The number of horizontal oil wells has been increasing rapidly in the past few years because of several advantages of their application. However, further improvement of oil production rate of horizontal wells is limited by the encroachment of the water crest when bottom water exists. This paper focuses on the theoretical and numerical analysis of water-oil-interface cresting behavior in horizontal wells. The objectives of this investigation include: (1) to find a simple approach to determination of the maximum water-free production rate of horizontal wells with water-oil-interface cresting, and (2) to determine the location of the water-oil-interface under critical condition.
The maximum water-free oil production rate (critical rate), which is defined as the oil producing rate at which the unstable water crest forms, is determined analytically for horizontal oil wells using conformal mapping theory. The resulting solution shows that the critical oil production rate is proportional to the conductivity and thickness of the oil reservoir, and water-oil density contrast. This critical oil rate is also a function of the critical crest height and wellbore location in the oil bearing formation.
The lateral extension of the water crest under critical condition is also determined analytically. This solution indicates that the water-oil-interface cresting is a local phenomena in an oil reservoir. The water crest extends laterally within one thickness of the oil reservoir.
Example calculations are confirmed by a numerical reservoir simulator which has matched field data. This solution provides a new approach to evaluating performance of horizontal wells.