Revisiting Current Techniques for Analyzing Reservoir Performance: A New Approach for Horizontal-Well Pseudosteady-State Productivity Index
- Salam Al-Rbeawi (METU-Northern Cyprus Campus, Turkey)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2019
- Document Type
- Journal Paper
- 71 - 91
- 2019.Society of Petroleum Engineers
- Horizontal wells, Reservoir performance, Single and dual porous media, Productivity index
- 8 in the last 30 days
- 154 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The objective of this paper is to revisit currently used techniques for analyzing reservoir performance and characterizing the horizontal-well productivity index (PI) in finite-acting oil and gas reservoirs. This paper introduces a new practical and integrated approach for determining the starting time of pseudosteady-state flow and constant-behavior PI. The new approach focuses on the fact that the derivative of PI vanishes to zero when pseudosteady-state flow is developed. At this point, the derivative of transient-state pressure drop and that of pseudosteady-state pressure drop become mathematically identical. This point indicates the starting time of pseudosteady-state flow as well as the constant value of pseudosteady-state PI. The reservoirs of interest in this study are homogeneous and heterogamous, single and dual porous media, undergoing Darcy and non-Darcy flow in the drainage area, and finite-acting, depleted by horizontal wells. The flow in these reservoirs is either single-phase oil flow or single-phase gas flow.
Several analytical models are used in this study for describing pressure and pressure-derivative behavior considering different reservoir configurations and wellbore types. These models are developed for heterogeneous and homogeneous formations consisting of single and dual porous media (naturally fractured reservoirs) and experiencing Darcy and non-Darcy flow. Two pressure terms are assembled in these models; the first pressure term represents the time-dependent pressure drop caused by transient-state flow, and the second pressure term represents time-invariant pressure drop controlled by the reservoir boundary. Transient-state PI and pseudosteady-state PI are calculated using the difference between these two pressures assuming constant wellbore flow rate. The analytical models for the pressure derivatives of these two pressure terms are generated. Using the concept that the derivative of constant PI converges to zero, these two pressure derivatives become mathematically equal at a certain production time. This point indicates the starting time of pseudosteady-state flow and the constant behavior of PI.
The outcomes of this study are summarized as the following:
- Understanding pressure, pressure derivative, and PI behavior of bounded reservoirs drained by horizontal wells during transient- and pseudosteady-state production
- Investigating the effects of different reservoir configurations, wellbore lengths, reservoir homogeneity or heterogeneity, reservoirs as single or dual porous media, and flow pattern in porous media whether it has undergone Darcy or non-Darcy flow
- Applying the concept of the PI derivative to determine the starting time of pseudosteady-state stabilized PI
The novel points in this study are the following:
- The derivative of the PI can be used to precisely indicate the starting time of pseudosteady-state flow and the constant behavior of PI.
- The starting time of pseudosteady-state flow determined by the convergence of transient- and pseudosteady-state pressure derivative or by the PI curve is always less than that determined from the curves of total pressure drop and its derivative.
- Non-Darcy flow may significantly affect the transient-state PI, but pseudosteady-state PI is slightly affected by non-Darcy flow.
- The starting time of pseudosteady-state flow is not influenced by non-Darcy flow.
- The convergence of transient- and pseudosteady-state pressure derivatives is affected by reservoir configurations, wellbore lengths, and porous-media characteristics.
|File Size||1 MB||Number of Pages||21|
Ahmed, T. 2010. Reservoir Engineering Handbook, fourth edition. Burlington, Massachusetts: Gulf Professional Publishing.
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.
Al-Rbeawi, S. J. H. and Tiab, D. 2011. Transient Pressure Analysis of Horizontal Wells in a Multi-Boundary System. Presented at the SPE Production and Operations Symposium, Oklahoma City, Oklahoma, 27–29 March. SPE-142316-MS. https://doi.org/10.2118/142316-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.
Babu, D. K. and Odeh, A. S. 1988. Productivity of a Horizontal Well, Appendices A and B. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18334-MS. https://doi.org/10.2118/18334-MS.
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., Raghavan, R. et al. 2011. Practical Solution for Pressure Transient Response of Fractured Horizontal Wells in Unconventional Shale Reservoirs. SPE Res Eval & Eng 14 (6): 663–676. SPE-125043-PA. https://doi.org/10.2118/125043-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): 237–243. SPE-26180-PA. https://doi.org/10.2118/26180-PA.
Daviau, F., Mouronval, G., Bourdarot, G. et al. 1988. Pressure Analysis for Horizontal Wells. SPE Form Eval 3 (4): 720–724. SPE-14251-PA. https://doi.org/10.2118/14251-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.
Ding, Y., Herzhaft, B., and Renard, G. 2006. Near-Wellbore Formation Damage Effects on Well Performance—A Comparison Between Underbalance and Overbalance Drilling. SPE Prod & Oper 21 (1): 51–57. SPE-86558-PA. https://doi.org/10.2118/86558-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. A Well Configuration in Anisotropic Reservoirs. SPE Form Eval 11 (4): 257–262. SPE-27980-PA. https://doi.org/10.2118/27980-PA.
Forchheimer, P. 1901. Wasserbewegung Durch Boden (Movement of Water Through Soil). Z. Ver. Deutsch. Ing. 45: 1781–1788.
Goode, P. A. and Kuchuk, F. J. 1991. Inflow Performance of Horizontal Wells. SPE Res Eng 6 (3): 319–323. SPE-21460-PA. https://doi.org/10.2118/21460-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): 1–10. SPE-149807-PA. https://doi.org/10.2118/149807-PA.
Helmy, M. W. and Wattenbarger, R. A. 1998. New Shape Factor for Wells 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.
Johansen, T. E., Hender, D. G., and James, L. A. 2017. Productivity Index for Arbitrary Well Trajectories in Laterally Isotropic, Spatially Anisotropic Porous Media. SPE J. 22 (2): 699–711. SPE-184408-PA. https://doi.org/10.2118/184408-PA.
Jones, S. C. 1987. Using the Inertial Coefficient, B, To Characterize Heterogeneity in Reservoir Rock. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 27–30 September. SPE-16949-MS. https://doi.org/10.2118/16949-MS.
Kazemi, H. 1969. Pressure Transient Analysis of Naturally Fractured Reservoirs With Uniform Fracture Distribution. SPE J. 9 (4): 451–462. SPE-2156-A. https://doi.org/10.2118/2156-A.
Kuchuk, F., Morton, K., and Biryukov, D. 2016. Rate-Transient Analysis for Multistage Fractured Horizontal Wells in Conventional and Un-Conventional Homogeneous and Naturally Fractured Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Dubai, 26–28 September. SPE-181488-MS. https://doi.org/10.2118/181488-MS.
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, Release 2017a. Natick, Massachusetts: MathWorks.
Matthews, C. S. 1986. Transient, Semisteady-State, and Steady-State Flow. J Pet Technol 38 (4): 385–386. SPE-15278-PA. https://doi.org/10.2118/15278-PA.
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.
Mukherjee, H. and Economides, M. J. 1991. A Parametric Comparison of Horizontal and Vertical Well Performance. SPE Form Eval 6 (2): 209–216. SPE-18303-PA. https://doi.org/10.2118/18303-PA.
Newman, M. S. and Yin, X. 2013. Lattice Boltzmann Simulation of Non-Darcy Flow in Stochastically Generated 2D Porous Media Geometries. SPE J. 18 (1): 12–26. SPE-146689-PA. https://doi.org/10.2118/146689-PA.
Nie, R.-S., Jia, Y.-L., Meng, Y. et al. 2012. New Type Curves for Modeling Productivity of Horizontal Well With Negative Skin Factors. SPE Res Eval & Eng 15 (4): 486–497. SPE-163045-PA. https://doi.org/10.2118/163045-PA.
Olarewaju, J. S. and Lee, W. 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.
Ozkan, E. 1988. Performance of Horizontal Wells. PhD dissertation, University of Tulsa, Oklahoma.
Ozkan, E. and Raghavan, R. 1991a. New Solutions for Well-Test-Analysis Problems: Part 1—Analytical Considerations. SPE Form Eval 6 (3): 359–368. SPE-18615-PA. https://doi.org/10.2118/18615-PA.
Ozkan, E. and Raghavan, R. 1991b. New Solutions for Well-Test-Analysis Problems: Part 2—Computational Considerations and Applications. SPE Form Eval 6 (3): 369–378. SPE-18616-PA. https://doi.org/10.2118/18616-PA.
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.
Ozkan, E., Sarica, C., and Haci, M. 1999. Influence of Pressure Drop Along the Wellbore on Horizontal-Well Productivity. SPE J. 4 (3): 288–301. SPE-57687-PA. https://doi.org/10.2118/57687-PA.
Serra, K., Reynolds, A. C., and Raghavan, R. 1983. New Pressure Transient Analysis Methods 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.
Tang, Y., Yildiz, T., Ozkan, E. et al. 2005. Effects of Formation Damage and High-Velocity Flow on the Productivity of Perforated Horizontal Wells. SPE Res Eval & Eng 8 (4): 315–324. SPE-77534-PA. https://doi.org/10.2118/77534-PA.
Valko, P. P., Doublet, L. E., and Blasingame, T. A. 2000. Development and Application of the Multiwell Productivity Index (MPI). SPE J. 5 (1): 21–31. SPE-51793-PA. https://doi.org/10.2118/51793-PA.
Wang, X. and Economides, M. 2009. Advanced Natural Gas Engineering. Houston: Gulf Publishing Company.
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.
Yildiz, T. 2006. Productivity of Selectively Perforated Horizontal Wells. SPE Prod & Oper 21 (1): 75–80. SPE-90580-PA. https://doi.org/10.2118/90580-PA.
Zeng, F. and Zhao, G. 2008. Semianalytical Model for Reservoirs With Forchheimer’s Non-Darcy Flow. SPE Res Eval & Eng 11 (1): 280–291. SPE-100540-PA. https://doi.org/10.2118/100540-PA.
Zinati, F. F., Jansen, J.-D., and Luthi, S. M. 2012. Estimating the Specific Productivity Index in Horizontal Wells From Distributed-Pressure Measurements Using an Adjoint-Based Minimization Algorithm. SPE J. 17 (3): 742–751. SPE-135223-PA. https://doi.org/10.2118/135223-PA.