Final Project I. Calibration Drawdown Prediction Particle Tracking Presentation of Results

Final Project

Particle Tracking

FLOW NETS The streamfunction,  (from Hornberger et al., 1998)

A flow net consists of equipotential lines and streamlines. (from Hornberger et al., 1998) A flow net consists of equipotential lines and streamlines.

(used to trace flow lines) Particle Tracking (used to trace flow lines) distance = velocity x time

Particle Tracking (used to trace flow lines) Groundwater flow model MODFLOW Note: need to input effective porosity, ne Darcy’s law v = KI / ne Particle tracking code MODPATH, Path3D

Particle tracking simulates advection of contaminant “particles”. Transport models (e.g., MT3D) simulate advection, dispersion and chemical reactions. Retardation caused by linear adsorption reactions can be simulated using particle tracking, since the velocity can be adjusted: vc = v/Rd Rd is the retardation coefficient.

Steps in Particle Tracking Need to interpolate velocities from nodal point values since particle tracking is done in a continuous coordinate system. Need to track the movement of the particles in the computed velocity field.

Interpolation Schemes Linear (MODPATH, Path3D) Bilinear Reverse distance (FLOWPATH)

Tracking distance = velocity x time dx/dt = vx dx = vx dt

Tracking Schemes Semianalytical (MODPATH) Euler (FLOWPATH) Runge Kutta (Path3D) Taylor Series (WHPA)

Profile Models (e.g., the Toth Problem) z h = c x + zo x z x

Profile Models The profile should be oriented parallel to flow. Axisymmetric profiles (useful to simulate pumping) Slice orientation and layer orientation

Layer Orientation Profile – unconfined aquifer 2D confined aquifer for homogeneous, anisotropic aquifers  We can simulate a profile by using 1 confined layer in MODFLOW.

Problem 6.1a Specified head cells Active cells MODFLOW computes fluxes between specified head cells and active cells. MODFLOW does not compute fluxes between specified head cells; you need to compute those manually.

active cells with injection wells Qp= Q1 + Q2 Q1 Q2 active cells with injection wells Active cells In problem 6.1b, you use injection wells to simulate recharge to the profile. Calculate the injection rate as the net flux into each of the cells in the top row.

Problem Set 6 illustrates: Use of a confined MODFLOW layer to simulate an unconfined aquifer in profile view. Procedure for switching from specified head to specified flux boundary conditions.

Problems dealing with the water table In a profile model or a 3D model, the water table typically forms the upper boundary of the model. In transient problems the water table fluctuates and the position of the water table is unknown. MODFLOW utilizes the Dupuit assumptions to calculate the water table in unconfined layers. Recharge typically occurs to the top active cell.

Alternatives to MODFLOW for water table problems Finite element codes with deformable elements allow the element to deform as the water table moves. Codes that incorporate the unsaturated zone.

Models that incorporate the unsaturated zone solve for the position of the water table by locating where pressure head (hp) equals zero. h = z + hp = z + p/g Total head = elevation head + pressure head 2D USGS codes for flow in partially saturated media (unsaturated zone and saturated zone) VS2DTI (for water and solutes) VS2DHI (for water and heat) Other codes include: SUTRA, HYDRUS and many others.

Example problem run with VS2D Infiltration into a cross section Possible seepage face Example problem run with VS2D Infiltration into a cross section with a slope low K layer perched water Pressure head = 0 defines the water table

Flow through a dam