Modification of the Kozeny-Carman Equation To Quantify Formation Damage by Fines in Clean, Unconsolidated Porous Media
- Eva D. Krauss (University of Colorado Denver) | David C. Mays (University of Colorado Denver)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- November 2014
- Document Type
- Journal Paper
- 466 - 472
- 2014.Society of Petroleum Engineers
- 1.2.3 Rock properties, 2.4.3 Sand/Solids Control, 1.8 Formation Damage, 5.3.4 Integration of geomechanics in models
- permeability, fines, Kozeny-Carman, formation damage
- 2 in the last 30 days
- 553 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Estimating formation permeability as a function of porosity, grain size, and the quantity and structure of fines is important in reservoir engineering. One can use the Kozeny-Carman equation to estimate the permeability of clean, unconsolidated media as a function of porosity and grain size, but it does not account for the quantity and structure of deposited fines. This study shows how incorporating of the volume of fines and a dimensionless bulk factor into the Kozeny-Carman equation can be used to model how the quantity and structure of deposited fines control permeability. Several experimental studies from the literature are analyzed, representing a range of fines (type and diameter), porous media, fluids, and Darcy velocity. These studies indicate that, when other variables are held constant, experiments conducted at a higher Darcy velocity result in less plugging. For each experiment, a dimensionless bulk factor in the Kozeny-Carman equation was fitted, with use of the root-mean-square method, to best match the experimental data. Fitted values of the bulk factor were then correlated with the Péclet number to investigate how the structure of fines, quantified by the bulk factor, depends on the characteristics of the porous media, the depositing colloids, and the Darcy velocity. Larger bulk factors are observed at a lower Péclet number, when diffusive transport dominates, which could result from more-dendritic deposits. Smaller bulk factors are observed at higher Péclet numbers, when advective transport dominates, which could result from deposits that are more compact. By understanding how the bulk factor, and, therefore, the extent of permeability reduction, depends on the Péclet number, one can optimize pumping schemes. The primary application of this work is to optimize well-pumping rates to prevent or manage plugging that results from the deposition of fines in initially clean, unconsolidated porous media, including both geologic formations and gravelpacks used for sand control.
|File Size||440 KB||Number of Pages||7|
Acharya, R.C., van der Zee, S.E.A.T.M., and Leijnse, A. 2004. Porosity-Permeability Properties Generated With a New 2-Parameter 3D Hydraulic Pore-Network Model for Consolidated and Unconsolidated Porous Media. Adv. Water Resour. 27: 707–723. http://dx.doi.org/10.1016/j.advwatres.2004.05.002.
Armstrong, R. and Ajo-Franklin, J. 2011. Investigating Biomineralization Using Synchrotron Based X-ray Computed Microtomography. Geophys. Res. Lett. 38: L08406. http://dx.doi.org/10.1029/2011GL046916.
Babadagli, T. and Al-Salmi, S. 2004. A Review of Permeability-Prediction Methods for Carbonate Reservoirs Using Well-Log Data. SPE Res. Eval. Eng. 7 (2): 75–88. SPE-87824-PA. http://dx.doi.org/10.2118/87824-PA.
Beard, D.C. and Weyl, P.K. 1973. Influence of Texture on Porosity and Permeability of Unconsolidated Sand. AAPG Bull. 57 (2): 349–369. http://dx.doi.org/10.1306/819A4272-16C5-11D7-8645000102C1865D.
Berg, R.R. 1970. Method for Determining Permeability From Reservoir Rock Properties. Gulf Coast Assoc. Geol. Soc. T. 20: 303–317.
Boller, M.A. and Kavanaugh, M.C. 1995. Particle Characteristics and Head Loss Increase in Granular Media Filtration. Water Res. 29 (4): 1139–1149. http://dx.doi.org/10.1016/0043-1354(94)00256-7.
Carlson, J., Gurley, D., King, G. et al. 1992. Sand Control: Why and How? Oilfield Rev. 4 (4): 41–53.
Carman, P.C. 1997. Fluid Flow Through Granular Beds. Chemical Engineering Research & Design 75: S32–S48. http://dx.doi.org/10.1016/S0263-8762(97)80003-2.
Chang, J.W. 1985. Mathematical Modeling of Deep Bed Filtration: Microscopic Approach. MS thesis EV-85-3, Asian Institute of Technology, Bangkok, Thailand.
Chen, C., Packman, A.I., and Gaillard, J.F. 2008. Pore-Scale Analysis of Permeability Reduction Resulting From Colloid Deposition. Geophys. Res. Lett. 35: L07404. http://dx.doi.org/10.1029/2007GL033077.
Civan, F. 2000. Reservoir Formation Damage-Fundamentals, Modeling, Assessment, and Mitigation. Houston, Texas: Gulf Publishing Company.
Clavaud, J.-B. 2008. Intrinsic Electrical Anisotropy of Shale: The Effect of Compaction. Petrophysics. 49 (3): 243–260.
Fitts, C.R. 2002. Groundwater Science. San Diego, California: Academic Press.
Hurtado, N., Aldana, M., and Torres, J. 2009. Comparison Between Neuro-Fuzzy and Fractal Models for Permeability Prediction. Computat. Geosci. 13 (2): 181–186. http://dx.doi.org/10.1007/s10596-008-9095-9.
Kim, Y.S. and Whittle, A.J. 2006. Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging. Transport Porous Med. 65 (1): 53–87. http://dx.doi.org/10.1007/s11242-005-6087-2.
Kozeny, J. 1927. Über Kapillare Leitung des Wassers im Boden. Sitzungsber Akad. Wiss., Wien 136 (2a): 271–306.
Krauss, E.D. 2012. Modification of the Kozeny-Carman Equation to Quantify Formation Damage by Fines in Clean Unconsolidated Porous Media, MS thesis, Department of Civil Engineering, University of Colorado Denver, Denver, Colorado.
Liu, X. and Civan, F. 1996. Formation Damage and Filter Cake Buildup in Laboratory Core Tests: Modeling and Model-Assisted Analysis. SPE Form Eval 11 (1): 26–30. SPE-25215-PA. http://dx.doi.org/10.2118/25215-PA.
Maini, B., Wassmuth, F., and Schramm, L.L. 1996. Fines Migration in Petroleum Reservoirs. In Suspensions: Fundamentals and Applications in the Petroleum Industry, ed. L.L. Schramm, 321–375. Washington, DC: American Chemical Society.
Manga, M., Beresnev, I., Brodsky, E.E. et al. 2012. Changes in Permeability by Transient Stresses: Field Observations, Experiments, and Mechanisms. Rev. Geophys. 50: RG2004. http://dx.doi.org/10.1029/2011RG000382.
Marandi, G.B., Mahdavinia, G.R., and Ghafary, S. 2011. Collagen-g-poly(Sodium Acrylate-co-Acrylamide)/Sodium Montmorillonite Superabsorbent Nanocomposites: Synthesis and Swelling Behavior. J. Polymer Res. 18 (6): 1487–1499. http://dx.doi.org/10.1007/s10965-010-9554-6.
Mays, D.C. 2005. Hydrodynamics of Particle Clogging in Saturated Granular Media: Analysis and Experiments, PhD thesis, Department of Civil and Environmental Engineering, University of California Berkeley, Berkeley, California.
Mays, D.C. 2010. Contrasting Clogging in Granular Media Filters, Soils, and Dead-End Membranes. J. Environ. Eng-ASCE 136 (5): 475–480. http://10.1061/(ASCE)EE.1943-7870.0000173.
Mays, D.C., Cannon, O.T., Kanold, A.W. et al. 2011. Static Light Scattering Resolves Colloid Structure in Index-Matched Porous Media, J. Colloid Interf. Sci. 363 (1): 418–424. http://dx.doi.org/10.1016/j.jcis.2011.06.046.
Mays, D.C. and Hunt, J.R. 2005. Hydrodynamic Aspects of Particle Plugging in Porous Media. Environ. Sic. Technol. 39 (2): 577–584. http://dx.doi.org/10.1021/es049367k.
Mays, D.C. and Hunt, J.R. 2007. Hydrodynamic and Chemical Factors in Clogging by Montmorillonite in Porous Media. Environ. Sci. Technol. 41 (16): 5666–5671. http://dx.doi.org/10.1021/es062009s.
Mohan, K.K., Vaidya, R.N., Reed, M.G. et al. 1993. Water Sensitivity of Sandstones Containing Swelling and Non-Swelling Clays Colloid. Surface A 73: 237–254. http://dx.doi.org/10.1016/0927-7757(93)80019-B.
Muecke, T.W. 1978. Formation Fines and Factors Controlling Their Movement in Porous Media. Presented at the SPE Symposium on Formation Damage Control, Lafayette, Louisiana, 15–16 February. SPE-7007-MS. http://dx.doi.org/10.2118/7007-MS.
Naar, J., Wygal, R.J., and Henderson, J.H. 1962. Imbibition Relative Permeability in Unconsolidated Porous Media. SPE J. 2 (1): 13–17. SPE-213-PA. http://dx.doi.org/10.2118/213-PA.
Narayan, R., Coury, J.R., Masliyah, J.H. et al. 1997. Particle Capture and Plugging in Packed-Bed Reactors. Ind. Eng. Chem. Res. 36 (11): 4620–4627. http://dx.doi.org/10.1021/ie970101e.
Nelson, P.H. 1994. Permeability-Porosity Relationships in Sedimentary Rocks. The Log Analyst 35 (3): 36–62.
Nooruddin, H.A. and Hossain, M.E. 2011. Modified Kozeny-Carman Correlation for Enhanced Hydraulic Flow Unit Characterization. J. Petrol. Sci. Eng. 80: 107–115.
Ojha, C.S.P. and Graham, J.D. 1992. Appropriate Use of Deep-Bed Filtration Models. J. Environ. Eng. 118 (6): 964–980. http://dx.doi.org/10.1061/(ASCE)0733-9372(1992)118:6(964).
O’Melia, C.R. and Ali, W. 1978. The Role of Retained Particles in Deep Bed Filtration. Prog. Water Res. 10 (5–6): 167–182.
Panda, M.N. and Lake, L.W. 1995. A Physical Model of Cementation and Its Effects on Single-Phase Permeability. AAPG Bull. 79 (3): 431–443. http://dx.doi.org/10.1306/8D2B1552-171E-11D7-8645000102C1865D.
Perera, Y.A.P. 1982. Comparison of Performance of Radial and Upflow Filters, MS thesis EV-82-10, Asian Institute of Technology, Bangkok, Thailand.
Poesio, P. and Ooms, G. 2004. Formation and Ultrasonic Removal of Fouling Particle Structures in a Natural Porous Material. J. Petrol. Sci. Eng. 45 (3): 159–178. http://dx.doi.org/10.1016/j.petrol.2004.07.008.
Quirk, J.P. 1994. Interparticle Forces: A Basis for the Interpretation of Soil Physical Behavior. Adv. Agronomy 53: 121–183.
Schlumberger. 2013. Oilfield Glossary, http://www.glossary.oilfield.slb.com/ (accessed 16 October 2013).
Sen, T.K., Mahajan, S.P., and Khilar, K.C. 2002. Colloid-Associated Contaminant Transport in Porous Media: 1. Experimental Studies. AIChE J. 48 (10): 2366–2374. http://dx.doi.org/10.1002/aic.690481026.
Tindall, J.A. and Kunkel, J.R. 1999. Unsaturated Zone Hydrology for Scientists and Engineers. Upper Saddle River, New Jersey: Prentice Hall.
Tobiason, J.E. and Vigneswaran, B. 1994. Evaluation of a Modified Model for Deep Bed Filtration. Water Res. 28 (2): 335–342. http://dx.doi.org/10.1016/0043-1354(94)90271-2.
Udegbunam, E. and Amaefule, J.O. 1998. An Improved Technique for Modeling Initial Reservoir Hydrocarbon Saturation Distributions: Applications in Illinois (USA) Aux Vases Oil Reservoirs. J. Petrol. Sci. Eng. 21 (3): 143–152. http://dx.doi.org/10.1016/S0920-4105(98)00075-8.
Veerapaneni, S. and Wiesner, M.R. 1997. Deposit Morphology and Head Loss Development in Porous Media. Environ. Sci. Technol. 31 (10): 2738–2744. http://dx.doi.org/10.1021/es960979h.
Vernik, L. 2000. Permeability Prediction in Poorly Consolidated Siliciclastics Based On Porosity and Clay Volume Logs. Petrophysics 41 (2): 138–147.
Vigneswaran, S. and Chang, J.S. 1989. Experimental Testing of Mathematical Models Describing the Entire Cycle of Filtration. Water Res. 23 (11): 1413–1421. http://dx.doi.org/10.1016/0043-1354(89)90081-X.
Wiesner, M.R. 1999. Morphology of Particle Deposits. J. Environ. Eng. 125 (12): 1124–1132. http://dx.doi.org/10.1061/(ASCE)0733-9372(1999)125:12(1124).
Wu, T. and Berg, R.R. 2003. Relationship of Reservoir Properties for Shaly Sandstones Based on Effective Porosity. Petrophysics 44 (5): 328–341.
Zamani, A. and Maini, B. 2009. Flow of Dispersed Particles Through Porous Media—Deep Bed Filtration. J. Petrol. Sci. Eng. 69 (1): 71–88. http://dx.doi.org/10.1016/j.petrol.2009.06.016.
Zeinijahromi, A., Lemon, P., and Bedrikovetsky, P. 2011. Effects of Induced Fines Migration on Water Cut During Waterflooding. J. Petrol. Sci. Eng. 78 (3): 609–617. http://dx.doi.org/10.1016/j.petrol.2011.08.005.