Horizontal wells and multilateral wells have been applied in conventional and unconventional resource to improve recovery of hydrocarbon by increasing the contact of wellbores with reservoirs. In order to estimate production rate, many analytical models have been developed in the past years. One of the commonly used models is the Babu and Odeh's model which introduces a concept of partial penetration skin factor to transfer an analytical model for vertical wells to horizontal well mode. The partial penetration skin, SR, which accounts for the deviation of production for a partially-penetrated well in a reservoir (more likely in horizontal well scenarios) from a fully-penetrated well, is estimated by a correlation based on the reservoir simulation results. The correlation is one of the key elements in the Babu and Odeh's model, and it made the model flexible and convenient to use. The limit of the correlation is that the error of the calculation is increasing as the ratio of wellbore length to reservoir dimension decreases. Meanwhile, to consider the influence of permeability heterogeneity and wellbore pressure drop on well performance in these models, a segment approach is also commonly used for a horizontal well which divides the entire wellbore into smaller piece while calculating the pressure and flow relationship. When a well is segmented, the segmented well length is most likely lower than the limit of the partial penetration skin correlation applies. This raises a question of how the partial penetration skin should be distributed for different segments. The conventional method is to only apply the SR to the toe and heel segments when segment a wellbore, since the centered segments are considered fully-penetrated. This sometimes results in unreasonably low flow rate in these two segments compared to the segments in the middle. The toe and the heel segments should have high flow rate because of the larger drainage area contacted at these segments compared with the center segments in partial-penetrated wells. A new approach to distribute the partial penetration skin is needed to solve this problem.

In this work, we discuss several approaches to reasonably distribute the total partial penetration skin over different segments. A new approaches is proposed to take into account of the effect of contact area, location of segments, as well as the drainage area on inflow performance. The result shows a more reasonable flow rate distribution for different segments of the new approach when compared with reservoir simulation results. This modification to the conventional approach for the segmented horizontal inflow model makes the analytical model more reasonable and applicable. Examples in the paper illustrate how to use the new approach to estimate horizontal well inflow performance.

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