Research Papers: Petroleum Engineering

A Semi-Analytical Method for Modeling Two-Phase Flow Behavior in Fractured Carbonate Oil Reservoirs

[+] Author and Article Information
Suran Wang, Yongchao Xue, Yonghui Wu, Pin Jia, Zheng Sun

State Key Laboratory of Petroleum
Resources and Prospecting,
China University of Petroleum,
Beijing 102249, China

Linsong Cheng

State Key Laboratory of Petroleum
Resources and Prospecting,
China University of Petroleum,
Beijing 102249, China
e-mail: lscheng@cup.edu.cn

Shijun Huang

State Key Laboratory of Petroleum
Resources and Prospecting,
China University of Petroleum,
Beijing 102249, China
e-mail: fengyun7407@163.com

Minghong Bai, Junfeng Wang

The first Gas Production Plant,
Sinopec Southwest Oil and Gas Company,
Deyang 610800, Sichuan, China

1Corresponding authors.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received August 4, 2018; final manuscript received November 13, 2018; published online January 9, 2019. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 141(7), 072902 (Jan 09, 2019) (11 pages) Paper No: JERT-18-1609; doi: 10.1115/1.4042237 History: Received August 04, 2018; Revised November 13, 2018

It is quite common for oil/gas two-phase flow in developing fractured carbonate oil reservoirs. Many analytical models proposed for black oil wells in fractured carbonate reservoirs are limited to single-phase flow cases and conventional methods have been the use of numerical simulations for this problem. In this approach, a novel semi-analytical method is proposed to integrate the complexities of phase change, pressure-dependent pressure-volume-temperature (PVT) properties, two-phase flow behavior, and stress-dependent fracture permeability characteristics. A dual-porosity, black oil model considering the phase change and two-phase flow is applied to model the fractured carbonate reservoirs. To linearize the model, only flow equations of oil phase are used to develop the mathematical model. Nonlinear parameters and producing gas–oil ratio (GOR) are updated with coupled flowing material balance equations, followed by a novel proposed procedure for history matching of field production data and making forecasts. The semi-analytical method is validated with a commercial simulator Eclipse. The results show that both of the production rate curves of oil and gas phase using the proposed model coincide with the numerical simulator. The results also show that the effects of pressure-dependent fracture permeability, fracture porosity, and exterior boundary on production rate are significant. Stress sensitivity influences production rate during the whole process, reducing the cumulative production. Fracture porosity influences production rate during the intermediate flow periods. The exterior boundary affects production rate mainly in the early and intermediate production periods. Finally, a field example from the eastern Pre-Caspian basin is used to demonstrate the practicability of the method. Acceptable history match is achieved and the interpreted parameters are all reasonable.

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Kniazeff, V. J. , and Naville, S. A. , 1965, “ Two-Phase Flow of Volatile Hydrocarbons,” SPE J., 5(1), pp. 37–44.
Thiebot, B. M. , and Sakthikumar, S. S. , 1991, “ Cycling Fractured Reservoirs Containing Volatile Oil: Laboratory Investigation of the Performance of Lean Gas or Nitrogen Injection,” SPE Middle East Oil Show Conference, Bahrain, Nov. 16–19, SPE Paper No. SPE-21427-MS.
Ghorbani, D. , and Kharrat, R. , 2000, “ Fluid Characterization of an Iranian Carbonate Oil Reservoir Using Different PVT Packages,” SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, Indonesia, Apr. 17–19, SPE Paper No. SPE-68745-MS.
Kang, Z. , Wu, Y. , Li, J. , Wu, Y. , and Zhang, J. , 2006, “ Modeling Multiphase Flow in Naturally Fractured Vuggy Petroleum Reservoirs,” SPE Annual Technical Conference and Exhibition, San Antonio, TX, Sept. 24–27, SPE Paper No. SPE-102356-MS.
Gringarten, A. C. , Ogunrewo, O. , and Uxukbayev, G. , 2011, “ Assessment of Individual Skin Factors in Gas Condensate and Volatile Oil Wells,” SPE EUROPEC/EAGE Annual Conference and Exhibition, Vienna, Austria, May 23–26, SPE Paper No. SPE-143592-MS.
Warren, J. E. , and Root, P. J. , 1963, “ The Behavior of Naturally Fractured Reservoirs,” AIME Trans., 228, pp. 245–255.
Kazemi, H. , 1969, “ Pressure Transient Analysis of Naturally Fractured Reservoirs With Uniform Fracture Distribution,” SPE J., 11(4), pp. 451–462.
De Swaan, O. A. , 1976, “ Analytical Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing,” SPE J., 16(3), pp. 117–122.
Jalali, Y. , and Ershaghi, I. , 1987, “ Pressure Transient Analysis of Heterogeneous Naturally Fractured Reservoirs,” SPE California Regional Meeting, Ventura, CA, Apr. 8–10, SPE Paper No. SPE-16341-MS.
Nie, R. , Men, Y. , Jia, Y. , Zhang, F. , Yang, X. , and Niu, X. , 2012, “ Dual Porosity and Dual Permeability Modeling of Horizontal Well in Naturally Fractured Reservoir,” Transp. Porous Med., 92(1), pp. 213–235. [CrossRef]
Nie, R. , Jia, Y. , Meng, Y. , Wang, Y. , Yuan, J. , and Xu, W. , 2012, “ New Type Curves for Modeling Productivity of Horizontal Well With Negative Skin Factors,” SPE Reservoir Eval. Eng., 15(4), pp. 486–497. [CrossRef]
Yang, D. , Zhang, F. , Styles, J. A. , and Gao, J. , 2015, “ Performance Evaluation of a Horizontal Well With Multiple Fractures by Use of a Slab-Source Function,” SPE J., 20(03), pp. 652–662. [CrossRef]
Obinna, E. D. , and Hassan, D. , 2016, “ Characterizing Tight Oil Reservoirs With Dual- and Triple-Porosity Models,” ASME J. Energy Resour. Technol., 138(3), p. 032801. [CrossRef]
Wu, Y. , Cheng, L. , Huang, S. , Jia, P. , Zhang, J. , Lan, X. , and Huang, H. , 2016, “ A Practical Method for Production Data Analysis From Multistage Fractured Horizontal Wells in Shale Gas Reservoirs,” Fuel, 186, pp. 821–829. [CrossRef]
He, Y. , Cheng, S. , Qin, J. , Wang, Y. , Chen, Z. , and Yu, H. , 2018, “ Pressure-Transient Behavior of Multisegment Horizontal Wells With Nonuniform Production: Theory and Case Study,” ASME J. Energy Resour. Technol., 140(9), p. 093101. [CrossRef]
Arps, J. J. , 1945, “ Analysis of Decline Curves,” AIME Trans., 160(1), pp. 228–247. [CrossRef]
Ilk, D. , Rushing, J. A. , Perego, A. D. , and Blasingame, T. A. , 2008, “ Exponential vs. Hyperbolic Decline in Tight Gas Sands: Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves,” SPE Annual Technical Conference and Exhibition, Denver, CO, Sept. 21–24, SPE Paper No. SPE-116731-MS.
Wu, Y. S. , 2002, “ Numerical Simulation of Single-Phase and Multiphase Non-Darcy Flow in Porous and Fractured Reservoirs,” Transp. Porous Med., 49(2), pp. 209–240. [CrossRef]
Al-Shaalan, T. M. , Fung, L. S. K. , and Dogru, A. H. , 2003, “ A Scalable Massively Parallel Dual-Porosity Dual-Permeability Simulator for Fractured Reservoirs With Super-k Permeability,” SPE Annual Technical Conference and Exhibition, Denver, CO, Oct. 5–8, SPE Paper No. SPE-84371-MS.
Degraff, J. M. , Meurer, M. E. , Landis, L. H. , and Lyons, S. L. , 2005, “ Fracture Network Modeling and Dual-Permeability Simulation of Carbonate Reservoirs,” International Petroleum Technology Conference, Doha, Qatar, Nov. 21–23, Paper No. IPTC 10954-MS.
Uba, H. M. , Chiffoleau, Y. , Pham, T. , Divry, V. , Kaabi, A. , and Thuwaini, J. , 2007, “ Application of a Hybrid Dual Porosity/Dual Permeability Representation of Large-Scale Fractures to the Simulation of a Giant Carbonate Reservoir,” SPE Middle East Oil and Gas Show and Conference, Bahrain, Mar. 11–14, SPE Paper No. SPE-105560-MS.
Chong, H. , Dilmore, R. , and Wang, J. , 2017, “ Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model,” ASME J. Energy Resour. Technol., 139(1), p. 012903.
Yi, Y. , Li, J. , and Ji, L. , 2017, “ Numerical Determination of Critical Condensate Saturation in Gas Condensate Reservoirs,” ASME J. Energy Resour. Technol., 139(6), p. 062801. [CrossRef]
Perrine, R. L. , 1956, “ Analysis of Pressure-Buildup Curves,” Drilling and Production Practice, New York, Jan. 1, Paper No. API 56-482.
Martin, J. C. , 1959, “ Simplified Equations of Flow in Gas Drive Reservoirs and the Theoretical Foundation of Two-Phase Pressure Buildup Analyses,” AIME Trans., 216, pp. 309–311.
Fetkovich, M. J. , 1973, “ The Isochronal Testing of Oil Wells,” Fall Meeting of the Society of Petroleum Engineers of AIME, Las Vegas, NV, Sept. 30–Oct. 3, SPE Paper No. SPE-4529-MS.
Raghavan, R. , 1976, “ Well Test Analysis: Wells Producing by Solution Gas Drive,” SPE J., 16(4), pp. 196–208.
Raghavan, R. , 1989, “ Performance of Wells in Solution-Gas-Drive Reservoirs,” SPE Form. Eval., 4(4), pp. 611–620. [CrossRef]
O'Sullivan, M. J. , 1981, “ A Similarity Method for Geothermal Well Test Analysis,” Water Resour. Res., 17(2), pp. 390–398. [CrossRef]
Bui, T. D. , Mamora, D. D. , and Lee, W. J. , 2000, “ Transient Pressure Analysis for Partially Penetrating Wells in Naturally Fractured Reservoirs,” SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium and Exhibition, Denver, CO, Mar. 12–15, SPE Paper No. SPE-60289-MS.
Clarkson, C. R. , and Qanbari, F. , 2014, “ A Semi-Analytical Forecasting Method for Unconventional Gas and Light Oil Wells: A Hybrid Approach for Addressing the Limitations of Existing Empirical and Analytical Methods,” SPE Reservoir Eval. Eng., 18(1), pp. 260–263.
Clarkson, C. R. , and Qanbari, F. , 2015, “ An Approximate Semi-Analytical Two-Phase Forecasting Method for Multifractured Tight Light-Oil Wells With Complex Fracture Geometry,” J. Can. Petrol. Technol., 54(6), pp. 489–508. [CrossRef]
Zhang, M. , and Ayala, L. F. , 2016, “ Analytical Study of Constant Gas–Oil-Ratio Behavior as an Infinite-Acting Effect in Unconventional Two-Phase Reservoir Systems,” SPE J., 22(1), pp. 1–11.
Zhang, F. , and Yang, D. , 2017, “ Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation,” ASME J. Energy Resour. Technol., 140(3), p. 032903. [CrossRef]
Sun, Z. , Li, X. , Shi, J. , Yu, P. , Huang, L. , Xia, J. , Sun, F. , Zhang, T. , and Feng, D. , 2017, “ A Semi-Analytical Model for Drainage and Desorption Area Expansion During Coal-Bed Methane Production,” Fuel, 204, pp. 214–226. [CrossRef]
Tan, Y. , Li, H. , Zhou, X. , Jiang, B. , Wang, Y. , and Zhang, N. , 2018, “ A Semi-Analytical Model for Predicting Horizontal Well Performances in Fractured Gas Reservoirs With Bottom-Water and Different Fracture Intensities,” ASME J. Energy Resour. Technol., 140(10), p. 102905. [CrossRef]
Sun, Z. , Li, X. , Shi, J. , Zhang, T. , and Sun, F. , 2017, “ Apparent Permeability Model for Real Gas Transport Through Shale Gas Reservoirs Considering Water Distribution Characteristic,” Int. J. Heat Mass Transfer, 115, pp. 1008–1019. [CrossRef]
Bøe, A. , Skjaeveland, S. , and Whitson, C. , 1989, “ Two-Phase Pressure Test Analysis,” SPE Form. Eval., 4(4), pp. 604–610. [CrossRef]
Kissling, W. , McGuinness, M. , and McNabb, A. , 1992, “ Analysis of One-Dimensional Horizontal Two-Phase Flow in Geothermal Reservoirs,” Transp. Porous Med., 7(3), pp. 223–253. [CrossRef]
Ayala, L. F. , and Kouassi, J. P. , 2007, “ The Similarity Theory Applied to the Analysis of Two-Phase Flow in Gas-Condensate Reservoirs,” Energy Fuels, 21(3), pp. 1592–1600. [CrossRef]
Guo, J. , Nie, R. , and Jia, Y. , 2014, “ Unsteady-State Diffusion Modeling of Gas in Coal Matrix for Horizontal Well Production,” AAPG Bull., 98(9), pp. 1669–1697. [CrossRef]
Stehfest, H. , 1970, “ Numerical Inversion of Laplace Transforms,” ACM Commun., 13(1), pp. 47–49. [CrossRef]
Kuchuk, F. J. , 2009, “ Radius of Investigation for Reserve Estimation From Pressure Transient Well Tests,” SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, Mar. 15–18, SPE Paper No. SPE-120515-MS.


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Fig. 1

Description of the dual-porosity model in this paper: (a) dual-porosity model flow scheme and (b) dual-porosity model with spherical matrix

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Fig. 2

Flow chart of history matching procedure using proposed semi-analytical method

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Fig. 3

PVT properties of oil and gas phase used for numerical model and semi-analytical model: (a) PVT properties of the oil phase and (b) PVT properties of the gas phase

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Fig. 4

Relative permeability curve used for numerical model and semi-analytical model

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Fig. 5

Results comparison of production rate between numerical simulation and the semi-analytical method for validation case: (a) log–log plot of oil production rate and (b) log–log plot of gas production rate

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Fig. 6

Results comparison of cumulative production between numerical simulation and the semi-analytical method for validation case: (a) Cartesian plot of cumulative oil production and (b) Cartesian plot of cumulative gas production

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Fig. 7

Influence of stress sensitivity of fracture on production rate: (a) influence of stress sensitivity on oil production rate and (b) influence of stress sensitivity on gas production rate

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Fig. 8

Influence of Φf on production rate: (a) influence of Φf on oil production rate and (b) influence of Φf on gas production rate

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Fig. 9

Effect of radial distance of external boundary on production rate: (a) effect of radial distance of external boundary on oil production rate and (b) effect of radial distance of external boundary on gas production rate

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Fig. 10

History matching results for field case: (a) Cartesian plot of oil production and (b) Cartesian plot of gas production



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