### Water Breakthrough Time in a Vertical Oil Well

Consider an oil reservoir with an underlying water zone. An oil well that is producing from this reservoir will experience the phenomenon of water breakthrough if the well produces above its critical rate. Since economic considerations often demand high flowrates, this can be a real risk.

This Excel spreadsheet uses the Sobocinski-Cornelius method to calculate the water breakthrough time.  This method was published in 1965, and was derivied from laboratory tests. It uses these equations.

where

• Bo is the oil formation volume factor
• μo is the oil viscosity (cp)
• μw is the water viscosity (cp)
• φ is the porosity
• h is the oil column thickness (ft)
• hp is the perforated interval (ft)
• Qo is the oil production rate (STB day-1)
• α is 0.5 if M <=1, or 0.6 otherwise
• M is the water-oil mobility ratio
• tBT is the time to breakthrough
• tD is the dimensionless time (Sobocinski-Cornelius method)
• Z is the dimensionless cone height
• ρw is the water viscosity (lb ft-3)
• ρo is the oil density (lb ft-3)