S3 XA9643079 IAEA-TECDOC-910 Manual on mathematical models in isotope hydrogeology INTERNATIONAL ATOMIC ENERGY AGENCY October 1996 VOL 2 8 Nl 0 6 The IAEA does not normally maintain stocks of reports in this series. However, microfiche copies of these reports can be obtained from INIS Clearinghouse International Atomic Energy Agency Wagramerstrasse 5 P.O. Box 100 A-1400 Vienna, Austria Orders should be accompanied by prepayment of Austrian Schillings 100,— in the form of a cheque or in the form of IAEA microfiche service coupons which may be ordered separately from the INIS Clearinghouse. IAEA-TECDOC-910 Manual on mathematical models in isotope hydrogeology ijO ^ l INTERNATIONAL ATOMIC ENERGY AGENCY The originating Section of this publication in the IAEA was: Isotope Hydrology Section International Atomic Energy Agency Wagramerstrasse 5 P.O. Box 100 A-1400 Vienna, Austria MANUAL ON MATHEMATICAL MODELS IN ISOTOPE HYDROGEOLOGY IAEA, VIENNA, 1996 IAEA-TECDOC-910 ISSN 1011-4289 © IAEA, 1996 Printed by the IAEA in Austria October 1996 FOREWORD Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Applications of isotope methods aim at providing an improved understanding of the overall hydrological system as well as estimating physical parameters of the system related to flow dynamics. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. Water resources assessment and management requires a multidisciplinary approach involving chemists, physicists, hydrologists and geologists. Existing modelling procedures for quantitative interpretation of isotope data are not readily available to practitioners from diverse professional backgrounds. Recognizing the need for guidance on the use of different modelling procedures relevant to specific isotope and/or hydrological systems, the IAEA has undertaken the preparation of a publication for this purpose. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Y. Yurtsever, Division of Physical and Chemical Sciences, was the IAEA technical officer responsible for the final compilation of this report. It is expected that the manual will be a useful guidance to scientists and practitioners involved in isotope hydrological applications, particularly in quantitative evaluation of isotope data in groundwater systems. EDITORIAL NOTE In preparing this publication for press, staff of the IAEA have made up the pages from the original manuscripts as submitted by the authors. The views expressed do not necessarily reflect those of the governments of the nominating Member States or of the nominating organizations. Throughout the text names of Member States are retained as they were when the text was compiled. The use of particular designations of countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and institutions or of the delimitation of their boundaries. The mention of names of specific companies or products (whether or not indicated as registered) does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement or recommendation on the part of the IAEA. The authors are responsible for having obtained the necessary permission for the IAEA to reproduce, translate or use material from sources already protected by copyrights. CONTENTS SUMMARY ....................................................................................................................... 7 Lumped parameter models for interpretation of environmental tracer data................... 9 P. Maloszewski, A. Zuber Numerical models of groundwater flow for transport ..................................................... 59 L.F. Konikow Quantitative evaluation of flow systems, groundwater recharge and transmissivities using environmental traces................................................................. 113 E.M. A dar Basic concepts and formulations for isotope geochemical modelling of groundwater systems ................................................................................................155 R.M. Kalin List of related IAEA publications ...................................................................................... 207 SUMMARY The IAEA has, during the last decade, been actively involved in providing support to development and field verification of the various modelling approaches in order to improve the capabilities of modelling for reliable quantitative estimates of hydrological parameters related to the dynamics of the hydrological system. A Co-ordinated Research Programme (CRP) on Mathematical Models for Quantitative Evaluation of Isotope Data in Hydrology was implemented during 1990-1994. The results of this CRP were published as IAEA-TECDOC- 777, in which the present state-of-the-art in modelling concepts and procedures with results obtained from applied field research are summarized. The present publication is a follow-up to the earlier work and can be considered to be a supplement to TECDOC-777. Methodologies based on the use of environmental (naturally occurring) isotopes are being routinely employed in the field of water resources and related environmental investigations. Temporal and/or spatial variations of commonly used natural isotopes (i.e. stable isotopes of hydrogen, oxygen and carbon; radioactive isotopes of hydrogen and carbon) in hydrological systems are often employed for two main purposes: (i) improved understanding of the system boundaries, origin (genesis) of water, hydraulic interconnections between different sub-systems, confirmation (or rejection) of boundary conditions postulated as a result of conventional hydrological investigations; (ii) quantitative estimation of dynamic parameters related to water movement such as travel time of water and its distribution in the hydrological system, mixing ratios of waters originating from different sources and dispersion characteristics of mass transport within the system. Methodologies of isotope data evaluations (as in i) above) are essentially based on statistical analyses of the data (either in the time or the space domain) which would contribute to the qualitative understanding of the processes involved in the occurrence and circulation of water, while the quantitative evaluations, as in (ii) above, would require proper conceptual mathematical models to be used for establishing the link between the isotopic properties with those of the system parameters. The general modelling approaches developed so far and verified through field applications for quantitative interpretations of isotope data in hydrology cover the following general formulations: Lumped parameter models , that are based on the isotope input-output relationships (transfer function models) in the time domain, Distributed parameter numerical flow and transport models for natural systems with complex geometries and boundary conditions, Compartmental models (mixing cell models), as quasi-physical flow and transport of isotopes in hydrological systems, Models for geochemical speciation of water and transport of isotopes with coupled geochemical reactions. 7 While the modelling approaches cited above are still at a stage of progressive development and refinement, the IAEA has taken the initiative for the preparation of guidance material on the use of existing modelling approaches in isotope hydrology. The need for such a manual on the basic formulations of existing modelling approaches and their practical use for isotope data obtained from field studies was recognized during the deliberations of the earlier CRP mentioned above. Other relevant IAEA publications available in this field are listed at the end of this publication. Use of specific models included in each of the available general methodologies, and data requirements for their proper use will be dictated by many factors, mainly related to the type of hydrological system under consideration, availability of basic knowledge and scale of the system. Groundwater systems are often much more complex in this regard, and use of isotopes is much more widespread for a large spectrum of hydrological problems associated with proper assessment and management of groundwater resources. Therefore, this manual,