The Power of Spreadsheet Models. Mary P. Anderson 1, E. Scott Bair 2 ABSTRACT
|
|
- Egbert Sutton
- 6 years ago
- Views:
Transcription
1 MODFLOW 00 and Other Modeling Odysseys Proceedings, 00, International Ground Water Modeling Center, Colorado School of Mines, Golden, CO, p The Power of Spreadsheet Models Mary P. Anderson, E. Scott Bair University of Wisconsin, Madison, WI, USA Ohio State University, Columbus, OH, USA ABSTRACT Prior to using MODFLOW, students need experience with simpler codes that provide hands-on experience setting up boundary and initial conditions, coding simple solution algorithms, and handling numerical errors. The best way to do this is using spreadsheet models; faculty no longer can expect students to know a common computer language, but students are familiar with spreadsheets. Many aspects of flow and transport modeling may be taught using spreadsheets. Students can quickly set up a spreadsheet model of a simple problem (e.g, the two-dimensional Toth regional flow system problem), watch the iterative solution on-screen, and view the final distributions of heads or concentrations. The same problem may be solved later using MODFLOW. Spreadsheets can be set up to calculate water balances, compute and graph calibration statistics, and perform sensitivity analyses. With the basic principles of modeling in hand, students are introduced to more complex concepts used in MODFLOW such as conductances and head dependent fluxes. Spreadsheets can be designed to mimic packages in MODFLOW such as Zonebudget, River, Well, and Recharge. Thus, spreadsheets provide an easy way to teach finite-difference theory and modeling concepts, as well as their implementation in MODFLOW. INTRODUCTION One of the challenges of teaching numerical techniques applied to groundwater modeling is that students no longer know a common computer language. With the keen interest in graphically-oriented languages like C++, languages like Fortran, the stalwart for scientific computation for the past three decades, are no longer taught at many colleges and universities. Most students are familiar with spreadsheets. The ease with which a spreadsheet can be set up, programmed, solved, and the results statistically analyzed and graphically displayed makes the concepts and notations used in finite-difference modeling easier to understand. In fact, spreadsheet models provide a more effective way to teach finite-difference methods and the hydrologic concepts and argon underlying groundwater modeling than the use of programming languages such as Fortran. Furthermore, an introduction to modeling via spreadsheets eases the transition to using MODFLOW. Olsthoorn (985) and Ousey (986) first described how spreadsheets are used to solve simple finitedifference problems. Olsthoorn (998) provided a summary and additional discussion. The initial excitement over the potential of the method (e.g., Campbell, 985), however, did not lead to widespread use of spreadsheet models in the literature or in practice. This is probably owing to the fact that while ideal for solving simple problems, the use of spreadsheets is awkward for solving the complex models typically needed to represent field situations. Furthermore, pre- and post-processing programs for MODFLOW now allow for a more user-friendly environment than in the mid-980s. Nevertheless, for pedagogical purposes, spreadsheet models are far superior to complex codes such as MODFLOW. Furthermore, spreadsheets like EXCEL not only solve the finite-difference equations but also contain a built in pre-processor of geologic and hydrologic data and a post-processor of results. SIMPLE BEGINNINGS The two-dimensional Laplace equation is written as follows:
2 h + h y 0 () When approximated using finite differences and assuming that x y, the equation becomes: h h + h + h h 0 () i+, + i, i, + i, 4 i, Solving for h i, yields: m m+ m m+ m+ hi+, + hi, + hi, + + hi, h i, (3) 4 where iteration indices (m, m+) have been introduced. Gauss-Seidel iteration is invoked if we always use the most recently computed head values (m+ values) in the solution and if the calculation progresses through the grid from top to bottom and from left to right. (The spreadsheet automatically uses Gauss-Seidel iteration when the iteration option is selected.) When implemented in a spreadsheet solution for a typical cell, D3 for example, the solution is written as follows: D4 + D + C3 + E3 D3 (4) 4 Specified head boundary conditions are represented by simply entering the appropriate head value in the boundary cell. Specified flux conditions are also easily represented; a spreadsheet model with specified flux boundary conditions can be used to illustrate the difference between mesh-centered and blockcentered models. Consider the two-dimensional spreadsheet model shown in Figure, which represents a version of the Toth regional flow problem (Toth, 96). The top boundary represents the water table under specified head conditions whereas the side boundaries are under no flow conditions representative of groundwater divides and the bottom boundary is a no flow boundary reflecting the presence of an impermeable layer. Figure. Mesh-centered grid for the Toth regional flow problem In a mesh-centered grid, a flux boundary is located directly on a node. For the model shown in Figure, the boundary condition for cells that lie along the side boundaries is represented by a central difference h approximation of 0, or
3 h h 0 (5) i+, i, For the boundary cells in column A in Figure, this implies that h i+, h i-, and for cell A3, this means that the head in the node to the left of A3 equals the head in B3. Hence, equation 3 simplifies to * B3 + A + A4 A3 (6) 4 In a block-centered grid, the no flow boundary is at the edge of the cell, or half way between two nodes. For the model shown in Figure, which represents a version of the Toth regional flow problem with a block-centered grid, the left-hand side boundary is located between the nodes in column A and B, so that the head in A3 equals the head in B3. When set up with imaginary nodes that are outside the problem domain (located in columns A and M and row 7) the standard finite difference equation (equation 3) is written for all cells inside the problem domain. Figure. Block-centered grid for the Toth regional flow problem In Figures and above, a simple water balance accounting scheme was introduced, where K is hydraulic conductivity and Q is the flux across the water table. Total recharge (R) into the model equals total discharge (D) leaving the model and a simple error is computed as the difference between R and D. In another assignment, distributed recharge and point withdrawals from wells can be introduced using a finite-difference approximation to Poisson s equation, which can be written for both confined aquifers and for unconfined aquifers under the Dupuit assumptions (e.g., the Island Recharge Problem in Wang and Anderson, 98, p , 66). For a confined aquifer, where T is transmissivity and R is a sink/source term, the Poisson equation is written as h h R + (7) y T and the spreadsheet equation is modified by the addition of the term, a R/T, where x y a. Both distributed recharge and point sources and sinks (pumping wells) can be introduced and the students can test the effects of varying R and T and changing the boundary conditions. Water balance calculations must be modified to include the sink/source terms, thereby giving students hands on experience formulating water balance equations. An SOR iterative solution procedure can also be introduced.
4 One-dimensional problems can be used to convey complex concepts while maintaining mathematical simplicity. For example, a one-dimensional transient problem can be used to introduce transient solution techniques (i.e., explicit and implicit solutions) and illustrate how storage is introduced into a transient water budget. Figure 3 shows a spreadsheet model set up to solve the one-dimensional transient reservoir problem in Wang and Anderson (98, p ). The governing equation is h S h (8) T t Each line of the spreadsheet, starting with line 5 represents the solution at a given time level. A time step of 5 minutes is used in this simulation (cell B and column L). The initial conditions are shown in line 4. Boundary conditions are specified head at both ends of the system (columns A and K). Notice the instantaneous drop in water level in the boundary cell K4 to meters. An implicit solution with Gauss-Seidel iteration is used; the solution at t5 minutes is shown in line 5 with subsequent time steps following line 5. Figure 3. Spreadsheet model of a one-dimensional transient flow problem using an implicit finite difference approximation
5 Figure 4. Water balance computation for the spreadsheet model shown in Figure 3 A water balance also can be introduced as shown in Figure 4. Columns R through Z contain the computed release of water from storage for each node. Column N contains the flow into the model from the left-side constant head boundary, whereas column O contains the flow out of the model through the right-side constant head boundary. Column P is column N plus the total amount of water released from storage (the sum of columns R through Z) and represents the total amount of water flowing into the model. The values in column P should equal the amounts in column O for each time step. The percent error in the water balance is shown in column Q. ADVANCED TOPICS The Block-Centered Flow (BCF) Package in MODFLOW, among other functions, computes the conductance components of the finite-difference equations and the flux between adacent cells. The flux between adacent cells (i, ) and (i+, ) along a row can be written as q Kb y( hi, hi x ) +, i, qi+, (9) This formulation is applicable only when x is constant and the aquifer is isotropic and homogeneous. If K i, K i+, a weighted average value of K must be used. This requires the concepts of harmonic mean and conductance to be introduced. The harmonic mean hydraulic conductivity between nodes (i, ) and (i+, ) is Harmonic Mean K i, i +, (0) and is equal to the conductance, C, across the interface between x i, and x i+, when x y and b. In this case, the flux is computed as K i, K + K q i, qi +, i, i+, i +, C( h h ) ()
6 Conductances must be computed for every shared cell face. In a one-dimensional model conductances are computed for every cell face in the positive x direction (q i, q i+, ) and for every cell face in the negative x direction (q i-, q i, ) to account for water entering and exiting the two faces of the cell. In a two-dimensional model conductances are computed at all four cell faces and in a three-dimensional model conductances at all six cell faces. Again we can use a one-dimensional problem to introduce complex concepts. The left side of Figure 5 shows a spreadsheet of a one-dimensional, steady-state, heterogeneous flow system bounded by two specified head nodes and solved using a Laplace formulation modified for heterogeneous conditions. The spreadsheet computes conductances and fluxes between cells in the positive x direction (C >>> and q >>>) and in the negative x direction (<<< C and <<< q). In the simulation shown, the values of hydraulic conductivity, K, change from 00 (columns B through F), to 0 (column G), to 00 (columns H through L). The graph at the bottom of the spreadsheet shows the effect of the heterogeneities on the computed heads. The spreadsheet also is programmed to compute the difference in flux across the right face and the left face of each cell (q diff), a water balance, and the error. Once the concept of conductance is understood in one dimension, it is relatively easy to expand the model to two dimensions. The logistics of creating two-dimensional models lends itself to linking spreadsheets so that conductances and fluxes are computed on separate spreadsheets that are linked to the main spreadsheet that is used to compute heads and to display results. Linking spreadsheets also is a convenient way to add source and sink terms such as recharge, wells, and the effects of rivers and drains. If each of these sources/sinks is assigned a separate linked spreadsheet, the structure of the spreadsheet model is similar to the modular structure of MODFLOW. Figure 5. Advanced topics introduced using a simple one-dimensional spreadsheet model
7 For example, the right side of Figure 5 shows the same one-dimensional flow system shown on the left side except sources/sinks from recharge, wells, and river interaction are added and a Poisson formulation is used. The volumetric rate of well withdrawal (-00 in cell Q5) is specified on the main spreadsheet. The volumetric rates of recharge and water entering or exiting river cells are computed on linked spreadsheets. The total volumetric rate of water entering or exiting each cell is calculated in the main spreadsheet (cells P7-X7) and is used as the R term in the finite-difference equation for each cell. This type of spreadsheet model enables students to learn more MODFLOW argon and to see how MODFLOW computes different source/sink terms. The linked spreadsheet used to compute volumetric rates of water entering or exiting the model from river cells (Figure 5, right side) is set up as five onedimensional arrays: one array for the head in each river cell (H riv ), one array for the vertical hydraulic conductivities of the riverbed (K riv ), arrays for the width (W) and length (L) of the river in each cell, and one array for the riverbed thickness (M). The values in these arrays are combined according to the same formulae used in MODFLOW to compute riverbed conductance (C riv ) C K rivlw M riv () and then used to compute the volumetric rate of flow into or out of the model from the river q riv C ) (3) riv ( hriv hcell It is also easy to program the main spreadsheet to compute water balances of specific zones, like Zonebudget in MODFLOW, to make contour plots of simulated heads and residuals, to compute calibration statistics such as mean absolute error and root mean squared error, and to make a graph of simulated versus measured heads. As a term proect, students in the second author s flow modeling class develop a two-dimensional, steady-state, spreadsheet model of the flow system in the Aberona River valley at Woburn, Massachusetts. The leukemia cases associated with water from municipal wells G and H at this site are the focus of the book A Civil Action (Harr, 995). The geology and hydrology of the site including synoptic sets of water levels and measured streamflow gains/losses (Myette and others, 987) are used to incorporate some of the complexity of the buried valley aquifer, riparian wetland, and outwash and icecontact deposits into the model. Linked spreadsheets incorporate pumping wells, river/aquifer interaction, and spatially variable hydraulic conductivity, layer thickness, and recharge. To calibrate their models, students statistically and graphically compare simulated and measured heads and calculate a local water balance to compute simulated streamflow gains/losses along the same reach of the Aberona River gaged by the USGS (Myette and others, 987). In a follow-up course on solute transport modeling, students develop a one-dimensional, explicit, finitedifference solution to the advection-dispersion equation incorporating chemical retardation (R f ) R f C t D x C ( v C) x (4) The solution addresses transport in a steady-state, heterogeneous flow field with spatially variable recharge, where the velocity field is determined using a Poisson formulation. The concentration (C) at cell i at time step t is determined by
8 C t i C t α v t t t t ( Ci+ Ci ) α xvi / ( Ci Ci ) t t t ( v C v C ) t x i+ / i + / + / i i i i R f x x R f x (5) where Di α xv is hydrodynamic dispersion (molecular diffusion is ignored) and the terms i v and i / v i+/ are flow velocities at the interfaces between cells i and i- and cells i and i+, respectively (modified from Zheng and Bennett, 995, p. 6). This introduces students to the concepts of stability and numerical dispersion as the solution is unstable if Peclet and Courant constraints are not met. Students apply the model to the movement of TCE from the W.R. Grace site toward wells G and H at Woburn, Massachusetts. The attempt is made to calibrate the one-dimensional model to water levels measured along a flowpath from W.R. Grace to the Aberona River, to measured streamflow gains, and to (limited) historic TCE data by adusting values of hydraulic conductivity, aquifer thickness, recharge rates, dispersivity, and chemical retardation. Students then compare their numerical results to those computed using an Ogata-Banks analytical solution, which assumes a uniform velocity field (i.e. hydraulic conductivity, aquifer thickness, and porosity are constants). CONCLUSIONS AND LIMITATIONS Spreadsheets can be used to introduce students to many concepts involved in numerical modeling of flow and transport, including mesh and block-centered grids, Gauss-Seidel and SOR iteration, explicit and implicit solutions to transient equations, water budgets, and stability and numerical dispersion. Spreadsheets also offer a convenient and easy way to analyze and graph results. Linked spreadsheets allow students to create sophisticated two-dimensional models that mimic the structure and equations of parts of MODFLOW including the BCF, Well, River, Recharge, and Zonebudget packages. There are few limitations to the creativity and types of small problems that can be addressed using spreadsheet models. Spreadsheet models, like all model codes, need to be verified by reproducing analytical solutions. The graphical displays and statistical calculations created for spreadsheet models also must be verified to check for proper assignment of cells and programming. Verification of spreadsheet models is mandatory because of the ease with which small but significant programming errors can be introduced and propagated using the copy and paste command. Developing code verification tests is a creative exercise that challenges students to use the breadth and depth of their hydrogeologic knowledge. The biggest difficulty with using spreadsheet models is associated with managing, linking, and debugging large numbers of arrays. This is particularly true for two-dimensional models of transient flow and solute transport. Once the maor numerical techniques have been presented and implemented using simple spreadsheet models, students can be introduced to professional codes like MODFLOW. Many of these codes have steep learning curves, but allow for three-dimensional problems and processes that are not computationally tractable using spreadsheets such as variable-density flow, multi-phase flow, and partially saturated flow. Although use of professional codes as part of a graduate curriculum in groundwater hydrology is subect to pedagogical debate, it does provide students with experience using tools they may later use as groundwater professionals. This experience is very appealing to some employers. As professional educators, however, it is the hands-on knowledge of the underlying concepts of numerical modeling techniques developed by constructing simple spreadsheet models that we believe improves and enhances the learning process. REFERENCES Campbell, A. M., 985, Discussion of: The power of the electronic worksheet: modeling without special programs and reply by T.N. Olsthoorn, Ground Water, 3(4), Harr, J., 995, A Civil Action, Random House, New York, 500 p.
9 Myette, C.F., J.C. Olympio, and D.G. Johnson, 987, Area of influence and zone of contribution to Superfund-site Wells G and H, Woburn, Massachusetts; U. S. Geological Survey, Water- Resources Investigations Report , p. Olsthoorn, T.N., 985. The power of the electronic worksheet: modeling without special programs, Ground Water, 3(3), Olsthoorn, T.N., 998. Groundwater modelling: calibration and the use of spreadsheets, Delft University Press, 4 p. Ousey, J.R., 986. Modeling steady-state groundwater flow using microcomputer spreadsheets, Journal Geological Education, 34, Toth, J., 96, A theory of groundwater motion in small drainage basins in central Alberta, Canada, Journal of Geophysical Research, 67(), Wang, H.F., and M.P. Anderson, 98, Introduction to Groundwater Modeling: Finite Difference and Finite Element Methods, W.H. Freeman, 56 p. Zheng, C., and G.D. Bennett, 995, Applied Contaminant Transport Modeling, Theory and Practice: van Nostrand Reinhold, New York, New York, 440 p.
GMS 8.0 Tutorial MT3DMS Advanced Transport MT3DMS dispersion, sorption, and dual domain options
v. 8.0 GMS 8.0 Tutorial MT3DMS dispersion, sorption, and dual domain options Objectives Learn about the dispersion, sorption, and dual domain options in MT3DMS Prerequisite Tutorials None Required Components
More informationFORENSIC GEOLOGY A CIVIL ACTION
NAME 89.215 - FORENSIC GEOLOGY A CIVIL ACTION I. Introduction In 1982 a lawsuit was filed on behalf of eight Woburn families by Jan Schlictmann. The suit alleged that serious health effects (childhood
More informationIDAWRA: Groundwater-flow model for the Wood River Valley aquifer system, south-central Idaho February 1, 2017, 11:30-1:00
Idaho Section of the American Water Resources Association IDAWRA: Groundwater-flow model for the Wood River Valley aquifer system, south-central Idaho A three-dimensional numerical model of groundwater
More informationHydrogeology and Simulated Effects of Future Water Use and Drought in the North Fork Red River Alluvial Aquifer: Progress Report
Hydrogeology and Simulated Effects of Future Water Use and Drought in the North Fork Red River Alluvial Aquifer: Progress Report Developed in partnership with the Oklahoma Water Resources Board S. Jerrod
More informationJ. Environ. Res. Develop. Journal of Environmental Research And Development Vol. 8 No. 1, July-September 2013
SENSITIVITY ANALYSIS ON INPUT PARAMETERS OF 1-D GROUNDWATER FLOW GOVERNING EQUATION : SOLVED BY FINITE-DIFFERENCE AND THOMAS ALGORITHM IN MICROSOFT EXCEL Goh E.G.* 1 and Noborio K. 2 1. Department of Engineering
More informationSenior Thesis. BY Calliope A. Voiklis 2000
Senior Thesis MODFLOW Model of The Ohio State University, Columbus Campus BY Calliope A. Voiklis 2000 Submitted as partial fulfillment of The requirements of the degree of Bachelor of Science in Geological
More information11/22/2010. Groundwater in Unconsolidated Deposits. Alluvial (fluvial) deposits. - consist of gravel, sand, silt and clay
Groundwater in Unconsolidated Deposits Alluvial (fluvial) deposits - consist of gravel, sand, silt and clay - laid down by physical processes in rivers and flood plains - major sources for water supplies
More informationIntroduction to Well Hydraulics Fritz R. Fiedler
Introduction to Well Hydraulics Fritz R. Fiedler A well is a pipe placed in a drilled hole that has slots (screen) cut into it that allow water to enter the well, but keep the aquifer material out. A well
More informationMATLAB Solution of Flow and Heat Transfer through a Porous Cooling Channel and the Conjugate Heat Transfer in the Surrounding Wall
MATLAB Solution of Flow and Heat Transfer through a Porous Cooling Channel and the Conjugate Heat Transfer in the Surrounding Wall James Cherry, Mehmet Sözen Grand Valley State University, cherryj1@gmail.com,
More informationTRANSIENT MODELING. Sewering
TRANSIENT MODELING Initial heads must be defined Some important concepts to keep in mind: Initial material properties and boundary conditions must be consistent with the initial heads. DO NOT start with
More informationRT3D Rate-Limited Sorption Reaction
GMS TUTORIALS RT3D Rate-Limited Sorption Reaction This tutorial illustrates the steps involved in using GMS and RT3D to model sorption reactions under mass-transfer limited conditions. The flow model used
More informationFrozen Ground Containment Barrier
Frozen Ground Containment Barrier GEO-SLOPE International Ltd. www.geo-slope.com 1200, 700-6th Ave SW, Calgary, AB, Canada T2P 0T8 Main: +1 403 269 2002 Fax: +1 888 463 2239 Introduction Frozen soil barriers
More informationGroundwater Hydrology
EXERCISE 12 Groundwater Hydrology INTRODUCTION Groundwater is an important component of the hydrologic cycle. It feeds lakes, rivers, wetlands, and reservoirs; it supplies water for domestic, municipal,
More informationGroundwater Simulation
Review Last time Measuring Water Levels Water Level Fluctuations Examples Fluctuations due to well tests, ET, recharge, atms. pressure, earth tides, river stage, ocean tides, surface loading, etc. Todd,
More information1D Verification Examples
1 Introduction 1D Verification Examples Software verification involves comparing the numerical solution with an analytical solution. The objective of this example is to compare the results from CTRAN/W
More informationBaseflow Analysis. Objectives. Baseflow definition and significance
Objectives Baseflow Analysis. Understand the conceptual basis of baseflow analysis.. Estimate watershed-average hydraulic parameters and groundwater recharge rates. Baseflow definition and significance
More informationSimulation of hydrologic and water quality processes in watershed systems using linked SWAT-MODFLOW-RT3D model
Simulation of hydrologic and water quality processes in watershed systems using linked model Ryan Bailey, Assistant Professor Xiaolu Wei, PhD student Rosemary Records, PhD student Mazdak Arabi, Associate
More information4.11 Groundwater model
4.11 Groundwater model 4.11 Groundwater model 4.11.1 Introduction and objectives Groundwater models have the potential to make important contributions in the mapping and characterisation of buried valleys.
More informationModular 3-D Transport model. for accommodating add-on reaction packages. Downloads & a wealth of information at: and.
MT3DMS Modular 3-D Transport model MS denotes the Multi-Species i structure t for accommodating add-on reaction packages Downloads & a wealth of information at: http://hydro.geo.ua.edu/mt3d/ edu/mt3d/
More informationSecond-Order Linear ODEs (Textbook, Chap 2)
Second-Order Linear ODEs (Textbook, Chap ) Motivation Recall from notes, pp. 58-59, the second example of a DE that we introduced there. d φ 1 1 φ = φ 0 dx λ λ Q w ' (a1) This equation represents conservation
More informationGAM Run by Ali H. Chowdhury Ph.D., P.G. Texas Water Development Board Groundwater Resources Division (512)
GAM Run 7-18 by Ali H. Chowdhury Ph.D., P.G. Texas Water Development Board Groundwater Resources Division (512) 936-0834 July 13, 2007 EXECUTIVE SUMMARY The groundwater availability model for the Hill
More informationSimulation of Unsaturated Flow Using Richards Equation
Simulation of Unsaturated Flow Using Richards Equation Rowan Cockett Department of Earth and Ocean Science University of British Columbia rcockett@eos.ubc.ca Abstract Groundwater flow in the unsaturated
More informationAssessing Groundwater Vulnerability and Contaminant Pathways at MCAS Beaufort, SC
Assessing Groundwater Vulnerability and Contaminant Pathways at MCAS Beaufort, SC James M. Rine, John M. Shafer, Elzbieta Covington Abstract A project to assess the vulnerability of groundwater resources
More informationGroundwater Modeling for Flow Systems with Complex Geological and Hydrogeological Conditions
Available online at www.sciencedirect.com Procedia Earth and Planetary Science 3 ( 2011 ) 23 28 2011 Xi an International Conference on Fine Geological Exploration and Groundwater & Gas Hazards Control
More informationNapa Valley Groundwater Sustainability: A Basin Analysis Report for the Napa Valley Subbasin
Napa Valley Groundwater Sustainability: A Basin Analysis Report for the Napa Valley Subbasin A report prepared pursuant to California Water Code Section 10733.6(b)(3) EXECUTIVE SUMMARY (354.4(A)) 1 1.0
More informationv. 8.0 GMS 8.0 Tutorial RT3D Double Monod Model Prerequisite Tutorials None Time minutes Required Components Grid MODFLOW RT3D
v. 8.0 GMS 8.0 Tutorial Objectives Use GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated by an actively growing microbial population that exists in both soil
More informationGroundwater Flow and Solute Transport Modeling
Groundwater Flow and Solute Transport Modeling Ye Zhang Dept. of Geology & Geophysics University of Wyoming c Draft date February 13, 2016 Contents Contents i 0.1 Introduction..............................
More informationContaminant Modeling
Contaminant Modeling with CTRAN/W An Engineering Methodology February 2012 Edition GEO-SLOPE International Ltd. Copyright 2004-2012 by GEO-SLOPE International, Ltd. All rights reserved. No part of this
More information1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #9: Numerical Modeling of Groundwater Flow
1.7, Groundwater Hydrology Prof. Carles Harvey Lecture Packet #9: Numerical Modeling of Groundwater Flow Simulation: Te prediction of quantities of interest (dependent variables) based upon an equation
More informationSurface Processes Focus on Mass Wasting (Chapter 10)
Surface Processes Focus on Mass Wasting (Chapter 10) 1. What is the distinction between weathering, mass wasting, and erosion? 2. What is the controlling force in mass wasting? What force provides resistance?
More informationNumerical Solution of One-dimensional Advection-diffusion Equation Using Simultaneously Temporal and Spatial Weighted Parameters
Australian Journal of Basic and Applied Sciences, 5(6): 536-543, 0 ISSN 99-878 Numerical Solution of One-dimensional Advection-diffusion Equation Using Simultaneously Temporal and Spatial Weighted Parameters
More informationEarth dam steady state seepage analysis
Engineering manual No. 32 Updated 3/2018 Earth dam steady state seepage analysis Program: FEM Water Flow File: Demo_manual_32.gmk Introduction This example illustrates an application of the GEO5 FEM module
More informationChapter 2 Linear Optimization
Chapter 2 Linear Optimization Abstract The purpose of this chapter is to cover the basic concept of linear optimization analysis and its applications in water resources engineering. The graphical and simplex
More informationFinding Large Capacity Groundwater Supplies for Irrigation
Finding Large Capacity Groundwater Supplies for Irrigation December 14, 2012 Presented by: Michael L. Chapman, Jr., PG Irrigation Well Site Evaluation Background Investigation Identify Hydrogeologic Conditions
More informationarxiv:physics/ v1 19 Feb 2004
Finite Difference Time Domain (FDTD) Simulations of Electromagnetic Wave Propagation Using a Spreadsheet David W. Ward and Keith A. Nelson Department of Chemistry Massachusetts Institute of Technology,
More informationRT3D Double Monod Model
GMS 7.0 TUTORIALS RT3D Double Monod Model 1 Introduction This tutorial illustrates the steps involved in using GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated
More informationFreezing Around a Pipe with Flowing Water
1 Introduction Freezing Around a Pipe with Flowing Water Groundwater flow can have a significant effect on ground freezing because heat flow via convection is often more effective at moving heat than conduction
More informationC2VSim Fine Grid (C2VSim-FG) Version Development & Applications
C2VSim Fine Grid (C2VSim-FG) Version Development & Applications 2014 CWEMF Annual Meeting February 24, 2014 Presenters: Ali Taghavi & Mesut Cayar Collaborators: Reza Namvar (RMC), Jim Blanke (RMC), Tariq
More informationSimulation of Ground-Water Flow in the Cedar River Alluvial Aquifer Flow System, Cedar Rapids, Iowa
Prepared in cooperation with the City of Cedar Rapids Simulation of Ground-Water Flow in the Cedar River Alluvial Aquifer Flow System, Cedar Rapids, Iowa Scientific Investigations Report 2004-5130 U.S.
More informationGeophysical Surveys for Groundwater Modelling of Coastal Golf Courses
1 Geophysical Surveys for Groundwater Modelling of Coastal Golf Courses C. RICHARD BATES and RUTH ROBINSON Sedimentary Systems Research Group, University of St. Andrews, St. Andrews, Scotland Abstract
More informationRT3D Double Monod Model
GMS TUTORIALS RT3D Double Monod Model This tutorial illustrates the steps involved in using GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated by an actively
More informationGEOL.3250 Geology for Engineers Glacial Geology
GEOL.3250 Geology for Engineers Glacial Geology NAME Part I: Continental Glaciation Continental glaciers are large ice sheets that cover substantial portions of the land area. In the region of accumulation
More informationFlow toward Pumping Well, next to river = line source = constant head boundary
Flow toward Pumping Well, next to river = line source = constant head boundary Plan view River Channel after Domenico & Schwartz (1990) Line Source Leonhard Euler 1707-1783 e i" +1 = 0 wikimedia.org Charles
More informationRegional groundwater mapping and model
Regional groundwater mapping and model Boyd, Dwight 1, Steve Holysh 2, and Jeff Pitcher 1 1 Grand River Conservation Authority, Canada; 2 Regional Municipality of Halton, Canada The Grand River forms one
More informationVISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES
VISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES Kathryn W. Thorbjarnarson Department of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California
More informationSoils, Hydrogeology, and Aquifer Properties. Philip B. Bedient 2006 Rice University
Soils, Hydrogeology, and Aquifer Properties Philip B. Bedient 2006 Rice University Charbeneau, 2000. Basin Hydrologic Cycle Global Water Supply Distribution 3% of earth s water is fresh - 97% oceans 1%
More informationEnhancing Computer-Based Problem Solving Skills with a Combination of Software Packages
3420 Enhancing Computer-Based Problem Solving Sills with a Combination of Software Pacages Mordechai Shacham Dept. of Chemical Engineering, Ben Gurion University of the Negev Beer-Sheva 84105, Israel e-mail:
More informationCase Study: University of Connecticut (UConn) Landfill
Case Study: University of Connecticut (UConn) Landfill Problem Statement:» Locate disposal trenches» Identify geologic features and distinguish them from leachate and locate preferential pathways in fractured
More informationSemi-Analytical 3D solution for assessing radial collector well pumping. impacts on groundwater-surface water interaction
1 2 Semi-Analytical 3D solution for assessing radial collector well pumping impacts on groundwater-surface water interaction 3 Ali A. Ameli 1 and James R. Craig 2 4 5 1 Global Institute for Water Security,
More informationSeepage through a dam embankment
Elevation GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com Introduction Seepage through a dam embankment The objective of this example is look at a rather simple case of flow through
More informationImpact of the Danube River on the groundwater dynamics in the Kozloduy Lowland
GEOLOGICA BALCANICA, 46 (2), Sofia, Nov. 2017, pp. 33 39. Impact of the Danube River on the groundwater dynamics in the Kozloduy Lowland Peter Gerginov Geological Institute, Bulgarian Academy of Sciences,
More informationA NOVEL APPROACH TO GROUNDWATER MODEL DEVELOPMENT. Thomas D. Krom 1 and Richard Lane 2
A NOVEL APPROACH TO GROUNDWATER MODEL DEVELOPMENT Thomas D. Krom 1 and Richard Lane 2 1 Touch Water Ltd., P.O. Box 143, Lincoln, Christchurch, New Zealand; email: touchwater@gmail.com 2 Applied Research
More informationLocation of protection zones along production galleries: an example of methodology
Tracers and Modelling in Hydrogeology (Proceedings of the TraM'2000 Conference held at Liège, Belgium, May 2000). IAHS Publ. no. 262, 2000. 141 Location of protection zones along production galleries:
More information1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #5: Groundwater Flow Patterns. Local Flow System. Intermediate Flow System
1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #5: Groundwater Flow Patterns c Local Flow System 10,000 feet Intermediate Flow System Regional Flow System 20,000 feet Hydrologic section
More informationRATE OF FLUID FLOW THROUGH POROUS MEDIA
RATE OF FLUID FLOW THROUGH POROUS MEDIA Submitted by Xu Ming Xin Kiong Min Yi Kimberly Yip Juen Chen Nicole A project presented to the Singapore Mathematical Society Essay Competition 2013 1 Abstract Fluid
More informationTechnical Memorandum No
Pajaro River Watershed Study in association with Technical Memorandum No. 1.2.10 Task: Evaluation of Four Watershed Conditions - Sediment To: PRWFPA Staff Working Group Prepared by: Gregory Morris and
More informationWisconsin s Hydrogeology: an overview
2012 Soil and Water Conservation Society Conference Stevens Point, WI Feb 9, 2012 Wisconsin s Hydrogeology: an overview Ken Bradbury Wisconsin Geological and Natural History Survey University of Wisconsin-Extension
More informationSpreadsheet Implementation for Momentum Representation of Gaussian Wave Packet and Uncertainty Principle
European Journal of Physics Education Vol. 3 Issue 0 Tambade Spreadsheet Implementation for Momentum Representation of Gaussian Wave Packet and Uncertainty Principle Popat S. Tambade pstam3@rediffmail.com
More information13 Watershed Delineation & Modeling
Module 4 (L12 - L18): Watershed Modeling Standard modeling approaches and classifications, system concept for watershed modeling, overall description of different hydrologic processes, modeling of rainfall,
More informationv GMS 10.4 Tutorial RT3D Double-Monod Model Prerequisite Tutorials RT3D Instantaneous Aerobic Degradation Time minutes
v. 10.4 GMS 10.4 Tutorial RT3D Double-Monod Model Objectives Use GMS and RT3D to model the reaction between an electron donor and an electron acceptor, mediated by an actively growing microbial population
More informationCHAPTER 9 SUMMARY AND CONCLUSIONS
CHAPTER 9 SUMMARY AND CONCLUSIONS The following are the important conclusions and salient features of the present study. 1. The evaluation of groundwater potential is a prerequisite for any kind of planning
More informationENVIRONMENTAL EFFECTS OF GROUNDWATER WITHDRAWAL IN SOUTH NYÍRSÉG
PhD thesis ENVIRONMENTAL EFFECTS OF GROUNDWATER WITHDRAWAL IN SOUTH NYÍRSÉG János Szanyi Szeged, 2004 ENVIRONMENTAL EFFECTS OF GROUNDWATER WITHDRAWAL IN SOUTH NYÍRSÉG Preliminaries, the aims of the dissertation
More informationDetermination of Density 1
Introduction Determination of Density 1 Authors: B. D. Lamp, D. L. McCurdy, V. M. Pultz and J. M. McCormick* Last Update: February 1, 2013 Not so long ago a statistical data analysis of any data set larger
More informationChapter 8 Fetter, Applied Hydrology 4 th Edition, Geology of Groundwater Occurrence
Chapter 8 Fetter, Applied Hydrology 4 th Edition, 2001 Geology of Groundwater Occurrence Figure 8.42. Alluvial Valleys ground-water region. Fetter, Applied Hydrology 4 th Edition, 2001 Fetter, Applied
More informationCREDENTIALS. HERBERT E. JOHNSTON 185 Manville Hill Rd, Unit 203 Cumberland, Rhode Island (401)
CREDENTIALS HERBERT E. JOHNSTON 185 Manville Hill Rd, Unit 203 Cumberland, Rhode Island 02864-3617 (401) 658 4747 e-mail: hjohns1931@aol.com OCCUPATION: Hydrogeologist POSITIONS: o Groundwater consultant
More informationDeflated CG Method for Modelling Groundwater Flow Near Faults. L.A. Ros
Deflated CG Method for Modelling Groundwater Flow Near Faults Interim Report L.A. Ros Delft, Utrecht January 2008 Delft University of Technology Deltares Supervisors: Prof.dr.ir. C. Vuik (TU Delft) Dr.
More informationFUNDAMENTALS OF ENGINEERING GEOLOGY
FUNDAMENTALS OF ENGINEERING GEOLOGY Prof. Dr. HUSSEIN HAMEED KARIM Building and Construction Engineering Department 2012 Preface The impulse to write this book stemmed from a course of geology given by
More informationCode-to-Code Benchmarking of the PORFLOW and GoldSim Contaminant Transport Models using a Simple 1-D Domain
Code-to-Code Benchmarking of the PORFLOW and GoldSim Contaminant Transport Models using a Simple 1-D Domain - 11191 Robert A. Hiergesell and Glenn A. Taylor Savannah River National Laboratory SRNS Bldg.
More informationUsing Spreadsheets to Teach Engineering Problem Solving: Differential and Integral Equations
Session 50 Using Spreadsheets to Teach Engineering Problem Solving: Differential and Integral Equations James P. Blanchard University of Wisconsin - Madison ABSTRACT Spreadsheets offer significant advantages
More informationGroundwater Modeling of the NorthMet Plant Site
Groundwater Modeling of the NorthMet Plant Site Supporting Document for Water Modeling Data Package Volume 2 Plant Site Prepared for Poly Met Mining Inc. January 2015 4700 West 77th Street Minneapolis,
More informationTowards Seamless Interactions Between Geologic Models and Hydrogeologic Applications
Towards Seamless Interactions Between Geologic Models and Hydrogeologic Applications Ross, M. 1, M. Parent 2, R. Martel 1, and R. Lefebvre 1 1 Institut National de la Recherche Scientifique (INRS-ETE),
More informationEvaluation and optimization of multi-lateral wells using. MODFLOW unstructured grids. Modelling multi-lateral wells using unstructured grids
1 2 3 4 5 6 7 8 Evaluation and optimization of multi-lateral wells using MODFLOW unstructured grids 9 10 Modelling multi-lateral wells using unstructured grids 11 12 13 14 15 *1,2 Marcell Lux, 1 János
More informationGG655/CEE623 Groundwater Modeling. Aly I. El-Kadi
GG655/CEE63 Groundwater Modeling Model Theory Water Flow Aly I. El-Kadi Hydrogeology 1 Saline water in oceans = 97.% Ice caps and glaciers =.14% Groundwater = 0.61% Surface water = 0.009% Soil moisture
More informationWeighted residual (s=1.0)
Prepared in cooperation with the U.S. Department of Energy MODFLOW-2000, THE U.S. GEOLOGICAL SURVEY MODULAR GROUND-WATER MODEL USER GUIDE TO THE OBSERVATION, SENSITIVITY, AND PARAMETER-ESTIMATION PROCESSES
More informationFlow to a Well in a Two-Aquifer System
Flow to a Well in a Two-Aquifer System Bruce Hunt 1 and David Scott Abstract: An approximate solution for flow to a well in an aquifer overlain by both an aquitard and a second aquifer containing a free
More informationPRELIMINARY. Select Geophysical Methods and Groundwater Modeling: Examples from USGS studies. Claudia Faunt and a cast of others
Select Geophysical Methods and Groundwater Modeling: Examples from USGS studies Claudia Faunt and a cast of others Current Preliminary Studies Stanford Water in the West Groundwater Data Workshop Series:
More informationNUMERICAL SOLUTION OF TWO-REGION ADVECTION-DISPERSION TRANSPORT AND COMPARISON WITH ANALYTICAL SOLUTION ON EXAMPLE PROBLEMS
Proceedings of ALGORITMY 2002 Conference on Scientific Computing, pp. 130 137 NUMERICAL SOLUTION OF TWO-REGION ADVECTION-DISPERSION TRANSPORT AND COMPARISON WITH ANALYTICAL SOLUTION ON EXAMPLE PROBLEMS
More informationSaltwater injection into a fractured aquifer: A density-coupled mass-transport model
Saltwater injection into a fractured aquifer: A density-coupled mass-transport model Junfeng Luo 1, Martina aus der Beek 2, Joachim Plümacher 2, Sven Seifert 1, Bertram Monninkhoff 1 1 DHI-WASY GmbH, Volmerstr.
More informationDipartimento di Scienze Matematiche
Exploiting parallel computing in Discrete Fracture Network simulations: an inherently parallel optimization approach Stefano Berrone stefano.berrone@polito.it Team: Matìas Benedetto, Andrea Borio, Claudio
More informationSimulating the groundwater discharge to wetlands. Mukwonago Basin Example and Potential Application in Dane County
Simulating the groundwater discharge to wetlands Mukwonago Basin Example and Potential Application in Dane County Conceptual Model Topography is major control on flow to wetlands Land Surface Water Table
More informationInverse Modelling for Flow and Transport in Porous Media
Inverse Modelling for Flow and Transport in Porous Media Mauro Giudici 1 Dipartimento di Scienze della Terra, Sezione di Geofisica, Università degli Studi di Milano, Milano, Italy Lecture given at the
More informationPollution. Elixir Pollution 97 (2016)
42253 Available online at www.elixirpublishers.com (Elixir International Journal) Pollution Elixir Pollution 97 (2016) 42253-42257 Analytical Solution of Temporally Dispersion of Solute through Semi- Infinite
More informationSimple closed form formulas for predicting groundwater flow model uncertainty in complex, heterogeneous trending media
WATER RESOURCES RESEARCH, VOL. 4,, doi:0.029/2005wr00443, 2005 Simple closed form formulas for predicting groundwater flow model uncertainty in complex, heterogeneous trending media Chuen-Fa Ni and Shu-Guang
More informationIPMO2-1. Groundwater Modelling of Chiang Rai Basin, Northern Thailand. Sattaya Intanum* Dr.Schradh Saenton**
IPMO2-1 Groundwater Modelling of Chiang Rai Basin, Northern Thailand Sattaya Intanum* Dr.Schradh Saenton** ABSTRACT Chiang Rai basin, situated in Chiang Rai and Phayao provinces covering an area of 11,000
More informationLecture Outlines PowerPoint. Chapter 5 Earth Science 11e Tarbuck/Lutgens
Lecture Outlines PowerPoint Chapter 5 Earth Science 11e Tarbuck/Lutgens 2006 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors
More informationStudy of heterogeneous vertical hyporheic flux via streambed temperature at different depths
168 Remote Sensing and GIS for Hydrology and Water Resources (IAHS Publ. 368, 2015) (Proceedings RSHS14 and ICGRHWE14, Guangzhou, China, August 2014). Study of heterogeneous vertical hyporheic flux via
More informationTexas A & M University and U.S. Bureau of Reclamation Hydrologic Modeling Inventory Model Description Form
Texas A & M University and U.S. Bureau of Reclamation Hydrologic Modeling Inventory Model Description Form JUNE, 1999 Name of Model: Two-Dimensional Alluvial River and Floodplain Model (MIKE21 CHD & CST)
More informationABSTRACT INTRODUCTION
Development and Calibration of Dual-Permeability Models in Complex Hydrogeologic Settings: An Example from the T-Tunnel Complex, Rainier Mesa, Nevada National Security Site Donald M. Reeves, Rishi Parashar,
More informationRT3D BTEX Degradation with Multiple Electron Acceptors
GMS TUTRIALS RTD BTEX Degradation with Multiple Electron Acceptors This tutorial illustrates the steps involved in using GMS and RTD to model BTEX degradation using a multiple electron acceptor model.
More informationEVALUATION OF CRITICAL FRACTURE SKIN POROSITY FOR CONTAMINANT MIGRATION IN FRACTURED FORMATIONS
ISSN (Online) : 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology An ISO 3297: 2007 Certified Organization, Volume 2, Special Issue
More informationAPPENDIX Tidally induced groundwater circulation in an unconfined coastal aquifer modeled with a Hele-Shaw cell
APPENDIX Tidally induced groundwater circulation in an unconfined coastal aquifer modeled with a Hele-Shaw cell AaronJ.Mango* Mark W. Schmeeckle* David Jon Furbish* Department of Geological Sciences, Florida
More informationA GUI FOR EVOLVE ZAMS
A GUI FOR EVOLVE ZAMS D. R. Schlegel Computer Science Department Here the early work on a new user interface for the Evolve ZAMS stellar evolution code is presented. The initial goal of this project is
More informationRiver Processes. Drainage Basin Morphometry
Drainage Basin Morphometry River Processes Morphometry - the measurement and mathematical analysis of the configuration of the earth s surface and of the shape and dimensions of its landforms. Horton (1945)
More information12 SWAT USER S MANUAL, VERSION 98.1
12 SWAT USER S MANUAL, VERSION 98.1 CANOPY STORAGE. Canopy storage is the water intercepted by vegetative surfaces (the canopy) where it is held and made available for evaporation. When using the curve
More informationSupplemental Materials. Modeling Flow into Horizontal Wells in a Dupuit-Forchheimer Model
Supplemental Materials Modeling Flow into Horizontal Wells in a Dupuit-Forchheimer Model Henk Haitjema, Sergey Kuzin, Vic Kelson, and Daniel Abrams August 8, 2011 1 Original publication Modeling Flow into
More informationAppendix D. Model Setup, Calibration, and Validation
. Model Setup, Calibration, and Validation Lower Grand River Watershed TMDL January 1 1. Model Selection and Setup The Loading Simulation Program in C++ (LSPC) was selected to address the modeling needs
More informationFollow links Class Use and other Permissions. For more information, send to:
COPYRIGHT NOTICE: Stephen L. Campbell & Richard Haberman: Introduction to Differential Equations with Dynamical Systems is published by Princeton University Press and copyrighted, 2008, by Princeton University
More informationNumerical investigation of the river-groundwater interaction characteristics in the downstream desert of the Heihe River, China
Numerical investigation of the river-groundwater interaction characteristics in the downstream desert of the Heihe River, China B.B. WANG1,a, W.R. HUANG1,a *, Y.CAI1,a, F.TENG1,a, Q.ZHOU1,a 1 Department
More informationResidence Time Distribution in Dynamically Changing Hydrologic Systems
Residence Time Distribution in Dynamically Changing Hydrologic Systems Jesus D. Gomez and John L. Wilson Hydrology Program New Mexico Tech December 2009 1 Introduction Age distributions (ADs) encapsulate
More information