## Abstract

Simulation grid blocks of naturally fractured reservoirs contain thousands of fractures with variable flow properties, dimensions, and orientations. This complexity precludes direct incorporation into field-scale models. Macroscopic laws capturing their integral effects on multiphase flow are required. Numerical discrete fracture and matrix simulations show that ensemble relative permeability as a function of water saturation (k_{ri}[S_{w}]), water breakthrough, and cut depend on the fraction of the cross-sectional flux that occurs through the fractures. This fracture-matrix flux ratio [q _{fqm}] can be quantified by steady-state computation. Here we present a new semianalytical model that uses q_{fqm} and the fracture-related porosity fjf) to predict k_{ri}(S_{w}) capturing that, shortly after the first oil is recovered, the oil relative permeability (kro) becomes less that that of water (k_{rw}), and k _{rw}k_{ro} approaches q_{f}/q_{m} as soon as the most conductive fractures become water saturated. To include a capillary-driven fracture-matrix transfer into our model, we introduce the nonconventional parameter A_{fw}/_{Sw}), the fraction of the fracture-matrix interface area in contact with the injected water for any grid-block average saturation. The A_{fw}/_{Sw}) is used to scale the capillary transfer modeled with conventional transfer functions and expressed in terms of a rate- and capillary-pressure- dependent k_{ro}. All predicted parameters can be entered into conventional reservoir simulators. We explain how this is accomplished in both, single- and dual-continua formulations. The predicted grid-block-scale fractional flow (f _{i}[S_{w}]) is convex with a near-infinite slope at the initial saturation. The upscaled flow equation therefore does not contain an S _{w} shock but a long leading edge, capturing the progressively widening saturation fronts observed in numerical experiments published previously.

Original language | English |
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Pages (from-to) | 1621-1632 |

Number of pages | 12 |

Journal | AAPG Bulletin |

Volume | 93 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |