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Ground-Water Flow and Solute Transport for the PHAST Simulator Ken Kipp and David Parkhurst

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Outline Concepts Assumptions Governing Equations Numerical Implementation

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Basic Concepts Conservation of an extensive variable in an open system – –Mass – –Solute mass – –Solute moles – –Electrons – –Redox state Mechanisms of transport – –Flow in porous media – –Advection – –Dispersion – –Diffusion Mechanism of chemical reaction – –Mass action equilibria – –Kinetics

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Water Balance Rate of water accumulation = Rate of water addition by advection + Rate of water addition by point sources

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Solute Component Balance Rate of solute accumulation = Rate of solute addition by advection + Rate of solute addition by dispersion Rate of solute addition by diffusion + Rate of solute addition by equilibrium reactions Rate of solute addition by kinetic reactions + Rate of solute addition by point sources + +

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Simplifying Assumptions Single phase Liquid water Saturated porous media Darcy flow Isothermal Dilute solutions Constant density and viscosity Compressible porous media for confined flow Isotropic dispersion with empirical modification One set of diffusion and dispersion parameters No pure diffusive solute sources

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Ground-Water Flow Equation Interstitial velocity (Darcy flow) Conservation of water mass (volume)

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Flow Equation Parameters Hydraulic conductivity (L/T) Specific storage (1/L), confined flow

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Flow Equation Results Head field h(x,t) Velocity field v(x,t) Boundaries –Flow rates –Cumulative amounts Assumed independent of solute transport

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Solute Transport Equation Conservation of solute mass for each component i

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Solute Transport Parameters Porosity Dispersion coefficient tensor –Dispersivities –Effective molecular diffusivity Modified dispersion coefficients for restricted anisotropic dispersion –Split into and –Applies to horizontal flow in layered anisotropic aquifer Dispersion Models Isotropic dispersion

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Dispersive Processes

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Solute Transport Equation Results Component concentration fields c i (x,t) Breakthrough curves Peak concentrations Boundaries –Solute flow rates –Cumulative solute amounts

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Water and Porous-Matrix Properties Intrinsic water properties – –Density, – –Compressibility – –Viscosity Intrinsic porous matrix properties – –Permeability – –Porosity – –Compressibility – –Dispersivity Combined properties for simulator – –Hydraulic conductivity – –Storage coefficient – –Effective molecular diffusivity

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Boundary Conditions for Flow No flux (default) Specified head – –adjacent open body of water – –determined from field data or larger model Specified flux – –precipitation – –determined from field data or larger model Leakage flux –adjacent leaky aquifer –extension of simulation region River leakage flux Well –injection or production well –observation well Free surface –water table; unconfined flow –atmospheric pressure

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Boundary Conditions for Solute Transport Specified concentrations – –Only with specified head boundary – –Adjacent open body of water Associated advective component fluxes – –Can be used with all boundary conditions – –Open boundary with incoming ground-water flux – –Outgoing flux leaves at resident boundary concentration

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Leakage Boundary Condition Leaky boundary – –Fluid flux a function of head – –Associated concentration for advective solute flux Assumptions and limitations – –One-dimensional Darcian flow in confining layer – –Neglect transient fluid storage in confining layer – –Neglect transient solute storage in confining layer – –Outer aquifer conditions not affected by leakage flux

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Leakage Flux

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River Leakage Boundary Condition River leakage boundary – –Fluid flux a function of head – –Associated concentration for advective solute flux Assumptions and limitations – –One-dimensional Darcian flow in river bed – –Neglect transient fluid storage in river bed – –Neglect transient solute storage in river bed – –River conditions not affected by leakage flux – –Limit on maximum recharge flux from river

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River Geometry

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River Leakage Flux

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Free-Surface Boundary Conditions Two b.c. since location is an unknown 1. Atmospheric pressure 2. Kinematic condition neglected Linear extrapolation of pressure to locate free surface elevation Free surface allowed in any cell Only one free surface at any horizontal location Cells resaturate initially from below

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Well-Bore Model Methods – –Local well model with steady-state head profile at each cell layer – –Concentration from production well is layer- flow-rate weighted average Options – –Specified flow rate (injection, production) – –Observation well Allocation of flow – –By mobility – –By product of mobility and head difference

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Well Geometry

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Wells Assumptions and limitations – –Well bore is finite radius cylinder incorporated as a source term – –Local steady-state radial-flow well-bore equation – –Hydrostatic pressure distribution in well bore – –Net flow in well bore must not reverse direction – –No reactions are considered in well bore

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Initial Condition Options Head distribution – –Defined by zones Uniform value Piecewise linear – –Water-table condition – –Steady-state flow field Concentration distribution – –Defined by zones Uniform value Piecewise linear

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Solving the Flow and Reactive- Transport Equations Finite difference approximations Equation discretization – –Point-distributed mesh – –Zonation of spatial properties – –Backwards-in-time or centered-in-time – –Upstream-in-space or centered-in-space Operator splitting the reactive-transport equations

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Discretization

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Point-Distributed Grid Elements and nodes Porous-media properties defined by element

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Point-Distributed Grid Cells and nodes Boundary and initial conditions defined by cell (node)

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Zones for Property Definition Selection of elements

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Zones for Property Definition Selection of cells and nodes

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Application of Boundary Conditions

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Well Discretization

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Temporal Discretization Using Finite Differences Generic equation Centered-in-time, Crank-Nicolson; = 0.5 Backward-in-time, Fully implicit; = 1 Intermediate weighting; 0.5 <= <= 1

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Operator Splitting Separating transport from reaction calculations Solute Transport Equations (simplified): Finite Difference Equations:

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Sequential Non-lterative Approach Transport step: Reaction step:

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Summary Sequential Solution of Coupled Equation System – –Discretize in space and time yielding finite difference equations – –Operator split the reactive-transport equations – –Solve sequentially for each time step Flow Solute transport for each component Equilibrium and kinetic chemical reactions

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PHAST Information Flow Chart

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Types of PHAST Simulations 1. 1. Steady-state ground-water flow 2. 2. Transient ground-water flow 3. 3. Steady-state ground-water flow and transient reactive transport 4. 4. Transient ground-water flow and transient reactive transport

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