Horizontal and vertical wells are commonly used in the production of oil lying above a water zone, or above a gas zone or sandwiched between the gas and the water. Under such conditions, water or gas coning is a very common problem. Experimental, empirical and analytical works have been done in determining the critical oil production rate and the breakthrough time if production is supercritical. Aside from numerical simulations, post-breakthrough production predictions have been restricted to experimental and empirical techniques employing statistical regression.

In this work, employing analytically derived breakthrough time expressions for vertical and horizontal wells, a technique have been developed to semi-analytically predict the rate of oil and water production after cone breakthrough in vertical and horizontal wells. The results of this new procedure were compared with predictions from numerical simulations and some common literature correlations. Though the analytical technique tended to under-predict oil production, it presented a trend which conformed more to the numerical simulation results than the correlations tested. It thus can be used for checking more complex numerical simulations and can serve as a backbone for developing consistent post-breakthrough correlations.

Simplified correlations for the determination of breakthrough time for vertical and horizontal wells were also developed from the semi-analytical formulations. To the best knowledge of the authors, this is the first semi-analytical post-breakthrough modeling of vertical and horizontal wells.


Work on coning had generally been pursued along the path of preventing or delaying cone generation and evolution, the time to breakthrough if advancement is not checked and the performance of the well after cone breakthrough. A number of empirical and analytical studies have been conducted to model and determine these properties (Joshi, 1991). Correlations and models for the determination of critical rate of oil production, time to breakthrough when producing at super-critical rate and the performance of the well after breakthrough have been developed for vertical and horizontal wells. These models may be experimental, empirical or analytical. After breakthrough performance model available are generally not analytical.

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