Modeling%20Multiphase%20Flow%20in%20Variably%20Saturated%20Media

1
Modeling Multiphase Flow in Variably Saturated
Media

• For BAE 558
• By Kate Burlingame
• 5/7/07

2
Introduction

• 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.

3
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

4
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 http//www.permacultu
  re.com/newsletter/alaskapipeline.jpg

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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 (LNAPLs), 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
• Darcys Law
• Mass balance for multiphase system (Miller,
  1995)
• T volume fraction
• ? mass fraction
• ? density
• ? macroscopic phase velocity vector
• I general interphase mass transfer term
• R general species reaction term
• S Solute Source
• i species qualifier
• a phase qualifier
• Darcys 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 Millers 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 Darcys 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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STOMP

• 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 STOMP Experiment 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 media Results
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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.

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References

• Environmental Technology Directorate. 2007.
  Technologies Products Subsurface Transport
  Over Multiple Phases (STOMP). Pacific Northwest
  National Labobratories. Available at
  http//environment.pnl.gov/resources/resource_desc
  ription.asp?id3typetech. 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
  http//www.uscg.mil/hq/g-m/nmc/response/stats/CHPT
  2004.pdf. 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 users 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.