Estimating the Effect of Production Rate and Tubing Intake Depth on Water/Oil or Gas/Oil Ratios
Authors: Hawthorne Robert G. 
Published: December 2007

This paper was prepared for the 40th Annual California Regional Meeting of the Society of Petroleum Engineers of AIME, to be held in San Francisco, Calif., Nov. 6–7, 1969. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
This paper presents a simple calculation for placing limits on water and gas coning in oil wells. The well is assumed to penetrate a formation which contains a water and an oil layer, or a gas and an oil layer. Vertical permeability is assumed to have the limiting permeability is assumed to have the limiting condition of either zero, or infinity (the Dupuit assumption). Also, a sharp flow boundary is assumed between the two fluids (no relative permeability effects). permeability effects).Formulas are given to compute water and oil or oil and gas rates at the limiting vertical permeability conditions. The basic derivations permeability conditions. The basic derivations were given by Teplov; one particular solution was given by van Lookeren. They show how production ratios are affected by gross production production ratios are affected by gross production rate and tubing intake position. In most cases, the differences between the results for the two limiting conditions are small.
The use of the formulas is illustrated with three sample problems. Graphs are given of the functions employed to facilitate computation of other specific problems.
The results show that the maximum pumping rate gives the highest oil rate, usually without undue increases in water/oil ratio. If pump capacity is limited, it is best to place the pump as high as possible and still pump at pump as high as possible and still pump at capacity.

Introduction
In the production of oil, overlying gas or underlying water will often be produced with the oil by the phenomenon of coning. This is caused by the lowering of pressure at the producing interval of the well, which results in producing interval of the well, which results in the vertical flow of gas or water against the restricting force of gravity. As excessive gas or water production is costly and wasteful of reservoir energy, an understanding of coning is important for the application of control methods. Previous papers on coning deal with the problem of maximum oil production rates which problem of maximum oil production rates which can be sustained gas or water free. (For example, see References 1, 2, 3). More recently, numeric and analog models have been used to analyze the transient period from the start of production until the cone reaches the wellbore. production until the cone reaches the wellbore. (References 4, 5, 6). Little information is available as to production rates after the coning fluids begin to be produced. A paper by van Lookeren showed how inverted water coning could be used to increase the gas free oil production rate.