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Foam Transport in Porous Media – a Review

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Foam Transport in Porous Media – a Review PNNL-18918 Prepared for the U.S. Department of Energy Under Contract DE-AC05-76RL01830 Foam Transport in Porous Media – A Review ZF Zhang VL Freedman L Zhong November 2009 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor Battelle Memorial Institute, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORY operated by BATTELLE for the UNITED STATES DEPARTMENT OF ENERGY under Contract DE-AC05-76RL01830 Printed in the United States of America Available to DOE and DOE contractors from the Office of Scientific and Technical Information, P.O. Box 62, Oak Ridge, TN 37831-0062; ph: (865) 576-8401 fax: (865) 576-5728 email: [email protected] Available to the public from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Rd., Springfield, VA 22161 ph: (800) 553-6847 fax: (703) 605-6900 email: [email protected] online ordering: http://www.ntis.gov/ordering.htm PNNL-18918 Foam Transport in Porous Media – A Review ZF Zhang VL Freedman L Zhong November 2009 Prepared for the U.S. Department of Energy under Contract DE-AC05-76RL01830 Pacific Northwest National Laboratory Richland, Washington 99352 Executive Summary Amendment solutions with or without surfactants have been used to remove contaminants from soil. However, they have drawbacks in that amendment solutions often mobilize the plume, and its movement is controlled by gravity and preferential flow paths. Foam is an emulsion-like, two-phase system in which gas cells are dispersed in a liquid and separated by thin liquid films called lamellae. The potential advantages of using foams in sub-surface remediation include providing better control on the volume of fluids injected, uniformity of contact, and the ability to contain the migration of contaminant-laden liquids. It is expected that foam can serve as a carrier of amendments for vadose zone remediation, e.g., at the Hanford Site. As part of the U.S. Department of Energy’s EM-20 program, a numerical simulation capability will be added to the Subsurface Transport Over Multiple Phases (STOMP) flow simulator. The primary purpose of this document is to review the modeling approaches of foam transport in porous media. However, as an aid to understanding the simulation approaches, some experiments under unsaturated conditions and the processes of foam transport are also reviewed. Foam may be formed when the surfactant concentration is above the critical micelle concentration. There are two main types of foams –ball foam (microfoam) and polyhedral foam. The characteristics of bulk foam are described by properties such as foam quality, texture, stability, density, surface tension, disjoining pressure, etc. Foam has been used to flush contaminants such as metals, organics, and nonaqueous phase liquids from unsaturated soil. Ball foam, or colloidal gas aphrons, reportedly have been used for soil flushing in contaminated site remediation and was found to be more efficient than surfactant solutions on the basis of weight of contaminant removed per gram of surfactant. Experiments also indicate that the polyhedral foam can be used to enhance soil remediation. The transport of foam in porous media is complicated in that the number of lamellae present governs flow characteristics such as viscosity, relative permeability, fluid distribution, and interactions between fluids. Hence, foam is a non-Newtonian fluid. During transport, foam destruction and formation occur. The net result of the two processes determines the foam texture (i.e., bubble density). Some of the foam may be trapped during transport. According to the impacts of the aqueous and gas flow rates, foam flow generally has two regimes – weak and strong foam. There is also a minimum pressure gradient to initiate foam flow and a critical capillary for foam to be sustained. Similar to other fluids, the transport of foam is described by Darcy’s law with the exception that the foam viscosity is variable. Three major approaches to modeling foam transport in porous media are the empirical, semi-empirical, and mechanistic methods. Mechanistic approaches can be complete in principle but may be difficult for obtaining reliable parameters, whereas empirical and semi-empirical approaches can be limited by the detail used to describe foam rheology and mobility. Mechanistic approaches include the bubble population-balance model, the network/percolation theory, the catastrophe theory, and the filtration theory. All these methods were developed for modeling polyhedral foam, with the exception that the filtration theory method was developed for modeling ball foam (microfoam). iii Acknowledgments Funding for this work was provided by the U.S. Department of Energy’s EM-22 project managed by Dawn M. Wellman and EM-20 project managed by Mark D. Freshley. v Acronyms and Abbreviations ATF automatic transmission fluid CBF common black films CGA colloidal gas aphrons CMC critical micelle concentration DNAPL dense non-aqueous phase liquid MRF mobility reduction factor NBF Newton black films NAPL non-aqueous phase liquid PCP Pentachlorophenol TCE Trichloroethylene vii Symbols Roman Letters: aL Langmuir constant a,b, c constants As intermediate variable B backbone fraction in the percolation model C surfactant concentration Cm mean curvature of a lamella 0 Cs, Cs aqueous concentration of surfactant cg,cc constants for foam generation and coalesce cf constant db, dp particle diameter dg diameter of the spherical grain of filter media (collector) dt tube diameter D a constant or dispersion coefficient Dw diffusivity of water es, eo, ev exponents E a constant f foam quality, (-) f* a specific foam quality that divides the high and low foam quality fb fraction of bonds in the percolation theory 0 fb fraction of bonds without surfactant c fb percolation threshold fc, fk, and fp functions fsn fraction of throat blocked fw fractional flow of water ’ fw slope of the fw vs. Sw curve F percolation fraction g gravity constant G conductivity in the percolation model Gp pressure gradient min Gp minimum pressure gradient to keep foam moving h film thickness H the Hamaker constant, usually assumed to be 10-20 J k permeability ka pseudo first-order rate coefficient for attachment kb the Boltzmann constant kr relative permeability krf relative permeability of foam krg relative permeability of gas without foam krw relative permeability of the aqueous phase krnw relative permeability of the nonaqueous phase k1 generation rate constant k-1 coalescence rate constant ix 0 k-1 scaling constant K effective hydraulic conductivity l the length of a single pore Ls length of liquid slugs between the bubbles LBD dimensionless bubble length Lb average cluster length ml mass of liquid in foam nf bubble density or foam texture max nf maximum bubble density or foam texture nff flowing foam bubble density nft trapped foam bubble density n average number of pores in a gas channel blocked by a single pore throat nL number of lamellae per unit length NR, Npe, NG, dimensionless numbers NLo Ns dimensionless bubble group Nc capillary number P pressure Pc capillary pressure cr Pc the critical capillary pressure rup rup Pc rupture capillary pressure corresponding to Pd Pd disjoining pressure el Pd disjoining pressure due to electrostatic repulsion vw Pd disjoining pressure van der Waals attraction sh Pd disjoining pressure steric/hydration forces max Pd maximum disjoining pressure rup Pd the disjoining pressure at which the film ruptures q Darcy velocity/flux qg gas Darcy velocity/flux qw aqueous Darcy velocity/flux qf foam Darcy velocity/flux qw nonaqueous Darcy velocity/flux qt total flux of the aqueous and nonaqueous phases Q source/since term r net change of nf per unit time rg, rc bubble generation and coalescence rates rc radius of curvature of plateau border in foam lamella rcap capillary radius rb foam bubble radius Pf foam pressure R ideal gas constant or retardation factor Rf expansion factor of foam S saturation Si saturation corresponding to the point a tangent line is drawn in the fw vs. Sw curve Sf foam saturation x Sff flowing foam saturation Sft trapped foam saturation max Sft maximum trapped foam saturation Sg gas saturation Sgr residual gas saturation Si initial saturation Snw nonaqueous phase saturation So oil saturation Sw aqueous saturation * Sw limiting aqueous saturation Swc connate water saturation Swr residual aqueous saturation t time T absolute temperature U approach velocity Up buoyant rise velocity of the bubbles vg gas velocity vw aqueous velocity vf foam velocity Vg volume of gas in foam Vl volume of liquid in foam Vf bulk volume of foam x spatial variable Greek Letters: α model parameter αL longitudinal dispersivity γB the exponent
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