Beig, Mikala

Fang, Yi-Lin

Fujita, Yoshiko

Kelly, Shelly

Redden, George D.

Reddy, Michael M.

Scheibe, T.D.

Smith, Robert W.

Tartakovsky, A.M.

Taylor, Joanna

Scheibe, T. D.

Tartakovsky, A. M.

UNT Digital Library

Fluid Flow, Solute Mixing andPrecipitation In Porous MediaIdaho National Laboratory    George D. Redden    Yoshiko FujitaPacific Northwest National Laboratory    Yi-Lin Fang    T.D. Scheibe    A.M. TartakovskyUniversity of Idaho    Mikala Beig    Joanna Taylor    Robert W. SmithU.S. Geological Survey    Michael M. ReddyArgonne National Laboratory    Shelly KellySupport from the U.S. Department of Energy, Environmental Remediation SciencesProgram, under contracts DE-AC07-05ID14517 and DE-AC06-76RLO 1830Theme:ReactantMixingModification ofPermeability or FlowPathsPrecipitationPrediction and Control of Subsurface ProcessesMixing: Dispersion vs. Diffusion• Diffusion– Molecular-scale mixing precipitationFlux = -Ddiff(∇C)• Dispersion– Macroscopic volume-averaged concentrationFlux = ΘDdisp(∇C)Issues and challenges:• Evolution of the spatial distribution of propertiesand processes• Volume averaging of properties and processes insystems characterized by mixing zones (at allscales).  For example:How should volume-averaged concentrationbe used to predictreaction rates?Averaged concentrationsmay exist only in mixingzones, which can be smalland transient.Issues and challenges:• HysteresisPrecipitation path(advection > diffusion)Dissolution path(diffusion > advection)Precipitation• Mineral precipitation• Biomass growth• Biofilm formation• Colloid filtrationImpact:• Fate and transport, sequestration• Field-scale kinetics vs. laboratory kinetics• Understanding the evolution of subsurfaceproperties (MNA)• Developing amendment introductionstrategies• Understanding “Rapid” engineered eventsFlagship experiment:• Hypotheses– Precipitation can be induced in the mixing zonebetween solutions containing reactive substrate(intuitively obvious, but interested in possibledeviation of flow paths)– Permeability of a mixing zone where mineralprecipitation occurs does not go to zero.  (If itdid, both sides of the mixing zone would beundersaturated)Premodeling using Smoothed Particle Hydrodynamics:Parallel flow with mixing and precipitationExperimental approach: Parallel flow, mixing andprecipitation at a solution-solution interface, “2-D”Solution A Solution BTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixingBlue dye Red dyeTracer test showing fluid-fluid interfaceand mixing (second attempt)Propagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cm~0.5mm silica sandPropagation of calcium carbonate(second attempt)And Biofilms…?Tracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationTracer test following precipitationImpact on permeabilityAfter carbonateprecipitation:Averagepermeabilitydecreased by ~ 100Before carbonateprecipitation100mM Na 2CO3, 1 cm/minSample Position: 2.5cmSample Position: 45cmSEM images5 µm20 µm5 µm2 µm20 µm10 µm100mM CaCl 2, pH ~7, 1 cm/minPlans: Precipitation Kinetics• Extend outside conventional conditions• Ion ratios• Correlation to Sr uptake and speciation 2-D flow experiments• Full characterization• propagation of precipitates in physicallyheterogeneous systems° Low permeability inclusions° High permeability flow paths• propagation of precipitates in chemicallyheterogeneous systems° calcite seeds° clay on sand SPH and continuum-scale model refinementPrecipitation Kinetics(see A.E. Nielsen (1983))• R = k’(Ω-1)                                                  Adsorption (linear)• R = k’’(Ω-1)2                                                Spiral growth (parabolic)• R = [kex Ω7/6(Ω-1)2/3(lnΩ)1/6] exp(-Kex/lnΩ) Surface nucleation    ~ (Ω-1)5/6 exp(-Kex/lnΩ)    ~ exp(-Kex/lnΩ)• R = k’’’(Ω-1)n …PracticalWhere: ks are rate constants      Ω = [Π(aiν)]/Ksp   (saturation ratio) aiν is the activity of component i with stoichiometry ν      Ksp = solubility product• Also, Ostwald Ripening, Ostwald Step Rule• Colloid filtration?  Biomass growth?Precipitation KineticsFrom Shiraki and Brantley (1995, GCA, vol. 59, pp. 1457-1471).CombinedPrecipitation Kinetics and Sr2+sequestration: Experimental Approach• Goals:– Test growth rate functions – apply in models– Test influence of ion ratios and modifiers– Morphologies, modes, products – interpretive– Sr2+ uptake and speciation• Method - constant composition– Batch reactors– Seeding – to confine the role of homogeneousnucleation– Stirring -  maintain uniform concentrations andreduce the influence of diffusive transport tosurface layers.– Maintain chemical composition (as opposed to“free drift”) -  to prolong the state ofsupersaturation.• Will these relationships help predict what happens inthe field?– Subsurface mixing zones are not stirred reactors.Diffusion will influence precipitation kinetics and,subsequently, distributions of saturation states.– Relative rate at which solutes are replenished orconsumed – can result in non-stoichiometric,varying ion ratios• R = kf(Ca2+)p(CO32-)q – kb      (Zhong and Mucci, 1993,GCA, vol. 57; Lin and Singer, 2005, GCA, vol. 69)Precipitation Kinetics: Relevant to Field?Pre-modeling:Simulating pore-scale precipitation usingSmoothed Particle Hydrodynamics• Lagrangian, gridless, particle-based• Used to establish a basis for parameters andconceptual basis for continuum approach• Precipitation of A and B via Cintermediate/d dt! != "# v2/ 1/ /extd dt P! µ != " + " +v v F2/A A A BA ABdC dt D C k C C= ! "2/B B A BB ABdC dt D C k C C= ! "• Continuity:• Conservation of momentum:• Diffusion/reaction:2/C C C AB A BdC dt D C k C C= ! +2/A A A BA ABdC dt D C k C C= ! "A  +  B  =  CintermediateCintermediate =  Csolid , driven by (C - Ceq)Hypothetical intermediate:Irreversible formation of Cintermediate:Irreversible formation of Cintermediate:• Initial Saturation index• Saturation index duringprecipitation• Steady-state condition atsolution-solution interface– Preservation of lessstable solid phases– Co-existence of multiplephases• Flow variations– Velocities and ratios– Changing map ofDamköhler (reaction ratevs. advection), andPeclet (advection vs.diffusion) numbers-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1distance from precipitation axisarbitrary concentration or saturation ratio Ca2+CO32-S.R.-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1distance from precipitation axisarbitrary concentration or saturation ratio Ca2+ CO32-S.R.Ca2+ CO32- Distance from precipitation axisDistance from precipitation axisContinuum-scale simulation: mixing0.0020000.0040000.0060000.0080000.00100000.00120000.00140000.00160000.00180000.00200000.00-25 -15 -5 5 15 25Distance from centerline (cm)Saturation Index0.0020000.0040000.0060000.0080000.00100000.00120000.00140000.00160000.00180000.00200000.00-25 -15 -5 5 15 25Distance from centerline (cm)Saturation IndexMixing without and with precipitationPresentations, Publications:Redden, G. and A. M. Tartakovsky (2006). Merging Experiments, Sensing, and Modeling for Predicting Coupled Biogeochemical ProcessBehavior Posters. American Geophysical Union 2006 Fall Meeting, San Francisco, American Geophysical Union.Redden, G. D., Y. Fang, T. Scheibe, A. Tartakovsky, D. T. Fox, T. A. White, Y. Fujita and M. E. Delwiche (2005). Calcium carbonateprecipitation along solution-solution interfaces in porous media. American Geophysical Union 2005 Fall Meeting, San Francisco,CA.Redden, G. D., Y. Fang, T. Scheibe, A. Tartakovsky, D. T. Fox, T. A. White, Y. Fujita and M. E. Delwiche (2005). "Calcium carbonateprecipitation along solution-solution interfaces in porous media." EOS Trans. AGU 86(52): Abstract B33C-1042.Redden, G. D., Y. Fang, T. Scheibe, A. M. Tartakovsky, D. T. Fox and T. A. White (2006). Metal precipitation and mobility in systemswith fluid flow and mixing: Illustrating coupling and scaling issues. American Chemical Society, 231st ACS National Meeting,Atlanta, GA, American Chemical Society.Redden, G. D., Y. Fang, T. D. Scheibe, A. M. Tartakovsky, D. T. Fox, Y. Fujita and T. A. White (2006). Fluid Flow, Solute Mixing andPrecipitation in Porous Media. INRA 2006 Environmental Subsurface Science Symposium, Moscow, ID.Scheibe, T. D., Y. Fang, A. M. Tartakovsky and G. Redden (2006). Hydrogeologic controls on subsurface biogeochemistry: field-scaleeffects of heterogeneous coupled physical and biogeochemical processes. 2006 Philadelphia Annual Meeting (22–25 October2006). Geological Society of America. Philadelphia, Geological Society of America.Scheibe, T. D., A. M. Tartakovsky, Y. Fang and G. D. Redden (2006). Models of Coupled Flow, Transport and Mineral Precipitation at aMixing Interface in Intermediate-Scale Experiments. American Geophysical Union 2006 Fall Meeting, San Francisco, AmericanGeophysical Union.Scheibe, T. D., A. M. Tartakovsky, G. Redden, P. Meakin and Y. Fang (2006). Pore-scale simulations of reactive transport with smoothedparticle hydrodynamics. Society for Industrial and Applied Mathematics Annual Meeting, Boston, MA.Tartakovsky, A., T. Scheibe, G. Redden, Y. Fang, P. Meakin and P. Saripalli (2006). Smoothed particle hydrodynamics model for pore-scale flow, reactive transport and mineral precipitation. CMWR XVI - Computational Methods in Water Resources conference,XVI International Conference, Copenhagen, Denmark.Tartakovsky, A., T. Scheibe, G. Redden and P. Meakin (2006). "Pore-scale smoothed particle hydrodynamics model of the mixing inducedprecipitation.", submitted to Water Resources ResearchTartakovsky, A. M., T. D. Scheibe, P. Meakin, G. Redden and Y. Fang (2006). Multiscale Lagrangian Particle model for ReactiveTransport and Mineral Precipitation in Porous Media. American Geophysical Union 2006 Fall Meeting, San Francisco, AmericanGeophysical Union.Tartakovsky, A. M., T. D. Scheibe, G. Redden, Y. Fang, P. Meakin and K. P. Saripalli (2006). Smoothed particle hydrodynamics model forpore-scale flow, reactive transport and mineral precipitation. XVI International Conference on Computational Methods in WaterResources, Copenhagne, Denmark.Connections:• Field Investigations of Microbially Facilitated CalcitePrecipitation for Immobilization of Strontium-90 andOther Trace Metals in the Subsurface– University of Idaho; Robert W. Smith, PI• Hybrid Numerical Methods for Multiscale Simulations ofSubsurface Biogeochemical Processes– PNNL; Tim Scheibe, PI• Collaboration opportunities for:– Microbial characterization methods– Geotechnical propertiesParallel flow: mixing and precipitation at a solution-solution interface, 3-D, X-ray tomographyCaCl2 NaHCO3Inner perimeterof columnCalciumcarbonate6 cmInjection of a supersaturated solutionDirection of FlowPropagation of calcium carbonate50mM Na2CO3 50mM CaCl2Darcy Flow ~ 1cm/min60 cmApplication: nested dipole application+ -Fluid A Fluid B Fluid AFluid BReaction Zone-+Example 1: In situ generation and mixingof reactants and geophysical monitoring• Application: Formation of calcium carbonate andco-precipitation (immobilization) of strontium• Reactions (simplified):     (NH2)2CO + 3H2O                    HCO3- + 2NH4+ + OH-                 HCO3- + Ca2+    CaCO3(s)  +  H+        HCO3- + Ca2+ + Sr2+   (Ca,Sr)CO3(s)  +  H+           Ksp calcite = (Ca2+)(CO32-) ~ 10-8.4• An abiotic analog to a microbially mediatedprocessureaseureaCO32-urea(Ca,Sr)CO3Questions:• Impact of flow rate– Location of pecipitation– Efficiency of reaction = f(mixing)• Impact of premeability reduction– Constant flow– Constant gradientureaCO32-ureaCaCO3Ultimate Modeling ObjectivePrefer a macroscopic continuum scale description–  Practical–  Can simulate larger systemsPerform pore-scale modeling to:–  Validate continuum approach–  Provide basis for empirical or effective parametersused in continuum approach–  Reduce level of detail as much as possibleContinuum model/d dt! != "# v2/ 1/ /extd dt P! µ != " + " +v v F2/A A A BA ABdC dt D C k C C= ! "2/B B A BB ABdC dt D C k C C= ! "Continuity:• Conservation of momentum:• Diffusion/reaction:2/C C C AB A BdC dt D C k C C= ! +A  +  B  =  Csolidt = 2000 t = 4000 t = 6000Pe = 2.8Pe = 0.9Supersaturation and velocity profilesContours of saturation indext = 1000 t = 6000t = 3000Pe = 2.8Pe = 0.9Impact of Peclet number (advection/diffusion)- anon

Fluid Flow, Solute Mixing and Precipitation In Porous Media

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Fluid Flow, Solute Mixing and Precipitation In Porous Media

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