Presentation on theme: "SDSU GEOL Numerical Modeling of Ground-Water Flow"— Presentation transcript:
1 SDSU GEOL 651 - Numerical Modeling of Ground-Water Flow SDSU Coastal Waters LaboratoryUSGS San Diego Project Office1st Floor conference room4165 Spruance RoadSan Diego CATuesdays 4 -7 PM
2 Introductions Claudia C. Faunt Ph.D. in Geological Engineering from Colorado School of MinesHydrologist with U.S. Geological Survey(619)Office 2nd floor NE corner
3 Introductions Please introduce yourself explain who you are where you are fromwhat your current endeavor is (for example, MS student; state government hydrologist; or consulting hydrologist)explain why you would like to learn more about ground-water modeling (knowing your motives helps me improve the class)
4 Course Organization Organizational Meeting Grading (details next week) Part of the first class meeting will be dedicated to an organizational meeting, at which time a general outline of the class topics, and any desired changes in schedule will be discussed.Grading (details next week)25% miscellaneous assignments25% paper critique assignment50% final project (paper and presentation)Syllabus
5 Course Organization Classes First few mostly lectures Majority First half lecturesSecond halfProblem set related to lectureModel project work
6 Course Topics Introduction, Fundamentals, and Review of Basics Conceptual ModelsBoundary ConditionsAnalytical ModelingNumerical Methods (Finite Difference and Finite Element)Grid Design and Sources/SinksIntroduction to MODFLOWTransient ModelingModel CalibrationSensitivity AnalysesParameter EstimationPredictionsTransport ModelingAdvanced Topics including new MODFLOW packagesOthers?
7 Tentative Syllabus (subject to change to adjust our pace) Handout
9 OUTLINE: What is a ground-water model? Objectives Why Model? Types of problems that we modelTypes of ground-water modelsSteps in a geohydrologic projectSteps in the modeling process
10 What is a ground-water model? A replica of a “real-world” ground-water system
11 OBJECTIVE: UNDERSTAND why we model ground-water systems and problems KNOW the TYPES of problems we typically modelUNDERSTAND what a ground-water model isKNOW the STEPS in the MODELING PROCESSKNOW the STEPS in a GEOHYDROLOGIC PROJECT and how the MODELING PROCESS fits inKNOW HOW to FORMULATE & SOLVE very SIMPLE ground-water MODELSCOMPREHEND the VALUE of SIMPLE ground water MODELS
12 Why model? SOLVE a PROBLEM or make a PREDICTION THINKING TOOL Understand the system and its responses to stresses
13 Types of problems that we model WATER SUPPLYWATER INFLOWWATER OUTFLOWRATE AND DIRECTIONCONCENTRATION OF CHEMICAL CONSTITUENTSEFFECT OF ENGINEERED FEATURESTEST ANALYSIS
14 Types of ground-water models CONCEPTUAL MODELGRAPHICAL MODELPHYSICAL MODELANALOG MODELMATHEMATICAL MODELWe will focus on numerical models in this class
15 Conceptual Model Qualitative description of the system Think of a cartoon
16 Graphical Model FLOW NETS limited to steady state, homogeneous systems, with simple boundary conditions
17 Physical Model SAND TANK which poses scaling problems, for example the grains of a scaled down sand tank model are on the order of the size of a house in the system being simulated
19 Analog Model ELECTRICAL CURRENT FLOW circuit board with resistors to represent hydraulic conductivity and capacitors to represent storage coefficientdifficult to calibrate because each change of material properties involves removing and resoldering the resistors and capacitors
22 Mathematical Model MATHEMATICAL DESCRIPTION OF SYSTEM SIMPLE – ANALYTICALprovides a continuous solution over the model domainCOMPLEX - NUMERICALprovides a discrete solution - i.e. values are calculated at only a few pointswe are going to focus on numerical models
24 Numerical Modeling Formation of conceptual models Manipulation of modeling softwareRepresent a site-specific ground-water systemThe results are referred to as:A model orA model application
25 Steps in a geohydrologic project 1. Define the problem 2. Conceptualize the system 3. Envision how the problem will affect your system 4. Try to find an analytical solution that will provide some insight to the problem 5. Evaluate if steady state conditions will be indicative of your problem (conservative/non-conservative) 6. Evaluate transients if necessary but always consider conditions at steady state
26 Steps in a geohydrologic project 7. SIT BACK AND ASK - DOES THIS RESULT MAKE SENSE? 8. CONSIDER WHAT YOU MIGHT HAVE LEFT OUT ENTIRELY AND HOW THAT MIGHT AFFECT YOUR RESULT 9. Decide if you have solved the problem or if you needa. more field datab. a numerical model (time, cost, accuracy)c. both
27 Steps in a geohydrologic project 9a. If field data are needed, use your analysis to guide data collectionwhat data are needed?what location should they be collected from?
28 Steps in a geohydrologic project 9b. If a numerical model is needed, select appropriate code and when setting up the modelkeep the question to be addressed in mindkeep the capabilities and limitations of the code in mindplan at least three times as much time as you think it will takedraw the problem and overlay a grid on itnote input values formaterial properties,boundary conditions, andinitial conditionsrun steady-state first!plan and conduct transient runsalways monitor results in detail
29 Steps in a geohydrologic project 10.Keep the question in focus and the objective in mind 11.Evaluate Sensitivity 12.Evaluate Uncertainty
30 Steps in a geohydrologic project KEEP THESE THOUGHTS IN MIND:1. Numerical models are valuable thinking tools to help you understand the system. They are not solely for calculating an "answer". They are also useful in illustrating concepts to others.2. A numerical modeling project is likely a major undertaking.3. Capabilities of state-of-the-art models are often primitive compared to the analytical needs of current ground-water problems.4. Data for model input is sparse therefore there is a lot of uncertainty in your results. Report reasonable ranges of answers rather than single values.5. DO NOT get discouraged! 99% of modeling is getting the model set up and working. The predictive phase comprises only a small percentage of the total modeling effort.
31 Components of Modeling Project Statement of objectivesData describing the physical systemSimplified conceptual representation of the systemData processing and modeling softwareReport with written and graphical presentations
32 Steps in the Modeling Process Modeling objectivesData gathering and organizationDevelopment of a conceptual modelNumerical code selectionAssignment of properties and boundary conditionsCalibration and sensitivity analysisModel execution and interpretation of resultsReporting
35 Model AccuracyDependant of the level of understanding of the flow systemRequirements:Some level of site investigationAccurate conceptualizationOld quote:“All models are wrong but some are useful”Accuracy is always a trade-off betweenresources andgoals
36 Determination of Modeling Needs What is the general type of problem to be solved?What features must be simulated to answer the questions about the system?—study objectiveCan the code simulate the hydrologic features of the site?What dimensional capabilities are needed?What is the best solution method?What grid discretization is required for simulating hydrologic features?
37 Modeling Code Administration Is there support for the code?Is there a user’s manual?What does it cost?Is the code proprietary?Are user references available?Is the code widely used?
38 Types of Modeling Codes Objective based:Ground-water supplyWell field designProcess Based:Saturated or unsaturated flowContaminate transportPhysical System BasedMathematical
39 Components of a Mathematical Model Governing Equation (Darcy’s law + water balance eqn) with head (h) as the dependent variableBoundary ConditionsInitial conditions (for transient problems)
40 Solution Methods In order of increasing complexity: AnalyticalAnalytical ElementNumericalFinite differenceFinite elementEach solves the governing equation of ground-water flow and storageDifferent approaches, assumptions and applicability
41 Analytical Methods Classical mathematical methods Resolve differential equations into exact solutionsAssume homogeneityLimited to 1-D and some 2-D problemsCan provide rough approximationsExamples are the Theis or Theim equations
43 Toth Problem Water Table Groundwater Groundwater AQUIFER divide divide Impermeable RockSteady state system: inflow equals outflow
44 Toth Problem Laplace Equation 2D, steady state Water Table Groundwater divideGroundwaterdivideLaplace EquationImpermeable Rock2D, steady state
45 Finite Difference Methods Solves the partial differential equationApproximates a solution at points in a square or rectangular gridCan be 1-, 2-, or 3-DimensionalRelatively easy to constructLess flexibility, especially with boundary conditions
46 Finite difference models may be solved using:a computer program or code (e.g., a FORTRAN program)a spreadsheet (e.g., EXCEL)
49 MODFLOW a computer code that solves a groundwater flow model using finite difference techniquesSeveral versions availableMODFLOW 88MODFLOW 96MODFLOW 2000MODFLOW 2005
50 Finite Element Methods Allows more precise calculationsFlexible placement of nodesGood at defining irregular boundariesLabor intensive setupMight be necessary if the direction of anisotropy varies in the aquifer
51 Structural features create anisotropy in this karst system
53 Class FocusWill use USGS finite-difference model, MODFLOW, for class presentations and exercisesMore details on mathematics and simplifications used in MODFLOW later
54 Governing Equations for Ground Water Flow Conditions and requirements:Mass of water must be conserved at every point in the systemRate and direction of flow is related to head by Darcy’s LawWater and porous medium behave as compressible, elastic materials, so the volume of water “ stored” in the system can change as a function of head
55 Governing Equations for Ground Water Flow Many forms depending on the assumptions that are valid for the problem of interest.In most cases, it is assumed that the density of ground water is spatially and temporally constant.
56 Governing Equations for Ground Water Flow Conservation of MassStarting point for developing 3-D flow equationMass In – Mass Out = Change in Mass Stored(If there is no change in storage, the condition is said to be steady-state. If the storage changes, the condition is said to be transient.)Small control volume over time in 3 directions-finite difference and differential forms-to be useful must be able to express flow rates and change in storage in terms of head (measurable variable) --- Darcy’s Law
57 Governing Equations for Ground Water Flow Darcy’s Law1856 experiment measured flow through sand packgeneralized relationship for flow in porous media
58 Darcy’s LawRelates direction and rate of ground-water flow to the distribution of head in the ground-water systemwhere, Q = volumetric flow rate (discharge), A = flow area perpendicular to L (cross sectional area), K = hydraulic conductivity, L= flow path length (L = x1 - x0), and h = hydraulic head
59 From D.L. Baker online tutorial Darcy’s LawIf the soil did not have uniform properties, then we would have to use the continuous form of the derivative:Notice the minus sign on the right hand side of Darcy’s Law. We do this because in standard notation Q is positive in the same direction as increasing x, and we take x1 > x0. Notice that since H0 > H1, the slope of H(x), DH/Dx, is negative. If it had been the other way around, with H1 > H0, then the negative sign would ensure that Q would be flowing the other way.*** hydraulic head always decreases in the direction of flow ***From D.L. Baker online tutorial
60 HeadHead is defined as the elevation to which ground water will rise in a cased well. Mathematically, head (h) is expressed by the following equation:wherez = elevation head and P/pg = pressure head (water table = 0).
62 Darcy’s Law Dupuit Simplification Mainly used for unconfined aquifers Dupuit's simplification uses the approximate gradient (difference in h over the distance x rather than the flow path length, l), and uses the average head to determine the height of the flow area.Mainly used for unconfined aquifers
63 "Darcy tube" to flow in simple aquifers LaPlace’s Equation:Steady groundwater flow must satisfy not only Darcy's Law but also the equation of continuity3-Dimensional Steady State flow: Homogeneous, Isotropic Conditions where there are no changes in storage of fluidd2h/dx2+d2h/dy2+d2h/dz2=0Steady-state version of diffusion equationthe change of the slope of the head field is zero in the x directionhydraulic head is a harmonic function, and has many analogs in other fields
64 Assignment: If you chose to purchase Applied Groundwater Modeling: read the Preface and Chapters 1 and 2.Begin thinking about class projectBegin looking at journal articles
65 Pre- and Post- Processors Many commercially available programsBest allow placement of model grid over a base mapAllow numerical output to be viewed as contours, flow-path maps, etcSome popular codes are:GMS (Ground Water Modeling System)Visual MODFLOWGroundwater VistasMFI (USGS for setting up smaller models)