### Abstract

Horizontal wells are a proven and well acknowledged technology to enhance well productivity through an increase in reservoir contact compared to that of a vertical well under the same conditions. In the last three decades, a considerable effort has been directed to study flow around horizontal wells by many investigators. These studies have mainly focused on proposing practical tools (in the form of skin factor) for long-term well productivity estimation. The skin factor proposed can be applied in an equivalent (one dimensional radial) open-hole system replicating the flow around the actual complex three dimensional (3-D) flow geometry of the Horizontal well. However, all these studies concentrate on single-phase Darcy flow conditions.

In gas condensate reservoirs, in addition to the three dimensional (3-D) nature of flow geometry, the flow behavior is further complicated by the phase change and the variation of relative permeability (kr) due to the coupling (increase in kr by an increase in velocity or decrease in IFT) and inertia (a decrease in kr by an increase in velocity) effects. Therefore, simulating such a complex 3-D flow using numerical commercial simulators requires a three dimensional fine grid compositional approach, which is very impractical, cumbersome and sometimes trigger convergence problems due to numerical instability. In fact, the introduction of a quick and reliable tool for long term productivity calculation is much needed in such systems.

This work is aimed at the development of a practical, general, and easy-to-use method for defining an effective wellbore radius of an equivalent open-hole system, replicating flow around the 3-D Horizontal well in gas condensate reservoirs.

Accordingly, a 3-D compositional finite element based in-house simulator was developed to accurately model gas and gas condensate flow around horizontal wells. A large data bank was generated, covering the impact of a wide range of pertinent geometric and flow parameters on the well performance. Then a general approach is proposed for estimation of an effective wellbore radius of an equivalent open-hole radial 1-D system replicating flow around the 3-D Horizontal well system. The effective wellbore radius varies with fluid properties, velocity, IFT, reservoir and wellbore conditions. The results of the proposed formulation, which benefits from suitable dimensionless numbers, has been tested against the simulator results not used in its development confirming the integrity of the approach. Also, the proposed formulation is applicable for both single-phase non-Darcy and two-phase gas condensate flow systems.

With this approach, no numerical simulation is needed and instead a simple excel spread-sheet can predict the horizontal well performance, significantly facilitating engineering and management decisions relating to the application of horizontal well technologies.

In gas condensate reservoirs, in addition to the three dimensional (3-D) nature of flow geometry, the flow behavior is further complicated by the phase change and the variation of relative permeability (kr) due to the coupling (increase in kr by an increase in velocity or decrease in IFT) and inertia (a decrease in kr by an increase in velocity) effects. Therefore, simulating such a complex 3-D flow using numerical commercial simulators requires a three dimensional fine grid compositional approach, which is very impractical, cumbersome and sometimes trigger convergence problems due to numerical instability. In fact, the introduction of a quick and reliable tool for long term productivity calculation is much needed in such systems.

This work is aimed at the development of a practical, general, and easy-to-use method for defining an effective wellbore radius of an equivalent open-hole system, replicating flow around the 3-D Horizontal well in gas condensate reservoirs.

Accordingly, a 3-D compositional finite element based in-house simulator was developed to accurately model gas and gas condensate flow around horizontal wells. A large data bank was generated, covering the impact of a wide range of pertinent geometric and flow parameters on the well performance. Then a general approach is proposed for estimation of an effective wellbore radius of an equivalent open-hole radial 1-D system replicating flow around the 3-D Horizontal well system. The effective wellbore radius varies with fluid properties, velocity, IFT, reservoir and wellbore conditions. The results of the proposed formulation, which benefits from suitable dimensionless numbers, has been tested against the simulator results not used in its development confirming the integrity of the approach. Also, the proposed formulation is applicable for both single-phase non-Darcy and two-phase gas condensate flow systems.

With this approach, no numerical simulation is needed and instead a simple excel spread-sheet can predict the horizontal well performance, significantly facilitating engineering and management decisions relating to the application of horizontal well technologies.

Original language | English |
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Title of host publication | SPE EUROPEC 2015 |

Publisher | Society of Petroleum Engineers |

ISBN (Print) | 9781613994054 |

DOIs | |

Publication status | Published - 3 Jun 2015 |

Event | SPE EUROPEC 2015/77th EAGE Conference and Exhibition - Madrid, Spain Duration: 1 Jun 2015 → 4 Jun 2015 |

### Conference

Conference | SPE EUROPEC 2015/77th EAGE Conference and Exhibition |
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Abbreviated title | SPE EUROPEC 2015 |

Country | Spain |

City | Madrid |

Period | 1/06/15 → 4/06/15 |

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## Cite this

Ghahri, P., Alatefi, S., & Jamiolahmady, M. (2015). A New, Accurate and Simple Model For Calculation of Horizontal Well Productivity in Gas and Gas Condensate Reservoirs. In

*SPE EUROPEC 2015*[SPE-174345-MS] Society of Petroleum Engineers. https://doi.org/10.2118/174345-MS