# Factoring Permeability Anisotropy in Complex Carbonate Reservoirs in Selecting an Optimum Field Development Strategy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- (a)
- X-direction$$\mathrm{Fracture}\text{}\mathrm{type}\text{}{\mathrm{k}}_{\mathrm{xf}}=0.8384\xb7{e}^{\left(0.356\xb7\mathsf{\phi}\right)}$$$$\mathrm{Matrix}\text{}\mathrm{type}\text{}{\mathrm{k}}_{\mathrm{xm}}=0.1037\xb7{e}^{\left(0.264\xb7\mathsf{\phi}\right)}$$
- (b)
- Y-direction$$\mathrm{Fracture}\text{}\mathrm{type}\text{}{\mathrm{k}}_{\mathrm{yf}}=0.216\xb7{e}^{\left(0.468\xb7\mathsf{\phi}\right)}$$$$\mathrm{Matrix}\text{}\mathrm{type}\text{}{\mathrm{k}}_{\mathrm{ym}}=0.0725\xb7{e}^{\left(0.273\xb7\mathsf{\phi}\right)}$$
- (c)
- Z-direction$$\mathrm{Fracture}\text{}\mathrm{type}\text{}{\mathrm{k}}_{\mathrm{zf}}=0.2979\xb7{e}^{\left(0.302\xb7\mathsf{\phi}\right)}$$$$\mathrm{Matrix}\text{}\mathrm{type}\text{}{\mathrm{k}}_{\mathrm{zm}}=0.0418\xb7{e}^{\left(0.286\xb7\mathsf{\phi}\right)}$$

_{Wn}—normalised water saturation, S

_{WCR}—critical water saturation, S

_{OWCR}—critical oil saturation, S

_{GL}—gas saturation.

## 3. Results and Discussions

- Model 2 calculations made minimum difference between the options (oil production is 30,000 m
^{3}, watercut is 0.01). - Model 2 calculations indicated notably low watercut performance during development and values at the end of development. Model 2 did not expose flooding risks in higher reservoir porosity and permeability zones, and permeability anisotropy.
- In Model 1 calculations, the difference between the options in terms of cumulative oil production was 145,000 m
^{3}. In terms of watercut at the end of development, the difference was insignificant, while the watercut trends were completely different. Model 1, with allowance for anisotropy, shows that different orientation of horizontal wellbores considerably impacted the cumulative production and watercut. - Model 1 calculations suggested that Option 1, i.e., the orientation of horizontal wellbores along the strike, was a better choice. With the probability of fracture zones and permeability anisotropy, a faster flooding from the injection wells was predicted for the perpendicular wellbore option; there was a substantial risk of the horizontal wellbore heel flooding, which would cause the rapid flooding of wells.

## 4. Conclusions

- -
- three-dimensional parameters reflecting the directivity of fracture intensity distribution in the lateral and vertical strike were integrated into the fluid flow simulation model;
- -
- rock reservoirs in the reservoir volume were classified into fractured and porous;
- -
- permeability–porosity petrophysical correlations describing lateral and vertical anisotropy were plotted for different rock types and factored into the fluid flow model;
- -
- phase permeabilities were differentiated by rock type;
- -
- the fluid flow model was history-matched, the discrepancy in the cumulative oil production not exceeding 5%;
- -
- predicted options for the reservoir development were calculated;
- -
- it was discovered that Model 2 (with no allowance for anisotropy) does not allow reliable estimates of fluid flow processes in a complex carbonate reservoir;
- -
- Model 1 calculations showed Option 1 as the most effective, as it allows the production of 145,000 m
^{3}more oil compared to Option 2.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Lake, L.W. Short Course Manual, Enhanced Oil Recovery Fundamentals; SPE: Richardson, TX, USA, 1985; p. 449. [Google Scholar]
- Novokreshchenny, D.V.; Raspopov, A.V. Perspectives of development of technologies of radial opening of a layer on deposits of the Perm region. Oil Ind.
**2014**, 3, 54–57. [Google Scholar] - Pivovar, A.V.; Kolesov, V.A.; Kalistratov, S.A.; Zagrivniy, F.A.; Mishakov, M.V. Influence of Geological Conditions on Wear-out of the Bits in the Riphean Deposits of the Yurubcheno-Tokhomskoye Field. Oil Ind.
**2022**, 1, 50–53. [Google Scholar] [CrossRef] - Zaripov, A.T.; Razumov, A.R.; Beregovoy, A.N.; Knyazeva, N.A.; Vasilyev, E.P.; Amerkhanov, M.I. Improved Production Performance of Heavy Oil Reservoirs with Compacted and Shaled-Out Interlayers. Oil Ind.
**2021**, 7, 28–31. [Google Scholar] [CrossRef] - Putilov, I.S.; Vinokurova, E.E.; Guliaeva, A.A.; Yuzhakov, A.L.; Popov, N.A. Creation of a Conceptual Geological Model based on Lithological-Petrographic Research on the Example of the Permo-Carboniferous Deposit of the Usinskoe Deposit. Perm J. Pet. Min. Eng.
**2020**, 3, 214–222. [Google Scholar] [CrossRef] - Ke, X.Y.; Zhao, J.; Li, Z.; Guo, Y.; Kang, Y. Production Simulation of Oil Reservoirs with Complex Fracture Network using Numerical Simulation. Energies
**2022**, 15, 4050. [Google Scholar] [CrossRef] - Churanova, N.Y.; Khayrullin, M.M.; Chorniy, A.V.; Solovyev, A.V.; Kurelenkov, S.K. Reservoir Properties Distribution Forecast in a Complex Carbonate Reservoir and Drilling Risk Evaluation. In Proceedings of the Russian Petroleum Technology Conference, Moscow, Russia, 15–17 October 2018. [Google Scholar] [CrossRef]
- Fonta, O.; Verma, N.; Matar, S.; Divry, V.; Al-Qallaf, H. The Fracture Characterization and Fracture Modeling of a Tight Carbonate Reservoir. SPE Reserv. Eval. Eng.
**2007**, 10, 695–710. [Google Scholar] [CrossRef] - Tavakoli, V. Carbonate Reservoir Heterogeneity: Overcoming the Challenges; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar] [CrossRef]
- Gimazov, A.A.; Fokeeva, E.E.; Khairullin, R.U.; Minikhanov, D.M. Integrated Approach to Adapting and Forecasting the Parameters of Secondary Porosity for the R. Trebs Oilfield. Oil Ind.
**2018**, 10, 20–23. [Google Scholar] [CrossRef] - Lu, X.B.; Gao, B.Y.; Chen, S.M. Study on Characteristics of Paleokarst Reservoir in Lower Ordovician Carbonate of Tahe Oil Field. Kuangwu Yanshi
**2003**, 23, 87–92. [Google Scholar] - Jiu, B.; Huang, W.; Mu, N.; Li, Y. Types and Controlling Factors of Ordovician Paleokarst Carbonate Reservoirs in the Southeastern Ordos Basin, China. J. Petrol. Sci. Eng.
**2021**, 198, 108162. [Google Scholar] [CrossRef] - Lopez, D.D.; Pickup, G.E.; Corbett, P.W.M. The Effects of Relative Permeability and Capillary Pressure Curves on a 2D Karst Reservoir Model. In Proceedings of the 77th EAGE Conference and Exhibition, Madrid, Spain, 1–4 June 2015; pp. 1–5. [Google Scholar] [CrossRef]
- Du, Y.; Wang, J.; Fang, J.; Wang, Z.; Xin, J.; Ma, W.; Wang, H.; Huang, T.; Chen, M.; Fu, X. The Karst Reservoir Evolution and Genesis of Abnormal High Permeability Zone of the Upper Cretaceous Khasib Formation in Central Iraq. Sci. Geol. Sinica
**2015**, 50, 1218–1234. [Google Scholar] [CrossRef] - Alkhimenkov, Y.A.; Bayuk, I.O. Analysis of Anisotropy Parameters of Fractured Carbonate Reservoir. In Proceedings of the 6th EAGE Saint Petersburg International Conference and Exhibition, Saint Petersburg, Russia, 7–10 April 2014; pp. 1–5. [Google Scholar] [CrossRef]
- Grigoriev, A.V.; Laevsky, Y.M.; Yakovlev, P.G. On a Double Porosity Model of Fractured-Porous Reservoirs Based on a Hybrid Flow Function. Numerical Anal. Appl.
**2018**, 11, 121–133. [Google Scholar] [CrossRef] - Krivoshchekov, S.N.; Kochnev, A.A.; Kozyrev, N.D.; Mengaliev, A.G. Modification of Permeability Cube of Geologic and Hydrodynamic Model Under various Volumes of Input Data. IOP Conf. Ser. Earth Environ. Sci.
**2022**, 988, 042020. [Google Scholar] [CrossRef] - Nie, R.S.; Meng, Y.F.; Jia, Y.L.; Zhang, F.X.; Yang, X.T.; Niu, X.N. Dual porosity and dual permeability modeling of horizontal well in naturally fractured reservoir. Transp. Porous Media
**2012**, 92, 213–235. [Google Scholar] [CrossRef] [Green Version] - Hutahaean, J.; Demyanov, V.V.; Christie, M. Many-objective optimization algorithm applied to history matching. In Proceedings of the 2016 IEEE Symposium Series on Computational Intelligence, Athens, Greece, 6–9 December 2016; pp. 1–8. [Google Scholar] [CrossRef]
- Anifowose, F.A.; Abdulraheem, A.; Al-Shuhail, A.; Schmitt, D.P. Improved Permeability Prediction From Seismic and Log Data using Artificial Intelligence Techniques. In Proceedings of the SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 10–13 March 2013. [Google Scholar] [CrossRef]
- Subasi, A.; El-Amin, M.F.; Darwich, T.; Dossary, M. Permeability prediction of petroleum reservoirs using stochastic gradient boosting regression. J. Ambient Intell. Human Comput.
**2020**, 13, 3555–3564. [Google Scholar] [CrossRef] - Chen, G.; Meng, Y.; Huan, J.; Wang, Y.; Xiao, L.; Zhang, L.; Feng, D. A new predrilling reservoir permeability prediction model and its application. J. Petrol. Sci. Eng.
**2021**, 210, 110086. [Google Scholar] [CrossRef] - Zolotukhin, A.; Gayubov, A. Machine learning in reservoir permeability prediction and modelling of fluid flow in porous media. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 700, 012023. [Google Scholar] [CrossRef] - Takougang, E.M.T.; Bouzidi, Y.; Ali, M.Y. Characterization of small faults and fractures in a carbonate reservoir using waveform inversion, reverse time migration, and seismic attributes. J. Appl. Geophys.
**2019**, 161, 116–123. [Google Scholar] [CrossRef] - Thararoop, P.; Karpyn, Z.; Gitman, A.; Ertekin, T. Integration of seismic attributes and production data for infill drilling strategies—A virtual intelligence approach. J. Petrol. Sci. Eng.
**2008**, 63, 43–52. [Google Scholar] [CrossRef] - Iturrarán-Viveros, U.; Parra, J.O. Artificial Neural Networks applied to estimate permeability, porosity and intrinsic attenuation using seismic attributes and well-log data. J. Appl. Geophys.
**2014**, 107, 45–54. [Google Scholar] [CrossRef] - Yang, P.; Sun, Z.; Liang, X.; Li, H.; Dan, G. Seismic strategy for predicting highly profitable wells in the fractured-vuggy carbonate reservoirs. Petrol. Explor. Dev.
**2013**, 40, 537–541. [Google Scholar] [CrossRef] - Boadu, F.K. Predicting the transport properties of fractured rocks from seismic information: Numerical experiments. J. Appl. Geophys.
**2000**, 44, 103–113. [Google Scholar] [CrossRef] - Katterbauer, K.; Arango, S.; Sun, S.; Hoteit, I. Multi-data reservoir history matching for enhanced reservoir forecasting and uncertainty quantification. J. Petrol. Sci. Eng.
**2015**, 128, 160–176. [Google Scholar] [CrossRef] - Moradi, A.; Samani, N.A.; Kumara, A.S.; Moldestad, B.M.E. Evaluating the Performance of Advanced Wells in Heavy Oil Reservoirs Under Uncertainty in Permeability Parameters. Energy Reports
**2022**, 8, 8605–8617. [Google Scholar] [CrossRef] - Wang, Z.; Ge, H.; Wei, Y.; Wang, Y.; Jia, K.; Xu, N.; Zhang, Y.; Du, S. Characterizing the Microscopic Anisotropic Permeabilities of Tight Oil Reservoirs Impacted by Heterogeneous Minerals. Energies
**2022**, 15, 6552. [Google Scholar] [CrossRef] - Kozyrev, N.D.; Kochnev, A.A.; Mengaliev, A.G.; Putilov, I.S.; Krivoshchekov, S.N. Refinement of the Geological and Hydrodynamic Model of a Complex Oil Reservoir by Means of a Comprehensive Data Analysis. Bull. Tomsk Polytech. Univ. Geo Assets Eng.
**2022**, 331, 164–177. [Google Scholar] [CrossRef] - Mengaliev, A.G.; Martyushev, D.A. Accounting the Parameter of Anisotropy of Permeability in Geological and Hydrodynamic Models of Carbonate Objects (on the Example of the Gagarin Deposit). Bull. Tomsk Polytech. Univ. Geo Assets Eng.
**2020**, 331, 7–17. [Google Scholar] [CrossRef] - Clavaud, J.-B.; Maineult, A.; Zamora, M.; Rasolofosaon, P.; Schlitter, C. Permeability Anisotropy and its Relations with Porous Medium Structure. J. Geophys. Res. Solid Earth
**2008**, 113. [Google Scholar] [CrossRef] - Aziz, E.A.A.E.; Gomaa, M.M. Petrophysical Analysis of Well Logs and Core Samples for Reservoir Evaluation: A Case Study of Southern Issaran Field, Gulf of Suez Province, Egypt. Environ. Earth Sci.
**2022**, 81, 341. [Google Scholar] [CrossRef] - Kovalenko, Y.F.; Karev, V.I.; Gavura, A.V.; Shafikov, R.R. About Necessity of Taking into Account the Anisotropy of Strength and Filtration Rocks Properties in Geomechanical Modeling of Wells. Oil Ind.
**2016**, 11, 114–117. [Google Scholar] - Yermekov, R.I.; Merkulov, V.P.; Chernova, O.S.; Korovin, M.O. Features of Permeability Anisotropy Accounting in the Hydrodynamic Model. J. Min. Inst.
**2020**, 243, 299–304. [Google Scholar] [CrossRef] - Kolbikov, S.; Kuznetsova, Y.; Smirnov, A. Method of Anisotropy Modeling and its Application to Hydrodynamic Simulation. In Proceedings of the SPE Russian Petroleum Technology Conference, Moscow, Russia, 15–17 October 2018. [Google Scholar] [CrossRef]
- Martyushev, D.A.; Galkin, V.I.; Ponomareva, I.N. Study of Regularities of Distribution of Filtering Properties within Complexly Constructed Carbonate Reservoirs. Bull. Tomsk Polytech. Univ. Geo Assets Eng.
**2021**, 332, 117–126. [Google Scholar] [CrossRef] - Shipaeva, M.; Sudakov, V.; Khairtdinov, R.; Sattarov, A. Analysis of Flow Distribution in Fractured-Cavernous Carbonate Reservoir Basing on Tracer Tests and Isotope Survey. In Proceedings of the 19th International Multidisciplinary Scientific GeoConference SGEM, Albena, Bulgaria, 28 June–7 July 2019; pp. 635–642. [Google Scholar] [CrossRef]
- Dmitriev, N.M.; Maksimov, V.M. Determining Equations of Two-Phase Flows through Anisotropic Porous Media. Fluid Dyn.
**1998**, 33, 224–229. [Google Scholar] [CrossRef] - Pergament, A.K.; Tomin, P.Y. The Study of Relative Phase-Permeability Functions for Anisotropic Media. Math. Models Comp. Sim.
**2012**, 4, 1–9. [Google Scholar] [CrossRef] - Johnson, E.F.; Bossler, D.P.; Naumann, V.O. Calculation of relative permeability from displacement experiments: Transl. AIME
**1959**, 216, 370–376. [Google Scholar] [CrossRef] - Khromova, I.; Link, B.; Marmelevskyi, N. Comparison of Seismic-Based Methods for Fracture Permeability Prediction. First Break
**2011**, 29, 37–44. [Google Scholar] [CrossRef] - Marmalevskyi, N.; Khromova, I.; Kostyukevych, A. Duplex Wave AVO for Predicting Properties of Subvertical Boundaries. In Proceedings of the 4th EAGE St. Petersburg International Conference and Exhibition on Geosciences, St. Petersburg, Russia, 5–8 April 2010. [Google Scholar] [CrossRef]
- Jin, S.; Xu, S.; Walraven, D. One-Return Wave Equation Migration: Imaging of Duplex Waves. In Proceedings of the 2006 SEG Annual Meeting, New Orleans, LO, USA, 1–6 October 2006; SEG Technical Program Expanded Abstracts. pp. 2338–2342. [Google Scholar] [CrossRef]
- Dubrova, G.B.; Khromova, I.; Kostyukevych, A.; Luo, D.; Liang, W.; Li, B. Duplex Wave Migration Based AVO for Determination Properties of Vertical Boundaries. In Proceedings of the 73rd EAGE Conference and Exhibition Incorporating SPE EUROPEC, Vienna, Austria, 23–27 May 2011. [Google Scholar] [CrossRef]
- Marmalevskyi, N.; Gorbachev, S.; Gornyak, Z.; Dubrova, G.; Link, B. Velocity Detection by Duplex Wave Migration. In Proceedings of the 5th EAGE St. Petersburg International Conference and Exhibition on Geosciences, St. Petersburg, Russia, 2–5 April 2012. [Google Scholar] [CrossRef]
- Khromova, I. Migration of duplex waves-a method for mapping of fracture zones of tectonic genesis. Oil Gas Geol.
**2008**, 3, 37–47. (In Russian) [Google Scholar] - Galkin, S.V.; Efimov, A.A.; Krivoshchekov, S.N.; Savitskiy, Y.V.; Cherepanov, S.S. X-ray tomography in petrophysical studies of core samples from oil and gas fields. Rus. Geol. Geophys.
**2015**, 5, 782–792. [Google Scholar] [CrossRef] - Zakrevsky, K.E. Geological 3D Modeling. M. European Association of Geoscientists & Engineers. 2011. Available online: https://www.earthdoc.org/content/books/9789462820043 (accessed on 20 November 2022).
- Yarus, J.M. Stochastic Modeling and Geostatistics; AAPG: Tulsa, OK, USA, 1994; p. 231. [Google Scholar]
- Richmond, P.C.; Watson, A.T. Estimation of multiphase flow functions from displacement experiments. SPE Res. Eng.
**1990**, 5, 121–127. [Google Scholar] [CrossRef] - Li, K.; Horne, R.N. Comparison of Methods to Calculate Relative Permeability from Capillary Pressure in Consolidated Water-Wet Porous Media. Water Resources Res.
**2006**, 42. [Google Scholar] [CrossRef] [Green Version] - Ghoodjani, E.; Bolouri, S.H. A Novel Two-Parameter Relative Permeability Model. J. Porous Media
**2012**, 15, 1061–1066. [Google Scholar] [CrossRef]

**Figure 1.**Classification of the reservoir in the volume according to the aperture of the distribution of duplex waves: (

**a**) in the X-direction, (

**b**) in the Y-direction, (

**c**) in the Z-direction.

**Figure 2.**Results of x-ray tomography study of rock samples: (

**a**) XY slice; (

**b**) YZ slice; (

**c**) 3D model of pore space.

**Figure 3.**Permeability–porosity correlation: (

**a**) in the X-direction, (

**b**) in the Y-direction, (

**c**) in the Z-direction.

Parameter | Fractures Type (Mean, mD) | Matrix Type (Mean, mD) | t-Test/p-Value | F-Test/p-Value |
---|---|---|---|---|

Permeability (X direction) | 63 | 19 | 2.26/0.02 | 11.4/<0.01 |

Permeability (Y direction) | 38 | 12 | 1.86/0.04 | 4.0/<0.01 |

Permeability (Z direction) | 8 | 22 | −1.92/0.05 | 5.1/<0.01 |

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**MDPI and ACS Style**

Krivoshchekov, S.; Kochnev, A.; Kozyrev, N.; Ozhgibesov, E.
Factoring Permeability Anisotropy in Complex Carbonate Reservoirs in Selecting an Optimum Field Development Strategy. *Energies* **2022**, *15*, 8866.
https://doi.org/10.3390/en15238866

**AMA Style**

Krivoshchekov S, Kochnev A, Kozyrev N, Ozhgibesov E.
Factoring Permeability Anisotropy in Complex Carbonate Reservoirs in Selecting an Optimum Field Development Strategy. *Energies*. 2022; 15(23):8866.
https://doi.org/10.3390/en15238866

**Chicago/Turabian Style**

Krivoshchekov, Sergey, Alexander Kochnev, Nikita Kozyrev, and Evgeny Ozhgibesov.
2022. "Factoring Permeability Anisotropy in Complex Carbonate Reservoirs in Selecting an Optimum Field Development Strategy" *Energies* 15, no. 23: 8866.
https://doi.org/10.3390/en15238866