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Modeling Multiphase Flow in Variably Saturated Media. For: BAE 558 By: Kate Burlingame 5/7/07. Introduction.

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Modeling multiphase flow in variably saturated media l.jpg

Modeling Multiphase Flow in Variably Saturated Media

For: BAE 558

By: Kate Burlingame


Introduction l.jpg

  • Non Aqueous Phase Liquids, or NAPLs, are common contaminants of soils that are not miscible in water. Once introduced to a soil, the NAPL contaminant will therefore remain in a separate liquid phase.

  • Understanding how this separate liquid phase behaves in the vadose zone is essential to understanding how long the contaminant will remain present, the approximate area a spill of a given volume will occupy, and how deep the NAPL will penetrate. Predictions of this behavior assist in soil and aquifer clean-up operations.

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Introduction (continued)

  • This presentation will examine the key parameters used in modeling land NAPL spills and will provide a brief description of how each parameter affects the transport of the NAPL

  • The STOMP code, a leading model currently in use, will be analyzed and evaluated

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Benefits of Computer Simulation

  • A study by the US Coast guard estimates that around 1.5 million gallons of oil were spilled in the United States in the year of 2004

  • 83% these spills occurred either inland or in the contiguous zone

    Image below was obtained at:

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Benefits of Computer Simulation continued

  • In order to effectively design remediation strategies for these spill sites, as well as spills or leakages of other organics, accurate characterization of contaminated areas must be achieved.

  • This characterization is currently performed by taking measurements at the field due to the lack of an accurate, efficient simulator.

  • However, an accurate simulation, able to predict the amount and location of a NAPL beneath the soil surface and estimate the persistence of the NAPL after the spill or leak, would reduce time and costs associated with site cleanup (Simmons, 2003).

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Parameters used to describe modeling-Properties of the liquid

  • Density

    There are two major types of NAPLs: those that are less dense than water (LNAPL’s), and those that are denser than water (DNAPLs). This property of the NAPL is of primary importance in predicting the behavior of the NAPL, as DNAPLs will continue to sink below the porous media until reaching an impermeable layer. LNAPLs, on the other hand, will float on top of water found in the soil matrix or aquifer. Also, while LNAPLs will travel in the direction of the slope of the water table, DNAPLs will travel with the slope of the lower boundary of material in a soil. DNAPLs deposit a greater fraction of free product to the aquifer.

  • Viscosity

    Viscosity quantifies the internal energy of an object and describes how rapidly a liquid flows over a surface (Simmons, 2003). Viscosity, therefore, will act as a resistive force to the wetting front progression. It is important to note that viscosity is a function of temperature, and therefore the rate at which the liquid flows is dependent upon the temperature of the soil and atmosphere.

  • Interfacial Tension

    Interfacial Tension, or surface tension, is the potential energy associated with the area of contact between two liquids. These forces are important in fluid flow in both the horizontal and vertical directions.

  • Vapor Pressure

    Vapor pressure is indicative of a liquid's evaporation rate. Volatile substances are substances that have a high vapor pressure at normal temperatures, and therefore evaporate easily. This is an important factor in determining not only how the NAPL will behave in the vadose zone, but also in determining remediation techniques for the site. For example, a volatile substance responds more readily to soil vapor extraction than a non-volatile substance.

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Parameters used to describe modeling-Properties of the soil

  • Soil-Water Retention Curve

    This soil property describes how much moisture is retained in the soil for a given pressure.

  • Porosity

    Porosity is the ratio of the volume of voids in a soil compared to the volume of the soil. This property determines the amount of water, NAPL, or gas that a soil may imbibe and retain.

  • Permeability

    The permeability and hydraulic conductivity of a soil describes the ability of that soil to transport a fluid.

  • Surface Gradient

    The slope of the surface that the spill occurs on plays a fundamental role in determining the direction and magnitude of the spill.

  • Soil texture

    The soil texture, including grain size distribution, has a key influence on many properties of the soil.

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Parameters used to describe modeling: Properties of the spill

  • Amount of liquid spilled

  • The rate at which the liquid is spilled

    • Rapid spills will cover a broader area and will leave a larger residual saturation in the vadose zone.

    • Because of the large amount of NAPL remaining in the unsaturated zone, less free product is available to contaminate the aquifer.

    • Slow spills, or leaks, on the other hand, will contaminate an extensive area while still delivering a large amount of NAPL to the aquifer.

    • Slow leaks are also more prone to lateral movement

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Important Mathematical Relationships

  • Primary equations:

    • Darcy’s Law:

    • Mass balance for multiphase system (Miller, 1995):

    • Θ: volume fraction

    • ω: mass fraction

    • ρ: density

    • υ: macroscopic phase velocity vector

    • I: general interphase mass transfer term

    • R:general species reaction term

    • S: Solute Source

    • i: species qualifier

    • α: phase qualifier

    • Darcy’s law accounts for loss of momentum of each fluid phase when moving through interconnected pore space. When coupled with the conservation of mass, the law determines an equation for fluid flow (Simmons, 2003).

    • Most multiphase environmental model simulations do not include an energy balance equation (Miller, 1995)

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Common assumptions

  • Due to the fact that the equations governing three-phase flow in heterogeneous unsaturated media are so complex, it is difficult, if not impossible, to develop an accurate representative computer model. It is thus necessary to make assumptions to simplify the equations. According to Miller’s study, there are five common assumptions made to achieve this simplification:

  • the solid phase is immobile

  • the solid phase is inert (not chemically active)

  • a portion of components in the system can be ignored

  • all relevant species of a system can be represented by a smaller representative group of species

  • local chemical equilibrium exists among phases

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Effect of Assumptions

  • These assumptions all eliminate variables that increase the complexity of the equation.

  • For example, assuming that the solid phase is immobile eliminates three unknowns.

  • It is difficult to determine the exact effect that these assumptions will have on the accuracy of the simulation; however, all assumptions made are reasonable.

  • Many experiments make additional assumptions

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Conditions required to write a computer model

  • Miller goes on to summarize the nine basic parameters a computer model must have in order to be accurate:

    • a set of balance equations that describe the system

    • A multiphase from of Darcy’s law and the conservation of mass equation

    • Equations of state and appropriate thermodynamic relations

    • Relationships between fluid pressures, saturations, and permeabilities for flow through the media

    • If an energy transport equation is considered, it is necessary to include relationships for diffusion, dispersion, and conduction

    • Thermodynamic equilibrium and mass transfer rate relationships for all considered species

    • Reaction relationships of both reversible and irreversible reactions

    • All sources and sinks

    • Auxilliary conditions

  • It is important to note that, even with simplifying assumptions, computer simulations require an enormous amount of information and remain quite convoluted.

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Subsurface Transport Over Multiple Phases (STOMP)

  • The computer model Subsurface Transport Over Multiple Phases (STOMP) was designed by Mark White of Pacific Northwest Laboratory in order to simulate the flow and transport of fluids in variably saturated soil.

  • The simulator was designed specifically to simulate spill zones contaminated with volatile organics and radioactive material.

  • According to a description by the Environmental Technology Directorate, “the simulator's modeling capabilities address a variety of subsurface environments, including nonisothermal conditions, fractured media, multiple-phase systems, nonwetting fluid entrapment, soil freezing conditions, nonaqueous phase liquids, first-order chemical reactions, radioactive decay, solute transport, dense brines, nonequilibrium dissolution, and surfactant-enhanced dissolution and mobilization of organics.”

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  • How it works:

    • The STOMP modeling code uses Euler discretization and integrated volume finite difference discretization to solve the conservation of mass and conservation of energy partial differential equations.

    • The operator of the computer model defines the governing equations for the simulator, which can model up to four phases and recognizes a number of boundary conditions.

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Experimental Testing of STOMP

  • Experiments in the field are often prohibited

  • Difficult to test the model against existing spill sites because there is generally too little historical documented data for the site, making it difficult to develop initial and boundary conditions for the simulator.

  • Often, laboratory-controlled experiments offer the only means of evaluation.

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Experimental Testing of STOMP

  • Experiment 1: Hysteretic three phase flow

  • In an experiment conducted by R.J. Lenhard STOMP was used to simulate a three-phase flow situation with a fluctuating water table.

  • Hysteresis was considered in the experiment.

  • The results were compared to another, older computer model and tested against experimental results.

  • When simulating the experiment, the primary assumptions made were that the gas-phase pressure remained constant and the transport through the gas phase was negligible.

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Experimental Testing of STOMP

  • Experiment 1: Hysteretic three phase flow

  • Steps in experiment:

    • a water-saturated column, made up of coarse sand, was drained by lowering the water table.

    • NAPL was infiltrated into the system under atmospheric conditions, creating a three-phase system.

    • The moisture and NAPL contents were measured using gamma attenuation.

    • The water table was raised and lowered, allowing the fluids to drain and infiltrate, simulating hysteretic conditions. (Lenhard, 1995).

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Experimental Testing of STOMP Experiment 1: Hysteretic three phase flow

  • Results at 57 and 67 cm elevations

  • Open circle= water saturations Closed circle= NAPL saturations

  • Thin line= STOMP water saturations

  • Thick line= STOMP NAPL saturations

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Experimental Testing of STOMPExperiment 1: Hysteretic three phase flow

Results at 47cm and 37 cm elevations:

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Experimental Testing of STOMPExperiment 2: Flow in layered porous media

  • This experiment was conducted by E.L. Wipfler in 2003

  • When conducting the simulation, Wipfler assumed that each sand layer was isotropic, all fluids were incompressible and immiscible, and that the air was infinitely mobile at constant pressure.

  • Hysteresis was not evaluated.

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Experimental Testing of STOMPExperiment 2: Flow in layered porous media

  • Experiment Steps:

    • A fine sand matrix and a coarse sand were layered in a plexiglass chamber.

    • Both layers were inclined at varying angles with respect to the water table.

    • The porous media was held at saturation for several hours and then allowed to drain until a steady-state was reached.

    • The LNAPL was distributed as a finite point source on the upper surface of the unsaturated sand.

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Experimental Testing of STOMPExperiment 2: Flow in layered porous mediaResults:

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Remaining Uncertainties

  • Still not commonly used in field applications. All laboratory experiments analyzed made assumptions that neglected key factors in NAPL movement in order to simplify the computer model. In reality, some of these parameters would affect the NAPL distribution; especially temperature, hysteresis, and anisotropic soil grain sizes.

  • The STOMP code requires detailed information about initial and boundary conditions in order to perform any simulation. This is an important obstacle in the application of the code at field sites.

  • The STOMP code has been proven to be accurate; the remaining challenges will be to modify the model such that it can be effectively used in field applications.

References l.jpg

  • Environmental Technology Directorate. 2007. Technologies & Products: Subsurface Transport Over Multiple Phases (STOMP). Pacific Northwest National Labobratories. Available at: Accessed April 2007.

  • Lenhard, R.J., M. Oostrom, and M.D. White. 1995. Modeling fluid flow and transport in variably saturated porous media with the STOMP simulator. 2. Verification and validation exercises. Advances in Water Resources 18(6): 365-373.

  • Miller, Cass T., George Christakos, Paul T. Imhoff, John F. McBride and Joseph A. Pedit. 1996. Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches. Advances in Water Resources 21(2): 77-120.

  • Selker, John S., C. Kent Keller, and James T. McCord. 1999. Vadose Zone Processes, Boca Raton, FL.

  • Simmons, C.S. and J.M. Keller. 2003. Status of Models for Land Surface spills of Nonaqueous Liquids. Pacific Northwest National Laboratory PNNL-14350.

  • U.S. Coast guard, 2006. Pollution Incidents In and Around U.S. Waters. Available at: Accessed 20 April 2007.

  • Ward, Andy L., Z. Fred Zhang, and Glendon W. Gee. 2005. Upscaling unsaturated hydraulic parameters for flow through heterogeneous anisotropic sediments. Advances in Water Resources 29(2006): 268-280.

  • White, M.D. and M. Oostrom. 2003. STOMP version 3.0 user’s guide. Pacific Northwest National Laboratory PNNL-14286.

  • Williams, B. 2002. Unpublished data. Moscow, ID: University of Idaho.

  • Wipfler, E.L., M. Ness, G.D. Breedveld, A. Marsman, S.E.A.T.M. van der Zee. 2003. Inflitration and redistribution of LNAPL into unsaturated layered porous media. Journal of Contaminant Hydrology 71(2004): 47-66.

  • Yoon, Hongkyu, Albert J. Valocchi, and Charles J. Werth. 2006. Effect of soil moisture dynamics on dense nonaqueous phase liquid (DNAPL) spill zone architecture in heterogeneous porous media. Journal of Contaminant Hydrology 90(2007): 159-183.