Development and Application of Groundwater Flow and Solute Transport Models. Randolf Rausch

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1 Development and Application of Groundwater Flow and Solute Transport Models Randolf Rausch

2 Overview Groundwater Flow Modeling Solute Transport Modeling Inverse Problem in Groundwater Modeling

3 Groundwater Flow Modeling

$Flow modeling in fractured and$ $fractured / karstified sytems Double$

4 Flow modeling in fractured and karstified media Model approaches for fractured / karstified sytems Double porosity flow models Parameter identification

$fractures$

5 Problem: Flow in fractures and pipes

6 Large dynamics in head and discharge

7 Matrix and pipe network

8 Matrix and pipe network + observation wells

9 Interpolated head distribution

10 Interpolated head distribution and reality

$of fractured$ media Granite

$fractures and$ impermeable

11 Classification of fractured media Granite Sandstone Limestone Karstified Limestone Mesh of fractures and impermeable matrix Fractures with permeable matrix Fractured system with minor karstification Conduit system with a karstified rock matrix Waste Disposal Water Supply

$Equivalent continuum Two coupled fracture systems Fracture network and continuum Two$

12 Possible model approaches Single Porosity Model Double Porosity Model Discrete model Equivalent continuum Two coupled fracture systems Fracture network and continuum Two equivalent continua

Double continuum flow model Karst system Double continuum system Linear exchange depends on: head difference exchange coefficient Different aquifer

13 Double continuum flow model Karst system Double continuum system Linear exchange depends on: head difference exchange coefficient Different aquifer parameters: Hydraulic conductivity low in fissured system high in conduit system Storage coefficient: high in fissured system low in conduit system

14 System of coupled flow equations: ( ) ( ) (x,y,z,t) f and h (x,y,z,t) f h Solution : h h W t h S z h k z y h k y x h k x h h W t h S z h k z y h k y x h k x b a b a b b b b b zz b b yy b b xx b a a a a a a zz a a yy a a xx = = α + = α + =

$standard deviation heads from fracture system: large standard$ deviation same range as continuum b (conduit system) heads from matrix

15 Parameter identification interpretation of heads Classification by standard deviation heads from fracture system: large standard deviation same range as continuum b (conduit system) heads from matrix system: only one point with same standard deviation as continuum a (fissured system)

16 Double continuum model: Stubersheimer Alb steady state model calibration using measured head and discharge data distribution of hydraulic conductivity sensitivity study for transient flow: simulate the measured characteristics to investigate the exchange behavior

$exchange between fracture and matrix system$

17 Simulation results Double continuum model shows same characteristics as measured data Heads Transient exchange between fracture and matrix system Continuum a: smooth curve Continuum b: large dynamics Discharge

18 Solute Transport Modeling

19 Application of solute transport models interpretation of concentration data mass balance of contaminants predictions of pollutant plumes design of pump and treat management planning of monitoring strategy risk assessment in case of waste disposals

20 Simulation of a contamination plume

21 Relation between groundwater flow and transport models

22 Representation of transport processes Transport in 1-D-aquifer Advection Advection + Dispersion (+ Diffusion) Advection + Dispersion + Adsorption Advection + Dispersion + Adsorption + Decay

23 Transport equation c t = q n ( D c uc) + σ c c ) f ( in The temporal change of pollutant mass for every volume element is given by the in- / outflows from Dispersion Advection Reaction Sources / Sinks ( D c) ( uc) σ q n f ( c cin)

24 1-D transport equation c t = D 2 c 2 x u c x Measure for the relation advective / dispersive transport is given by the PECLET-number: P e = L u DL Lu = αl u L: typical length scale of transport problem P e = 0 pure dispersive transport P e = pure advective transport

25 Solution methods for transport equation - Analytical solutions Simple flow conditions / simple initial and boundary conditions, homogeneity - Neglecting Diffusion / Dispersion Path lines, travel times, concentration along path lines - Numerical Solutions Grid methods: FD, FV, FE Particle-Tracking Methods: MOC, Random-Walk

26 Numerical solution methods Grid Methods: Finite Differences Finite Elements Finite Volumes Particle-Tracking Methods: Method of Characteristics Random-Walk-Method

27 Problems with grid methods - Numerical dispersion - Oscillations Possible solution: grid refinement

28 Possible solution: adaptive grid Adaptive gridding methods consists in dynamically refining the grid size to eliminate numerical dispersion Example of grid refinement

29 Adaptive refinement: nested iteration

30 Error indicator for adaptive griding The selection of elements for refinement and coarsening is based on an error indicator. Typical error indicators are The gradient of the solution c, Concentration variation between neighbor elements. In case of time step methods the solution of the proceeding time step is considered.

31 Example of an adaptive refined grid from a simulation

32 The Inverse Problem in Groundwater Modeling

33 Direct problem Given: Wanted: parameters, boundary and initial conditions head / flow distribution (or concentration) Usually parameters are not known completely! Therefore: Calibration (i.e. completion of parameters) using measurements of heads / flows (or concentration) is required.

34 Inverse problem Given: Wanted: heads / flows, (concentrations) parameter distribution Problem: Ways out: ill-posedness No unique solution may exist Measurement errors make result unreliable Reduction of degrees of freedom and regression Introduction of a priori knowledge Joint use of head, flow and / or concentration measurements Estimate of uncertainty

35 Example for non uniqueness of the inverse problem Q = B T (h 1 -h 2 )/L Where: Q: discharge B: width T: transmissivity h: head L: length Identification problem of steady state calibration. Every T leads to the same head distribution, only Q varies!

36 Criterion for goodness of fit (maximum likelihood) Without prior knowledge minimize S( p = measured computed 2 1,..., pm) ( fi fi ( pk )) i or with a priori knowledge S( p = measured computed 2 prior 2 1,..., pm) ( fi fi ( pk )) wi + ( p j p j ) i j w i w j (p j parameter, f i heads or flow, w i weights) Minimization can be done manually ( trial and error ) or by automatic methods: e.g. MARQUARDT-LEVENBERG algorithm

37 Concepts for parameterization of spatial structures Reduction of degrees of freedom by: Zonation (N zones) Interpolation and pivot points

38 Spatial transmissivity distribution (Jurassic karst aquifer) Frequency distributions: all data valleys plateau

39 Umm Er Radhuma aquifer system in Saudi Arabia

Euphrates Geological and hydrogeological units of the Umm Er Radhuma aquifer system Tigris I R A N Tdm I R A Q Q K U W A I T Ka Tu HAFAR AL BATIN AL KHAFJI ARABIAN GULF AN NUYRIYAH Tsm AL JUBAYL

40 Euphrates Geological and hydrogeological units of the Umm Er Radhuma aquifer system Tigris I R A N Tdm I R A Q Q K U W A I T Ka Tu HAFAR AL BATIN AL KHAFJI ARABIAN GULF AN NUYRIYAH Tsm AL JUBAYL BURAYDAH AZ ZULFI BUQAYQ AD DAMMAM AL KHUBAR BAHRAIN Tdm Ka AL HUFUF QATAR RIYADH AL KHARJ Tr HARAD Q SALWAH U. A. E. Legend YABRIN Q Quaternary Tu Tsm Tsm Neogene LAYLA Tdm Dammam Tr Rus Tu Umm Er Radhuma Ka Aruma AS SULAYYIL Kilometers

41 Geological structure and stratification Geological Cross Sections

42 Geological structure and tectonic features Main Anticlinal Structures and Faults Colored sub crop surface: base of Umm Er Radhuma

43 Vertical hydraulic conductivity distribution Rus aquitard Dammam / Neogene

44 Muschelkalk lithology

45 Time needed for the change of rocks within an aquifer depends on rock type Important features for the Muschelkalk are: - the dissolution of evaporites, - and the karstification of carbonate rocks. The processes depend on the exposition to the ground surface.

46 Thickness reduction of the Mittlerer Muschelkalk by salt and sulphate dissolution

$fractures Acceleration$

47 Consequence: 50 m thickness reduction within a relative short time Cracking of rocks Intensification of fractures Acceleration of karstification

48 What are the major processes for dissolution? The main factor is the exposition to the ground surface. The exposition to the ground surface depends on the cuesta development.

49 Cuesta development in Baden-Württemberg Location of cuestas and rivers during Oligocene and Late Miocene (34 20 Ma)

50 Cuesta development in Baden-Württemberg Location of cuestas and rivers during Upper Miocene (11 5 Ma)

51 Cuesta development in Baden-Württemberg Location of cuestas and rivers during Lower Pleistocene ( Ma)

52 Cuesta development in northern Baden-Württemberg Cuesta development and location of Muschelkalk aquifers from Oligocene - Quarternary

53 Consequence Adjacent areas within the cuesta landscape developed successively over a long time and represent different states of karstification.

54 Present Muschelkalk aquifer systems 1-3: present areas of Muschelkalk aquifers

Development of karstification Area / Stage of Development 1 2 3 Start of karstification Not yet started Miocene Oligocene Salinar in Mittleren Muschelkalk no dissolution Salt mostly dissoluted,

55 Development of karstification Area / Stage of Development Start of karstification Not yet started Miocene Oligocene Salinar in Mittleren Muschelkalk no dissolution Salt mostly dissoluted, Sulphates start of dissolution Salt completely dissoluted, Sulphates mostly dissoluted Dolines, sinkholes none mo: numerous mo: numerous, but sealed mm + mu: many mm + mu: existing Areas with no surface runoff none mo: many mo + mm: rare (sealing) mu: existing Caves none mo: many mo: very rare (sealing) mm: none mu: existing Perched aquifers none mo: existing (wide areas) mm + mu: none mo: rare mu: existing

56 Palaeo-climatology Precipitation Fluctuations Temperature Fluctuations Precipitation [mm/year] COLE 2004 BRICE 1978 DIESTER-HAAS 1973 DIESTER-HAAS 1973 VAN ZINDEREN BAKKER 1980 BRICE 1978 BRICE 1978 VAN ZINDEREN BAKKER 1980 BRICE 1978 BUTZER 1958 BRICE BRICE BARTH BRICE 1978 COLE COLE BRICE ISSAR Temperature [ C] Years Before Present Years Before Present Recharge Estimation 60 Recharge [mm/y] Years Before Present

57 Isotopes information: estimation of river infiltration Temporal distribution of d18 O in river water and groundwater Spatial distribution of Iller infiltration

58 Isotopes information: groundwater age Simulated travel time to the Al Hassa oasis (mean residence time 12,000 a) Groundwater Age Umm Er Radhuma Aquifer 14 C-Groundwater Age and 3 H- Detection Line

59 Modeling under uncertainty worst case best case analysis scenario techniques sensitivity analysis stochastic modeling

60 Stochastic modeling Required: Parameter distribution, mean, variance, correlation length Result: Mean, deviation, confidence limits Methods: Monte Carlo Simulation FOSM (First Order Second Moment)

61 Monte Carlo method Principle: - generation of a large number N of equally probable random realizations of the aquifer - the ensemble of N calculated solutions (Z i ) is analyzed statistically Z = N i= 1 N Z i σ = N i= 1 ( Z i Z ) N 1 2

62 Delineation of groundwater protection area Sample problem: Pumping rate: Q = m 3 /s Groundwater recharge: I = 8 l/s/km 2

63 Statistical analysis of field data

64 Simulation steps using Monte Carlo method

65 Simulation steps using Monte Carlo method Repeated simulation of catchment areas Unconstrained sampling Sampling under calibration constraint

66 Simulation steps using Monte Carlo method Probability distribution

67 Convergence of Monte Carlo method A large number of realizations N may be necessary in order to get meaningful convergent statistics Problem: this number is not known a priori!

68 Never forget: a good model includes important features of reality a model does not replace data acquisition a good modeler explores the uncertainty of her/his predictions what we really want are robust decisions do not overstretch a model a model is not reality

The Hydrogeology of Al Hassa Springs

The 3 rd International Conference on Water Resources and Arid Environments (2008) and the 1 st Arab Water Forum The Hydrogeology of Al Hassa Springs Ali Saad Al Tokhais 1 and Randolf Rausch 2 1. Ministry