Analytical Modeling of Linear Flow in Pressure-Sensitive Formations
- S. Hamed Tabatabaie (IHS Global Canada) | Mehran Pooladi-Darvish (Futech Energy Corporation) | Louis Mattar (IHS Global Canada) | Mohammad Tavallali (IHS Global Canada)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2017
- Document Type
- Journal Paper
- 215 - 227
- 2017.Society of Petroleum Engineers
- Pressure-dependent Permeability , Drawdown Management , Productivity Loss , Permeability Modulus , distance of investigation
- 16 in the last 30 days
- 549 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The mathematical models commonly used to describe fluid flow through porous media are dependent on various simplifying assumptions, one of them being that the permeability is independent of pore pressure. However, during fluid withdrawal, reservoir permeability may be reduced because of deformation of the porous rock. The pressure dependence of permeability is more pronounced in tight formations. When dealing with pressure-sensitive formations, the assumption of a constant permeability is inappropriate.
In this study, analytical models are developed to model production from hydraulically fractured tight formations with pressure-dependent permeability, for both constant-pressure and constant-rate production scenarios. By deriving an explicit relationship between time and pseudotime, it is shown that the analytical liquid solutions can be directly applied to pressure-dependent permeability reservoirs.
This paper develops the appropriate transformation, and discusses its application by comparing the numerical solution of the nonlinear problem with the analytical solution proposed here. The close agreement between these solutions demonstrates the accuracy of the proposed methodology in forecasting the behavior of pressure-sensitive formations. We used the models developed in this work to address the following question: Is it possible that the permeability is decreased so much that a reduction in rate results when drawdown is increased? We show that the answer to the question is no. Depending on the strength of the nonlinearity, there could be a point beyond which the rate will not improve measurably as the flowing pressure is lowered. However, for a particular reservoir with a constant-permeability modulus, it is not possible to reduce the production rate by increasing the drawdown. This is contrary to previous publications that suggest that in a reservoir with pressure-dependent permeability, there is an optimum drawdown for maximum production. In a companion paper, we explore conditions where such an optimum drawdown could exist.
|File Size||682 KB||Number of Pages||13|
Agarwal, R. G. 1979. “Real Gas Pseudo-Time”–A New Function For Pressure Buildup Analysis Of MHF Gas Wells. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23–26 September. SPE-8279-MS. http://dx.doi.org/10.2118/8279-MS.
Akande, J. A. and Spivey, J. 2012. Considerations for Pore Volume Stress Effects in Over-pressured Shale Gas under Controlled Drawdown Well Management Strategy. Presented at the SPE Canadian Unconventional Resources Conference, Calgary, 30 October–1 November. SPE-162666-MS. http://dx.doi.org/10.2118/162666-MS.
Anderson, D. M. and Mattar, L. 2007. An Improved Pseudo-Time for Gas Reservoirs With Significant Transient Flow. J Can Pet Technol 46 (7): 49–54. PETSOC-07-07-05. http://dx.doi.org/10.2118/07-07-05.
Archer, R. A. 2008. Impact of Stress Sensitivity Permeability on Production Data Analysis. Presented at the SPE Unconventional Reservoirs Conference, Keystone, Colorado, 10–12 February. SPE-114166-MS. http://dx.doi.org/10.2118/114166-MS.
Behmanesh, H., Tabatabaie, S. H., Heidari Sureshjani, M. et al. 2014. Modification of the Transient Linear Flow Distance of Investigation Calculation for Use in Hydraulic Fracture Property Determination. Presented at the SPE Unconventional Resources Conference, The Woodlands, Texas, 1–3 April. SPE-168981-MS. http://dx.doi.org/10.2118/168981-MS.
Bello, R. O. 2009. Rate Transient Analysis in Shale Gas Reservoirs with Transient Linear Behavior. PhD dissertation, Texas A&M University, College Station, Texas.
Bin Tajul Amar, Z. H., Altunbay, M. and Barr, D. 1995. Stress Sensitivity in the Dulang Field – How It Is Related to Productivity. Presented at the SPE European Formation Damage Conference, The Hague, 15–16 May. SPE-30092-MS. http://dx.doi.org/10.2118/30092-MS.
Burnell, J. G., McNabb, A., Weir, G. J. et al. 1989. Two-Phase Boundary Layer Formation in a Semi-Infinite Porous Slab. Transport Porous Med. 4 (4): 395–420. http://dx.doi.org/10.1007/BF00165781.
Chen, Z. X. 1988. Some Invariant Solutions to Two-Phase Fluid Displacement Problems Including Capillary Effect. SPE Res Eng 3 (2): 691–700. SPE-14874-PA. http://dx.doi.org/10.2118/14874-PA.
Chen, S. and Li, H. 2008. A New Technique for Production Prediction in Stress-Sensitive Reservoirs. J Can Pet Technol 47 (3): 49–54. PETSOC-08-03-49. http://dx.doi.org/10.2118/08-03-49.
Clarkson, C. R. 2013. Production Data Analysis of Unconventional Gas Wells: Review of Theory and Best Practices. Int. J. Coal Geol. 109–110 (1 April): 101–146. http://dx.doi.org/10.1016/j.coal.2013.01.002.
Clarkson, C. R., Qanbari, F., Nobakht, M. et al. 2013. Incorporating Geomechanical and Dynamic Hydraulic-Fracture-Property Changes Into Rate-Transient Analysis: Example From the Haynesville Shale. SPE Res Eval & Eng 16 (3): 303–316. SPE-162526-PA.
Daungkaew, S., Hollaender, F. and Gringarten, A. C. 2000. Frequently Asked Questions in Well Test Analysis. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 1–4 October. SPE-63077-MS. http://dx.doi.org/10.2118/63077-MS.
Davies, J. P. and Davies, D. K. 2001. Stress-Dependent Permeability: Characterization and Modeling. SPE J. 6 (2): 224–235. SPE-71750-PA. http://dx.doi.org/10.2118/71750-PA.
El-Banbi, A. H. 1998. Analysis of Tight Gas Well Performance. PhD dissertation, Texas A&M University, College Station, Texas.
Gale, J. F., Laubach, S. E., Olson, J. E. et al. 2014. Natural Fractures in Shale: A Review and New Observations. AAPG Bull. 98 (11): 2165–2216. http://dx.doi.org/10.1306/08121413151.
Kikani, J. and Pedrosa, O. A. Jr. 1991. Perturbation Analysis of Stress-Sensitive Reservoirs. SPE Form Eval 6 (3): 379–386. SPE-20053-PA. http://dx.doi.org/10.2118/20053-PA.
Kuchuk, F. J. 2009. Radius of Investigation for Reserve Estimation from Pressure Transient Well Tests. Presented at the SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 15–18 March. SPE-120515-MS. http://dx.doi.org/10.2118/120515-MS.
Lee, W. J. and Holditch, S. A. 1982. Application of Pseudotime to Buildup Test Analysis of Low-Permeability Gas Wells With Long-Duration Wellbore Storage Distortion. J Pet Technol 34 (12): 2877–2887. SPE-9888-PA. http://dx.doi.org/10.2118/9888-PA.
Lei, Q., Xiong, W., Yuang, J. et al. 2007. Analysis of Stress Sensitivity and Its Influence on Oil Production From Tight Reservoirs. Presented at Eastern Regional Meeting, Lexington, Kentucky, 17–19 October. SPE-111148-MS. http://dx.doi.org/10.2118/111148-MS.
Lian, P. Q., Cheng, L. S. and Liu, L. F. 2011. Characteristics of Productivity Curves in Abnormal High-Pressure Reservoirs. Pet. Sci. Technol. 29 (2): 109–120. http://dx.doi.org/10.1080/10916461003681752.
Miller, R. S., Conway, M. and Salter, G. 2010. Pressure-Dependant Permeability in Shale Reservoirs Implications for Estimated Ultimate Recovery. Oral presentation given at the AAPG Hedberg Conference, Austin, Texas. 5–10 December.
Nobakht, M. and Clarkson, C. R. 2012a. A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition. SPE Res Eval & Eng 15 (3): 370–384. SPE-143989-PA. http://dx.doi.org/10.2118/143989-PA.
Nobakht, M. and Clarkson, C. R. 2012b. A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Rate Boundary Condition. SPE Res Eval & Eng 15 (1): 51–59. SPE-143990-PA. http://dx.doi.org/10.2118/143990-PA.
Nobakht, M., Clarkson, C. R. and Kaviani, D. 2012. New and Improved Methods for Performing Rate-Transient Analysis of Shale Gas Reservoirs. SPE Res Eval & Eng 15 (3): 335–350. SPE-147869-PA. http://dx.doi.org/10.2118/147869-PA.
Nur, A. and Yilmaz, O. 1985. Pore Pressure in Fronts in Fractured Rock Systems. Internal report, Department of Geophysics, Stanford University, Stanford, California.
Okouma Mangha, V., Guillot, F., Sarfare, M. et al. 2011. Estimated Ultimate Recovery (EUR) as a Function of Production Practices in the Haynesville Shale. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 30 October–2 November. SPE-147623-MS. http://dx.doi.org/10.2118/147623-MS.
Ostensen, R. W. 1986. The Effect of Stress-Dependent Permeability on Gas Production and Well Testing. SPE Form Eval 1 (3): 227–235. SPE-11220-PA. http://dx.doi.org/10.2118/11220-PA.
Ozisik, M. N. 1993. Heat Conduction, second edition. New York City: John Wiley & Sons.
Ozkan, E., Raghavan, R. S. and Apaydin, O. G. 2010. Modeling of Fluid Transfer From Shale Matrix to Fracture Network. Presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. SPE-134830-MS. http://dx.doi.org/10.2118/134830-MS.
Palacio, J. C. and Blasingame, T. A. 1993. Decline-Curve Analysis With Type Curves - Analysis of Gas Well Production Data. Presented at the Low Permeability Reservoirs Symposium, Denver, 26–28 April. SPE-25909-MS. http://dx.doi.org/10.2118/25909-MS.
Palmer, I. and Mansoori, J. 1998. How Permeability Depends on Stress and Pore Pressure in Coalbeds: A New Model. SPE Res Eval & Eng 1 (6): 539–544. SPE-52607-PA. http://dx.doi.org/10.2118/52607-PA.
Pedrosa, O. A. Jr. 1986. Pressure Transient Response in Stress-Sensitive Formation. Presented at the SPE California Regional Meeting, Oakland, California, 2–4 April. SPE-15115-MS. http://dx.doi.org/10.2118/15115-MS.
Qanbari, F. and Clarkson, C. R. 2013. Analysis of Transient Linear Flow in Tight Oil and Gas Reservoirs with Stress-Sensitive Permeability and Multi-Phase Flow. Presented at the SPE Unconventional Resources Conference Canada, Calgary, 5–7 November. SPE-167176-MS. http://dx.doi.org/10.2118/167176-MS.
Raghavan, R., Scorer, J. D. T. and Miller, F. G. 1972. An Investigation by Numerical Methods of the Effect of Pressure-Dependent Rock and Fluid Properties on Well Flow Tests. SPE J. 12 (3): 267–275. SPE-2617-PA. http://dx.doi.org/10.2118/2617-PA.
Raghavan, R. and Chin, L. Y. 2004. Productivity Changes in Reservoirs with Stress-Dependent Permeability. SPE Res Eval & Eng 7 (4): 308–315. SPE-88870-PA. http://dx.doi.org/10.2118/88870-PA.
Rosen, R., Mickelson, W., Sharf-Aldin, M. et al. 2014. Impact of Experimental Studies on Unconventional Reservoir Mechanisms. Presented at the SPE Unconventional Resources Conference, The Woodlands, Texas, 1–3 April. SPE-168965-MS. http://dx.doi.org/10.2118/168965-MS.
Settari, A. and Mourits, F. M. 1998. A Coupled Reservoir and Geomechanical Simulation System. SPE J. 3 (3): 219–226. SPE-50939-PA. http://dx.doi.org/10.2118/50939-PA.
Settari, A. T., Bachman, R. C. and Walters, D. A. 2005. How To Approximate Effects of Geomechanics in Conventional Reservoir Simulation. Presented at the SPE Annual Technical Conference and Exhibition. Dallas, 9–12 October. SPE-97155-MS. http://dx.doi.org/10.2118/97155-MS.
Settari, A. and Sen, V. 2008. Geomechanics in Integrated Reservoir Modeling. Presented at the Offshore Technology Conference, Houston, 5–8 May. OTC-19530-MS. http://dx.doi.org/10.4043/19530-MS.
Tabatabaie, S. H. 2014. Unconventional Reservoirs: Mathematical Modeling of Some Non-Linear Problems. PhD dissertation, University of Calgary, Calgary.
Tabatabaie, S. H., Mattar, L. and Pooladi-Darvish, M. 2013. Pseudotime Calculation in Low Permeability Gas Reservoirs. Presented at the SPE Unconventional Resources Conference Canada, Calgary, 5–7 November. SPE-167185-MS. http://dx.doi.org/10.2118/167185-MS.
Tabatabaie, S. H., Pooladi-Darvish, M. and Mattar, L. 2015. Draw-Down Management Leads to Better Productivity in Reservoirs with Pressure-Dependent Permeability–or Does It? Presented at the SPE/CSUR Unconventional Resources Conference, Calgary, 20–22 October. SPE-175938-MS. http://dx.doi.org/10.2118/175938-MS.
Thompson, J. M., Nobakht, M. and Anderson, D. M. 2010. Modeling Well Performance Data from Overpressured Shale Gas Reservoirs. Presented at the Canadian Unconventional Resources and International Petroleum Conference, Calgary, 19–21 October. SPE-137755-MS. http://dx.doi.org/10.2118/137755-MS.
Vairogs, J., Hearn, C. L., Dareing, D. W. et al. 1971. Effect of Rock Stress on Gas Production From Low-Permeability Reservoirs. J Pet Technol 23 (9): 1161–1167. SPE-3001-PA. http://dx.doi.org/10.2118/3001-PA.
Van Poollen, H. K. 1964. Radius-of-drainage and stabilization-time equations. Oil Gas J. 62 (37): 138–146.
Wattenbarger, R. A., El-Banbi, A. H., Villegas, M. E. et al. 1998. Production Analysis of Linear Flow into Fractured Tight Gas Wells. Presented at SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium and Exhibition, Denver, 5–8 April. SPE-39931-MS. http://dx.doi.org/10.2118/39931-MS.