-phase production windows are constructed to identify critical rates, the largest oil rate at which water (or gas) will not be produced. From comparisons to simulation, we show that critical flow rate estimates are accurate for aspect ratios greater than approximately 10. For aspect ratios less than 10, the critical rate estimates are always conservative.