# Research on Formation Pressure Prediction Method for Ultra-Deep Tight Sandstone Based on Collocated Cokriging

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Principle of Formation Pressure Prediction

#### 2.2. Cokriging Principle

#### 2.3. Collocated Cokriging Principle

#### 2.4. Workflow of Collocated Cokriging Method for Prediction

## 3. Numerical Simulation of Collocated Cokriging Method

#### 3.1. Fitting Experimental Model Variogram Functions

#### 3.2. Results

#### 3.3. Discussion

#### 3.4. Parameter Optimization for Collocated Cokriging

#### 3.4.1. Influence of Range on Experimental Results

#### 3.4.2. Influence of Anisotropy on Experimental Results

#### 3.4.3. Influence of Number of Conditioning Points on Experimental Results

## 4. Pressure Prediction of Actual Strata

#### 4.1. Data Introduction

#### 4.2. Results

#### 4.3. Discussion

## 5. Conclusions

- Compared with different kriging methods, the prediction results of the collocated cokriging method are more in line with experimental expectations. The calculation and fitting of the variogram function in the process of prediction directly affect the prediction results. When performing calculations, geological knowledge should be considered, appropriate models should be selected, and relevant parameters should be obtained reasonably to avoid using variogram functions that do not match the reality, thereby improving the prediction accuracy.
- Combining the Eaton formula with the collocated cokriging method for predicting formation pressure demonstrates feasibility. This method can be combined with seismic data, and the predicted results align with expectations, providing guidance for exploration and development in actual work areas.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zu, F.; Zhang, Z.L.; Feng, Q.H.; Fan, H. Abnormal formation pressure monitoring and predicting method. Oil Drill. Prod. Technol.
**2004**, 26, 35–38. [Google Scholar] [CrossRef] - Zhao, M.; Wei, C.J.; Wang, S.H. Algorithm research and realization of formation pressure prediction based on eaton method. J. Qingdao Univ.
**2017**, 30, 86–88+92. [Google Scholar] - Xie, Y.; Li, X.Y.; Zhai, Y. Establishing formation pressure profiles and guiding adjacent wells balanced drilling in new area by logging data. Pet. Instrum.
**2011**, 25, 46–48+103. [Google Scholar] - Li, H.; Yu, Z.T.; Yuan, H.S.; He, P.F. Application of formation pressure prediction technology in drilling in Bozhong A block. Petrochem. Ind. Appl.
**2018**, 37, 33–36. [Google Scholar] - Fan, X.Z.; Li, X.; Wu, Y.C.; Zhang, G.; Lou, Y.; Liu, S.; Zhu, Y. A formation pressure prediction method for well drilling in the Arctic permafrost region. Nat. Gas Ind.
**2022**, 42, 99–105. [Google Scholar] - Wang, B.; Yong, X.S.; Pan, J.G.; Yin, L.; Xu, D.N.; Kong, X.; Qu, J.H.; Tan, K.J.; Huang, Y. A new method to predecit pore pressure in low permeability reservoirs and its application. Prog. Geophys.
**2015**, 30, 695–699. [Google Scholar] [CrossRef] - Zhang, Q.; Zhi, Y.P. Applying seismic velocity to predicting formation pressure. Chin. J. Eng. Geophys.
**2015**, 30, 695–699. [Google Scholar] - Yang, H.; Zhou, P.G.; Sun, W.G.; Shi, J.G.; Chen, W.F. Using seismic data to predict formation pressure in piedmont structures at the southern margin of Junggar Basin. Xinjiang Pet. Geol.
**2017**, 38, 347–351. [Google Scholar] - Ma, H. Pore pressure prediction with seismic interval velocity by the modified Fillippone Method. Pet. Drill. Tech.
**2012**, 40, 56–61. [Google Scholar] [CrossRef] - Qian, L.P.; Wang, X.; Li, F.; Li, J.H.; Wang, J.; Qu, Y.W. Formation pore pressure prediction using Fillipone formula combined with equivalent medium theory. Oil Geophys. Prospect.
**2018**, 53, 224–229. [Google Scholar] - Shi, M.X.; Liu, Z.D.; Yang, X.F.; Yang, J.R.; Chen, X.J.; Liu, H.Z.; Cao, J.L. Review and prospect prediction technology for formation pore pressure by geophysical well logging. Prog. Geophys.
**2020**, 35, 1845–1853. [Google Scholar] [CrossRef] - Gao, R.N. Study on Sandstone Distribution in Yuncheng Based on Geostatistics. Shanxi Sci. Technol.
**2020**, 35, 37–41. [Google Scholar] - Ma, W.L.; Deng, S.Z. Application of Functional Kriging on the Well Productivity Prediction. Inn. Mong. Petrochem. Ind.
**2021**, 47, 92–96. [Google Scholar] - Li, S.H.; Wang, Y.B.; Li, J.; Liu, X.T.; Wang, J.; Gong, W.Q. Correcting the string effect of Kriging. OGP
**2012**, 47, 978–983. [Google Scholar] - Wang, C.Y.; Qu, Y.; Shuai, Y.M. Prediction of the Spatial Distribution of Gas Pipe Network Using Cokriging Method Based on ArcGIS Technologies. Geomat. Spat. Inf. Technol.
**2022**, 45, 28–32. [Google Scholar] - Du, W.F.; Peng, S.P. Coal seam Thickness Prediction With Geostatistics. Chin. J. Rock Mech. Eng.
**2010**, 29, 2762–2767. [Google Scholar] - Geng, M.X.; Huang, D.N.; Yu, P.; Yang, Q.J. Three-dimensional constrained inversion of full tensor gradiometer data based on cokriging method. Chin. J. Geophys.
**2016**, 59, 1849–1860. (In Chinese) [Google Scholar] [CrossRef] - Yu, Z.J.; Dong, D.D.; Song, W.Q.; Gao, Y.K.; Wu, S.G. Porosity prediction with co-Kriging method controlled by sedimentary facies. Prog. Geophys.
**2012**, 4, 1581–1587. [Google Scholar] [CrossRef] - Chen, J.Y.; Yu, X.H.; Li, S.L.; Hou, G.W. Application and method of predicting reservoir by collocated seismic attributes. Inn. Mong. Petrochem. Ind.
**2007**, 121, 1–3. [Google Scholar] - Wang, D.D.; Yang, X.F.; Zhou, Y.B.; Ma, Z.Z.; Liu, Y.M. Improving the accuracy of seismic inversion using the horizontal well data. Prog. Geophys.
**2019**, 34, 185–190. [Google Scholar] [CrossRef] - Zhang, S.P.; Yu, X.H. The application of collocated co-kriging stochastic modeling in reservoir description. Nat. Gas Geosci.
**2006**, 17, 378–381. [Google Scholar] - Niu, W.J.; Meng, X.H.; Li, J.G. A new estimation method of collocated CoKing combined with soft data. Coal Geol. Explor.
**2011**, 39, 13–17. [Google Scholar] [CrossRef]

**Figure 3.**Experimental variogram of Vp in six directions of plane (Blue dots are Experimental variation function value, and red lines are fitting lines.).

**Figure 4.**Elliptic variogram (different color points correspond to the range change in different directions).

**Figure 5.**Simulated prediction maps using simple kriging (

**a**), cokriging (

**b**), and collocated cokriging (

**c**).

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**MDPI and ACS Style**

Wei, Q.; Lin, Y.; Gao, G.; Gui, Z.; Wu, Z.; Liu, J.
Research on Formation Pressure Prediction Method for Ultra-Deep Tight Sandstone Based on Collocated Cokriging. *Processes* **2023**, *11*, 2010.
https://doi.org/10.3390/pr11072010

**AMA Style**

Wei Q, Lin Y, Gao G, Gui Z, Wu Z, Liu J.
Research on Formation Pressure Prediction Method for Ultra-Deep Tight Sandstone Based on Collocated Cokriging. *Processes*. 2023; 11(7):2010.
https://doi.org/10.3390/pr11072010

**Chicago/Turabian Style**

Wei, Qiang, Yaoting Lin, Gang Gao, Zhixian Gui, Zhendong Wu, and Jiaqi Liu.
2023. "Research on Formation Pressure Prediction Method for Ultra-Deep Tight Sandstone Based on Collocated Cokriging" *Processes* 11, no. 7: 2010.
https://doi.org/10.3390/pr11072010