To predict well performance for horizontal wells, several analytical models have been developed to generate inflow performance relationships (IPR) for single-phase wells. Similar to vertical wells, analytical solutions of IPR in two-phase flow horizontal wells are unavailable because of the complexity of relative permeability and the variable phase distribution in the reservoir. Correlations, lead by Vogel's equation, have been used for two-phase IPR calculations for vertical wells, and the methods have been adopted for horizontal well applications.

This paper reviews several two-phase correlations for horizontal wells (Bendakhlia and Aziz's equation, Cheng's equation, and Retnanto and Economides’ equation). Instead of using the original formula of Vogel's equation, these models include the effects of reservoir recovery factor or fluid bubble-point pressure on IPR behaviors. We also presented a modified Vogel's correlation for two-phase horizontal IPR following Kabir's work. The modified correlation uses Babu and Odeh's single-phase horizontal well model to calculate the absolute open flow potential, qo, max, and then uses the original Vogel's correlation to generate the relationship between flow rate and pressure. The reservoir anisotropy is considered in Babu and Odeh's model for horizontal well flow. The results of the modified Vogel's equation are compared with the reviewed two-phase correlations, and also checked against the results from a reservoir simulator (Eclipse™). It is found that the modified Vogel's equation results in close predictions of two-phase inflow performance for horizontal wells at normal recovery factors compared with the reservoir simulation results. At low recovery factor, it deviates from the simulation results more than some other correlations reviewed. For low bubble-point pressure fluids, flow conditions in the reservoir are more likely to be single-phase rather than two-phase, and gradually tranforms from single-phase to two-phase flow as the reservoir pressure declines. The modified Vogel's inflow equation does not capture this transient period; neither do the other correlations reviewed in this paper.

The modified Vogel correlation for two-phase flow horizontal wells is simple compared with the other models, and works as well as the other models at the normal flow condition. It can be used to estimate horizontal well performance conveniently.

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