GEOS 5311 Lecture Notes: Introduction toGroundwater Modeling

Dr. T. Brikowski

Spring 2013

0file:introduction.tex,v (1.10, January 23, 2013), printed January 23, 2013

Purpose of the Class

I Learn to apply quantitative modeling techniques wisely toobtain useful and valid results

I An enormous number of quantitative tools exist in hydrology(see Section 2)

I The challenge is to learn basic rules and principles that areuseful no matter which tool is selected

I We will do this in lecture, gaining hands-on experience usingone general computer interface (GMS1, and the most commonflow (MODFLOW) and transport (MT3D) model programs.Note GMS development was funded by the USACE.

1http://www.aquaveo.com

What is modeling?

I Model - any construction that approximates a field situationI conceptual model: a qualitative approximation of a system

used to understand its gross character (“this is how we think itworks . . . ”)

I mathematical model: mathematical construction, based ongoverning equation(s) and boundary/initial conditions that arethought to approximate a field setting

I numerical model: computer approximation of mathematicalmodel

Mathematical Model Solutions

I To make predictions or analyses, the system of governingequations must be solved

I Solutions take two basic forms:I analytic solution: an exact or algebraic solution of the

mathematical model, requires simple problemI numerical solution: an approximate solution, usually generated

on a computer, allows for great complexity

Uses of Models

I Predicting response of system to specific, isolated changes

I Studying effect of various processes on the system

I Limited ability to predict future state of systemI because of limitations in data (most often

incompletely-characterized heterogeneity)I because of limitations in theory (poorly understood

phenomena, e.g. hysteretic behavior in unsaturated flow)

Future Directions

I historically groundwater modeling was motivated by (inapproximate order of development):

I introduction of EPA regulation of hazardous chemical spills(CERCLA/Superfund), e.g. Love Canal

I Federal waste storage projects, e.g. Yucca Mountain, WIPPsite, Rocky Flats, Pantex

I future large-scale projects or concepts:I climate-change impacts on water supply

I future tools:

GSFLOW free USGS program for coupledgroundwater-surfacewater interaction (see USGSwebsite)

VIC main model currently used for runoff forecastingin the Western U.S. See U. Washington website

Hydrologic Model Types

Model types can be sorted most generally by their governingequation (van der Heijde et al. 1985; Mangold and Tsang 1991)(also IGWMC software reviews2):

I Flow model - solves water mass balance equation, dependentvariable is pressure or head, velocity is a derived quantity

I Transport model - solves water and dissolved species massbalance equation, dependent variable is concentration. Moredifficult to solve numerically.

2http://igwmc.mines.edu

Available Flow Models: USGS

See USGS WRD website3 for more details.

I Prickett-Lonnquist (aka PLASM, Prickett and Lonnquist1971)

I The most popular flow modeling program from mid-1970’s tomid-1980’s.

I Finite difference (ADI), original versions requiredcustomization for each setting (i.e. no provision for generalboundary conditions).

I Modflow (Harbaugh 2005; Harbaugh et al. 2000; McDonaldand Harbaugh 1988)

I industry standard for 20 yearsI 3-D saturated flow (confined or unconfined), finite difference

(block-centered grid).I Written to be a modular (easily-updatable) version of

Prickett-Lonnquist. Many add-on modules available (e.g. Hill1990).

I Sutra (Voss 1984)I 2-D variable-density flow code (i.e. includes buoyancy effects)

Available Flow Models: USGS (cont.)

I models fluid flow or transport of a single (density-affecting)species, i.e. heat or Cl−.

I Developed for work on saline-water intrusion problems,applicable to simple geothermal-hydrothermal settings.

3http://water.usgs.gov

Other Flow Models

Other useful flow models:I TOUGH+ (supercedes TOUGH, Pruess 1991, 2004; Pruess

et al. 1999)I multi-phase (gas and liquid) flow code, developed for work in

nuclear waste disposal, derived from geothermal modelingcodes.

I integrated finite difference (boundary conditions specified“unnaturally”, unstructured grid). Difficult to use successfullysince models highly non-linear equations.

I about the only useable code for volatile organic compounds(e.g. underground gasoline vapors)

I WhAEM, ModAEM, GFLOW2000I uses Analytic Element Method (Haitjema 1995; Strack 1989),

really just superimposed analytic solutions

I FEMwaterI Finite Element flow code, allows great flexibility in grids (2D

and 3D)

I HYDRUS2D/3D

Other Flow Models (cont.)

I vadose zone modeling, very popularI most used as Modflow package

Available Transport Models: USGS

See USGS WRD website4 for more details.

I Method-of-Characteristics (or ’MOC’, Konikow andBredehoeft 1978)

I Solves flow equation on discrete time steps, then transport asa steady-state process at each time step.

I Robust approach (stable for large time and space steps), butlimited accuracy. The most commonly used model in the 70’sand early 80’s.

I MT3D (Zheng 1992, 1995)I Adds MOC to Modflow.I Probably the most popular transport model in use today. Also

robust and computationally efficient.

4http://water.usgs.gov

Other Transport Codes

I RT3D:I Reactive transport code, adds rock/matrix chemical reaction

to MT3D. From PNL.I same capabilities now in MT3D

I TRACR3D (Los Alamos National Lab, (Travis and Birdsell1991). Efficiently written finite-difference program, includestwo-phase flow, deformable and reactive porous mediamodeling.

Reaction Models

I These compute water-rock reactions, including evolution ofwaters along a flowpath.

I Essentially a multi-component mass and electrical chargebalance, with thermodynamic rules (reactions) used todetermine distribution of species

I Main codes are:I PHREEQC (Parkhurst 1995, USGS)

I Charge balance, speciation & saturation index calculations(i.e. chemical significance of individual analyses);

I reaction-path modeling (prediction of water-rock interaction,or deduction of paths from analyses at differing locations).

I Command-line interface, but quite robust and applicable formany problems

I Geochemist’s Workbench (Bethke 1996). Nice point-and-clickinterface, similar functionality as PHREEQC, with more abilityto model reaction paths. Expensive.

Reaction Models (cont.)

I EQ3/EQ6 (Wolery 1979): water-rock interactions over widerange of T & P. Most useful for nuclear waste problems,hydrothermal systems, etc. The most complicated andthorough reaction model readily available.

Coupled-Process Models

At the leading edge of current modeling practice are models thatattempt to “do it all”:

I usually simulate combined flow, transport anddeformation/deposition.

I primarily involved in oilfield reservoir models (e.g. secondaryand tertiary production efforts)

I also important for advanced waste disposal problems, e.g.high level nuclear waste (TOSPEC, Yucca Mountain)

I many appear as new modules for Modflow:

PHAST reactive transport combining Modflow withPHREEQC. See PHAST homepage

HYDRUS vadose zone model for “accurate” rechargeestimation to saturated zone. See overviewarticle

Why model?

I Hypothesis testing

I System exploration (interpretation, study of process) e.g.(Brikowski and Norton 1989)

I PredictionI the basic goal of most consulting contracts (i.e. this is what

pays well)I VERY RISKY because (Konikow 1986; Konikow and

E. P. Patten 1985):I geologic systems will always be incompletely characterized

[‘surprise”, ][]Bredehoeft-2005I conditions may change in the future

Use and Misuse of Models

I General procedures in modeling (Mercer and Faust1980, 1981)

I Hypothesis testing: Aquifer-Lake interaction (Krabbenhoftand Anderson 1986)

I System exploration: Heat pipe phenomena (Pruess 1985)

I Misuse: Inputs pre-determine results (Fehn and Cathles 1979)

Demonstration of Modeling Procedure

For example, development of a model of Hays, KS valley aquifer

I Develop conceptual model of siteI Typically will have surface topography/culture (e.g. USGS

topo maps, Hays location figure), geologic maps/cross-sections, and some borehole information (usually well lithologylogs, some hydrologic tests or observations, Hays boreholesfigure)

I From this break system down into hydrostratigraphic units,system boundaries and source/sinks

I at Hays years of observation indicate three units, bedrockCretaceous shale of very low permeability, overlying Qalsand-gravel aquifer of high permeability, generally overlain byQt silt-clay overbank deposits of moderate-low permeability

I lateral aquifer boundaries are generally defined by the geologicmap (Kc-QT contact at the surface)

I vertical boundaries (top and bottom) are defined fromborehole information (demo of shale-top picking in GMS)

I other properties, such as hydraulic conductivity, are fitparameters for model

Demonstration of Modeling Procedure (cont.)

I Calibrate model

I carry out flow model, calculate residual error with observedhead

Models

Two main models of this system have been made

I DOE-Yucca Mountain (Eddebbarh et al. 2003; Zyvoloski et al.2003). Limited to region around waste repository

I USGS Model (Belcher et al. 2010)I includes entire flow system

USGS Study

To avoid adding lots of unreadable figures, start with list of PDFpage #s to Belcher et al. (2010), accessible at UTD here

I Ultimate scale: 27 hydrgeologic units, 16 layers of definedthickness, a finite-difference grid consisting of 194 rows and160 columns, and uniform cells 1,500 meters (m) on each side.

I Decide boundary of system (Setting, p. 6)

I potentially complicated hydrologic subdivisions (schematicblock diagram, p. 138)

I Hydrostratigraphic units (internal heterogeneity):I what kind of rocks possible (Surficial geology, p. 24)I deep carbonates important (large 2ndary porosity) and very

thick (E-W deep fence diagram, p. 26)I surficial volcanics lower perm, have visible chemical impact

(surface map, p. 27)I structure (normal faults) important, (structure map, p. 31)I vertical zonation crucial in this area (deep high conductivity

layers, see x-secns., p. 34, maps p. 42, 48-50)

USGS Study (cont.)I again carbonates most important (maps p. 62-3)I some confining beds present (map. p 66)I together with structural juxtaposition stratigraphy quite

complicated (3D block diagram, p. 74)I Walker Lane-related strike-slip faults thought to be deep

conduits for groundwater flow (3D block digram, p. 81)I also faults as flow barriers (p. 83)

I Boundary fluxes (recharge-discharge)I potentiometric surface map, with recharge-discharge areas (p.

100)I anthropogenic (pumping) effects (p. 106, see abandoned farms

in Google Maps)I pumping can be included, but with significant errors (p. 110)I precipitation-infiltration is main water source (p. 112-3)I inter-basin flow possible, even across flow system boundaries

(small compared to pump rate, p. 115)I also ungauged natural springs (p. 155), at least providing

water level estimate

I Calibration data (history matching)

USGS Study (cont.)

I use holes-of-opportunity, usually poorly distributed (p. 122)and records questionable

I Build model gridI grid map view, p. 166,I hydrostratigraphic unit list, p. 167I assign hydrolithology (and therefore rock properties) in 3D (p.

174, explan. p 171)I block & fence diagrams of model units, p. 182-184, 243-6,

263)I viewable as thickness maps also (e.g. volcanic-sed p. 203,

lower carbonate aquifer p. 231)I model layers vs. hydrostraigraphy (p. 261)I fence diagram of model units (p. 263)I simulated recharge & discharge (p. 266-7)

I Calibration resultsI head errors (p. 331, large in Eleana Range, good in Amargosa

Valley)

References

Belcher, W.R., D’Agnese, F.A., O’Brien, G.M.: Death valley regionalgroundwater flow system, nevada and california; hydrogeologicframework and transient groundwater flow model; introduction. U.S. Geological Survey Professional Paper pp. 3 – 17 (2010),http://pubs.usgs.gov/pp/1711/

Bethke, C.M.: Geochemical Reaction Modeling: Concepts andApplications. Oxford University Press, New York (1996)

Brikowski, T.H., Norton, D.: Influence of magma chamber geometry onhydrothermal activity at mid-ocean ridges. Earth Planet. Sci. Lett.93, 241–255 (1989)

Eddebbarh, A.A., Zyvoloski, G.A., Robinson, B.A., Kwicklis, E.M.,Reimus, P.W., Arnold, B.W., Corbet, T., Kuzio, S.P., Faunt, C.:The saturated zone at Yucca Mountain: an overview of thecharacterization and assessment of the saturated zone as a barrier topotential radionuclide migration. J. Contam. Hydrology 62-63,477–493 (April-May 2003), http://www.sciencedirect.com/science/article/pii/S0169772202001547

References (cont.)

Fehn, U., Cathles, L.M.: Hydrothermal convection at slow-spreadingmid-ocean ridges. Tectonophysics 55(1-2), 239–260 (1979)

Haitjema, H.M.: Analytic Element Modeling of Groundwater Flow.Academic Press, San Diego, CA (1995), iSBN 0-12-316550-4

Harbaugh, A.W.: Modflow-2005, the u.s. geological survey modularground-water model–the ground-water flow process. Techniques andMethods Book 6-A16, U. S. Geol. Survey, Denver, CO (2005),http://pubs.usgs.gov/tm/2005/tm6A16/PDF/TM6A16.pdf

Harbaugh, A.W., Banta, E.R., Hill, M.C., McDonald, M.G.:Modflow-2000, the u.s. geological survey modular ground-watermodel – user guide to modularization concepts and the ground-waterflow process. Open File Rept. OFR00-92, U. S. Geol. Survey,Denver, CO (2000), http://water.usgs.gov/nrp/gwsoftware/modflow2000/ofr00-92.pdf, 121 p

van der Heijde, P., Bachmat, Y., Bredehoeft, J., Andrews, B., Holtz, D.,Sebastian, S.: Groundwater Management: The use of numericalmodels, Water Resources Monograph, vol. 5. Amer. Geophys.Union, Washington, D.C. (1985)

References (cont.)

Hill, M.C.: Preconditioned conjugate-gradient 2 (pcg2), a computerprogram for solving ground-water flow equations. Water-resour.investig. rept. 90-4048, U.S. Geol. Survey, Denver, CO (1990)

Konikow, L.F.: Predictive accuracy of a groundwater model - lessonsfrom a post-audit. Ground Water 24, 173–184 (1986)

Konikow, L.F., Bredehoeft, J.D.: Computer model of two-dimensionalsolute transport and dispersion in ground water, vol. 7, chap. Chp.C2. U. S. Geol. Survey (1978)

Konikow, L.F., E. P. Patten, J.: Groundwater forecasting. In: Anderson,M., Burt, T. (eds.) Hydrological Forecasting. John Wiley (1985)

Krabbenhoft, D.P., Anderson, M.P.: Use of a numerical ground-waterflow model for hypothesis testing. Ground Water 24, 49–55 (1986)

Mangold, D.C., Tsang, C.F.: A summary of subsurface hydrological andhydrochemical models. Rev. Geophys. 29, 51–79 (1991)

McDonald, M.G., Harbaugh, A.W.: A modular three-dimensionalfinite-difference ground-water flow model. Techniques of WaterResour. Investig. A1, Book 6, 200 (1988)

References (cont.)Mercer, J.W., Faust, C.R.: Ground-water modeling: An overview.

Ground Water 18, 108–115 (1980)

Mercer, J.W., Faust, C.R.: Ground-Water Modeling. Nat. Water WellAssn. (1981)

Parkhurst, D.L.: User’s guide to PHREEQC-A computer program forspeciation, reaction-path, advective-transport, and inversegeochemical calculations. Water-Resources Investig. Rept. 95-4227(1995), http://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc/

Prickett, T.A., Lonnquist, C.G.: Selected digital computer techniques forgroundwater resource evaluation. Bulletin, Illinois State WaterSurvey, Urbana, IL (1971)

Pruess, K.: A quantitative model of vapor dominated geothermalreservoirs as heat pipes in fractured porous rocks. Geotherm.Resour. Council Transact. 9, 353–361 (1985)

Pruess, K.: Tough2 - a general-purpose numerical simulator ofmultiphase fluid and heat flow. Lbl-29400/uc-251, LawrenceBerkeley Laboratory, Berkeley, CA (1991)

References (cont.)Pruess, K.: The TOUGH codes; a family of simulation tools for

multiphase flow and transport process in permeable media. VadoseZone J. 3(3), 738–746 (Aug 2004)

Pruess, K., Oldenburg, C., Moridis, G.: Tough2 user’s guide, version 2.0.Report LBNL-43134, Lawrence Berkeley Nat. Lab, Berkeley, CA(NOV 1999), http://esd.lbl.gov/tough2/LBNL_43134.pdf

Strack, O.D.L.: Groundwater Mechanics. Prentice Hall, Englewood Cliffs,NJ (1989)

Travis, B.J., Birdsell, K.H.: Tracr3d: A model of flow and transport inporous media– model description and user’s manual. La-11798-m,Los Alamos Nat. Lab., Los Alamos, NM (1991)

Voss, C.I.: A finite-element simulation model for saturated-unsaturated,fluid-density-dependent groundwater flow with energy transport orchemically-reactive single-species solute transport. Water Resour.Investig Rept. 84-4369, U.S. Geol. Surv. (1984)

Wolery, T.J.: Calculation of chemical equilibrium between aqueoussolution and minerals: the eq3/6 software package. Ucrl-52658,Lawrence Livermore Nat. Lab., Livermore, CA (1979)

References (cont.)

Zheng, C.: MT3D: A modular three-dimensional transport model forsimulation of advection, dispersion and chemical reactions ofcontaminants in groundwater systems. S.S. Papdopulos &Associates, Inc., Bethesda, MD (1992)

Zheng, C.: Applied Contaminant Transport Modeling. van Nostrand(1995), iSBN 0-442-01348-5

Zhou, Y., Li, W.: A review of regional groundwater flow modeling.Geoscience Frontiers 2(2), 205 – 214 (2011),http://www.sciencedirect.com/science/article/pii/

S167498711100020X

Zyvoloski, G., Kwicklis, E., Eddebbarh, A.A., Arnold, B., Faunt, C.,Robinson, B.A.: The site-scale saturated zone flow model for YuccaMountain: calibration of different conceptual models and theirimpact on flow paths. J. Contam. Hydrology 62-63, 731–750(April-May 2003), http://www.sciencedirect.com/science/article/pii/S0169772202001900