Productivity-Index Behavior for Hydraulically Fractured Reservoirs Depleted by Constant Production Rate Considering Transient-State and Semisteady-State Conditions
- Salam Al-Rbeawi (METU–Northern Cyprus Campus, Turkey)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Operations
- Publication Date
- April 2018
- Document Type
- Journal Paper
- 2018.Society of Petroleum Engineers
- Productivity index, Fractured formations, Horizontal wells, Reservoir performance
- 3 in the last 30 days
- 198 since 2007
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This paper introduces a new approach for studying productivity-index (PI) behavior of fractured oil and gas reservoirs during transient- and pseudosteady-state conditions. This approach focuses on the fact that PI derivative could vanish at a certain production time, indicating the beginning of pseudosteady state, wherein the PI demonstrates constant value. The reservoirs in this study are considered depleted by horizontal wells intersecting multiple hydraulic fractures where Darcy flow and non-Darcy flow may control flow patterns in the porous media. The PI is calculated assuming constant production rate and considering pressure profile for early- and intermediate-production time when transient condition dominates fluid flow and late-production time when pseudosteady state is reached.
The outcomes of this study can be summarized as understanding PI behavior at early- and intermediate-production time when transient flow is dominant in the porous media and late-production time when pseudosteady-state condition is reached; indicating the effect of reservoir configuration on PI and the time when this index approaches constant value; and introducing a study for the influence of non-Darcy flow in the PI.
The most-interesting points in this study are the following. First, that PI reaches constant value when the rates of change with time for the two pressure drops--transient and pseudosteady state--are equal. Second, the time for approaching constant PI in a small drainage area is faster than for a large area. Third, that PI is affected by non-Darcy flow at early- and intermediate-production time; however, the effect is not seen at late-production time. Last, that PI could exhibit constant behavior for severe non-Darcy flow at early- and intermediate-production times even though transient-state condition dominates fluid flow in the porous media.
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Al-Otaibi, A. M. and Wu, Y.-S. 2010. Transient Behavior and Analysis of Non-Darcy Flow in Porous and Fractured Reservoirs According to the Barree and Conway Model. Presented at the SPE Western Regional Meeting, Anaheim, California, 27–29 May. SPE-133533-MS. https://doi.org/10.2118/133533-MS.
Aulisa, E., Ibragimov, A., and Walton, J. 2009. A New Method for Evaluating the Productivity Index of Nonlinear Flows. SPE J. 14 (4): 693–706. SPE-108984-PA. https://doi.org/10.2118/108984-PA.
Barree, R. D. and Conway, M. W. 2004. Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 26–29 September. SPE-89325-MS. https://doi.org/10.2118/89325-MS.
Barree, R. D. and Conway, M. 2009. Multiphase Non-Darcy Flow in Proppant Packs. SPE Prod & Oper 24 (2): 257–268. SPE-109561-PA. https://doi.org/10.2118/109561-PA.
Brown, M., Ozkan, E., Raghvan, R. et al. 2011. Practical Solutions for Pressure-Transient Responses of Fractured Horizontal Wells in Unconventional Shale Reservoirs. SPE Res Eval & Eng 14 (6): 663–676. SPE-125043-PA. https://doi.org/10.8221/125043-PA.
Camacho-V., R., Vasquez-C., M., Roldan-C., J. et al. 1996. New Results on Transient Well Tests Analysis Considering Nonlaminar Flow in the Reservoir. SPE Form Eval 11 (4): 237–244. SPE-26180-PA. https://doi.org/10.2118/26180-PA.
de Swaan O., A. 1976. Analytic Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing. SPE J. 16 (3): 117–122. SPE-5346-PA. https://doi.org/10.2118/5346-PA.
Diyashev, I. R. and Economides, M. J. 2006. The Dimensionless Productivity Index as a General Approach to Well Evaluation. SPE Prod & Oper 21 (3): 394–401. SPE-94644-PA. https://doi.org/10.2118/94644-PA.
Economides, M. J., Brand, C. W. and Frick, T. P. 1996. Well Configurations in Anisotropic Reservoirs. SPE Form Eval 11 (4): 257–262. SPE-27980-PA. https://doi.org/10.2118/27980-PA.
Economides, M. J., Hill, A. D., Ehlig-Economides, C. et al. 2013. Petroleum Production Systems, second edition. Westford, Massachusetts: Prentice Hall.
Forchheimer, P. 1901. Wasserbewegung Durch Boden. Z. Ver. Deut. Ing. 45: 1781–1788.
Fuentes-Cruz, G. and Valko, P. P. 2015. Revisiting the Dual-Porosity/Dual-Permeability Modeling of Unconventional Reservoirs: The Induced-Interporosity Flow Field. SPE J. 20 (1): 124–141. SPE-173895-PA. https://doi.org/10.2118/173895-PA.
Hagoort, J. 2004. Non-Darcy Flow Near Hydraulically Fractured Wells. SPE J. 9 (2): 180–185. SPE-80419-PA. https://doi.org/10.2118/80419-PA.
Hagoort, J. 2008. Stabilized Well Productivity in Double-Porosity Reservoirs. SPE Res Eval & Eng 11 (5): 940–947. SPE-110984-PA. https://doi.org/10.2118/110984-PA.
Hagoort, J. 2011. Semisteady-State Productivity of a Well in a Rectangular Reservoir Producing at Constant Rate or Constant Pressure. SPE Res Eval & Eng 14 (6): 677–686. SPE-149807-PA. https://doi.org/10.2118/149807-PA.
Helmy, M. W. and Wattenbarger, R. A. 1998. New Shape Factor for Well Produced at Constant Pressure. Presented at the SPE Gas Technology Symposium, Calgary, 15–18 March. SPE-39970-MS. https://doi.org/10.2118/39970-MS.
KAPPA Engineering. 2017. SAPHIR NL - Pressure Transient Analysis, https://www.kappaeng.com/software/saphir/overview.
Lai, B., Miskimins, J. L. and Wu, Y.-S. 2012. Non-Darcy Porous-Media Flow According to the Barree and Conway Model: Laboratory and Numerical-Modeling Studies. SPE J. 17 (1): 70–79. SPE-122611-PA. https://doi.org/10.2118/122611-PA.
MathWorks. 2017. MATLAB and Simulink (22.214.171.1248062), https://www.mathworks.com/products/simulink.html.
Medeiros, F., Ozkan, E., and Kazemi, H. 2008. Productivity and Drainage Area of Fractured Horizontal Wells in Tight Gas Reservoirs. SPE Res Eval & Eng 11 (5): 902–911. SPE-108110-PA. https://doi.org/10.2118/108110-PA.
Mohan, J., Pope, G. A., and Sharma, M. M. 2009. Effect of Non-Darcy Flow on Well Productivity of a Hydraulically Fractured Gas-Condensate Well. SPE Res Eval & Eng 12 (4): 576–585. SPE-103025-PA. https://doi.org/10.2118/103025-PA.
Olarewaju, J. S. and Lee, J. 1989. New Pressure-Transient Analysis Model for Dual-Porosity Reservoirs. SPE Form Eval 4 (3): 384–390. SPE-15634-PA. https://doi.org/10.2118/15634-PA.
Ozcan, O., Sarak, H., Ozkan, E. et al. 2014. A Trilinear Flow Model for a Fractured Horizontal Well in a Fractal Unconventional Reservoir. Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. SPE-170971-MS. https://doi.org/10.2118/170971-MS.
Ozkan, E., Brown, M. L., Raghavan, R. et al. 2011. Comparison of Fractured-Horizontal-Well Performance in Tight Sand and Shale Reservoirs. SPE Res Eval & Eng 14 (2): 248–259. SPE-121290-PA. https://doi.org/10.2118/121290-PA.
Raghavan, R. S., Chen, C.-C., and Agarwal, B. 1997. An Analysis of Horizontal Wells Intercepted by Multiple Fractures. SPE J. 2 (3): 235–245. SPE-27652-PA. https://doi.org/10.2118/27652-PA.
Serra, K. V., Reynold, A. C., and Raghavan, R. 1983. New Pressure Transient Analysis Method for Naturally Fractured Reservoirs. J Pet Technol 35 (12): 2271–2283. SPE-10780-PA. https://doi.org/10.2118/10780-PA.
Spivey, J. P., Brown, K. G., Sawyer, W. K. et al. 2004. Estimating Non-Darcy Flow Coefficient from Buildup-Test Data with Wellbore Storage. SPE Res Eval & Eng 7 (4): 256–269. SPE-88939-PA. https://doi.org/10.2118/88939-PA.
Warren, J. E. and Root, P. J. 1963. The Behavior of Naturally Fractured Reservoirs. SPE J. 3 (3): 245–255. SPE-426-PA. https://doi.org/10.2118/426-PA.
Wei, Y., He, D., Wang, J. et al. 2015. A Coupled Model for Fractured Shale Reservoirs with Characteristics of Continuum Media and Fractal Geometry. Presented at the SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, Australia, 9–11 November. SPE-176843-MS. https://doi.org/10.2118/176843-MS.
Zeng, F. and Zhao, G. 2008. Semianalytical Model for Reservoirs with Forchheimer’s Non-Darcy Flow. SPE Res Eval & Eng 11 (2): 280–291. SPE-100540-PA. https://doi.org/10.2118/100540-PA.