A new comprehensive formula for productivity prediction of horizontal well

The horizontal well productivity prediction formula doesn’t take into account the characteristics of typical linear flow and elliptic flow in horizontal wells, so its productivity prediction result is optimistic. The characteristics of typical flows in horizontal wells were analyzed, and accordingly the flow region in an oil reservoir is divided into three zones, i.e., the external plane radial flow, the central plane linear flow and elliptic flow, and the internal vertical radial flow. Then, a comprehensive horizontal well productivity calculation formula was newly derived by virtue of the water and electricity similarity principle and the equivalent percolation resistance method. Finally, its adaptability was analyzed. It is indicated that the commonly used formulas are the simplified or approximate versions of the new formula in the special situations. The calculation results of the new formula show that with the increase of the length or penetration ratio of horizontal well, the effect of plane linear flow and elliptic flow increases gradually, and its productivity presents the characteristic of increasing approximately linearly first and then gently. When the horizontal well is very long or its penetration ratio is approximate to 1, its flow characteristic is similar to that in vertically fractured wells. This new comprehensive formula can calculate the productivity of short and long horizontal wells and predict the productivity of horizontal well with different drainage shapes and injection-production well patterns.