Research Papers: Petroleum Wells-Drilling/Production/Construction

Analytical Modeling of Non-Darcy Flow-Induced Conductivity Damage in Propped Hydraulic Fractures

[+] Author and Article Information
M. K. Rahman

Baker Hughes,
Perth, Australia
e-mail: khalil.rahman@bakerhughes.com

M. M. Salim

Kuala Lumpur, Malaysia
e-mail: msalim6@slb.com

M. M. Rahman

The Petroleum Institute,
Abu Dhabi, UAE
e-mail: mrahman@pi.ac.ae

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the Journal of Energy Resources Technology. Manuscript received May 14, 2011; final manuscript received June 6, 2012; published online October 29, 2012. Assoc. Editor: Desheng Zhou.

J. Energy Resour. Technol 134(4), 043101 (Oct 29, 2012) (8 pages) doi:10.1115/1.4007658 History: Received May 14, 2011; Revised June 06, 2012

This paper presents a simple analytical method to model the non-Darcy flow effect on the production performance of hydraulically fractured wells by modifying the fracture conductivity. The method is suitable to conveniently incorporate the non-Darcy flow effect in a production prediction model usually used for fracture treatment design and optimization. The method is validated against published information of field productivity and production prediction by other complex methods. The method is then used to demonstrate that the non-Darcy effect is one of the major sources for the loss of fracture conductivity, even at a low flow rate well, and hence the source for discrepancy between the predicted and actual productivities. Finally, the implication of neglecting the non-Darcy effect in fracture treatment optimization is also investigated, emphasizing the need to incorporate this effect even for low flow rate wells.

Copyright © 2012 by ASME
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Rahman, M. M., Rahman, M. K., and Rahman, S. S., 2001, “An Integrated Model for Multiobjective Design Optimization of Hydraulic Fracturing,” J. Pet. Sci. Eng., 31, pp. 41–62. [CrossRef]
Vincent, M. C., Pearson, C. M., and Kullman, J., 1999, “Non-Darcy and Multiphase Flow in Propped Fractures: Case Studies Illustrate the Dramatic Effect on Well Productivity,” SPE Western Regional Meeting, Alaska, May 26–28, SPE Paper No. 54630-MS. [CrossRef]
Vincent, M. C., 2002, “Proving It—A Review of 80 Published Field Studies Demonstrating the Importance of Increased Fracture Conductivity,” SPE Annual Technical Conference and Exhibition, Sept. 29–Oct. 2, SPE Paper No. 77675-MS. [CrossRef]
Handren, P., Pearson, C. M., Kullman, J., Coleman, R. J., Foreman, J., Froebel, K., and Caron, J., 2001, “The Impact of Non-Darcy Flow on Production From Hydraulically Fractured Gas Wells,” SPE Production and Operations Symposium, Oklahoma, Mar. 25–28, SPE Paper No. 67299-MS. [CrossRef]
Holditch, S. A., and Morse, R. A., 1976, “The Effect of Non-Darcy Flow on the Behaviour of Hydraulically Fractured Gas Wells,” J. Pet. Technol., 28, pp. 1169–1179. [CrossRef]
Agarwal, R. G., Gardner, D. C., Kleinsteiber, S. W., and Fussel, D. D., 1998, “Analyzing Well Production Data Using Combined Type Curve and Decline Curve Analysis Concepts,” SPE Annual Technical Conference and Exhibition, Louisiana, Sept. 27–30, SPE Paper No. 49222-MS. [CrossRef]
Umnuayponwiwat, S., Ozkan, E., Pearson, C. M., and Vincent, M., 2000, “Effect of Non-Darcy Flow on the Interpretation of Transient Pressure Responses of Hydraulically Fractured Wells,” SPE Annual Technical Conference and Exhibition, Texas, Oct. 1–4, SPE Paper No. 63176-MS. [CrossRef]
Gil, J. A., Ozkan, E., and Raghavan, R., 2003, “Fractured Well-Test Design and Analysis in the Presence of Non-Darcy Flow,” SPE Res. Eval. Eng., 6(3), pp. 185–196. [CrossRef]
Friedel, T., and Voight, H., 2006, “Investigation of Non-Darcy Flow in Tight-Gas Reservoirs With Fractured Wells,” J. Pet. Sci. Eng., 54(3–4), pp. 112–128. [CrossRef]
Lopez-Hernandez, H. D., Valko, P., and Pham, T. T., 2004, “Optimum Fracture Treatment Design Minimizes the Impact of Non-Darcy Flow Effects,” SPE Annual Technical Conference and Exhibition, Texas, Sept. 26–29, SPE Paper No. 90195-MS. [CrossRef]
Miskimins, J. L., Lopez-Hernandez, H. D., and Barree, R. D., 2005, “Non-Darcy Flow in Hydraulic Fractures: Does It Really Matter?,” SPE Annual Technical Conference and Exhibition, Texas, Oct. 9–12, SPE Paper No. 96389-MS. [CrossRef]
Evans, R. D., and Carroll, H. B., Jr., 1981, “Modeling of Hydraulically Fractured Gas Wells Completed in Noncontinuous Lenticular Formations,” ASME J. Energy Resour. Technol., 103, pp. 153–158. [CrossRef]
Rubin, M. B., 1983, “A Quantitative Evaluation of Two Classical Approximations Used to Predict the Extent of Vertical Hydraulic Fractures,” ASME J. Energy Resour. Technol., 105, pp. 512–527. [CrossRef]
Palmer, I. D., and Luiskutty, C. T., 1986, “Comparison of Hydraulic Fracture Models for Highly Elongated Fractures of Variable Height,” ASME J. Energy Resour. Technol., 108, pp. 107–115. [CrossRef]
Lee, T. S., Advani, S. H., and Lee, J. K., 1990, “Three-Dimensional Modeling of Hydraulic Fractures in Layered Media: Part II—Calibrations, Parametric Sensitivity and Field Simulations,” ASME J. Energy Resour. Technol., 112, pp. 10–19. [CrossRef]
Valko, P., and Economides, M. J., 1995, Hydraulic Fracture Mechanics, John Wiley & Sons, Chichester, England.
Ishida, T., Chen, Q., Mizuta, Y., and Roegiers, J., 2004, “Influence of Fluid Viscosity on the Hydraulic Fracturing Mechanism,” ASME J. Energy Resour. Technol., 126, pp. 190–200. [CrossRef]
Cinco-Ley, H., and Samaniego-V., F., 1981, “Transient Pressure Analysis for Fractured Wells,” J. Pet. Technol., 33, pp. 1746–1766. [CrossRef]
Valko, P., Oligney, R. E., and Economides, M. J., 1997, “High Permeability Fracturing of Gas Wells,” Gas TIPS (Fall), 3, pp. 31–40.
Rahman, M. K., Rahman, M. M., and Joarder, A. H., 2007, “Analytical Production Modeling for Hydraulically Fractured Gas Reservoirs,” Pet. Sci. Technol., 25(5–6), pp. 683–704. [CrossRef]
Geertsma, J., 1974, “Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media,” Soc. Pet. Eng. J., 14, pp. 445–450. [CrossRef]
Dranchuk, P. M., and Abou-Kassem, J. H., 1975, “Calculation of Z-Factors for Natural Gases Using Equations of State,” J. Can. Pet. Technol., 14, pp. 34–36. [CrossRef]
Londono, F. E., Archer, R. A., and Blasingame, T. A., 2005, “Correlations for Hydrocarbon-Gas Viscosity and Gas Density—Validation and Correlation of Behaviour Using a Large-Scale Database,” SPE Res. Eval. Eng., 8, pp. 561–572. [CrossRef]
Penny, G. S., and Jin, L., 1995, “The Development of Laboratory Correlations Showing the Impact of Multiphase Flow, Fluid and Proppant Selection Upon Gas Well Productivity,” SPE Technical Conference and Exhibition, Dallas, Oct. 22–25, SPE Paper No. 30494-MS. [CrossRef]
Flowers, J. R., Hupp, M. T., and Ryan, J. D., 2003, “The Results of Increased Fracture Conductivity on Well Performance in a Mature East Texas Gas Fields,” SPE Annual Technical Conference and Exhibition, Colorado, Oct. 5–8, SPE Paper No. 84307-MS. [CrossRef]


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Fig. 1

Flow chart of proposed analytical model

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Fig. 4

Effect of increasing fracture conductivity on non-Darcy affected dimensionless fracture conductivity

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Fig. 3

Validation of the proposed model with Handren et al. [4] for (a) RCS 20/40 and (b) LWC 20/40 proppants

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Fig. 2

Convergence test of the proposed method for non-Darcy flow effect calculation

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Fig. 5

Effect of dimensionless fracture conductivity on Darcy and non-Darcy flow rates

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Fig. 6

Darcy and non-Darcy IPR curves for a hydraulically fractured reservoir

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Fig. 7

Effect of reservoir permeability on Darcy and non-Darcy flow rates through a fracture

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Fig. 8

Effect of fracture half-length on Darcy and non-Darcy flow rates in (a) moderately tight reservoirs and (b) extremely tight reservoirs

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Fig. 9

Effect of fracture half-length on Darcy and non-Darcy flow rates in relatively high permeability reservoirs

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Fig. 10

Comparison of cumulative productions from treatments optimized with Darcy and non-Darcy flow models




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