New Propped-Fracture-Conductivity Models for Tight Gas Sands
- Obadare O. Awoleke (University of Alaska, Fairbanks) | Ding Zhu (Texas A&M University) | A. D. Hill (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2016
- Document Type
- Journal Paper
- 1,508 - 1,517
- 2016.Society of Petroleum Engineers
- dimensional analysis, regression, fracture conductivity model , fractional factorial design
- 2 in the last 30 days
- 630 since 2007
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In this work, we developed two models of fracture conductivity in the presence of proppant-pack damage. The models are derived from the analysis of experiments relating dynamic fracture conductivity to flowback rate, reservoir temperature, polymer loading, presence of breaker, closure stress, and proppant concentration.
The first model is purely empirical, and it is modeled after fracture-conductivity studies conducted in previous work. The experimental design and planning table were derived from fractional-factorial designs. This meant that we could uniquely quantify the effect of all the dependent variables and also ensure that the factors are not correlated. We tested the empirical model for adequacy--that is, ensuring the model residuals are normally distributed with no obvious trend and approximately constant variance. Because empirical models are generally constrained by the data on which they are built, we developed a semiempirical model dependent on dimensional analysis and nonlinear regression. Dimensionless products from the dimensional analysis procedure form the backbone of this semiempirical model.
We used subset-regression analysis to determine the optimal regression model and found that model was adequate. We also found two dimensionless groups and used them to develop the semiempirical model. We thereafter corrected the semiempirical model for the effect of temperature. Both the purely empirical model and the semiempirical model match experimental data with reasonable accuracy.
These models can be used as a first approximation for the short-term fracture conductivity of field hydraulic fractures. We also present methodology by which engineers can develop empirical models, assess uncertainty, and test for regression-model adequacy given noisy data.
|File Size||1 MB||Number of Pages||10|
Awoleke, O. O. 2013. Dynamic Fracture Conductivity—An Experimental Investigation Based on Factorial Analysis. PhD dissertation, Texas A&M University, College Station, Texas (May 2013).
Awoleke, O. O., Romero, J., Zhu, D. et al. 2012. Experimental Investigation of Propped Fracture Conductivity in Tight Gas Reservoirs Using Factorial Design. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 6–8 February. SPE-151963-MS. http://dx.doi.org/10.2118/151963-MS.
Berg, R. R. 1970. Method for Determining Permeability from Reservoir Rock Properties. Gulf Cost Association of Geological Societies Transactions 20: 303–317.
Birkhoff, G. 1950. Hydrodynamics: A Study in Logic, Fact and Similitude. New York City: Dover Publications.
Buckingham, E. 1914. On Physically Similar Systems; Illustrations of the Use of Dimensional Equations. Phys. Rev. 4 (4): 345–376. http://dx.doi.org/10.1103/PhysRev.4.345.
Cooke, C. E. Jr. 1973. Conductivity of Fracture Proppants in Multiple Layers. J Pet Technol 25 (9): 1101–1107. SPE-4117-PA. http://dx.doi.org/10.2118/4117-PA.
Cooke, C. E. Jr. 1975. Effect of Fracturing Fluids on Fracture Conductivity. J Pet Technol 27 (10): 1273–1282. SPE-5114-PA. http://dx.doi.org/10.2118/5114-PA.
Fredd, C. N., McConnell, S. B., Boney, C. L. et al. 2001. Experimental Study of Fracture Conductivity for Water-Fracturing and Conventional Fracturing Applications. SPE J. 6 (3): 288–298. SPE-74138-PA. http://dx.doi.org/10.2118/74138-PA.
Howard, P. 2012. Lecture Notes on Mathematical Modeling. Class Notes, Texas A&M University, College Station, Texas.
Lacy, L. L., Rickards, K. R. and Bilden, D. M. 1998. Fracture Width and Embedment Testing in Soft Reservoir Sandstone. SPE Drill & Compl 13 (1): 25–29. SPE-36421-PA. http://dx.doi.org/10.2118/36421-PA.
Li, K., Gao, Y., Lyu, Y. et al. 2015. New Mathematical Models for Calculating Proppant Embedment and Fracture Conductivity. SPE J. 20 (3): 496–507. SPE-155954-PA. http://dx.doi.org/10.2118/155954-PA.
Marpaung, F., Chen, F., Pongthunya, P. et al. 2008. Measurement of Gel Cleanup in a Propped Fracture With Dynamic Fracture Conductivity Experiments. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 21–24 September. SPE-115653-MS. http://dx.doi.org/10.2118/115653-MS.
McDaniel, B. W. 1986. Conductivity Testing of Proppants at High Temperature and Stress. Presented at the SPE California Regional Meeting, Oakland, California, 2–4 April. SPE-15067-MS. http://dx.doi.org/10.2118/15067-MS.
McDaniel, B. W. 1987. Realistic Fracture Conductivities of Proppants as a Function of Reservoir Temperature. Presented at the Low Permeability Reservoirs Symposium, Denver, 18–19 May. SPE-16453-MS. http://dx.doi.org/10.2118/16453-MS.
Much, M. G. and Penny, G. S. 1987. Long-Term Performance of Proppants Under Simulated Reservoir Conditions. Presented at the Low Permeability Reservoirs Symposium, Denver, 18–19 May. SPE-16415-MS. http://dx.doi.org/10.2118/16415-MS.
Palmer, A. C. 2008. Dimensional Analysis and Intelligent Experimentation. Singapore: World Scientific.
Penny, G. S. 1987. An Evaluation of the Effects of Environmental Conditions and Fracturing Fluids Upon the Long-Term Conductivity of Proppants. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 27–30 September. SPE-16900-MS. http://dx.doi.org/10.2118/16900-MS.
R Core Team. 2015. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
Van der Vlis, A. C., Haafkens, R., Schipper, B. A. et al. 1975. Criteria for Proppant Placement and Fracture Conductivity. Presented at Fall Meeting of Society of Petroleum Engineers of AIME, Dallas, 28 September–1 October. SPE-5637-MS. http://dx.doi.org/10.2118/5637-MS.
Volk, L. J, Raible C. J., Carroll, H. B. et al. 1981. Embedment Of High Strength Proppant Into Low-Permeability Reservoir Rock. Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, 27–29 May. SPE-9867-MS. http://dx.doi.org/10.2118/9867-MS.
Zhang, J. 2014. Creation and Impairment of Hydraulic Fracture Conductivity in Shale Formations. PhD dissertation, Texas A&M University, College Station, Texas (August 2014).