Modeling Multiphase Modeling Multiphase Flow in Variably Flow in Variably Saturated MediaSaturated Media

For: BAE 558For: BAE 558

By: Kate BurlingameBy: Kate Burlingame

5/7/075/7/07

IntroductionIntroduction Non Aqueous Phase Liquids, or NAPLs, are Non Aqueous Phase Liquids, or NAPLs, are

common contaminants of soils that are not common contaminants of soils that are not miscible in water. Once introduced to a soil, miscible in water. Once introduced to a soil, the NAPL contaminant will therefore remain the NAPL contaminant will therefore remain in a separate liquid phase. in a separate liquid phase.

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

Introduction (continued)Introduction (continued)

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

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

Benefits of Computer Benefits of Computer SimulationSimulation

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

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

Image below was obtained at: http://www.permaculture.com/newsletter/alaskapipeline.jpgImage below was obtained at: http://www.permaculture.com/newsletter/alaskapipeline.jpg

Benefits of Computer Benefits of Computer Simulation continuedSimulation continued

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

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

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

Parameters used to describe Parameters used to describe modeling-modeling- Properties of the Properties of the

liquidliquid DensityDensity

There are two major types of NAPLs: those that are less dense than water (LNAPL’s), and 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 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 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 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 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 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 lower boundary of material in a soil. DNAPLs deposit a greater fraction of free product to the aquifer. the aquifer.

ViscosityViscosityViscosity quantifies the internal energy of an object and describes how rapidly a liquid 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 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 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, and therefore the rate at which the liquid flows is dependent upon the temperature of the soil and atmosphere. temperature of the soil and atmosphere.

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

Vapor PressureVapor PressureVapor pressure is indicative of a liquid's evaporation rate. Volatile substances are 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 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 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. 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 For example, a volatile substance responds more readily to soil vapor extraction than a non-volatile substance. non-volatile substance.

Parameters used to describe Parameters used to describe modeling-modeling- Properties of the Properties of the

soilsoil Soil-Water Retention CurveSoil-Water Retention Curve

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

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

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

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

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

Parameters used to describe Parameters used to describe modeling:modeling: Properties of the Properties of the

spillspill Amount of liquid spilledAmount of liquid spilled

The rate at which the liquid is spilled The rate at which the liquid is spilled – Rapid spills will cover a broader area and will Rapid spills will cover a broader area and will

leave a larger residual saturation in the vadose leave a larger residual saturation in the vadose zone. zone.

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

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

– Slow leaks are also more prone to lateral Slow leaks are also more prone to lateral movementmovement

Important Mathematical Important Mathematical Relationships Relationships

Primary equations:Primary equations:– Darcy’s Law: Darcy’s Law:

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

– Θ: volume fractionΘ: volume fraction– ω: mass fractionω: mass fraction– ρ: densityρ: density– υ: macroscopic phase velocity vectorυ: macroscopic phase velocity vector– II: general interphase mass transfer term: general interphase mass transfer term– RR:: general species reaction termgeneral species reaction term– S: S: Solute Source Solute Source – ii: species qualifier : species qualifier – α: α: phase qualifier phase qualifier– Darcy’s law accounts for loss of momentum of each fluid phase when moving through 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 interconnected pore space. When coupled with the conservation of mass, the law determines an equation for fluid flow (Simmons, 2003). an equation for fluid flow (Simmons, 2003).

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

Common assumptionsCommon assumptions Due to the fact that the equations governing three-phase Due to the fact that the equations governing three-phase

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

1.1. the solid phase is immobilethe solid phase is immobile2.2. the solid phase is inert (not chemically active)the solid phase is inert (not chemically active)3.3. a portion of components in the system can be ignoreda portion of components in the system can be ignored4.4. all relevant species of a system can be represented by a all relevant species of a system can be represented by a

smaller representative group of speciessmaller representative group of species5.5. local chemical equilibrium exists among phaseslocal chemical equilibrium exists among phases

Effect of AssumptionsEffect of Assumptions

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

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

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

Many experiments make additional Many experiments make additional assumptionsassumptions

Conditions required to write a Conditions required to write a computer modelcomputer model

Miller goes on to summarize the nine basic parameters a Miller goes on to summarize the nine basic parameters a computer model must have in order to be accurate: computer model must have in order to be accurate: 1.1. a set of balance equations that describe the systema set of balance equations that describe the system2.2. A multiphase from of Darcy’s law and the conservation of mass A multiphase from of Darcy’s law and the conservation of mass

equationequation3.3. Equations of state and appropriate thermodynamic relationsEquations of state and appropriate thermodynamic relations4.4. Relationships between fluid pressures, saturations, and permeabilities Relationships between fluid pressures, saturations, and permeabilities

for flow through the mediafor flow through the media5.5. If an energy transport equation is considered, it is necessary to include If an energy transport equation is considered, it is necessary to include

relationships for diffusion, dispersion, and conductionrelationships for diffusion, dispersion, and conduction6.6. Thermodynamic equilibrium and mass transfer rate relationships for all Thermodynamic equilibrium and mass transfer rate relationships for all

considered speciesconsidered species7.7. Reaction relationships of both reversible and irreversible reactionsReaction relationships of both reversible and irreversible reactions8.8. All sources and sinksAll sources and sinks9.9. Auxilliary conditionsAuxilliary conditions

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

Subsurface Transport Over Subsurface Transport Over Multiple Phases (STOMP)Multiple Phases (STOMP)

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

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

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

STOMPSTOMP

How it works:How it works:– The STOMP modeling code uses Euler The STOMP modeling code uses Euler

discretization and integrated volume discretization and integrated volume finite difference discretization to solve the finite difference discretization to solve the conservation of mass and conservation of conservation of mass and conservation of energy partial differential equations.energy partial differential equations.

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

Experimental Testing of Experimental Testing of STOMPSTOMP

Experiments in the field are often Experiments in the field are often prohibitedprohibited

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

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

Experimental Testing of Experimental Testing of STOMPSTOMP

Experiment 1: Hysteretic three phase flow Experiment 1: Hysteretic three phase flow In an experiment conducted by R.J. Lenhard In an experiment conducted by R.J. Lenhard

STOMP was used to simulate a three-phase flow STOMP was used to simulate a three-phase flow situation with a fluctuating water table. situation with a fluctuating water table.

Hysteresis was considered in the experiment. Hysteresis was considered in the experiment. The results were compared to another, older The results were compared to another, older

computer model and tested against experimental computer model and tested against experimental results. results.

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

Experimental Testing of Experimental Testing of STOMPSTOMP

Experiment 1: Hysteretic three phase Experiment 1: Hysteretic three phase flowflow

Steps in experiment:Steps in experiment:– a water-saturated column, made up of coarse a water-saturated column, made up of coarse

sand, was drained by lowering the water table.sand, was drained by lowering the water table.– NAPL was infiltrated into the system under NAPL was infiltrated into the system under

atmospheric conditions, creating a three-phase atmospheric conditions, creating a three-phase system. system.

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

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

Experimental Testing of STOMP Experimental Testing of STOMP

Experiment 1: Hysteretic three phase Experiment 1: Hysteretic three phase flowflow

Results at 57 and 67 cm elevations Results at 57 and 67 cm elevations Open circle= water saturations Closed circle= NAPL saturationsOpen circle= water saturations Closed circle= NAPL saturations Thin line= STOMP water saturations Thin line= STOMP water saturations Thick line= STOMP NAPL saturations Thick line= STOMP NAPL saturations

Experimental Testing of STOMPExperimental Testing of STOMP Experiment 1: Hysteretic three phase Experiment 1: Hysteretic three phase

flowflowResults at 47cm and 37 cm elevations: Results at 47cm and 37 cm elevations:

Experimental Testing of STOMPExperimental Testing of STOMPExperiment 2: Flow in layered porous Experiment 2: Flow in layered porous

mediamedia

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

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

Hysteresis was not evaluated. Hysteresis was not evaluated.

Experimental Testing of STOMPExperimental Testing of STOMPExperiment 2: Flow in layered porous Experiment 2: Flow in layered porous

mediamedia Experiment Steps:Experiment Steps:

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

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

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

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

Experimental Testing of STOMPExperimental Testing of STOMPExperiment 2: Flow in layered porous Experiment 2: Flow in layered porous

mediamedia Results:Results:

Remaining Uncertainties Remaining Uncertainties Still not commonly used in field applications. All Still not commonly used in field applications. All

laboratory experiments analyzed made laboratory experiments analyzed made assumptions that neglected key factors in NAPL assumptions that neglected key factors in NAPL movement in order to simplify the computer model. movement in order to simplify the computer model. In reality, some of these parameters would affect In reality, some of these parameters would affect the NAPL distribution; especially temperature, the NAPL distribution; especially temperature, hysteresis, and anisotropic soil grain sizes. hysteresis, and anisotropic soil grain sizes.

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

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

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

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Pacific Northwest National Laboratory PNNL-14350. Pacific Northwest National Laboratory PNNL-14350. U.S. Coast guard, 2006. Pollution Incidents In and Around U.S. Waters. Available at: 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/CHPT2004.pdf. Accessed 20 April 2007http://www.uscg.mil/hq/g-m/nmc/response/stats/CHPT2004.pdf. Accessed 20 April 2007.. Ward, Andy L., Z. Fred Zhang, and Glendon W. Gee. 2005. Upscaling unsaturated hydraulic Ward, Andy L., Z. Fred Zhang, and Glendon W. Gee. 2005. Upscaling unsaturated hydraulic

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

Williams, B. 2002. Unpublished data. Moscow, ID: University of Idaho.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 Wipfler, E.L., M. Ness, G.D. Breedveld, A. Marsman, S.E.A.T.M. van der Zee. 2003. Inflitration and

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