Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-07-07T06:18:37.187Z Has data issue: false hasContentIssue false
  • English
  • Français

Porosity-Size Relationship of Drilling Mud Flocs: Fractal Structure

Published online by Cambridge University Press:  28 February 2024

Hening Huang
Hening Huang*
Affiliation:
Atlantic Oceanographic and Meteorological Laboratory, National Oceanic and Atmospheric Administration, 4301 Rickenbacker Causeway, Miami, Florida 33149
Get access Rights & Permissions [Opens in a new window]

Abstract

The porosities of flocs formed from a used drilling mud were determined by measuring sizes and settling speeds of individual flocs. These flocs were produced in a Couette-type flocculator under a variety of combinations of fluid shear and solid concentrations. In the calculation of floc porosities, a floc settling model was employed that can consider the effects of creeping flow through a floc on its settling speed. Results show that floc structure can be well described as a fractal with a fractal dimension of 1.53–1.64 for the floc size range tested. The effects of flocculation conditions, such as fluid shear and solid concentration, on floc porosity and structure were examined. It was found that floc porosity and fractal dimension were not influenced by solid concentration, but they increased as fluid shear decreased. Empirical expressions for the porosity of drilling mud flocs are obtained from both the floc settling model and Stokes’ law. For solid volume fraction in flocs, the relative difference between these two expressions could be as much as 38%. However, the fractal dimensions estimated based on the two settling models are nearly the same.

Keywords

Drilling mudFlocsFractalPorosity
Type
Research Article
Information
Clays and Clay Minerals , Volume 41 , Issue 3 , June 1993 , pp. 373 - 379
Copyright
Copyright © 1993, The Clay Minerals Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adler, P. M., 1981 Streamlines in and around porous particles J. Colloid and Interface Sci. 81 2 531 – 535 10.1016/0021-9797(81)90434-3.CrossRefGoogle Scholar
Alldrege, A. L. and Gotschalk, C., 1988 In situ settling behavior of marine snow Limnol. Oceanogr. 33 3 339 – 351 10.4319/lo.1988.33.3.0339.CrossRefGoogle Scholar
Bevington, P. R., 1969 Data Reduction and Error Analysis for the Physical Sciences .Google Scholar
Brinkman, H. C., 1947 A calculation of the viscosity and the sedimentation velocity for solutions of large chain molecules taking into account the hampered flow of the solvent through each chain molecule Proc. K. Ned. Akad. Wet. (Amsterdam) 50 618 – 625.Google Scholar
Brinkman, H. C., 1947 Erratum for “A calculation of the viscosity and the sedimentation velocity for solutions of large chain molecules taking into account the hampered flow of the solvent through each chain molecule” Proc. K. Ned. Akad. Wet. (Amsterdam) 50 821.Google Scholar
Burban, P.-Y. Xu, Y.-J. McNeil, J. and Lick, W., 1990 Settling speeds of flocs in fresh water and seawater J. Geophys. Res. 95 18213 – 18220 10.1029/JC095iC10p18213.CrossRefGoogle Scholar
Concha, F. and Almendra, E. R., 1979 Settling velocities of particulate system, 1. settling velocities of individual spherical particles Inter. J. Mineral Processings 349 – 367.CrossRefGoogle Scholar
Epstein, N. and Neale, G., 1974 On the sedimentation of a swarm of permeable spheres Chem. Eng. Sci. 29 1841 – 1842 10.1016/0009-2509(74)87047-8.CrossRefGoogle Scholar
Gibbs, R. J., 1985 Estuarine flocs: Their size, settling velocity, and density J. Geophys. Res. 90 3249 – 3251 10.1029/JC090iC02p03249.CrossRefGoogle Scholar
Gibbs, R. J., 1985 Settling velocity, diameter, and density for flocs of illite, kaolinite, and montmorillonite J. Sedimentary Petrology 55 1 65 – 68.Google Scholar
Glasgow, L. A. and Hsu, J.-P., 1984 Floc characteristics in water and wastewater treatment Particulate Science and Technology 2 285 – 303 10.1080/02726358408906412.CrossRefGoogle Scholar
Goodarz-Nia, I., 1977 Floc density, porosity and void ratio in colloidal systems and aerosols J. Colloid and Interface Sci. 62 1 131 – 141 10.1016/0021-9797(77)90074-1.CrossRefGoogle Scholar
Haider, A. and Levenspiel, O., 1989 Drag coefficient and terminal velocity of spherical and nonspherical particles Powder Technology 58 63 – 70 10.1016/0032-5910(89)80008-7.CrossRefGoogle Scholar
Hawley, N., 1982 Settling velocity distribution of natural aggregates J. Geophys. Res. 87 9489 – 9498 10.1029/JC087iC12p09489.CrossRefGoogle Scholar
Huang, H., 1992 Transport properties of drilling muds and Detroit River sediments Santa Barbara University of California at.Google Scholar
Kajihara, M., 1971 Settling velocity and porosity of large suspended particle J. Oceanogr. Soc. Jpn. 27 158 – 162 10.1007/BF02109135.CrossRefGoogle Scholar
Klimpel, R. C. and Hogg, R., 1986 Effects of flocculation conditions on agglomerate structure J. Colloid and Interface Sci. 113 1 121 – 131 10.1016/0021-9797(86)90212-2.CrossRefGoogle Scholar
Krone, R. B., (1963) A study of rheologie properties of estuarial sediments, Techn. Bull., 7, Committee of Tidal Hydraulics, U.S. Army Corps of Engineers WES, Vicksburg, 91 pp.Google Scholar
Lagvankar, A. L. and Gemmell, R. S., 1968 A size-density relationship for flocs J. AWWA 60 1040 – 1046 10.1002/j.1551-8833.1968.tb03641.x.CrossRefGoogle Scholar
Li, D.-H. and Ganczarczyk, J. J., 1987 Stroboscopic determination of settling velocity, size and porosity of activated sludge flocs Wat. Res. 21 3 257 – 262 10.1016/0043-1354(87)90203-X.CrossRefGoogle Scholar
Magara, Y., Nambu, S. and Utosawa, K., 1976 Biochemical and physical properties of an activated sludge on settling characteristics Wat. Res. 10 71 – 77 10.1016/0043-1354(76)90160-3.CrossRefGoogle Scholar
Masliyah, J. H. and Polikar, M., 1980 Terminal velocity of porous spheres The Canadian J. Chem. Eng. 58 299 – 302 10.1002/cjce.5450580303.CrossRefGoogle Scholar
Matsumoto, K. and Suganuma, A., 1977 Settling velocity of a permeable model floc Chem. Eng. Sci. 32 445 – 447 10.1016/0009-2509(77)85009-4.CrossRefGoogle Scholar
Matsumoto, K. and Mori, Y., 1975 Settling velocity of floc—new measurement method of floc density J. Chem. Engrs., Jpn. 8 2 143 – 147 10.1252/jcej.8.143.CrossRefGoogle Scholar
McCave, I. N., 1975 Vertical flux of particles in the ocean Deep Sea Res. 22 491 – 502.Google Scholar
Meakin, P., 1984 Effects of cluster trajectories on cluster-cluster aggregation: A comparison of linear and Brownian trajectories in two- and three-dimensional simulations Phys. Rev. A: Gen. Phys. 29 997 – 999 10.1103/PhysRevA.29.997.CrossRefGoogle Scholar
Meakin, P., 1988 Fractal aggregates Advances in Colloid Interface Sci. 28 249 – 331 10.1016/0001-8686(87)80016-7.CrossRefGoogle ScholarPubMed
Mountain, R. D., Mulholland, G. W. and Baum, H., 1986 Simulation of aerosol agglomeration in the free molecular and continuum flow regimes J. Colloid and Interface Sci. 114 67 – 81 10.1016/0021-9797(86)90241-9.CrossRefGoogle Scholar
Neale, G., Epstein, N. and Nader, W., 1973 Creeping flow relative to permeable spheres Chem. Eng. Sci. 28 1865 – 1874 10.1016/0009-2509(73)85070-5.CrossRefGoogle Scholar
Ooms, G., Mijnlieff, P. F. and Beckers, H. L., 1970 Frictional force exerted by a flowing fluid on a permeable particle, with particular reference to polymer coils J. Chem. Phys. 53 4123 – 4130 10.1063/1.1673911.CrossRefGoogle Scholar
Rogak, S. N. and Flagan, R. C., 1990 Stokes drag on self-similar clusters of spheres J. Colloid and Interface Sci. 134 1 206 – 218 10.1016/0021-9797(90)90268-S.CrossRefGoogle Scholar
Sutherland, D. N., 1966 Comment on Void’s simulation of floc formation J. Colloid and Interface Sci. 22 300 10.1016/0021-9797(66)90037-3.CrossRefGoogle Scholar
Sutherland, D. N., 1967 A theoretical model of floc structure J. Colloid and Interface Sci. 25 373 – 380 10.1016/0021-9797(67)90043-4.CrossRefGoogle Scholar
Sutherland, D. N. and Tan, C. T., 1970 Sedimentation of a porous sphere Chem. Eng. Sci. 25 1948 – 1950 10.1016/0009-2509(70)87013-0.CrossRefGoogle Scholar
Tambo, N. and Watanabe, Y., 1979 Physical characteristics of flocs, I, The floc density function and aluminum floc Wat. Res. 13 409 – 419 10.1016/0043-1354(79)90033-2.CrossRefGoogle Scholar
Tsai, C. H., Iacobellis, S. and Lick, W., 1987 Flocculation of fine-grained lake sediments due to a uniform fluid shear stress J. Great Lakes Res. 13 2 135 – 146 10.1016/S0380-1330(87)71637-2.CrossRefGoogle Scholar
Tsao, H.-K. and Hsu, J.-P., 1989 Simulation of floc breakage in a batch-stirred tank J. Colloid and Interface Sci. 132 2 313 – 318 10.1016/0021-9797(89)90246-4.CrossRefGoogle Scholar
Void, M. J., 1963 Computer simulation of floc formation in a colloidal suspension J. Colloid Sci. 18 684 – 695 10.1016/0095-8522(63)90061-8.Google Scholar
Weitz, D. A. and Oliveria, M., 1984 Fractal structures formed by kinetic aggregation of aqueous gold colloids Physical Review Letters 52 1433 – 1436 10.1103/PhysRevLett.52.1433.CrossRefGoogle Scholar
Yusa, M., 1977 Mechanisms of pelleting flocculation Inter. J. Mineral Processing 4 293 – 305 10.1016/0301-7516(77)90010-2.CrossRefGoogle Scholar