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There are many types of carbonate reservoir rock spaces with complex shapes, and their primary pore structure changes dramatically. In order to describe the heterogeneity of K carbonate reservoir, equations of porosity, permeability and pore throat radii under different mercury injection saturations are fitted, and it shows that 30% is the best percentile.

There are several well-known models for the rock type discrimination. Leverett introduced the famous

In this paper, we focus on the high heterogeneity of

Darcy’s law is an equation that describes the flow of a fluid through porous medium. It can be expressed as follows:

Poiseuille’s equation can be used to determine the pressure drop of a constant viscosity fluid exhibiting laminar flow through a rigid pipe.

For homogenous plug samples, porosity can be calculated by the following equation:

By applying Darcy’s and Poiseuille’s Laws, a relationship between porosity and permeability can be derived as the following equation:

Converting (

For

It is shown in Figure

Correlation coefficients of fitting equations of porosity, permeability, and pore throat radii under different mercury injection saturations.

The fitting equation at mercury injection saturation of 30% is

Based on the pore throat distributions of plugs, we define five typical pore throat radii; they are separately 0.1

Rock type 1:

Rock type 2:

Rock type 3:

Rock type 4:

Rock type 5:

Rock type 6:

Rock type classification of

Capillary pressure curve is useful in characterizing rock type, because it is an indication of pore throat distribution within one rock type. According to the principle of rock typing, the plugs are classified into six groups. Rock type 6 is very tight with low porosity; the fluid cannot flow in this rock type. Therefore, it could be regarded as a barrier.

We use

The average porosity, average permeability, and

Average porosity, average permeability, and J function for each rock type.

Rock type | | | sqrt( | J function |
---|---|---|---|---|

1 | 117.32 | 3.26 | 59.99 | |

2 | 40.57 | 13.44 | 17.37 | |

3 | 7.64 | 12.48 | 7.82 | |

4 | 1.03 | 11.24 | 3.03 | |

5 | 0.11 | 8.76 | 1.12 | |

Capillary pressure curves of five rock types.

We have carried out relative permeability tests for 66 plugs; they cover from rock type 1 to rock type 5. Because of the heterogeneity of carbonate reservoir, we have not found any rules from the endpoint distributions of relative permeability curves, so we calculate the average value of each rock type, as shown in Table

Endpoint values of relative permeability curve of each rock type.

Rock type | Swi | Kro@Swi | Sorw | krw @ Sorw |
---|---|---|---|---|

1 | 0.33 | 0.69 | 0.41 | 0.42 |

2 | 0.20 | 0.65 | 0.31 | 0.31 |

3 | 0.23 | 0.59 | 0.33 | 0.28 |

4 | 0.26 | 0.55 | 0.35 | 0.25 |

5 | 0.30 | 0.52 | 0.38 | 0.20 |

Corey saturation function is derived to fit the average relative permeability curves [

Relative permeability curves of five rock types.

Each plug has a coring depth, and we can find the logging data at corresponding depth. The rock type number and the logging data of each plug compose a sample. By using these samples, a link is set up between rock types and log responses by the KNN (

3D rock type model.

The porosity model is built up based on logging data, seismic attribution, and sedimentary facies control. According to the relationship between porosity and permeability of each rock type, 3D permeability model can be established. The capillary pressure curve and the relative permeability curve are assigned to each rock type, and different flow units are generated.

The capillary pressure can be transformed into oil column height under formation conditions; (

According to (

As the numerical simulation model has been established, we have to testify the accuracy of the model. We use fixed oil production rate as the inner boundary condition, and the actual production process of the simulation area has been reappeared by the history matching. The fitting rates of the daily oil production rate and water cut are up to 99.8% and 93.6%.

Taking wells K2 and K8 as an example (their formation thickness is similar), we calculate the thickness proportion of different rock types of these two wells. As shown in Figure

The thickness proportion of different rock types of wells K2 and K8.

K2

K8

(1) By applying Darcy’s and Poiseuille’s Laws, the relationships among porosity, permeability, and different pore throat radii have been fitted, and the typical pore throat radius

(2)

(3) Based on geological model, the numerical simulation model has been established, and it can reflect the heterogeneity and the fluid distribution of formation very well and can be used to design the further development plan.

The authors declare that they have no conflicts of interest.

The authors are grateful for the financial support from the National Science & Technology Major Projects of China (Grant no. 2016ZX05033-003), the National Science Fund for Young Scholars of China (Grant no. 41702359), and the Corporate Science & Technology Projects of Sinopec (Grant no. P15129).