# Numerical Modeling and Simulation of Fractured-Vuggy Reservoirs Based on Field Outcrops

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Basic Assumptions

- Assuming that the system consists of three phases—oil, gas, and water—with each phase containing multiple components, they are treated as a single “pseudo component” with average fluid properties, and the two liquid components of oil and water only exist in the accompanying phase; gases not only exist in the gas phase but can also be dissolved in oil;
- The fractured vuggy reservoir is considered an isothermal medium system without considering the impact of heat exchange;
- Heat transport through the porous media is neglected in this study;
- The caves studied in this work are assumed to be filled-type, such that Darcy’s law is satisfactory in describing the flow behaviors in the cave;
- Geomechanical and geochemical effects on the rock porosity and permeability are not considered in this study;
- The influence of capillary force is not considered in fractures;
- Fractures and karst caves are the main storage spaces, while fractures also serve as connecting channels, neglecting the self-absorption and oil drainage effect of the matrix.

#### 2.2. Governing Equations

#### 2.3. Control Volume Finite-Difference Method

#### 2.4. Treatments of Boundary Conditions

#### 2.4.1. First Type of Boundary Conditions

^{50}orders of magnitude on the boundary [31,34] and ensures that other mesh geometric features remain unchanged. This method is also based on the principle of material balance.

#### 2.4.2. Second Type of Boundary Conditions

#### 2.4.3. Well Boundary Conditions

#### 2.5. Solution Methodology

## 3. Model Validation

^{3}and a viscosity of 1.757 $\times $ 10

^{−2}cP was injected from the inlet point (see Figure 3a) into a cylinder. A standard atmospheric pressure of 0.1 MPa was kept at the outlet point, connected to the other cylinder. A tiny tube connects the two cylinders, both of which are full of oil whose density and viscosity are 913.1 kg/m

^{3}and 5.0 cP, respectively. The two cylinders are analogs of the filled caves, whose total porous volume was 70.0 mL. After 90 min gas injection, the oil production rate observed from the outlet became so low and the cumulated oil production was 54.94 mL. The processes described above were simulated with the MSFLOW code, keeping the initial and boundary conditions consistent with the experiment. Figure 4 displays the comparison of oil production rate and oil recovery between numerical and experimental results, which exhibits good agreement with each other. This comparison indicates that the MSFLOW code could lead to satisfactory modeling results when simulating multiphase flow through the fractured-vuggy reservoir.

## 4. Numerical Results

#### 4.1. Discretization of Field Outcrop of Fractured-Vuggy Reservoirs

#### 4.2. Numerical Results and Discussion

^{3}, respectively. The compression coefficients are 1.1 $\times {10}^{-3}$, 0.998 $\times {10}^{6}$, and 1.0 $\times {10}^{-4}$ MPa

^{−1}, respectively. The bubble point pressure of the reservoir is 20.2 MPa, the bound water saturation and residual oil saturation are both 0.05, and the residual gas saturation is 0. At the initial time of simulation, the fractures and caves were full of oil, and the bottom pressure of the model was 59.0 MPa (see Figure 6). Figure 7 shows the relative permeability curve for fractures and filled caves. The pressure field in the simulation area is distributed according to a gravity gradient. By default, the model boundaries are all zero-flow boundary conditions, with an oil well liquid production rate of 0.1 m

^{3}/d, an initial time step of 1.0 h, and a maximum time step of 100 h. The time step is automatically adjusted according to the speed of convergence during the simulation.

#### 4.2.1. The Impact of the Location of Natural Water Bodies on Oil Recovery Efficiency

^{3}/d; the fracture permeability is given by the cubic law and the cave permeability is 5 D; the simulation time is based on the production shutdown standard of the production well with the water cut reaching 98%; the water bodies are located at the edge (Figure 8a) and the bottom (Figure 8b) of the model; and the oil saturation distribution, water cut curve, and cumulative oil production curve at the last moment are obtained. The simulation results show that the location of water bodies has a significant impact on oil recovery, with bottom water conditions resulting in a long period of anhydrous oil recovery, high cumulative oil production, and high extraction efficiency. When the water body is close to the production well, it can easily form a preferential channel, and the water body’s sweep range decreases. Oil in the fractures and caves located below the water body is difficult to extract. Figure 8 shows that the fractured-vuggy reservoirs have a complex oil–water contact relationship. Curves shown in Figure 9, Figure 10 and Figure 11 reflect the oil production performance, which implies that the displacement efficiency relies on the distance and the connected passages between the water body and the production well. Particularly, space connections between fractures and caves determine the shape of the waterflooding frontiers and, thus, longitudinal and transverse oil displacement efficiency. Fluctuation characteristics associated with water cut and oil production curves can be observed after approximately 200 d. This is because the permeability contrast between the fracture and the caves will amplify the contribution of individual caves to the fluid production. The caves have various volumes and, thus, present differing potentials for providing oil even under the same conditions. The fluctuation characteristics reflect the geometry and volume differences between the cave/s that contribute to the oil production in time sequence.

#### 4.2.2. The Influence of the Cave Permeability on Oil Recovery Efficiency

^{3}/d fluid production rate. The perforation depth and location of the oil well are shown in Figure 12. The fracture permeability is prescribed according to the cubic law. The simulation time is based on the shutdown standard of 98% water cut in the production well, and the cave permeability is set as 100 mD, 5 D, and 10 D, respectively. The oil saturation distribution, water cut curve, and cumulative oil production curve at the last moment can be calculated. The simulation results show that the higher the permeability of karst caves, the higher the degree of recovery (see Figure 13) and the longer the anhydrous oil recovery period (see Figure 14). When the permeability reaches a certain level, the influence of karst cave permeability on oil recovery efficiency becomes weaker (see Figure 13); the gravity capture effect is significant, and the bottom water roughly advances smoothly in a horizontal manner. After the production well is affected, it is immediately flooded with explosive water; the remaining oil is mainly distributed at the top and edges of the model, as well as at the top of single-fracture connected karst caves and multiple-fracture connected karst caves. Overall, the cave permeability does not have a significant impact on the water cut evolution and the oil production rate (see Figure 14 and Figure 15). Moreover, the remaining oil distributions of different cave permeabilities have a similar pattern. We believe that caves are mainly responsible for oil/gas storage, yet they have limited influence on oil displacement efficiency and production performance.

#### 4.2.3. The Influence of the Fracture Permeability on Oil Recovery Efficiency

^{3}/d. Different fracture permeabilities (i.e., 100 mD, 1 D, and 5D) were prescribed for three simulation cases with the intention of elucidating the influence of fracture permeability on oil recovery efficiency.

## 5. Conclusions

- The cave permeability has few impacts on the oil production, while the fracture permeability plays a significant role in determining the oil recovery;
- The higher the permeability of fractures, the longer the anhydrous oil recovery period and the higher the degree of recovery. When the permeability reaches a certain level, the impact of fracture permeability weakens;
- The location of the water body has a significant impact on the oil recovery effect. When the water body is close to the production well, it can easily form preferential channels, reduce the water body’s coverage, and thus, have a low oil recovery;
- The distribution of remaining oil is influenced by the connection mode of fractures and caves and the development scheme, usually distributed at the top and edges of the model, as well as at the top of single- and multiple-fracture connected caves.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Guo, W.; Fu, S.; Li, A.; Xie, H.; Cui, S.; Nangendo, J. Experimental research on the mechanisms of improving water flooding in fractured-vuggy reservoirs. J. Pet. Sci. Eng.
**2022**, 213, 110383. [Google Scholar] [CrossRef] - Li, Y.; Kang, Z.; Xue, Z.; Zheng, S. Theories and practices of carbonate reservoirs development in China. Pet. Explor. Dev.
**2018**, 45, 712–722. [Google Scholar] [CrossRef] - Zhang, F.; An, M.; Yan, B.; Wang, Y. Modeling the depletion of fractured vuggy carbonate reservoir by coupling geomechanics with reservoir flow. In Proceedings of the SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, United Arab Emirates, 8–10 May 2017. [Google Scholar]
- Lu, A. Carbonate Fractured Vuggy Reservoir Engineering Method Research. Ph.D. Thesis, China University of Petroleum, Qingdao, China, 2007. [Google Scholar]
- Li, B.; Tan, X.; Wang, F.; Lian, P.; Gao, W.; Li, Y. Fracture and vug characterization and carbonate rock type automatic classification using X-ray CT images. J. Pet. Sci. Eng.
**2017**, 153, 88–96. [Google Scholar] [CrossRef] - Wu, Y.-S.; Di, Y.; Kang, Z.; Fakcharoenphol, P. A multiple-continuum model for simulating single-phase and multiphase flow in naturally fractured vuggy reservoirs. J. Pet. Sci. Eng.
**2011**, 78, 13–22. [Google Scholar] [CrossRef] - Yao, J.; Huang, Z.-Q. Fractured Vuggy Carbonate Reservoir Simulation; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Neale, G.H.; Nader, W.K. The permeability of a uniformly vuggy porous medium. Soc. Pet. Eng. J.
**1973**, 13, 69–74. [Google Scholar] [CrossRef] - Liu, S.; Zhang, Y.; Du, H.; Liu, J.; Zhou, Z.; Wang, Z.; Huang, K.; Pan, B. Experimental study on fluid flow behaviors of waterflooding fractured-vuggy oil reservoir using two-dimensional visual model. Phys. Fluids
**2023**, 35, 062106. [Google Scholar] - Ju, X.; Zhao, X.; Zhou, B.; Zhang, R.; Wu, X.; Guo, D. Identification of reservoir water-flooding degrees via core sizes based on a drip experiment of the Zhenwu Area in Gaoyou Sag, China. Energies
**2023**, 16, 608. [Google Scholar] [CrossRef] - Lu, G.; Zhang, L.; Liu, Q.; Xu, Q.; Zhao, Y.; Li, X.; Deng, G.; Wang, Y. Experiment analysis of remaining oil distribution and potential tapping for fractured-vuggy reservoir. J. Pet. Sci. Eng.
**2022**, 208, 109544. [Google Scholar] [CrossRef] - Lyu, X.; Liu, Z.; Hou, J.; Lyu, T. Mechanism and influencing factors of EOR by N2 injection in fractured-vuggy carbonate reservoirs. J. Nat. Gas Sci. Eng.
**2017**, 40, 226–235. [Google Scholar] [CrossRef] - Liu, Z.; Zhao, H.; Shi, H. Experimental study on stress monitoring in fractured-vuggy carbonate reservoirs before and after fracturing. J. Pet. Sci. Eng.
**2022**, 218, 110958. [Google Scholar] [CrossRef] - Yang, W.; Zhang, D.; Lei, G. Experimental study on multiphase flow in fracture-vug medium using 3D printing technology and visualization techniques. J. Pet. Sci. Eng.
**2020**, 193, 107394. [Google Scholar] [CrossRef] - Yang, W.; Zhang, D. Experimental study on multiphase flow in 3D-printed heterogeneous, filled vugs. J. Pet. Sci. Eng.
**2022**, 208, 109497. [Google Scholar] [CrossRef] - Li, S.; Zhang, D. Development of 3-D curved fracture swarms in shale rock driven by rapid fluid pressure buildup: Insights from numerical modeling. Geophys. Res. Lett.
**2021**, 48, e2021GL092638. [Google Scholar] [CrossRef] - Wang, H.; Wang, Z.; Jiang, Y.; Song, J.; Jia, M. New approach for the digital reconstruction of complex mine faults and its application in mining. Int. J. Coal Sci. Technol.
**2022**, 9, 43. [Google Scholar] [CrossRef] - Chen, Y.; Zuo, J.; Liu, D.; Li, Y.; Wang, Z. Experimental and numerical study of coal-rock bimaterial composite bodies under triaxial compression. Int. J. Coal Sci. Technol.
**2021**, 8, 908–924. [Google Scholar] [CrossRef] - Li, S.; Feng, X.-T.; Zhang, D.; Tang, H. Coupled thermo-hydro-mechanical analysis of stimulation and production for fractured geothermal reservoirs. Appl. Energy
**2019**, 247, 40–59. [Google Scholar] [CrossRef] - Li, S.; Zhang, D. Three-dimensional thermoporoelastic modeling of hydrofracturing and fluid circulation in hot dry rock. J. Geophys. Res. Solid Earth
**2023**, 128, e2022JB025673. [Google Scholar] [CrossRef] - Fadlelmula, M.M.; Fraim, M.; He, J.; Killough, J.E. Discrete Fracture-vug Network Modeling in Naturally Fractured Vuggy Reservoirs Using Multiple-Point Geostatistics: A Micro-Scale Case; SPE: Kuala Lumpur, Malaysia, 2015. [Google Scholar]
- Lei, G.; Liao, Q.; Zhang, D. A new analytical model for flow in acidized fractured-vuggy porous media. Sci. Rep.
**2019**, 9, 8293. [Google Scholar] [CrossRef] - Li, S.; Kang, Z.; Feng, X.T.; Pan, Z.; Huang, X.; Zhang, D. Three-dimensional hydrochemical model for dissolutional growth of fractures in karst aquifers. Water Resour. Res.
**2020**, 56, e2019WR025631. [Google Scholar] [CrossRef] - Wu, Y.-S.; Ehlig-Economides, C.; Qin, G.; Kang, Z.; Zhang, W.; Ajayi, B.; Tao, Q. A Triple-Continuum Pressure-Transient Model for a Naturally Fractured Vuggy Reservoir; SPE: Kuala Lumpur, Malaysia, 2007. [Google Scholar]
- Kang, Z.; Wu, Y.-S.; Li, J.; Wu, Y.; Zhang, J.; Wang, G. Modeling Multiphase Flow in Naturally Fractured Vuggy Petroleum Reservoirs; SPE: Kuala Lumpur, Malaysia, 2006. [Google Scholar]
- Zhang, N.; Yao, J.; Xue, S.; Huang, Z. Multiscale mixed finite element, discrete fracture–vug model for fluid flow in fractured vuggy porous media. Int. J. Heat Mass Transf.
**2016**, 96, 396–405. [Google Scholar] [CrossRef] - Wang, M.; Cheung, S.W.; Chung, E.T.; Vasilyeva, M.; Wang, Y. Generalized multiscale multicontinuum model for fractured vuggy carbonate reservoirs. J. Comput. Appl. Math.
**2020**, 366, 112370. [Google Scholar] [CrossRef] - Guo, J.-C.; Nie, R.-S.; Jia, Y.-L. Dual permeability flow behavior for modeling horizontal well production in fractured-vuggy carbonate reservoirs. J. Hydrol.
**2012**, 464, 281–293. [Google Scholar] [CrossRef] - Jing, W.; Huiqing, L.; Zhengfu, N.; Zhang, H.; Cheng, H. Experiments on water flooding in fractured-vuggy cells in fractured-vuggy reservoirs. Pet. Explor. Dev.
**2014**, 41, 74–81. [Google Scholar] - Jing, W.; Huiqing, L.; Jie, X.; Zhang, H. Formation mechanism and distribution law of remaining oil in fracture-cavity reservoir. Pet. Explor. Dev.
**2012**, 39, 624–629. [Google Scholar] - Pruess, K. A General Purpose Numerical Simulator for Multiphase Fluid and Heat; LBL-29400; Lawrence Berkeley National Lab: Berkeley, CA, USA, 1991. [Google Scholar]
- Narasimhan, T.; Witherspoon, P. An integrated finite difference method for analyzing fluid flow in porous media. Water Resour. Res.
**1976**, 12, 57–64. [Google Scholar] [CrossRef] - Zhang, K.; Wu, Y.-S.; Pruess, K. User’s Guide for TOUGH2-MP-a Massively Parallel Version of the TOUGH2 Code; Ernest Orlando Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 2008. [Google Scholar]
- Wu, Y.-S. A virtual node method for handling well bore boundary conditions in modeling multiphase flow in porous and fractured media. Water Resour. Res.
**2000**, 36, 807–814. [Google Scholar] [CrossRef] - Wu, Y.-S. MSFLOW: Multiphase Subsurface Flow Model of Oil, Gas and Water in Porous and Fractured Media with Water Shut-Off Capability, Documentation and User’s Guide; Twange Int.: Houston, TX, USA; Walnut Creek, CA, USA, 1998. [Google Scholar]
- Huber, R.; Helmig, R. Multiphase flow in heterogeneous porous media: A classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach. Int. J. Numer. Methods Fluids
**1999**, 29, 899–920. [Google Scholar] [CrossRef] - MacDonald, R. Methods for numerical simulation of water and gas coning. Soc. Pet. Eng. J.
**1970**, 10, 425–436. [Google Scholar] [CrossRef] - Peaceman, D.W. A new method for representing multiple wells with arbitrary rates in numerical reservoir simulation. SPE Reserv. Eng.
**1995**, 10, 253–258. [Google Scholar] [CrossRef] - Tian, Y.; Xiong, Y.; Wang, L.; Lei, Z.; Zhang, Y.; Yin, X.; Wu, Y.-S. A compositional model for gas injection IOR/EOR in tight oil reservoirs under coupled nanopore confinement and geomechanics effects. J. Nat. Gas Sci. Eng.
**2019**, 71, 102973. [Google Scholar] [CrossRef] - Wu, Y.-S. Numerical simulation of single-phase and multiphase non-Darcy flow in porous and fractured reservoirs. Transp. Porous Media
**2002**, 49, 209–240. [Google Scholar] [CrossRef] - Pan, L. User Information Document for WinGridder Version 3.0; Ernest Orlando Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 2007. [Google Scholar]
- Li, S.; Zhang, K.; Wang, Y. Use WinGridder grid generator to achieve the fine description of complex geological features. Geotech. Investig. Surv.
**2012**, 40, 37–40. [Google Scholar] - Li, S.; Zhang, D.; Li, X. A new approach to the modeling of hydraulic-fracturing treatments in naturally fractured reservoirs. SPE J.
**2017**, 22, 1064–1081. [Google Scholar] [CrossRef]

**Figure 1.**Schematic of the characteristics of the fluid flow through multiscale fractures and caves within the fractured-vuggy reservoirs.

**Figure 2.**Space discretization and geometry data in the integral finite difference method [31].

**Figure 3.**Snapshots of the remaining oil in the cylinders with different porous volume numbers (PVs): (

**a**) 0.0 PVs; (

**b**) 0.25 PVs; (

**c**) 0.5 PVs; and (

**d**) 1.0 PVs.

**Figure 4.**Comparison of oil production rate and oil recovery between numerical and experimental results.

**Figure 5.**The workflow of modeling and discretization of a typical outcrop of fractured vuggy reservoirs: (

**a**) an outcrop picture of a fractured-vuggy reservoir; (

**b**) digital description of the fractures and caves; (

**c**) domain discretization; and (

**d**) digital extraction of the fractures and caves using computational grids.

**Figure 6.**Initial state of the studied domain: (

**a**) pressure distribution and (

**b**) oil saturation distribution of oil phase.

**Figure 8.**Oil saturation distribution of (

**a**) edge water and (

**b**) bottom water. Note that the grey rectangle zone denotes a production well and the red arrow denotes fluid extraction from the well.

**Figure 12.**Oil distributions with various cave permeabilities: (

**a**) 100 mD, (

**b**) 5 D, and (

**c**) 10 D. Note that the red arrow denotes fluid extraction from the well.

**Figure 16.**Oil distributions with various fracture permeabilities: (

**a**) 100 mD, (

**b**) 5 D, and (

**c**) 10 D. Note that the red arrow denotes fluid extraction from the well.

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**MDPI and ACS Style**

Li, S.; Kang, Z.; Zhang, Y.
Numerical Modeling and Simulation of Fractured-Vuggy Reservoirs Based on Field Outcrops. *Water* **2023**, *15*, 3687.
https://doi.org/10.3390/w15203687

**AMA Style**

Li S, Kang Z, Zhang Y.
Numerical Modeling and Simulation of Fractured-Vuggy Reservoirs Based on Field Outcrops. *Water*. 2023; 15(20):3687.
https://doi.org/10.3390/w15203687

**Chicago/Turabian Style**

Li, Sanbai, Zhijiang Kang, and Yun Zhang.
2023. "Numerical Modeling and Simulation of Fractured-Vuggy Reservoirs Based on Field Outcrops" *Water* 15, no. 20: 3687.
https://doi.org/10.3390/w15203687