Hard Rock Hydraulics:An Introduction to Modeling


IntroductionScope and level of this bookModeling uncertaintyReducing uncertaintyPractical examplesExample of the difficulty to detect karstic featuresExample of the value of published informationExample of the consequences of not detecting minor geologic featuresExample of anticipating future WT levelsExample of pumping-rates predictionsConcluding remarksNotesFundamentalsIntroductionBasic conceptsPseudo-continuityVolumetric and gravimetric relationsHomogeneous and anisotropic systemsHeterogeneous systemsObservation scalesHydraulic variablesScalars, vectors, and second-order tensorsGroundwater flow descriptionThe specific dischargeThe hydraulic gradientThe hydraulic conductivityIntroductionFractures and conduitsPseudo-continuity and pervious fracturesValid pseudo-continuity assumptionErratic discontinuitiesAssessment of the hydraulic conductivitiesExploring at the “sample scale”: back to 1930Exploring old Lugeon tests: 1958 to 1968Exploring integral sampling: 1968 to 1978Exploring inverse solution methods: 1978 to 1988Governing equations of groundwater flowEnergy conservation principle: Darcy’s lawBoundary conditionsAddendaEffective velocity and specific dischargeHydrodynamic gradientHydraulic conductivity for a group of random fracturesEnergy conservation principleMass conservation principleNotesReferencesApproximate solutionsOverviewDifferential operatorsUniqueness of solutionsApproximate errorsApproximation methodsPreliminariesCollocation methodLeast squares methodGalerkin’s methodOrthogonalityGalerkin’s approach“Weak” solutionsVariational notationAddendaClasses of second-order partial differential equationsMinimizing squared residualsMinimizing squared residuals changed by differential operatorsThe concept of orthogonalityNoteReferencesData analysisIntroductionAnalyzing geological dataAnalyzing hydrologic dataAnalyzing flow rate dataAnalyzing hydraulic conductivity dataMeaning of the hydraulic conductivityMapping of eigenvalues and eigenvectorsInterpolation of eigenvalues and eigenvectorsAnalyzing hydraulic head dataTraditional analysisIntegrated hydraulic head analysisNotesReferencesFinite differencesPreliminariesModeling hydrogeological systemsConceptsFinite difference basicsDifference equationsFinite differencesDifference equations for unsteady-state systemsSimultaneous difference equationsPreliminariesGauss–Seidel iterative routineCrank–Nicolson iterative routineFinite differences algorithms for hard rocksSteady-state solutionsDupuit’s approximationD algorithmsTransient solutionsNotesReferencesApplicationsPreliminariesFracture interconnectivityInterconnection between reservoirsPollution bypassing a wide riverThe problemThe anomaliesThe scanned images pieces of evidenceThe hydraulic properties of the megafractures netWhat happens during heavy rainsThe 3D model resultsThermal waters without hot pointsPreliminariesModel premisesGeneralitiesEffective mean regional porosityPermeabilityThe groundwater recharge discussionFundamentals of heat transportModeling resultsDimensions and parametersThe heat transfer processesModeling the thermalism gradual decayBibliographyIndex