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Water cut is a key evaluation parameter for reservoir development evaluation. Relative permeability curve reflects reservoir characteristics and fluid characteristics. It is important to figure out the influence law of oil relative permeability on water cut. Based on the 269 relative permeability curves of Bohai oilfields, the distribution of oil index of Bohai oilfields were studied. On the basis, combined with Corey expression of relative permeability and fractional flow equation, the theoretical relationship between oil index and water cut increasing rate was established. Three end points of water cut increasing rate curve were proposed and the influence law between three end points and oil index was studied. The results show that the oil index has a linear relationship with three end points. When the value of water oil mobile ratio is large than 1, with the increase of oil index, maximum value of water cut increasing rate gradually increase. When the value of water oil mobile ratio is less than 10, oil index has great effect on recovery percent when water cut increasing rate reaches to the maximum value as well as water cut when water cut increasing rate reaches to the maximum value. The application of SS field shows that the theoretical value is consistent with the field data.

Water cut is a key evaluation parameter for reservoir development evaluation. There are many factors affecting water cut. Generally, geological factors and dynamic factors are the two main classes. Relative permeability curve reflects reservoir characteristics and fluid characteristics [

Water index and oil index can directly reflect the shape of relative permeability, so the influence of water index and oil index on water cut increasing rate is very important. Wang Shuguang built the statistical regularity of oil-water relative permeability of Daqing oilfield [

Based on the 269 relative permeability curves of Bohai oilfields, the distribution of oil index of Bohai oilfields were studied. Based on Corey expression of relative permeability and fractional flow equation, the relationship between oil index and water cut increasing rate was established. The three end points of theoretical curve of water cut increasing rate were proposed and the influence law between three end points and oil index was studied.

Relative permeability of oil phase and water phase can be described in many ways, among them Corey expression is widely adopted by reservoir engineers [

K r w = K r w ( S o r ) S w d n w (1)

K r o = K r o ( S w i ) ( 1 − S w d ) ( 1 − S w d ) n o (2)

S w d = S w − S w i 1 − S w i − S o r (3)

where K r w is water relative permeability; K r w ( S o r ) is water relative permeability at residual oil saturation; S w d is normalized water saturation; n w is water index; K r o is oil relative permeability; K r o ( S w i ) is oil relative permeability at irreducible water saturation; S w i is irreducible saturation; n o is oil index; S w is average water saturation.

The logarithm expression of Equation (1) and Equation (2) are as follows:

lg ( K r w / K r w ( S o r ) ) = n w lg ( S w d ) (4)

lg ( K r o / ( K r o ( S w i ) ( 1 − S w d ) ) ) = n o lg ( S w d ) (5)

According to Equation (5), the oil index can be calculated. 269 relative permeability curves of Bohai oilfied was processed according to this method and the logarithm data of oil relative permeability are as shown in

As can be seen form

Water-oil mobility ratio can be defined as:

M = μ o B o K r w ( S o r ) μ w B w K r o ( S w i ) (6)

where M is water-oil mobility ratio; f w is water cut; μ w is formation viscosity, mPa∙s; B w is formation water volume factor; B o is formation oil volume factor.

Based on fractional flow equation, water cut can be described as follows:

f w = M S w d n w M S w d n w + ( 1 − S w d ) n o (7)

where f w is water cut.

According to the definition of normalized water saturation, normalized water saturation

S w d = 1 − S w i 1 − S w i − S o r R = k R (8)

where R is recovery percent of geologic reservoir; k is constant.

Combined with above equation water cut can be expressed as:

f w = M ( k R ) n w M ( k R ) n w + ( 1 − k R ) n o (9)

According to the definition of water cut increasing rate, water cut increasing rate can be expressed as:

f ′ w = M ( k R ) n w − 1 ( 1 − k R ) n o − 1 [ n w ( 1 − k R ) + n o k R ] [ M ( k R ) n w + ( 1 − k R ) n o ] 2 (10)

In order to study the effect of oil index on water cut increasing rate, we designed many projects with different oil index on the condition that other influencing factors keeps constant. The parameters of basic project is as shown in

Parameters | Value |
---|---|

Irreducible water saturation, f | 0.289 |

Residual oil saturation, f | 0.215 |

Water index | 2.00 |

Oil index | 1.5, 2.0, 2.5, 3.0 |

Porosity | 0.30 |

Water oil mobility raio | 10 |

Water relative permeability at residual oil saturation | 0.41 |

Oil relative permeability at irreducible water saturation | 1.00 |

The oil relative permeability with different oil index are shown in

The relation curve water cut increasing rate and water cut, water cut increasing rate and recovery percent (R) are shown respectively in

Three end points were proposed to describe the curve shape of water cut in

creasing rate. The three parameters are the maxima value of water cut increasing rate, the water cut when water cut increasing rate reaches to the maximum value and the recovery degree when water cut increasing rate reaches to the maximum value.

The relation curve between this three end points and oil index are respectively shown in Figures 5(a)-(c).

As can be seen from

As can be seen from

As can be seen from to the maximum value gradually increase.om

When the value of water oil mobility ratio is large than 10, oil index has little effect on recovery percent when water cut increasing rate reaches to the maximum value. And with the increase of oil index, recovery percent when water cut increasing rate reaches to the maximum value gradually increase.

This theoretical curve proposed in this paper has been applied to many water flooding reservoirs of Bohai Bay and the theoretical curve are consistent with field performance. This paper gives an example of SS oilfield to illustrate the application of this model.

SS oilfield belongs to Minghuazhen formation and shallow water delta deposits. The porosity of the reservoir is 0.30, permeability is 1682 × 10^{−3} μm^{2}, formation oil viscosity is 12 mPa∙s, formation water viscosity is 0.5 mPa∙s, irreducible water saturation is 0.29, residual oil saturation is 0.22, water index is 1.67, oil index is 1.95, oil relative permeability at irreducible water saturation is 1.00, water relative permeability at residual oil saturation is 0.31 (

According to this method, the theoretical curve between water increasing rate and water cut was established as well as the theoretical curve between water cut increasing rate and recovery percent (

Parameters | Value |
---|---|

Irreducible water saturation, f | 0.29 |

Residual oil saturation, f | 0.22 |

Water index | 1.67 |

Oil index | 1.95 |

Porosity | 0.30 |

Permeability, 10^{−3} μm^{2} | 1682 |

Formation oil viscosity, mpa∙s | 12 |

Formation water viscosity, mpa∙s | 0.5 |

Well distance, m | 360 |

Water relative permeability at residual oil saturation | 0.31 |

Oil relative permeability at irreducible water saturation | 1.00 |

Relative permeability curves of Bohai oilfied were analyzed and the average oil index of Bohai oilfied is 2.51. The oil index of Bohai oilfied mostly distributes in the range of 2.0 - 3.0.

The theoretical relationship between oil index and water cut increasing rate is established and three end points of water cut increasing rate curve were proposed. Oil index has a linear relationship with three end points.

When the value of water oil mobile ratio is larger than 1, with the increase of oil index, maximum value of water cut increasing rate gradually increase. When the value of water oil mobile ratio is less than 10, oil index has great effect on recovery percent when water cut increasing rate reaches to the maximum value as well as water cut when water cut increasing rate reaches to the maximum value.

The authors declare no conflicts of interest regarding the publication of this paper.

Zhang, Y.H., Liu, Y.X., Zhang, H.Y., Bie, M.J. and Sun, G.Y. (2018) The Influence Law of Oil Relative Permeability on Water Cut. Journal of Geoscience and Environment Protection, 6, 223-232. https://doi.org/10.4236/gep.2018.69017