Ground Water Hydroology: Understanding and Modeling Ground Water Systems - Prof. Eileen P., Study notes of Engineering

Download Ground Water Hydroology: Understanding and Modeling Ground Water Systems - Prof. Eileen P. and more Study notes Engineering in PDF only on Docsity! 1 ALL GROUND-WATER HYDROLOGY WORK IS MODELING A Model is a representation of a system. Modeling begins when one formulates a concept of a hydrologic system, continues with application of, for example, Darcy's Law or the Theis equation to the problem, and may culminate in a complex numerical simulation. MODELS can be used BENEFICIALLY and for DECEPTION GROUND WATER MODELING WHY MODEL? •To make predictions about a ground-water system’s response to a stress •To understand the System •To design field studies •Use as a thinking tool 2 t h sSWz h zKzy h yKyx h xKx ∂ ∂ =−⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ +⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ +⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ Geometry Material Properties (K, S, T, Φe, D, R, etc) Boundary Conditions (Head, Flux, Concentration etc) Stresses (changing boundary conditions) Characterize the system Governing equation of Ground Water Flow: Boundary Types Specified Head/Concentration: a special case of constant head (ABC, EFG) Constant Head /Concentration: could replace (ABC, EFG) Specified Flux: could be recharge across (CD) No Flow (Streamline): a special case of specified flux (HI) Head Dependent Flux: could replace (ABC, EFG) Free Surface: water-table, phreatic surface (CD) Seepage Face: h = z; pressure = atmospheric at ground surface (DE) infinite source/sink calculated head maintains flux infinite source/sink adjusts position adjusts length 5 PHYSICAL MODEL Geometry Materials Boundary Conditions ANALOG MODEL Geometry Material Properties Boundary Conditions Electrical analog model of the Champaign- Urbana Illinois area ground-water system (circa 1960). The top panel is a circuit of resistors and capacitors representing the regional model. Measuring the voltage at various locations in the circuit is equivalent to measuring head in the aquifer. The middle level includes a local model of a portion of the regional model at both the same scale and twice the scale. The lower area includes the controls for imposing current on the model. These models are very difficult to calibrate because each change of material properties involves removing and re-soldering the resistors and capacitors. 6 EMPIRICAL MODEL A Mathematical Fit to Data Unrelated to Process Equations e.g. Manning's Equation V = 1.49 R 2/3 S 1/2 n where: V = average velocity in fps R = hydraulic radius (flow area [ft2]/wetted perimeter[ft]) S = slope of energy gradient n = Manning friction factor GRAPHICAL MODEL - FLOW NET Geometry Material Properties Boundary Conditions 7 ANALYTICAL MODEL Closed form algebraic solution Geometry Material Properties Boundary Conditions Recall Dupuit, Flow to fixed heads with recharge: Note: Recharge is a fixed flux and head/gradient will be calculated to accommodate that recharge - e.g. High recharge >> High heads h1 and h2 are fixed heads and flux will be calculated to accommodate those heads - e.g. a high h1 will shift the divide to the left of the problem domain and produce large influx that joins the recharge and discharges to the right, if h2 is very low, that influx will be even higher ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −− − = x 2 Lw L2 hhKq 2 2 2 1 x L2 hh w K 2 Ld 2 2 2 1 −−= h1 h2 Lx=0 w qx d hx ( ) ( )xxL K w L2 xhhhh 2 2 2 12 1x −+ − −= 10 NUMERICAL FLOW MODELING DISCRETIZE Write equations of GW Flow between each node Darcy's Law Conservation of Mass Define Material Properties Boundary Conditions Initial Conditions Stresses At each node either H or Q is known, the other is unknown n equations & n unknowns solve simultaneously with matrix algebra Result H at each known Q node Q at each known H node Calibrate Steady State Transient Validate Sensitivity Predictions Similar Process for Transport Modeling only Concentration and Flux is unknown NUMERICAL MODELING – Finite Element Modeling 11 • More flexibility in designing Grid NUMERICAL MODELING – Finite Element Modeling Examples of Model Results with links to animations Flow and Transport Model East Texas Land Fill Plume http://inside.mines.edu/~epoeter/ _GW/23Modeling/etex2.avi Flow Model Hanford Reservation Waste Water Disposal http://inside.mines.edu/~epoeter/ _GW/23Modeling/flow_43_96.avi layer1 layer2 North-South cross section through plume 12 MODFLOW Block Centered 3D Finite Difference Ground Water Flow Model Developed by McDonald & Harbaugh at USGS in 1983 - enhanced many times since then Public Domain Most widely used Saturated Porous Media Flow model Many features available MODFLOW: MODFLOW ExecutableInput Files With Packages provided run calculation Based on Model Set-up Output GUI’s Facilitate your work Graphical User Interface 15 MODFLOW Head-dependent Flux Boundary Condition Packages DRAIN package For each river reach in each cell: MODFLOW requires that the user input Conductance, which is all of Darcy's Law except the head difference for Head Dependent Flux boundaries. Q = KA dh/dl Conductance = KA/thickness then MODFLOW calculates the flow as: Q = Conductance dh Conductance of the drain is calculated as: Kof material over which gradient is calculated * Area/thickness Area may be the cylindrical area midway between where the heads used for the gradient are located* length of the drain For recharge, a rate is specified for each cell MODFLOW calculates Q = rate * cell area MODFLOW Flux Boundary Condition Packages Recharge package Q is specified & forced in (or out) unless the cell “goes dry” in which case the modeler may choose to apply it to a lower layer Heads increase as recharge is increased Example alternative recharge distributions 16 When pumping a well in a MODFLOW grid cell Q is specified & withdrawn or injected unless the cell “goes dry” Calculated drawdown represents the average drawdown in the cell, not the actual drawdown in the well MODFLOW assigns one head value to each cell MODFLOW Flux Boundary Condition Packages Well package Cell cross section Next we will use MODFLOW and GMS (Ground Water Modeling System) to get a feel for ground water modeling 17 Locations of Production Wells Where you can adjust withdrawal rate As time allows, experiment with MODFLOW Using the GMS (Ground Water Modeling System) GUI (Graphical User Interface) By Downloading the Example Files and Associated Write up on the class web page for the Modeling Lecture