HYDROGEOLOGY

HYDROGEOLOGY

هیدروژئولوژی - مدل سازی و مدیریت آب زیرزمینی
HYDROGEOLOGY

HYDROGEOLOGY

هیدروژئولوژی - مدل سازی و مدیریت آب زیرزمینی

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مراحل یادگیری مدل سازی آب زیرزمینی

با سلام. خیلی از دانشجویان از مراحل یادگیری مدل سازی آب زیرزمینی سوال کرده بودند. برای شروع مدل سازی ابتدا باید اطلاعاتی در مورد کد مادفلو داشته باشید. یکی از منابع فارسی موجود، کتاب "مدل‌سازی کاربردی جریان و انتقال آلاینده در آبخوان" و دیگری کتاب نون کرسیک است. همچنین می توانید از فصل نهم کتاب Todd استفاده کنید.

در مرحله بعدی باید کار کردن با نرم افزار GMS یاد بگیرید که بهترین روش استفاده از راهنمای خود نرم افزار است که بعد از نصب در این آدرس یافت می شود:


  MyDocuments\GMS 7.1\Tutorials\


سپس راهنماها را به دقت و با ترتیب زیر مطالعه کنید:


  ابتدا پوشه های Intro - GIS- Geostatistics.

 

بعد از آن از پوشه MODFLOW فایل های زیر را مطالعه کنید:

  1. MODFLOW-GridApproach
  2. MODFLOW-ConceptualModelApproach
  3. MODFLOW-ModelCalibration
  4. MODFLOW-AutomatedParameterEstimation
  5. MODFLOW-ManagingTransientData


لازم به ذکر است در اینجا حداقل اطلاعات لازم برای مطالعه ذکر شده است و برای مدل سازی پیشرفه نیاز به اطلاعات خیلی بیشتری می باشد.









  •  تعدادی از منابع مورد استفاده در مدل سازی آب زیرزمینی:



  1.  نظری، رضا، عطاءاله جودوی (1393)، مدل‌سازی کاربردی جریان و انتقال آلاینده در آبخوان. چاپ اول، نشر آفتاب عالمتاب، مشهد، 240 صفحه.


    کرسیک، نون- ترجمه­ چیت سازان، منوچهر (1381). مدل­ سازی آبهای زیرزمینی، انتشارات دانشگاه شهید چمران اهواز.

-Todd, D. K. (2005). Groundwater Hydrology. John Wiley & Sons.

-Thangarajan Regional, M. (2003). RegionalGroundwater Modeling.Capital Publishing Company.

-Batu, Vedat. (2006). Applied flow and solute transport modeling in aquifers. Taylor & Francis Group Inc.

-Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G. (2000). MODFLOW-2000, User guide to modularization concepts and the ground-water flow process: U.S. Geological Survey Open-File Report 00-92, 121 p.

-Hill, Mary C. and Tiedeman, C. R. (2007). Effective groundwater model calibration. New Jersey: John Wiley & Sons, Inc

قیام مجدد اساتید دانشگاه‌های کشور علیه تقلب

قیام مجدد اساتید دانشگاه‌های کشور علیه تقلب

وبلاگ «اساتید علیه تقلب» پس از ایجاد برخی تغییرات، با آدرسی جدید فعالیت خود را از سر گرفت.

«اساتید علیه تقلب» نام وبلاگی است که توسط جمعی از اساتید برجسته دانشگاه های کشور اداره می شود. این وبلاگ که قبلا از سرویس بلاگر گوگل استفاده می کرد، از این پس در آدرس pap.blog.ir قابل دسترس کاربران خواهد بود.
در بخش معرفی این وبلاگ می خوانیم: "هدف ما مبارزه با تخلف و تقلب علمی در دانشگاه‌ها چه از سوی دانش‌جویان و چه از سوی اعضای هیات علمی است. متاسفانه ما شاهد گسترش حرکت‌های غیر اخلاقی در فضای علمی کشور هستیم که با انگیزه‌هایی چون اخذ مدرک، پذیرش یا ارتقای مرتبه‌ی دانشگاهی صورت می‌گیرد. ما با هرگونه تقلب مخالفیم و سکوت در برابر آن‌را هم جایز نمی‌دانیم. در این بلاگ قصد داریم برخی موارد و روش‌های تقلب‌ را بیان و ضمن آموزش به دانش‌جویان و تلاش برای اشاعه‌ی اخلاق و آداب حرفه‌ای در جمع خودمان‌، مسولان را وادار کنیم تا به مشکل تقلب و ریشه‌های آن واکنش جدی نشان دهند."

مقاله مدل سازی آب زیرزمینی دشت فیض آباد توسط نرم افزار GMS

برنامه ریزی منابع آب زیرزمینی در شرایط groundwater mining

مطالعه موردی: دشت فیض آباد

 

عطاءاله جودوی1- محمد زارع2

 

1دانشجوی دکتری آبشناسی، بخش علوم زمین، دانشگاه شیراز

2دانشیار گروه آبشناسی، بخش علوم زمین، دانشگاه شیراز

 

چکیده

    توسعه بدون برنامه کشاورزی و برداشت بیش از حد از منابع آب زیرزمینی دشت فیض آباد (واقع در شمال شرق ایران) باعث بوجود آمدن شرایط groundwater mining و پیامدهای این موضوع مانند افزایش شوری آب­ زیرزمینی شده­ است. به­ علت اقلیم خشک این منطقه، بیشتر آب مصرفی در بخش کشاورزی از منابع آب­ زیرزمینی تامین می­ شود. به­ منظور برنامه­ ریزی منابع آب­ زیرزمینی، مدل جریان آب­ زیرزمینی دشت فیض ­آباد بوسیله MODFLOW تهیه شد. واسنجی مدل بواسطه انطباق بین سطح آب محاسباتی و مشاهده ­ای انجام شد و نتایج قابل قبولی بدست آمد. برای ارزیابی تأثیر برنامه فعلی بهره ­برداری و پیشنهاد کردن راه حل مناسب، چهار سناریوی مدیریتی تنظیم گردید و سناریوها بوسیله مدل مورد آزمایش واقع شدند. بر پایه نتایج مدل، بیلان شبیه­ سازی شده نشان داد برای متوقف کردن افت سطح آب زیرزمینی لازم است میزان برداشت ماهانه 40% کاهش یابد و در فصل زمستان بهره برداری از آب زیرزمینی صورت نگیرد.     آآ

 

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در صورت نیاز به راهنمایی در مورد مدل سازی آب زیرزمینی، به این آدرس ایمیل بفرستید: atajoodavi@gmail.com 

منابع مفید برای پژوهش های مدیریت منابع آب

Sources of Information in Water Resources

Daene McKinney
University of Texas at Austin


  • Advances in Water Resources
  • American Water Works Association. Journal
  • Canadian Water Resources Journal
  • Environmental Science and Technology
  • Ground Water
  • Ground Water Monitoring Review
  • Ground Water Remediation and Monitoring
  • International Journal of Numerical Methods in Engineering
  • International Journal of Water Resources Development
  • Journal of American Water Resources Association
  • Journal of Contaminant Hydrology
  • Journal of Contemporary Water Research and Education
  • Journal of Environmental Engineering
  • Journal of Engineering Hydrology
  • Journal of Hydraulics
  • Journal of Hydrology
  • Journal of Irrigation and Drainage
  • Journal of Water Resources Planing and Management
  • Mathematical Geology
  • Nordic Hydrology
  • Transport in Porous Media
  • Water Pollution Control Federation. Journal (June issue)
  • Water Resources Bulletin
  • Water Resources Management
  • Water Resources Research
  • Water International
  • Water Policy
  • And many others .....

Selected Books


Handbooks

  • Handbook of Hydrology, D.R. Maidment (ed.), McGraw Hill, New York, 1994 (Engr.Library Reserve)
  • Handbook of Water Resources, L.W. Mays (ed.) , McGraw Hill, New York, 1996 (Engr.Library)

Water Resources Planning and Management

  • Biswas, A.K., Systems Approach to Water Management, McGraw-Hill, New York, 1976.
  • Buras, N., Scientific Allocation of Water Resources, American Elsevier, New York.
  • Esogbue, A.O., Dynamic Programming for Optimal Water Resources Systems, Prentice-Hall, 1989.
  • Goodman, A.S., Principles of Water Resources Planning, Prentice Hall, Englewood Cliffs, 1984.
  • Grigg, N. S., Water Resources Management, McGraw Hill, New York, 1996.
  • Haimes, Y. Y., Hierarchical Analysis of Water Resources Systems, McGraw Hill, 1977.
  • Haimes, Y.Y., W.A. Hall and H.T. Freedman, Multiobjective Optimization in Water Resources Systems, Elsevier Scientific, Amsterdam, 1975.
  • Haith, D.A., Environmental Sytems Optimization, John Wiley & Sons, New York, 1982.
  • Hall, W., and J. Dracup, Water Resources Systems Engineering, McGraw-Hill, New York, 1970, 627 H149W Engineering Library
  • Helweg, O.J., Water Resources Planning and Management, John Wiley & Sons, New York, 1986, 627 H149W Engineering Library
  • Linsley, R.K., and J.B. Franzini, Water Resources Engineering, McGraw-Hill, Inc., New York, 1979.
  • Loucks, D. P. et al., Water Resource Systems Planning and Analysis, Prentice Hall, Englewood Cliffs, 1981
  • Loucks, Daniel P. and Eelco van Beek, Water Resources Systems Planning and Management:  An Introduction to Methods, Models and Applications, UNESCO, Paris, 2006.
  • Maas, Arthur, Maynard M. Hufschmidt, Robert Dorfman, Harold A. Thomas, Stephen A. Marglin and Gordon M. Fair, Design of Water Resource Systems, Harvard, Cambridge, 1962
  • Major, D.C., and R.L. Lenton, Applied Water Resources Systems Planning,Prentice Hall, Englewood Cliffs, 1979

·       Major, D.C., Multiobjective Water Resource Planning, American Geophysical Union, Water Resources Monograph 4, 1977.

  • Mays, L.W., and Y-K, Tung, Hydrosystems Engineering and Management, McGraw Hill, 1992
  • Petersen, M.S., Water Resources Planning and Development, Prentice Hall, Englewood Cliffs, 1984
  • Revelle, C., Optimizing Reservoir Resources, John Wiley & Sons, New York, 1999.
  • Rogers, P., America's Water: Federal Roles and Responsibilities, MIT Press, Cambridge, 1993.
  • Stephenson, D., and Petersen, M.S., Water Resources Development in Developing Countries, Elsevier Science, New York, 1991
  • Viessman, W. Jr. and C. Welty, Water Management: Technology and Institutions, Harper & Row, Publishers, New York 1985
  • Willis, R.L., and W. W-G. Yeh, Groundwater Systems Planning and Management, Prentice Hall, Englewood Cliffs, 1987

·       Wilson, A.G., Geography and the Environment Systems: Analytical Methods, John Wiley and Sons, 1981.



Mathematical Programming and Optimization

  • Bradley, S.P., Hax, A.C., And Magnanti, T.L., Applied Mathematical Programming, Addison-Wesley, Reading, 1977
  • Fletcher, Practical Methods of Optimization, ...
  • Gill, P.E., W. Murray, and M.H. Wright, Practical Optimization, Academic Press, London, 1981
  • Gupta, S.K., Fundamentals of Operations Research and Management, Holden-Day, Inc., 1975.
  • Hadley, G., Linear Algebra, Addison Wesley, Reading, 1961
  • Hadley, G., Linear Programing, Addison Wesley, Reading, 196X
  • Hadley, G., Nonlinear and Dynamic Programming, Addison Wesley, Reading, 196X
  • Hillier, F. S. and G.J. Lieberman, Introduction to Operation Research, McGraw-Hill, Inc., New York, 1990.
  • Intrilligator, M.D., Mathematical Optimizatiron and Economic Theory, Prentice-Hall, Inc., Englewood Cliffs, 1971.
  • Luenberger, D.G., Linear and Nonlinear Programming, Addison Wesley, New York, 1984.
  • McCormick, G.P., Nonlinear Programming: Theory, Algorithms, and Applications, John Wiley and Sons, 1983.
  • Schrage, L., LINDO An Optimization Modeling System, Fourth Edition, The Scientific Press, 1991.
  • Taha, H.A., Operations Research: An Introduction, MacMillan, New York, 1987.
  • Wagner, H.M., Principles of Operations Research, Prentice-Hall, Inc., Englewood Cliffs, 1975.

Hydrology

  • Annear, T. et al., Instream Flows for Riverine Resource Stewardship, Instream Flow Council 2004 (revised ed.)
  • Bedient and Huber, W.C., Hydrology and Floodplain Analysis, Addison Wesley, Reading, Mass., 1988.
    See also:  http://doctorflood.rice.edu/envi512/appendixE.html
  • Brutsaert, W., Hydrology: An Introduction, Cambridge University Press, 2005
  • Bras, R.L., Hydrology: An Introduction to Hydrologic Science, Addison Wesley, Reading, Mass., 1990.
  • Chow, V.T., D.R. Maidment and L.W. Mays, Applied Hydrology, McGraw-Hill, Inc., New York, 1988.
  • Dingman, L.S., Physical Hydrology, MacMillan, New York, 1994.
  • Eagleson, P.S., Dynamic Hydrology, McGraw-Hill, Inc., New York, 1970.
  • Linsley, Jr., R.K., M.A., Kohler, and J.L. Paulhus, Applied Hydrology, McGraw-Hill, Inc., New York, 1982.
  • Viessman, Jr., W., G.L. Lewis, and J.W. Knapp, Introduction to Hydrology, Harper and Row, New York, 1989. (new edition??)

 Theory of Flow and Transport in Porous Media

  • Bear, J., Dynamics of Flow in Porous Media, Elsevier, 1972.
  • Bear, J., Groundwater Hydraulics, McGraw-Hill, 1979.
  • Bear, J., and Y. Bachmat, Introduction to Modeling of Transport Phenomena in Porous Media, D. Reidel, 1990.
  • Corey, A.T., Mechanics of Immiscible Fluids in Porous Media, Water Resources Publications, Littleton, CO, 1986.
  • Dagan, G., Flow and Transport in Porous Formations, Springer-Verlag, Berlin, 1989.
  • Domenico, P. and Schwartz, F., Physical and Chemical Hydrogeology, John Wiley and Sons, 1989.
  • Dullien, F.A.L., Porous Media: Fluid Transport and Pore Structure, 2nd ed., Academic, San Diego, 1992.
  • Fetter, C.W., Applied Hydrogeology, MacMillan, New York, 1994, 2001.
  • Fetter, C.W., Contaminant Hydrogeology, MacMillan, New York, 1993.
  • Freeze R.A., and J. Cherry, Groundwater, Prentice Hall, 1981
  • Gelhar, L.W., Stochastic Subsurface Hydrology, Prentice Hall, Inc., Englewood Cliffs, 1993.
  • Greenkorn, R.A., Flow Phenomena in Porous Media, Marcel Dekker, New York, 1983.
  • Kruesman, G. P. and N. A. de Ridder, Analysis and Evaluation of Pumping Test Data, ILRI Publication 47, International Institute for Land Reclamation and Improvement, Wageninger, 1991.
  • de Marsily, G, Quantitative Hydrogeology, Academic Press, 1986.
  • McWhorter, D. B., and Sunada, D. K., Groundwater Hydrology and Hydraulics, Water Resources Press, 1977.
  • Polubarinova-Kochina, P.Ya., Theory of Groundwater Movement, Princeton Univ. Press, Princeton, 1962.
  • Todd, D. K., Groundwater Hydrology, John Wiley and Sons, 1985.
  • deWiest, R. M., Geohydrology, John Wiley and Sons, 1965.
  • and a few more ....

Numerical Methods for Flow and Transport in Porous Media

  • Ahlfeld, David P. ,and Ann E. Mulligan. Optimal Management of Flow in Groundwater Systems. Academic Press, 2000.
  • Bear, J., and A. Verruijt, Modeling of Groundwater Flow and Pollution, D. Reidel, 1987.
  • Gorelick, S.M., Freeze, R.A., Donohue, D., and Keely, J. F. Groundwater Contamination: Optimal Capture and Containment, Lewis Publishers, 1993.

 

Steady State vs. Transient Modeling

Steady State vs. Transient Modeling

   Groundwater flow models describe their capabilities as either steady state and/or transient.  It is important when deciding upon groundwater modeling software to know which options are necessary for your needs.  This month's newsletter will describe the key differences between steady state and transient modeling.

   Steady state flow occurs when the magnitude and direction of flow is constant with time throughout the entire domain.  Conversely, transient flow occurs when the magnitude and direction of the flow changes with time.  In other words, the hydraulic head doesn't change with time in a steady state flow system, but does change during transient flow. This does not mean that in a steady state system there is no movement of groundwater, it simply means that the amount of water within the domain remains the same, and that the amount of water that flows into the system, is the same amount as flows out.

   The steady state flow conditions simplify the groundwater flow equation significantly. When steady state flow occurs, time is no longer an independent variable and thus the storage term in the groundwater flow equation disappears; since there is no change in the amount of water within the domain (no change in hydraulic head) there is obviously no change in the amount of water stored in the domain.  


  References:

 Fetter, C.Q. (1994). Applied Hydrogeology. Published by Maxwell Macmillan International, New York.

Freeze, R.A, and Cherry, J.A. (1979). Groundwater. Published by Prentice Hall, Inc., New Jersey.

MODFLOW

MODFLOW



MODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation. The program is used by hydrogeologists to simulate the flow of groundwater through aquifers. The code is free software, written primarily in Fortran, and can compile and run on DOS, Windows or Unix-like operating systems.


3-dimensional grid
Since its original development in the early 1980s, the USGS have released four major releases, and is now considered to be the de facto standard code for aquifer simulation. Currently, there are at least five actively developed commercial and non-commercial graphical user interfaces for MODFLOW.

Groundwater flow equation

The governing partial differential equation used in MODFLOW is:
\frac{\partial}{\partial x} \left[ K_{xx} 
\frac{\partial h}{\partial x} \right] + \frac{\partial}{\partial y} 
\left[ K_{yy} \frac{\partial h}{\partial y} \right] + 
\frac{\partial}{\partial z} \left[ K_{zz} \frac{\partial h}{\partial z} 
\right] + W = S_{S} \frac{\partial h}{\partial t}
where

Finite difference

The finite difference form of the partial differential in a discretized aquifer domain (represented using rows, columns and layers) is:
\begin{align}
& CR_{i,j-\tfrac{1}{2},k}\left(h^m_{i,j-1,k}-h^m_{i,j,k}\right) +
  CR_{i,j+\tfrac{1}{2},k}\left(h^m_{i,j+1,k}-h^m_{i,j,k}\right) + \\
& CC_{i-\tfrac{1}{2},j,k}\left(h^m_{i-1,j,k}-h^m_{i,j,k}\right) +
  CC_{i+\tfrac{1}{2},j,k}\left(h^m_{i+1,j,k}-h^m_{i,j,k}\right) + \\
& CV_{i,j,k-\tfrac{1}{2}}\left(h^m_{i,j,k-1}-h^m_{i,j,k}\right) +
  CV_{i,j,k+\tfrac{1}{2}}\left(h^m_{i,j,k+1}-h^m_{i,j,k}\right) + \\
& P_{i,j,k}\,h^m_{i,j,k} + Q_{i,j,k} = SS_{i,j,k}\left(DELR_j \cdot 
DELC_i \cdot THICK_{i,j,k}\right)
\frac{h^m_{i,j,k}-h^{m-1}_{i,j,k}}{t^m-t^{m-1}}
\end{align}
where
  • h^m_{i,j,k}\, is the hydraulic head at cell i,j,k at time step m
  • CV, CR and CC are the hydraulic conductances, or branch conductances between node i,j,k and a neighboring node
  • P_{i,j,k}\, is the sum of coefficients of head from source and sink terms
  • Q_{i,j,k}\, is the sum of constants from source and sink terms, where Q_{i,j,k}<0.0\, is flow out of the groundwater system (such as pumping) and Q_{i,j,k}>0.0\, is flow in (such as injection)
  • SS_{i,j,k}\, is the specific storage
  • DELR_j\,, DELC_i\, and THICK_{i,j,k}\, are the dimensions of cell i,j,k, which, when multiplied, represent the volume of the cell
  • t^m\, is the time at time step m

Limitations

  • The water must have a constant density, dynamic viscosity (and consequently temperature) throughout the modelling domain (SEAWAT is a modified version of MODFLOW which is designed for density-dependent groundwater flow and transport)
 \mathbf{K} = \begin{bmatrix} K_{xx} & 0 
& 0 \\ 0 & K_{yy} & 0 \\ 0 & 0 & K_{zz}\end{bmatrix}
 \
  • The principle components of anisotropy of the hydraulic conductivity used in MODFLOW is displayed on the right. This tensor does not allow non-orthogonal anisotropies, as could be expected from flow in fractures. Horizontal anisotropy for an entire layer can be represented by the coefficient "TRPY" (Data Item 3 Page 153 [2].


Computer codes for GROUNDWATER MODELING

Computer Codes


  1. MODFLOW
  2. MODFLOWP (Hill, 1992).
  3. MOC3D (Three-DimensionalMethod-of-Characteristics Ground-Water Flow and Transport Model).
  4.  MT3DMS (Modular 3-D Multi-Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems).
  5. RT3D (Multi-Species Reactive Flow and Transport Simulation Software).
  6. HST3D (Heat and Solute Transport in Three-Dimensional Groundwater Systems).
  7. FEMWATER (Three-Dimensional Finite Element Model of Water Flow Through Saturated-Unsaturated Media).
  8. Random-Walk (Random-Walk Solute TransportModel for Selected Groundwater Quality Evaluations).
  9. GMS (Groundwater Modeling System). GMS is a software pre-processor, post-processor, and graphic user interface (GUI) implementation of a number of public domain groundwater modeling computer codes, which include FEMWATER, MODFLOW, MODPATH, MT3DMS, RT3D, UTCHEM, and PEST. It was developed by the U.S. Army Engineer Research and Development Center for use by governmental agencies. It is available as a commercial software.
  10. SWAT (Soil and Water Assessment Tool). SWAT (Arnold and Fohrer, 2005; Neitsch et al., 2005) is a basin scale, continuous time model designed to predict the impact of management on water, sediments, and agricultural chemical yields in ungaged watersheds. Major model components include weather, hydrology, soil temperature and properties, plant growth, nutrients, pesticides, bacteria and pathogens, and land management. In SWAT, a watershed is divided into multiple sub-watersheds, which are then further subdivided into hydrologic response units that consist of homogeneous land use, management, and soil characteristics. SWAT is a public domain code supported by the U.S.D.A. Agricultural Research Service at the Grassland, Soil and Water Research Laboratory.
  11. HYDRUS (Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media).
  12. FEFLOW (Finite Element Subsurface Flow and Transport Simulation System).
  13. PEST (Model-independent parameter estimation).
  14. SUTRA (Model for 2D or 3D Saturated-Unsaturated, Variable-Density Ground-Water Flow, with Solute or Energy Transport).
  15. SEAWAT (Computer Programfor Simulation of Three-Dimensional Variable-Density Ground-Water Flow).
  16. CODESA-3D (Coupled Variable Density and Saturation 3D Model).
  17. SHARP (A Quasi-Three-Dimensional, Numerical FDMthat Simulates Freshwater and Saltwater Flow Separated by a Sharp Interface in a Layered Coastal Aquifer Systems).
  18. ParFlow (Modeling Surface and Subsurface Flow on High Performance Computers).
  19. TOUGH (Transport of Unsaturated Groundwater and Heat).
  20. NUFT (Nonisothermal, Unsaturated Flow and Transport with Chemistry).
  21. STOMP (Subsurface Transport Over Multiple Phases).
  22. SLAEM/MLAEM (Single/Multi-Layer Analytic Element Method).
  23. WHPA (Wellhead Protection Area).
  24. BIOPLUME. BIOPLUME is a two-dimensional computer code for simulating contaminant transport of a single and multiple hydrocarbons with oxygen-limited and reactant-limited bioreactions (Rafai et al., 1998), developed by EPA. Its transport code is based on the USGS MOC.
  25. NAPL Simulator. The NAPL Simulator is an EPA three-dimensional computer code based on Hermite collocation finite element discretization (Guarnaccia et al., 1997).
  26. UTCHEM (University of Texas Chemical Compositional Simulator). Originally a three-dimensional finite difference model for multiphase flow, multicomponent transport and chemical flooding, this code has been modified to become a general purpose NAPL simulator (University of Texas, 2000).
  27. BIOMOC (A Multispecies Solute-Transport Model with Biodegradation).
  28. PHREEQC (A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations).
  29. PHAST (Program for Simulating Ground-Water Flow, Solute Transport, and Multicomponent Geochemical Reactions).

Source: Bear, Jacob, Cheng, Alexander (2010), Modeling Groundwater Flow and Contaminant Transport.