Hydraulic Parameter Identification, Softcover reprint of the original 1st ed. 1999 Generalized Interpretation Method for Single and Multiple Pumping Tests

Hydraulic parameter identification is a crucial step in hydrogeological investigations. The book proposes a unique and generalized interpretation method for single and multiple pumping tests made in groundwater reservoirs with layered heterogeneity and with or without lateral anisotropy. This method eliminates the drawbacks of the numerous and frequently applied interpretation methods. The book also presents an introduction to inverse modeling, resulting in optimal parameter values with their joint confidence region and the corresponding residuals. Cross sections through this multidimensional region elucidate the relation between the shape of this region and some statistical parameters describing the reliability of the identified parameters. This method is demonstrated by means of five pumping or recharge tests.

1 / Introduction.- 1.1 Previous literature on pumping test interpretation.- 1.2 Proposed generalized interpretation method.- 1.3 Additional aims of the book.- 1.4 Arrangement of subject matter.- 2 / Hydraulic Parameters.- 2.1 Hydraulic parameters describing water conducting properties.- 2.1.1 Darcy’s law.- 2.1.2 Hydraulic head and fresh water head.- 2.1.3 Intrinsic permeability.- 2.1.4 Heterogeneity and anisotropy of geological formations with respect to hydraulic conductivity.- 2.1.4.1 Heterogeneity.- 2.1.4.2 Anisotropy.- 2.1.5 Generalized law of Darcy.- 2.1.6 Hydraulic conductivity ellipsoid.- 2.1.7 Classification of layers according to their water conductive properties.- 2.1.8 Hydraulic parameters derived from hydraulic conductivity.- 2.1.8.1 Transmissivity.- 2.1.8.2 Hydraulic resistance.- 2.1.8.3 Leakage factor.- 2.1.9 Methods to derive the hydraulic conductivity.- 2.1.9.1 Direct methods.- 2.1.9.2 Indirect methods.- 2.2 Hydraulic parameters describing water storing properties.- 2.2.1 Conservation of mass in a completely saturated volume of material fixed in space.- 2.2.2 Specific elastic storage.- 2.2.2.1 Compressibility of water.- 2.2.2.2 Effective stress concept.- 2.2.2.3 Compressibility of matrix.- 2.2.2.4 Movement of solids in deforming medium.- 2.2.3 Hydraulic parameters derived from specific elastic storage.- 2.2.3.1 Elastic storage coefficient.- 2.2.3.2 Diffusivity.- 2.2.4 Methods to derive specific elastic storage.- 2.2.4.1 Direct methods.- 2.2.4.2 Indirect methods.- 2.2.5 Storage coefficient near the water table.- 2.2.6 Hydraulic parameters derived from storage coefficient near watertable.- 2.2.7 Methods to derive storage coefficient near water table.- 2.2.7.1 Determination by pF-curves.- 2.2.7.2 Determination by pumping tests.- 2.2.7.3 Determination by inverse models of unsteady state flow.- 3 / Evolution of analytical models of pumping tests and their interpretation methods.- 3.1 Model of Thiem.- 3.1.1 Introduction.- 3.1.2 Derivation of basic differential equation.- 3.1.3 Solution of basic differential equation.- 3.1.4 Application of Thiem method.- 3.2 Model of Theis.- 3.2.1 Introduction.- 3.2.2 Derivation of basic differential equation.- 3.2.3 Solution of basic differential equation for constant discharge rate.- 3.2.4 Theis and Cooper-Jacob interpretation methods.- 3.2.5 Comments concerning Theis and Cooper-Jacob interpretation methods.- 3.3 Model of Jacob-Hantush.- 3.3.1 Introduction.- 3.3.2 Derivation of basic differential equation.- 3.3.3 Solution of basic differential equation for a constant discharge rate.- 3.3.4 Interpretation methods of De Glee, Hantush-Jacob, Hantush I-II and Walton.- 3.3.4.1 Interpretation of distance-drawdown curve at steady flow.- 3.3.4.2 Interpretation of time-drawdown curve.- 3.3.4.3 Comments concerning interpretation methods of semi-confined aquifer.- 3.4 Model of Hantush.- 3.4.1 Introduction.- 3.4.2 Derivation of basic differential equations.- 3.4.3 Initial and boundary conditions.- 3.4.4 Solution of basic differential equation.- 3.4.5 Interpretation methods derived from Hantush model.- 3.4.5.1 Interpretation of first part of time-drawdown curves.- 3.4.5.2 Interpretation of last part of time-drawdown curves.- 3.4.5.3 Interpretation of maximum drawdowns of cases 1 and 3.- 3.4.6 Concluding considerations about interpretation methods derived from Hantush model.- 3.5 Model of Hantush-Weeks.- 3.6 Model of Boulton-Cooley.- 3.7 Model of Neuman and Witherspoon.- 3.8 Retrospective view on analytical models and their derived interpretation methods.- 4 / Numerical model of pumping tests in a layered groundwater reservoir.- 4.1 Finite-difference grid.- 4.2 Mean drawdowns.- 4.2.1 Mean drawdown over horizontal plane through nodal circle in ring.- 4.2.2 Mean drawdown over cylindrical surface through nodal circle in ring.- 4.2.3 Mean drawdown over entire ring volume.- 4.2.4 Mean drawdown during a time step.- 4.3 Continuity equation in numerical model.- 4.3.1 Mean velocities through boundary surfaces of rings.- 4.3.2 Storage change in rings.- 4.3.3 In- and outflow difference of rings.- 4.3.4 Continuity equation for rings.- 4.3.5 Storage change for rings bounded by water table.- 4.3.6 In- and outflow difference of rings bounded by water table.- 4.3.7 Continuity equation for rings bounded by water table.- 4.4 Initial and boundary conditions.- 4.5 Solution of the numerical equations.- 4.5.1 Alternating direction implicit method.- 4.5.2 Verification of iteration process and number of iteration per time step.- 4.6 Verification of numerical model.- 4.6.1 Verification of numerical model with Theis model.- 4.6.2 Influence of grid parameters on results of numerical Theis model.- 4.6.3 Verification of numerical model with Jacob-Hantush model.- 4.6.4 Influence of grid parameters on results of Jacob-Hantush model.- 4.6.5 Verification of numerical model with Hantush model.- 4.6.6 Examination of validity limits of the Hantush asymptotic solution.- 4.6.7 Verification of numerical model with Hantush-Weeks model.- 4.6.8 Verification of numerical model with Boulton-Cooley model.- 4.6.9 Consequences of numerical model verification.- 4.7 Program package for numerical simulation of pumping tests.- 4.7.1 Program infinp.- 4.7.1.1 Input space-time grid parameters and hydraulic parameters.- 4.7.1.2 Input of observed drawdowns.- 4.7.3 Program sipur5.- 4.7.4 Program outpu5.- 4.7.5 Program sidap7.- 5 / Further developments of pumping test model.- 5.1 Drawdown of pumping tests with variable discharge rate.- 5.1.1 Theoretical considerations.- 5.1.2 Additional input data.- 5.1.3 Example of a pumping test with variable discharge rate.- 5.2 Drawdown in a laterally anisotropic aquifer.- 5.2.1 Theoretical considerations.- 5.2.2 Additional input data.- 5.2.3 Example of a pumping test in a laterally anisotropic aquifer.- 5.3 Drawdown in pumping wells.- 5.3.1 Theoretical considerations.- 5.3.2 Additional input data.- 5.3.3 Example of drawdowns in a pumped well during a step drawdown test.- 5.4 Drawdown due to a multiple well field.- 5.4.1 Theoretical considerations.- 5.4.2 Additional input data.- 5.4.3 Drawdown due to pumping on wells in laterally isotropic layers.- 5.4.4 Drawdown due to pumping on wells in laterally anisotropic layers.- 5.5 Drawdown in groundwater reservoir with lateral bounds.- 5.5.1 Drawdown in groundwater reservoir with lateral impervious boundary.- 5.5.2 Drawdown in groundwater reservoir with lateral constant head boundary.- 5.5.3 Drawdown in groundwater reservoir bounded by several straight boundaries.- 5.6 Drawdown in groundwater reservoir with lateral discontinuous conductivity change.- 5.6.1 Theoretical considerations.- 5.6.2 Additional input data.- 5.6.3 Example of drawdown approximation.- 5.7 Land subsidence due to groundwater withdrawal.- 5.7.1 Theoretical considerations.- 5.7.2 Additional input data and representation of results.- 5.7.3 Example of subsidence calculations.- 6 / Inverse model as tool for pumping test interpretation.- 6.1 Residual vector.- 6.1.1 Definition.- 6.1.2 Contributing factors of residuals.- 6.2 Sensitivity matrix —.- 6.2.1 Definition.- 6.2.2 Program package to calculate sensitivity matrix.- 6.2.3 Example of a sensitivity matrix.- 6.2.4 Graphical representation of sensitivities.- 6.3 Numerical nonlinear regression.- 6.3.1 Optimal values of hydraulic parameters.- 6.3.2 Uniqueness, identifiability and stability.- 6.3.3 Analysis of residuals.- 6.3.4 Joint confidence region of hydraulic parameters.- 6.3.4.1 Joint confidence region approximated by p-dimensional ellipsoid.- 6.3.4.2 Cross sections through joint confidence region.- 6.3.5 Condition indexes and matrix of marginal variance-decomposition proportions.- 6.3.6 Practical steps in interpretation by means of inverse model.- 6.4 Validation of inverse numerical model.- 6.5 Factors influencing accuracy of results.- 6.5.1 Influence of flow conceptualization.- 6.5.2 Influence of observed drawdown accuracy and discharge magnitude.- 6.5.3 Influence of observation time.- 6.5.4 Influence of observation distance.- 6.5.5 Conclusions.- 6.6 Program package for the nonlinear regression.- 6.6.1 Program solpu5.- 6.6.2 Program inpur5.- 6.6.3 Program etabdi.- 6.6.4 Program plprcr.- 6.6.5 Program susqln.- 6.6.6 Program susql3.- 6.6.7 Program sumsqr.- 6.6.8 Program sumsq2.- 6.7 Confidence interval for optimal estimated drawdown.- 6.7.1 Drawdown confidence intervals based on two- and three-dimensional cross sections through joint confidence interval of hydraulic parameters.- 6.7.2 Drawdown confidence intervals derived by optimization of constrained problem.- 6.7.3 Program packages to approximate drawdown confidence intervals.- 6.7.3.1 Program package confil.- 6.7.3.2 Program package confill.- 6.7.3.3 Program package confi3.- 6.7.3.4 Program package confl4.- 6.8 Hypothetical example to demonstrate nonlinear regression and approximation of drawdown confidence intervals.- 6.8.1 Conceptual model of ‘actual’ groundwater flow.- 6.8.2 Creation of ‘observed’ drawdowns.- 6.8.3 Conceptual model of groundwater flow used during interpretation.- 6.8.4 Interpretation by means of ordinary least square method.- 6.8.5 Joint confidence area of hydraulic parameters.- 6.8.6 Combined influence of hydraulic parameters at some observation points.- 6.8.7 Approximation of drawdown confidence intervals.- 7 / Example of performance and interpretation of pumping tests.- 7.1 Double pumping test in layered groundwater reservoir formed by Quaternary sediments.- 7.1.1 Lithostratigraphical cross section.- 7.1.2 Location of pumping and observation wells.- 7.1.3 Performance of double pumping test.- 7.1.4 Discretization of groundwater reservoir in numerical model.- 7.1.5 Hydraulic parameters derived from observed drawdown.- 7.1.6 Interpretation with ordinary least square method.- 7.2 Double pumping test in a laterally anisotropic aquifer formed by fractured rocks of Palaeozoic and Mesozoic age.- 7.2.1 Lithostratigraphical cross section.- 7.2.2 Location of pumping and observation wells.- 7.2.3 Discretization of groundwater reservoir in numerical model.- 7.2.4 Drawdowns used as input data.- 7.2.5 Hydraulic parameters derived from observed drawdowns.- 7.2.6 First interpretation results.- 7.2.7 Two-dimensional cross sections through exact joint confidence region.- 7.2.8 Three-dimensional cross sections through approximate joint confidence region.- 7.2.9 Condition indexes and matrix of marginal variance-decomposition.- 7.2.10 Observational constraints for unique solution.- 7.2.11 Second interpretation phase and post-optimization.- 7.2.12 Conclusion.- 7.3 Triple pumping test in layered groundwater reservoir formed by Tertiary sediments.- 7.3.1 Lithostratigraphical cross section.- 7.3.2 Location of pumping and observation wells.- 7.3.3 Performance of triple pumping test.- 7.3.4 Discretization of groundwater reservoir in numerical model.- 7.3.5 Hydraulic parameters derived from observed drawdowns.- 7.3.6 Interpretation of results.- 7.3.7 Outliers.- 7.3.8 Conclusions.- 7.4 Single pumping test to determine the conductivity of Tertiary silty clay.- 7.4.1 Lithostratigraphical cross-section.- 7.4.2 Location of pumping and observation wells.- 7.4.3 Performance of single pumping test.- 7.4.4 Discretization of groundwater reservoir in numerical model.- 7.4.5 Hydraulic parameters derived from observed drawdown.- 7.4.6 Interpretation results.- 7.5 Artificial recharge test in a natural bare dune valley.- 7.5.1 Lithological cross section and discretization of groundwater reservoir.- 7.5.2 Location of observation wells and performance of artificial recharge test.- 7.5.3 Hydraulic parameters derived from observed rises of hydraulic head.