Environmental Isotopes in the Hydrological Cycle Principles and Applications
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ENVIRONMENTAL ISOTOPES IN THE HYDROLOGICAL CYCLE Principles and Applications Vol. 6 esources Programme r Water Water Atoms for Peace International atomic energy agency and united Nations educational, scientific and cAtomsultural for Peace organization (reprinted with minor corrections) Ar H He C Kr C ENVIRONMENTAL ISOTOPES in the H HYDROLOGICAL CYCLE O C N S He Ar VOLUME VI MODELLING Co-ordinating editor Y. YURTSEVER Isotope Hydrology Section International Atomic Energy Agency, Vienna Contributing Authors A.Zuber, P.Małoszewski; M.E.Campana, G.A.Harrington, L.Tezcan; L.F.Konikow PREFACE TO volume VI This last volume in the series of textbooks on en- completed Co-ordinated Research Project by the vironmental isotopes in the hydrological cycle IAEA entitled “Use of isotopes for analysis of provides an overview of the basic principles of flow and transport dynamics in groundwater sys- existing conceptual formulations of modelling ap- tems” will also soon be published by the IAEA. proaches. While some of the concepts provided in This is the reason why the IAEA was involved in Chapter 2 and Chapter 3 are of general validity the co-ordination required for preparation of this for quantitative interpretation of isotope data; the volume; the material presented is a condensed modelling methodologies commonly employed overview prepared by some of the scientists that for incorporating isotope data into evaluations were involved in the above cited IAEA activities. specifically related to groundwater systems are This volume VI providing such an overview was given in this volume together with some illustra- included into the series to make this series self- tive examples. sufficient in its coverage of the field of Isotope Development of conceptual models for quantita- Hydrology. A special chapter on the methodolo- tive interpretations of isotope data in hydrogeolo- gies and concepts related to geochemical mod- gy and the assessment of their limitations and field elling in groundwater systems would have been verification has been given priority in the research most desirable to include. The reader is referred and development efforts of the IAEA during to IAEA-TECDOC-910 and other relevant publi- the last decade. Several Co-ordinated Research cations for guidance in this specific field. Projects on this specific topic were implemented Valuable contributions in the preparation of this and results published by the IAEA. Based on volume were accomplished by A.Zuber (Poland), these efforts and contributions made by a num- P.Maloszewski (Germany), M.E.Campana (USA), ber of scientists involved in this specific field, the G.A.Harrington (Australia), L.Tezcan (Turkey), IAEA has published two Technical Documents and L.F.Konikow (USA), as acknowledged with entitled “Mathematical models and their appli- each chapter cations to isotope studies in groundwater stud- ies, IAEA TECDOC-777, 1994” and “Manual on Vienne, mars 2000 Mathematical models in isotope hydrogeology – IAEA TECDOC-910, 1996”. Results of a recently Yuecel Yurtsever 491 CONTENTS OF volume VI 1. MODELLING INTRODUCTION ................................................................................................. 495 2. LUMPED PARAMETER MODELS ............................................................................................. 497 2.1. Introduction ............................................................................................................................ 497 2.2. Basic principles of the lumped-parameter approach for constant flow systems .................... 499 2.3. Models ................................................................................................................................... 500 2.3.1. The piston flow model ................................................................................................ 500 2.3.2. The exponential model ............................................................................................... 500 2.3.3. The combined exponential-piston flow model ........................................................... 501 2.3.4. The dispersion model ................................................................................................. 502 2.4. Cases of constant tracer input ................................................................................................ 502 2.5. Cases of variable tracer input ................................................................................................ 503 2.5.1. The tritium method ..................................................................................................... 503 2.5.2. The 3H-3He method .................................................................................................... 505 2.5.3. The krypton-85 method .............................................................................................. 506 2.5.4. The carbon-14 method ............................................................................................... 506 2.5.5. The oxygen-18 and deuterium method ...................................................................... 506 2.5.6. Other potential methods ............................................................................................. 507 2.6. Examples of 3H age determinations ....................................................................................... 508 2.7. Determination of hydrogeologic parameters from tracer ages .............................................. 508 2.8. The lumped-parameter approach versus other approaches .....................................................511 2.9. Concluding remarks ............................................................................................................... 512 3. COMPARTMENTAL MODEL APPROACHES TO GROUNDWATER FLOW SIMULATION 517 3.1. Introduction ............................................................................................................................ 517 3.2. A simple compartmental model: theory and application to a regional groundwater flow system ............................................................................................................................ 517 3.2.1. Theory ........................................................................................................................ 517 3.2.1.1. Tracer mass balance .................................................................................... 518 3.2.1.2. Transient flow ............................................................................................. 518 3.2.1.3. Age calculations ......................................................................................... 519 3.2.2. Application to the Nevada test site flow system ........................................................ 520 3.2.2.1. Introduction ................................................................................................ 520 3.2.2.2. Hydrogeology ............................................................................................. 520 3.2.2.3. Model development and calibration ........................................................... 521 3.2.2.4. Results and discussion ................................................................................ 522 3.2.2.5. Concluding remarks.................................................................................... 524 3.3. Constraining regional groundwater flow models with environmental isotopes and a compartmental mixing-cell approach ................................................................................. 524 3.3.1. Introduction ................................................................................................................ 524 3.3.2. Governing equations .................................................................................................. 525 3.3.3. Model design, input data and calibration procedure .................................................. 526 3.3.4. Application to the Otway basin, south Australia ........................................................ 526 3.4. Mixing-cell model for the simulation of environmental isotope transport ............................ 529 3.4.1. Introduction ................................................................................................................ 529 3.4.2. Mixing-cell model of flow and transport dynamics in karst aquifer systems ........... 531 3.4.2.1. Physical framework of the model ............................................................... 532 3.4.2.2. Hydrologic model ....................................................................................... 533 3.4.2.3. Transport model .......................................................................................... 534 3.4.3. Conclusions ................................................................................................................ 535 3.5. Summary and conclusions ..................................................................................................... 535 4. USE OF NUMERICAL MODELS TO SIMULATE GROUNDWATER FLOW AND TRANSPORT ................................................................................................................................. 541 4.1. Introduction ............................................................................................................................ 541 4.2. Models ................................................................................................................................... 542 4.3. Flow and transport