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:[[Chapter_5c#5.5.1 Introduction|Back to Chapter 5.5.1 Introduction]]
 +
 
 +
=Appendix 5-A=
 +
 
 +
== Introduction ==
 +
 
 +
<p><em>Geochemical  Modeling</em><br />
 +
  This  section describes the conceptual, thermodynamic, and kinetic fundamentals of  geochemical modeling and its application to prediction of mine water quality in  support of mine site characterization and remediation. The emphasis in this  section is on the basic processes that models attempt to represent with  discussions of the usefulness and the limitations of modeling. </p>
 +
<p>In principle, geochemical modeling  can be applied to all mine and process facilities, including mine portal effluent, subsurface waters  (wells or underground workings), waste dumps, process tailings piles, surface  waters, pit lakes, and open pits. The type of modeling used depends on both the  objectives and the type of source or pathway. A wide variety of codes are  available for these various environments but the critical factors are the  quality of their databases, the inherent assumptions, and, most importantly,  the knowledge and experience of the modeler.</p>
 +
<p>Three  basic approaches have been used with geochemical data: forward geochemical  modeling, inverse geochemical modeling, and geostatistical analyses. </p>
 +
<p>Forward  modeling is also known as simulating (i.e. potential reactions between rock and  water are simulated from initial conditions of a known rock type and  composition). Reactions are allowed to proceed in equilibrium or kinetic or  combined modes. Changes in temperature and pressure can be invoked, changes in  water flow rate can be invoked, and minerals can be allowed to precipitate as  they reach equilibrium solubility or dissolve as they become undersaturated.  Potential reactions can be simulated to see what the consequences are. This  type of modeling is the least constrained. A great many assumptions are either  invoked as input data or invoked as dictated by the program that may not apply  to the specific system being simulated. This approach assumes the modeler has a  significant amount of information on the ability of minerals to maintain  equilibrium solubility or their rates of reaction.</p>
 +
<p>Inverse  modeling assumes a water flow path is known and that water samples have been  analyzed along that flow path. Such data can then be converted into amounts of  minerals dissolved or precipitated along that flow path. Several assumptions  are still made regarding the choice of minerals and their relative proportions  contributing to the water chemistry, but the calculations are constrained with  actual data. Inverse modeling can also be done without any recourse to kinetic  or thermodynamic data, in which case it represents a relatively simple mass  balance calculation. When speciation and thermodynamic and kinetic properties  are included for additional constraints, the possible reactions become quite limited and the modeling is much more meaningful.</p>
 +
<p>Modeling  of any type does not lead to a unique solution but the possibilities are more  limited with greater amounts of carefully collected field data.  Martin et al. (2005) summarized the benefits  and limitations of geochemical modeling as follows:</p>
 +
<p><strong>Benefits</strong></p>
 +
<ul type="disc">
 +
  <li>Provide      insight into potential future conditions</li>
 +
  <li>Determine      which variables are most important in determining future conditions</li>
 +
  <li>Assess      the effects of alternative approaches to ARD management</li>
 +
  <li>Assess      potential effects of uncertain parameters</li>
 +
  <li>Establish      objectives and test conditions for field and laboratory studies</li>
 +
  <li>Integrate      available information</li>
 +
</ul>
 +
<p><strong>Limitations</strong></p>
 +
<ul type="disc">
 +
  <li>Insufficient      input data</li>
 +
  <li>Modeling      can be challenging and results misinterpreted</li>
 +
  <li>Uncertain      and variability of the results</li>
 +
  <li>Difference      between modeled and actual field conditions</li>
 +
</ul>
 +
 
 +
[[#top|Top of this page]]
 +
 
 +
== Approaches to Geochemical Modeling ==
 +
 
 +
<p><em>Speciation</em><br />
 +
  One of the most fundamental types of  geochemical modeling is speciation modeling. “Speciation” refers to the  distribution of chemical components or elements among the different possible  forms or species. Aqueous speciation is the distribution of chemical components  among dissolved free ions, ion pairs and triplets, and other complexes. This  concept is important because research has shown that a number of processes,  including mineral precipitation and dissolution, biological uptake and  toxicology, and sorption are all affected by speciation.</p>
 +
<p>Some species, such as redox species,  have to be determined analytically. This is because most geochemical modeling  codes erroneously assume that redox equilibrium is maintained while, in  reality, disequilibrium among redox species is the rule, not the  exception.  In particular, dissolved iron  is usually present in high concentration in ARD and can exist as the reduced  ferrous iron or as the oxidized ferric iron. For an accurate evaluation of iron  speciation, chemical analysis rather than speciation modeling is required. In  NMD and SD, dissolved iron is largely absent due to formation of sparingly-soluble  ferrihydrite or similar iron oxyhydroxide minerals. Solid speciation is the  distribution of chemical components among various solid phases. For example, iron  can precipitate from ARD as goethite, jarosite, schwertmannite, or  ferrihydrite. Identifying these phases would constitute solid speciation.</p>
 +
<p>Aqueous speciation results are used  in a variety of modeling objectives that include modeling of saturation-index  calculations for mass-transfer, modeling of mineral precipitation and dissolution,  modeling of adsorption and desorption, and reactive-transport modeling.</p>
 +
<p><em>Mass  Transfer (precipitation, dissolution, gas transfer)</em><br />
 +
  Modeling of mineral precipitation  and dissolution and gas-transfer reactions can take place conceptually in one  of three possible systems: equilibrium state, steady-state, or transient state. The equilibrium state assumes the system under investigation is isolated from  any external exchanges of energy or mass. Although an unrealistic concept,  equilibrium state is actually quite practical because many reactions  approximate equilibrium even though there are gradients in water pressure or  temperature. For example, in many groundwaters, calcite and gypsum quickly  reach their equilibrium solubility. Even with gradients in CO2  pressure or mixing with other sources of sulphate, these minerals adjust to  maintain saturation and the assumption of equilibrium may be valid. In  addition, even when geochemical reactions of interest do not reach equilibrium  rapidly, such reactions may achieve equilibrium over the time scale of the  modeling simulation (i.e. the life of a mine and beyond). Therefore, the  majority of geochemical modeling can be conducted under the assumption of  equilibrium conditions.</p>
 +
<p><em>Reactive  Transport (Coupled Models)</em><br />
 +
  Reactive-transport models that can  be applied to simulation of ARD, NMD, and SD are generally the subject of  active research, although several have been applied with considerable success.  The idea is to couple flow models with chemical reaction models to determine  the effects of flow on reactions and vice versa, including the effects of  dispersion. Such modeling is relatively straightforward for streams and rivers  because the flow path is not only visible but measurable. Considerable effort  has been made to develop quantitative reaction-transport models for streams  affected by acid mine drainage (Kimball et al., 1994; Runkel et al., 1996).  Progress in surface-water reactive-transport modeling has now advanced to the  point where it can guide remediation decisions for complex mine sites (Runkel  and Kimball, 2002; Kimball et al., 2003).</p>
 +
<p>Reactive-transport modeling for  groundwater has also progressed substantially over the last two decades and  many of the recent codes have been applied to mine sites. Three general types  of coupled models can be distinguished: those that model the groundwater only,  those that model the unsaturated zone only, and those that model both. The most  recent overview by Mayer et al. (2003) provides the theoretical foundations for  groundwater reactive-transport modeling, methods of coupling flow with  reaction, the various codes that have been used in mined environments, and case  studies. An excellent example of combining laboratory testing of waste rock  material with field measurements and modeling of small- to medium-scale test  plots of actual mine wastes to predict the consequent water quality over the  short term and the long term in a very sensitive environment is in progress at  the Diavik mine site near Yellowknife, Northwest Territories, Canada (Blowes et  al., 2007). This investigation may be one of the first to combine lab-scale  tests, field tests, and modeling, supported by the detailed characterization of  the rock and mineral composition and their weatherability.</p>
 +
 
 +
[[#top|Top of this page]]
 +
 
 +
== Role of Thermodynamic and Kinetic  Data ==
 +
 
 +
<p>Thermodynamic and, for some models,  kinetic data are part of the basic input to codes that compute reactions and  simulations for water-rock interactions. For some reactions, these data are  known accurately and precisely; for others they are non-existent or poorly  known. Thermodynamic measurements and evaluations are part of ongoing research.  Sometimes the conclusions of a modeling study can be greatly affected by these  databases and their uncertainties and sometimes not. Rarely are modeling  results evaluated from the point of view of the basic data, which reflects a  general lack of QA/QC common to many modeling efforts.</p>
 +
 
 +
== Scale-up  Considerations ==
 +
 
 +
<p>Drainage  quality prediction is made challenging by a number of factors that range in  scale from small to large. Small-scale factors that influence drainage quality  are related to reactions at the water-rock interface in the aqueous, gas and  solid phase. Information on reactive surface area and reaction rates generally  is limited. On a large scale, geology, climate, mining method, mineral  processing method, and waste management practices vary within and amongst  operations. Variability of these large-scale factors implies that it may not  always be feasible to apply information from one site to another. However,  advances are being made in this respect, for instance, through the use of  geo-environmental models that present unifying principles which link mine water  quality to the nature of the ore deposit, climate, and type of mine waste.</p>
 +
<p>Water  quality prediction typically necessitates the extrapolation of laboratory-scale  results to operational scale. This extrapolation must address factors such as  differences in particle size, climate conditions, water and gas transport, and  duration (i.e., how these variables affect drainage composition over decades,  centuries or longer). Although the construction of instrumented, large-scale  mine waste test cells has increased significantly in recent years and is  expected to yield valuable data, little information is currently available describing  the effects of these variables on well-characterized mine wastes over extended  periods of time. Use of models therefore is required to bridge the gap between  laboratory results and operational conditions (USEPA, 2003).</p>
 +
 
 +
[[#top|Top of this page]]
 +
 
 +
== Examples of Major Codes ==
 +
 
 +
<p>Some of the more popular codes used  primarily for groundwater geochemistry but also for mining-affected sites are  shown in Table A-5-1 below. More detail on geochemical modeling, modeling codes and  associated uses and limitations is presented in Alpers and Nordstrom (1999),  Mayer et al. (2003), and Maest and Kuipers (2005).  Section XXX on hydrogeological models in this Appendix  also provides additional information.</p>
 +
<p align="center"><strong> A-5-1: Summary of Geochemical  Modeling Codes</strong></p>
 +
<table border="1" align="center" cellpadding="0" cellspacing="0">
 +
  <tr>
 +
    <td width="130" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Codes</strong></p></td>
 +
    <td width="312" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Type</strong></p></td>
 +
    <td width="173" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Reference</strong></p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">PHREEQC, PHAST</p></td>
 +
    <td width="312" valign="top"><p align="center">USGS codes: mass transfer and reactive-transport</p></td>
 +
    <td width="173" valign="top"><p align="center">Parkhurst and Appelo (1999), Parkhurst et al. (2004)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">SOLMINEQ.GW</p></td>
 +
    <td width="312" valign="top"><p align="center">USGS code: mass transfer and high temperature</p></td>
 +
    <td width="173" valign="top"><p align="center">Perkins et    al. (1990)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">WATEQ4F</p></td>
 +
    <td width="312" valign="top"><p align="center">USGS code: speciation and low-temperature only</p></td>
 +
    <td width="173" valign="top"><p align="center">Ball and    Nordstrom (1991)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">MINTEQA2 </p></td>
 +
    <td width="312" valign="top"><p align="center">EPA supported code: speciation and mass transfer</p></td>
 +
    <td width="173" valign="top"><p align="center">USEPA    (1999)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">MIN3P </p></td>
 +
    <td width="312" valign="top"><p align="center">Waterloo code: saturated and unsaturated flow</p></td>
 +
    <td width="173" valign="top"><p align="center">Mayer et    al. (2002)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">TOUGH-AMD</p></td>
 +
    <td width="312" valign="top"><p align="center">Quebec code: gas and energy transfer without    reaction</p></td>
 +
    <td width="173" valign="top"><p align="center">Lefebvre    et al. (2002)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">RETRASO</p></td>
 +
    <td width="312" valign="top"><p align="center">Barcelona code: unsaturated and saturated flow and    reaction</p></td>
 +
    <td width="173" valign="top"><p align="center">Saaltink    et al. (2002)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">SULFIDOX</p></td>
 +
    <td width="312" valign="top"><p align="center">ANSTO code: gas and energy transfer</p></td>
 +
    <td width="173" valign="top"><p align="center">Ritchie    (2003)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">CRUNCH</p></td>
 +
    <td width="312" valign="top"><p align="center">Bern/LBL code: unsaturated and saturated flow and    reaction</p></td>
 +
    <td width="173" valign="top"><p align="center">Steefel    (2000)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">Geochemist’s Workbench</p></td>
 +
    <td width="312" valign="top"><p align="center">University of Illinois code: mass transfer,    saturated flow</p></td>
 +
    <td width="173" valign="top"><p align="center">Bethke    (1994, 1996)</p></td>
 +
  </tr>
 +
  <tr>
 +
    <td width="130" valign="top"><p align="center">EQ 3/6</p></td>
 +
    <td width="312" valign="top"><p align="center">Lawrence Livermore National Laboratory code: mass    transfer and reactive transport</p></td>
 +
    <td width="173" valign="top"><p align="center">Wolery and    Daveler (1992)</p></td>
 +
  </tr>
 +
</table>
 +
 
 +
[[#top|Top of this page]]
 +
 
 +
== Hydrological  Modeling ==
 +
 
 +
<p><em>Introduction</em><br />
 +
  In  a general sense, a hydrological model is an analog of a natural or  human-modified hydrological system. This generic definition encompasses models  of surface-water and groundwater systems. Scientists and engineers more  commonly use the term hydrological model to refer to models of surface-water  systems, and consider hydrogeological models for groundwater systems as a  separate subject. This section follows the latter convention, describing  hydrological models in the context of surface-water systems. Hydrogeological  models and their applications are presented in Section XXX.</p>
 +
<p>Hydrological  models range from simple algebraic calculations to complex reactive-transport  computer codes. Physical analogs, such as stream tables, can also be useful  simulations of complex surface-water systems. Hydrological models can be used  to predict the fate and transport of mine drainage through a surface-water  system, providing important input to human-health or ecological risk  assessments. Hydrological models can also be used to estimate the water-quality  and water-quantity evolution of pit lakes over time. Hydrological models can be  coupled with hydrogeological and geochemical models to incorporate the  interaction between surface water and groundwater into the simulation and  account for geochemical reactions.</p>
 +
<p>Selection  of an appropriate, quantitative hydrological model depends on the type of  output that is required and, critically, on the conceptual model of the system  being evaluated. A robust conceptual model will identify the important physical  and geochemical characteristics of the field-scale system being evaluated.  Based on that identification, an appropriate hydrological model can be selected  that quantitatively represents those important processes. For complex systems  or to assess a range of different types of processes, multiple hydrological  models can be applied to predict the fate, transport, and potential impacts of  mine discharges.</p>
 +
<p><em>Data Needs</em><br />
 +
  In  common with all models, the output from a hydrological model is only as  reliable as the data that are used to generate the model. Typical data  requirements for many hydrological models include:</p>
 +
<ul>
 +
  <li>Precipitation, either  local or distributed across a region</li>
 +
  <li>Evaporation from  surface-water bodies such as lakes and rivers</li>
 +
  <li>Potential or actual  evapotranspiration from vegetated areas and bare land</li>
 +
  <li>Surface slope and land  cover</li>
 +
  <li>Channel slope, width,  depth, and roughness for calculations of stream flow or conveyance capacity</li>
 +
  <li>Concentrations of  chemical constituents. These may be determined from on-site monitoring  programs, laboratory or field-scale testing programs, or estimated using  geochemical models</li>
 +
</ul>
 +
<p>Simple  quantitative models of surface-water flow such as the United States Natural  Resource Conservation Service (formerly known as the Soil Conservation Service  [SCS]) curve-number method (SCS, 1972) may only require a few of before listed  data elements. More detailed models, for instance those that incorporate  reactive transport (e.g., Runkel and Kimball, 2002), may require additional  information regarding the kinetics of reactions considered in the simulation.</p>
 +
<p>Governmental  agencies in many countries collect regional precipitation and evaporation data  that may be used for hydrological models. Precipitation data are commonly  collected with the greatest frequency through meteorological measuring  stations. Evaporation data, such as pan evaporation measurements, generally are  collected with less frequency. Some mine sites also collect these types of data  on a local scale that can be used to refine the regional data sets.</p>
 +
<p>Care  must be taken if combining different types of data from different locations.  The locations should be similar in terms of latitude, elevation, overall  climatic zone, and cloud cover for the combined data set to be reliable. If  this is not the case, statistical methods have been developed to estimate  precipitation at a special site from a known precipitation network </p>
 +
<p><em>Water-Balance and  Mixing-Cell Models</em><br />
 +
  Water-balance  models apply the principle of conservation of mass to quantitatively track  inflows and outflows from the various components of a conceptual model. Mass  and concentration of ARD-related constituents can be incorporated into this  approach through mixing-cell models. The hydrologic elements of a conceptual  model, such as surface-water reservoirs, open pits, and groundwater basins, can  be represented as a series of simulated reservoirs. The connections between the  reservoirs, such as the creeks or groundwater flow paths, can be represented by  quantitative estimates of capacity or flow. Concentrations of individual  constituents can be tracked along with water quantity to calculate the transfer  of chemical mass and mathematically mixed in the model to evaluate changes in  concentration over time in the reservoirs.</p>
 +
<p>Water-balance  and mixing-cell models can be implemented in standard spreadsheets. More  complex water-balance or mixing-cell models, incorporating additional physical  or chemical processes, can be addressed by using dynamic system simulators such  as GoldSim<sup>TM</sup> or STELLA<sup>TM</sup>.</p>
 +
<p><em>Rainfall  Runoff Models</em><br />
 +
  Appendix  A of USEPA (2003) describes the basic approaches to modeling runoff processes  based on precipitation inputs. Runoff can be thought of as the excess  precipitation after processes such as infiltration and surface abstraction are  evaluated. The most commonly applied model to estimate the volume of runoff is  the SCS curve-number method (SCS, 1972). The SCS curve-number method involves  estimating the vegetation and land-cover characteristics of a watershed or mine  facility, looking up the resulting curve number, and then applying that number  along with precipitation information to develop the runoff volume for a storm  event.</p>
 +
<p>The  unit-hydrograph method of runoff determination may be more appropriate for many  mine sites. The method is also described in SCS (1972). A hydrograph relating  runoff to precipitation is developed for a unit precipitation volume over an  area, for example 1 inch or 1 centimeter of rainfall. The unit hydrograph is  then used to estimate runoff from storms of greater or lesser intensity.</p>
 +
<p>Water  quality in well-mixed rivers and streams can be predicted using a code such as  QUAL2K developed by the USEPA (Chapra et al., 2007). QUAL2K represents a  modernized version of QUAL2E (Brown and Barnwell, 1987). QUAL2K is programmed  in the Visual Basic for Applications language and executed within the Microsoft  Excel spreadsheet environment. The program can simulate 1-dimensional flow,  changes in water quality along the flow path, and chemical interactions with  bed sediments.</p>
 +
<p>Distributed-parameter  rainfall-runoff models are more appropriate for larger watersheds with  heterogeneous flow characteristics. SWAT2000 (Neitsch et al., 2002) is a  distributed-parameter model developed by the Agricultural Research Service of  the U.S. Department of Agriculture to simulate runoff and water quality in  large, complex watersheds. SWAT2000 and similar models break a complex  watershed into hydrologic sub-units, each with a uniform set of  characteristics. Flow and water quality are calculated for each sub-unit, then  aggregated to provide predictions at a complex watershed scale.</p>
 +
<p><em>Pit Lake  Modeling</em><br />
 +
  Pit  lake formation and the evolution of water quality can be simulated using a  water-balance approach or with complex numerical codes. Water balance models  can be used to quantify the inflows to the pit lake as the pit fills after  mining and dewatering ceases. Potential inflows include direct precipitation  over the surface area of the lake, runoff entering the pit lake from the  surrounding watershed, and groundwater inflow through the walls and floor of  the pit. Outflows may include direct evaporation from the lake surface,  groundwater outflow, and potentially surface-water discharges if a spill  elevation is reached.</p>
 +
<p>A  chemical composition can be assigned to each inflow and outflow to extend the  water-balance model to include ARD-related impacts. For example, wall-washing  results can be used to estimate the mass input of chemical constituents from  seepage or overland flow coming in contact with reactive portions of the pit  wall. Geochemical speciation models can be used to predict the resulting  chemical quality of water in the pit.</p>
 +
<p>Rainfall-runoff  models can be used to develop the surface-water inflow portions of the water  balance. Groundwater inflow can be estimated using simple analytical equations  (Marinelli and Niccoli, 2000). The solution to drawdown in a large-diameter  pumping well presented by Papadopoulos and Cooper (1967) is often used to  approximate the groundwater inflow to a mine pit, and can also be used to  estimate recharge to the pit lake. Cimen (2001) and Aryafar (2007) present  additional analytical solutions that can be useful in pit-lake studies.</p>
 +
<p>Complex  numerical models can also be used to estimate the groundwater inflow to a pit  lake. SEEPW (Ref)  and FEFLOW (WASY, XXXX)  are finite-element, variably-saturated flow models that have been applied to  this problem. MODFLOW2005 (Ref),  including the LAK package, is a modular, 3-dimensional, finite-difference model  that can be used to simulate the groundwater components of pit-lake evolution.  Complex models such as these, however, require more data for parameterization  and calibration than the simpler approaches. Selection of more complex  simulation approaches should only be made if the conceptual model and project  needs require the additional computational burden.</p>
 +
<p>An  alternative to geochemical models for the prediction of pit-lake quality is a  code such as CE-QUAL-W2 developed by the U.S. Army Corps of Engineers Waterway  Experiment Station (Cole and Buchak, 1995). CE-QUAL-W2 is suitable for  applications to rivers, lakes, reservoirs, and estuaries.</p>
 +
<p><em>Watershed Models</em><br />
 +
  Watershed  models are used to simulate the hydrologic cycle, including surface water,  groundwater, and the interactions between the two, at the basin or watershed  scale. Watershed models can be used to predict ARD impacts on downstream users  and the evolution of ARD-related water quality through a flow system. Furman  (2008) summarizes the mathematics and computational tools used to simulate  coupled surface and subsurface flow processes.</p>
 +
<p>Watershed  models can be data-intense and numerically complex. The most widely used  watershed models are:</p>
 +
<ul>
 +
  <li>MIKE SHE, developed by  the Danish Hydraulic Institute (DHI) in Denmark</li>
 +
  <li>HEC-HMS, developed by  the U.S. Army Corps of Engineers Hydrologic Engineering Center</li>
 +
  <li>WMS (Watershed Modeling  System), a graphical interface developed by Environmental Modeling Systems,  Inc. for a number of modules including HEC-HMS, CE-QUAL-W2 and other codes</li>
 +
</ul>
 +
 
 +
[[#top|Top of this page]]
 +
 
 +
== Hydrogeological  Modeling ==
 +
 
 +
<p><em>Introduction</em><br />
 +
  Hydrogeological  models address water flow and contaminant transport below the land surface. As  with hydrological models, approaches to hydrogeological simulations range from  simple to complex. The universe of hydrogeological models includes physical and  electrical analogs. With the advent of powerful personal computers and  high-level programming languages, these approaches are rarely used in current  practice. Accordingly, this discussion of hydrogeological models will focus on  quantitative, mathematical approaches to subsurface water flow and contaminant  transport.</p>
 +
<p>A  large body of literature exists regarding hydrogeological modeling, as do a  number of computer programs. Zheng and Bennett (2002) provide an excellent  introduction to the topic of contaminant-transport modeling. Maest and Kuipers  (2005) provide a review of hydrogeological models more directly focused on ARD  prediction. Other references are provided in the discussion below.</p>
 +
<p>Three  basic types of hydrogeological models are available, in order from simple to  more complex:</p>
 +
<p>1.         Analytical  models of flow and contaminant transport<br />
 +
  2.         Analytic  element models<br />
 +
  3.         Numerical  models</p>
 +
<p>As  a general rule, hydrogeological models should be as simple as possible while  still representing the physical system with an adequate degree of precision and  accuracy. More complex models should only be selected when project needs  dictate, simpler models are demonstrably not adequate, and suitable data are  available for model parameterization and calibration.</p>
 +
<p>Hydrogeological  models are useful tools for predicting the potential generation and resulting  impacts of ARD. Models can be used to fill data gaps, either in space or in  time. They can also be used to test alternative conceptual models in an  iterative process designed to understand the complex natural or human-modified  subsurface system.</p>
 +
<p>Figure  5-19 in Chapter 5 of this GARD Guide presents a generalized approach to the  development, calibration, and use of models, including hydrogeological models.  The quantitative modeling process starts with a strong conceptual model, and  the quantitative model can then be used to update the conceptual model as  necessary. The majority of the effort for a hydrogeological model goes into the  calibration phase of the process, sometimes also referred to as inverse  modeling.</p>
 +
<p><em>Data Needs  for Model Parameterization</em><br />
 +
  <em>Basic Flow and Transport Models</em><br />
 +
  As  model complexity grows, the data requirements for model parameterization and  calibration also increase. Basic data requirements for any groundwater flow and  contaminant-transport model include:</p>
 +
<ul>
 +
  <li>Saturated hydraulic conductivity</li>
 +
  <li>Specific yield or storativity</li>
 +
  <li>Effective porosity (for calculations of contaminant transport)</li>
 +
</ul>
 +
<p><em>Unsaturated-Zone Models</em><br />
 +
  Simulating  flow and transport in the unsaturated zone typically requires additional  information regarding the flow characteristics of the unsaturated porous  medium. Unsaturated hydraulic conductivity is a function of the saturated  hydraulic conductivity and the degree of saturation of the porous medium. Additional data requirements for unsaturated-zone models include the parameters  for the function describing the relationship between saturation, matric  suction, and unsaturated hydraulic conductivity.</p>
 +
<p><em><u>Sorption and Retardation Factors</u></em><br />
 +
  Interaction  between the aquifer matrix and dissolved constituents can be an important  process for ARD-related hydrogeological models. Many contaminant-transport  models simulate this interaction through the use of a retardation factor.</p>
 +
<p>The  retardation factor is the ratio between the apparent velocity of the  contaminant front and the pore velocity of moving groundwater (Fetter, 1993).  In its simplest form, the retardation factor is calculated using a distribution  coefficient appropriate for a linear adsorption isotherm. More complex forms of  the retardation factor can be derived using different adsorption isotherms and  assumptions.</p>
 +
<p>Models  incorporating retardation thus require additional data, including:</p>
 +
<ul>
 +
  <li>Bulk density of the  aquifer matrix</li>
 +
  <li>Distribution coefficient  or other parameters defining the adsorption isotherm</li>
 +
  <li>Rate constants for non-equilibrium  sorption models</li>
 +
</ul>
 +
<p><em>Reactive-Transport Models</em><br />
 +
  As  discussed in Section XXXX  under geochemical modeling, detailed evaluation of the evolution of ARD-related  constituent concentrations over time and space in an aquifer may require the  use of a reactive-transport model. These types of models allow the simulation  of reactions between the dissolved constituents and the aquifer matrix and  reactions between the dissolved species themselves. Relative to the more basic  hydrogeological models, additional data are necessary to apply these models,  including:</p>
 +
<ul>
 +
  <li>Non-equilibrium rate  constants describing the reactions between dissolved constituents</li>
 +
  <li>Proportionality  constants or functions describing the solubility controls on individual species  under consideration</li>
 +
</ul>
 +
<p>Steefel  et al. (2005) and Mayer et al. (2003) provide overviews of reactive-transport  models and their associated data requirements.<br />
 +
  <em>Data Collection</em><br />
 +
  The  field data most commonly obtained in support of hydrogeological modeling are  the saturated hydraulic conductivity and storage coefficients (specific yield  or storativity). Saturated hydraulic conductivity can be measured on core  samples in the laboratory, by using single-well slug tests, or by using  multiple-well, long-term pumping tests.</p>
 +
<p>Slug  tests and pumping tests provide better estimates of saturated hydraulic  conductivity at the field scale than laboratory tests. Pumping tests conducted  with one or more pumping wells in combination with at least one additional  observation well can also provide data regarding the storage coefficients.  Butler (1998) provides an extensive description of the design and performance  of slug tests. Kruseman and de Ridder (2000) describe the design and  performance of pumping tests.</p>
 +
<p>The  relationship of unsaturated hydraulic conductivity to moisture content can be  measured in the field or laboratory, and the resulting data can be fitted to a  number of equations. Stephens (1995) provides a detailed description of data  collection and analysis related to unsaturated-zone hydrology.</p>
 +
<p><em>Other Data Sources</em><br />
 +
  Unsaturated  hydraulic conductivity characteristic curves can be estimated by several  methods. RETC (van Genuchten et al., 1991) and ROSETTA (Schaap, 2003?) are programs that  can be used to estimate unsaturated flow characteristics from more commonly  available data. SoilVision (SoilVision Systems, XXXX) contains a database of measured unsaturated  hydraulic conductivity characteristic curves in addition to a number of  algorithms to calculate unsaturated flow characteristics.</p>
 +
<p>Adsorption-isotherm  distribution coefficients for a number of metals are tabulated in Stenge and  Peterson (1989). Values are included for three different pH ranges and a range  of sorbent (organics, oxides, clays) contents.</p>
 +
<p><em>Analytical  Models</em><br />
 +
  Analytical  models are relatively simple methods for simulating groundwater flow and  contaminant transport. These models are formulated as closed-form equations  that can be solved directly without the use of numerical methods. Transient or  steady-state solutions for groundwater flow and contaminant transport with  simple retardation factors in one, two or three dimensions are available.<br />
 +
  Because  of their simplicity, data needs are relatively minor for analytical models.  Homogeneous, isotropic flow conditions are typically assumed. Analytical models  can be useful for screening-level evaluations. They can also be used for more  definitive assessments of groundwater flow and contaminant transport if the  assumptions are judged to be valid or insufficient data are available to  warrant a more complex approach.</p>
 +
<p>One  useful analytical model for the prediction of ARD-related transport is the  Ogata and Banks (1961) solution to the advection-dispersion equation. Domenico  and Schwartz (1990) extended that solution to include a retardation factor  based on a linear adsorption isotherm. The Domenico and Schwartz (1990) model  can be implemented in a spreadsheet format and adapted to a wide variety of  problems.</p>
 +
<p>STANMOD  (Simunek et al, 2003) is a public domain set of analytical solutions to the  advection-dispersion equation in one, two or three dimensions. A variety of  previously published solutions, already in the public domain, are included in  STANMOD.</p>
 +
<p><em>Analytic  Element Models</em><br />
 +
  Analytic  element modeling takes advantage of the principle of linear superposition to  solve groundwater flow and contaminant transport problems in more complex  systems than can be addressed by analytical models. Haitjema (1995) provides  the basic theoretical framework for the analytic element method and describes  its use.</p>
 +
<p>GFLOW  (Haitjema Software, 2007) is a groundwater flow model that implements the  analytic-element method. PhreFlow (Jankovic and Barnes, 2001) is a public  domain analytic-element model of 3-dimensional groundwater flow and contaminant  transport. WhAEM2000 (Kreamer et al., 2007) is a public domain and open source  general purpose ground-water flow modeling system, with strengths in  representing regional flow systems, and ground water/surface water  interactions. It was initially designed to facilitate capture zone delineation.</p>
 +
<p><em>Numerical  Models</em><br />
 +
  Numerical  models use iterative processes to solve the equations of groundwater flow and  contaminant transport in complex domains. Flow and transport under saturated,  unsaturated, or variably-saturated conditions in heterogeneous, anisotropic  systems with various boundary conditions can be simulated using these methods.  Numerical models can also require a substantial amount of data regarding  parameters and for input to the simulation.</p>
 +
<p>Two  numerical solution schemes, finite-difference and finite-element, are widely  used in hydrogeological models (Wang and Anderson, 1982). Finite-difference  models employ a rectangular discretization scheme to divide the model domain  into individual cells, within which flow characteristics such as hydraulic  conductivity are assumed to be uniform. Finite-element models employ either a  triangular or rectangular discretization scheme to divide the model domain into  individual elements of uniform characteristics.</p>
 +
<p>As  a general rule, finite-difference models are more computationally efficient for  a given problem compared to finite-element models. Finite-element models can be  fitted more closely to irregular boundaries and can handle internal boundaries  such as mine pits, underground workings, or faults with less numerical  instability than finite-difference models. The choice of numerical solution  scheme and computer code should be driven by the conceptual model, project  requirements, and available computer resources.</p>
 +
<p>The  MODFLOW family of computer codes (e.g., MODFLOW2005, Ref) contains examples of finite-difference  models. MODFLOW, originally released by the USGS in 1988 and upgraded  periodically since then, is probably the most widely used hydrogeological model  in the world.</p>
 +
<p>Finite-element  models are exemplified by FEFLOW (WASY, XXXX). FEFLOW is a commercially available code  that can be applied to a broad range of variably-saturated flow and transport  problems. Compared to MODFLOW it has more capabilities for modeling mine water  problems because the original program code was derived from a mining  background. </p>
 +
<p>Many  other finite-difference and finite-element models suitable for application to  ARD-prediction problems are available. Maest and Kuipers (2005) tabulate the  capabilities for a range of models.</p>
 +
<p><em>Commonly Available Models</em><br />
 +
  Table  A-5-2 summarizes the characteristics of several numerical model computer codes  that are widely used and can be applied to problems of ARD-related contaminant  transport. Some models are freely available in the public domain, while others  are proprietary products distributed by commercial companies. Table A-5-2 is  organized by computer program and by graphical user interface (GUI). More  information on GUI use and characteristics is presented below.</p>
 +
<p><em>Unsaturated-Zone Models</em><br />
 +
  Unsaturated-zone  models are often used to assist with predicting the formation and transport of  ARD within and through waste-rock dumps and unsaturated process tailings  impoundments. Commonly used unsaturated-zone models include HELP (Schroeder et  al., 1994), HYDRUS (Simunek et al., 2007), UNSATH (Fayer, 2000), and VADOSE/W  (GeoSlope International, 2002). HELP and UNSATH are available in the public  domain, as is the 1-dimensional version of HYDRUS.</p>
 +
<p><em>Fracture-Flow Models</em><br />
 +
  The  majority of hydrogeological models are strictly valid for simulating flow and  transport through continuous porous media only. However, some ARD problems  occur in subsurface systems dominated by flow and transport through discrete  fractures or fracture networks. Even if flow and transport are primarily  through fractures, porous-medium models may be adequate if the fracture density  is great and the fracture aperture is small. Some models allow a dual-porosity  formulation that can represent the flow through a fracture network as well as  flow through the porous media between fractures.</p>
 +
<p>If  the assumption of flow through continuous porous media is not valid, models  that represent the physics of fracture flow should be considered. Two such  models are FRACMAN (Golder, 2007) and FRACTRAN/FRAC3DVS (University of  Waterloo, 2004).</p>
 +
<p><em>Density-Dependent Flow and Transport</em><br />
 +
  Most  contaminant-transport models are based on the assumption that concentrations  are relatively dilute and the density of groundwater is not significantly  different from fresh water. Groundwater that is heavily impacted by ARD,  however, can have sufficiently large concentrations of metals, sulfate, and  other species that the density effects are significant. If the conceptual site  model indicates that density effects are important, a model capable of  accounting for variability in density should be selected.</p>
 +
<p>SEAWAT2000  (Guo and Langevin, 2002) is one such model, developed by the USGS to simulate 3-dimensional,  variable-density groundwater flow in porous media. It was developed by  combining MODFLOW and MT3DMS into a single program that solves the coupled flow  and solute-transport equations.</p>
 +
<p><em>Reactive-Transport Models</em><br />
 +
  Most  contaminant-transport models incorporate relatively simple reactions describing  interaction between dissolved constituents and the aquifer matrix. These  reactions are implemented in the form of retardation factors using one of  several adsorption isotherms. Interactions between dissolved constituents are  typically not considered.</p>
 +
<p align="center"><strong>Table A-5-2:  Hydrogeological Models and Graphical User Interfaces for those models</strong></p>
 +
<div align="center">
 +
<table border="1" cellspacing="0" cellpadding="2" width="1231">
 +
    <tr>
 +
      <td colspan="2" valign="top" nowrap="nowrap" bgcolor="#CCCCCC"><br />
 +
        <strong>GUI</strong></td>
 +
      <td width="96" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Groundwater Vistas</strong></p></td>
 +
      <td width="101" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Groundwater Modeling Systems</strong></p></td>
 +
      <td width="96" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Visual MODFLOW</strong></p></td>
 +
      <td width="88" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Argus ONE</strong></p></td>
 +
      <td width="88" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>PMWIN</strong></p></td>
 +
      <td width="489" valign="top" bgcolor="#CCCCCC"><p align="center"><strong>Description</strong></p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="105" nowrap="nowrap" rowspan="7"><p align="center">FLOW</p></td>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>SEEP2D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>A 2D finite-element groundwater model designed to be used on profile models such as cross-sections of earth dams or levees</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODAEM</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Analytic element model for simple flow and transport computations</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOW 88</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOW 96</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOW 2000</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOW 2005</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>FEMWATER</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>3D finite-element model used to simulate density-driven coupled flow and contaminant transport in saturated and    unsaturated zones</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="105" nowrap="nowrap" rowspan="15"><p align="center">SOLUTE<br />
 +
          TRANSPORT</p></td>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>ART3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>A three-dimensional analytic reactive transport model</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODPATH</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>A particle tracking code used with MODFLOW assuming particles are transported by advection</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>PATH3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>General particle tracking program for calculating ground-water paths and travel times in steady-state or transient, 2 or 3D    flow fields</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>PMPATH</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>Particle tracking</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MOC3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>3D method-of-characteristics ground-water flow and transport model integrated with MODFLOW-96</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MT3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>Simulation of single-species transport via advection, dispersion and simple chemical reactions</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MT3DMS</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">xXx </p></td>
 +
      <td width="489" valign="top"><p>Simulation of multi-species transport by advection, dispersion, and limited chemical reactions of dissolved constituents</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>PHT3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="489" valign="top"><p>A reactive transport model coupling MT3DMS and PHREEQC</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>RT3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="489" valign="top"><p>An advanced multi-species reactive transport model developed by the Battelle Pacific Northwest National Laboratory</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>SEAM3D</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Reactive transport model to simulate complex biodegradation problems involving multiple substrates and multiple electron    acceptors</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>SEAWAT 2000</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Simulation of 3D, transient, variable-density ground water flow</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOW-<br />
 +
      SURFACT</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Enhanced simulation capabilities and robust solution methods for handling complex saturated/unsaturated flow and transport</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOWT</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Version of MODFLOW that includes modules for simulating 3D contaminant transport</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>SWIFT</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>3D model to simulate groundwater flow, heat, brine  and radionuclide transport</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>UTCHEM</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>A multi-phase flow and transport model ideally suited for pump and treat simulations</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="105" nowrap="nowrap" rowspan="6"><p align="center">CALIBRATION</p></td>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODFLOW 2000</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Parameter inversion option built into MODFLOW 2000</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>UCODE</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="489" valign="top"><p>Developed by the USGS, UCODE is a universal inverse modeling code&nbsp;to solve parameter estimation problems</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>PEST</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="489" valign="top"><p>A model-independent, non-linear parameter estimator to assist in data interpretation, model calibration, and predictive analysis</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Stochastic</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Parameter inversion using Monte Carlo or Latin Hypercube</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Modac</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>An inverse model that calculates a K for every cell in the model (or in selected layers) using starting heads as the calibration    target</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Automated <br />
 +
      Sensitivity</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Automated sensitivity analysis that can be used for initial calibration or to test parameter sensitivity</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="105" nowrap="nowrap" rowspan="4"><p align="center">OPTIMIZE</p></td>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Somos</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Optimization modules to aid in optimally managing water resources</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Brute Force</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Optimization based on plume containment</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MODOFC</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>MODOFC is designed to allow the user to create and solve optimization problems for hydraulic control in groundwater systems</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>MGO</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p align="center">x</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top"><p>Optimizes groundwater management and remedial strategy based on various physical, environmental and budgetary constraints</p></td>
 +
    </tr>
 +
    <tr>
 +
      <td width="105" nowrap="nowrap" rowspan="10"><p align="center">GRAPHICS</p></td>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>GIS</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>AutoCAD</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Registered<br />
 +
      images</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Surfer</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>EQuIS</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Slicer</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Earth Vision</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>EVS</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Import, export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Tecplot</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>Export</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td width="118" nowrap="nowrap" valign="top"><p>Prop. 3D <br />
 +
      Visualization</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p>yes</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>yes</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="88" nowrap="nowrap" valign="top">&nbsp;</td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
    <tr>
 +
      <td nowrap="nowrap" colspan="2" valign="top"><p>Local Mesh Refinement?</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>yes</p></td>
 +
      <td width="101" nowrap="nowrap" valign="top"><p>yes</p></td>
 +
      <td width="96" nowrap="nowrap" valign="top"><p>no</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p>no</p></td>
 +
      <td width="88" nowrap="nowrap" valign="top"><p>yes</p></td>
 +
      <td width="489" valign="top">&nbsp;</td>
 +
    </tr>
 +
  </table>
 +
</div>
 +
<br clear="all" />
 +
<p>If  reactions between dissolved constituents, or precipitation and re-dissolution  of individual constituents are important processes, reactive-transport models  may be necessary to adequately represent the hydrogeological system. PHAST and  PHT3D are two potential choices for this type of model.</p>
 +
<p>PHAST  (Parkhurst et al, 2004) simulates multi-component, reactive solute transport in  three-dimensional saturated ground-water flow systems. The flow and transport  calculations are based on a modified version of HST3D (Kipp, 1997) that is  restricted to constant fluid density and constant temperature. The geochemical  reactions are simulated with the geochemical model PHREEQC, which is embedded  in PHAST.</p>
 +
<p>The  publicly-available code PHT3D (Prommer, 2002) couples MT3DMS and PHREEQC and  therefore works within the MODFLOW scheme. PHT3D provides the highest level of  coupling between constant density flow and fully reactive-transport codes.  Because PHT3D couples MT3DMS with PHREEQC, it cannot be used simultaneously  with SEAWAT2000, which also uses MT3DMS to couple MODFLOW.<br />
 +
  Models  available for fully coupled reactive flow and transport with density effects  are severely limited. PHWAT (Mao et al., 2006) incorporates PHREEQC-2 into  SEAWAT and provides the necessary capabilities. However, the model is still in  development and not available commercially. It can simulate multi-component  reactive transport with variable density groundwater flow.</p>
 +
<p><em>Graphical  User Interfaces</em><br />
 +
  The  raw input files for many hydrogeological models, including MODFLOW, are quite  user-unfriendly. Model inputs are typically via multiple text files using line-entry  and array format. Large models can be quite difficult to manage. Fortunately,  several GUIs have been developed that are user-friendly and simplify the  process of developing, calibrating, and using hydrogeological models.</p>
 +
<p>In  general, GUIs provide Windows-based interfaces that simplify pre- and  post-processing for MODFLOW and other hydrogeological models. Several GUIs  provide interfaces with AutoCAD, Geographic Information Systems (GIS), SURFER  (Golden Software, 2002) or other graphical programs to directly input material  properties and boundary conditions as well as visualize model outputs.</p>
 +
<p>GUIs  also provide interfaces with add-on modules such as calibration and  optimization routines, including UCODE and PEST. Some GUIs provide interfaces  with these codes in addition to the inverse-modeling routines contained within  MODFLOW. Further, a suite of optimization codes can be used to evaluate a  variety of hydrologic issues related to groundwater pumping, plume management,  cost effectiveness, and receptor management for contaminated areas.</p>
 +
<p>Local  Mesh Refinement (LMR) provides the ability to create submodels within a  regional model. While submodels cannot be used simultaneously with a regional  model, they can be used to refine calibration or predictions within a smaller  area after solving the regional model. Some GUIs provide this function while  others do not</p>
 +
<p>Table  A-5-3 provides a comparison of capabilities of five widely used GUIs:</p>
 +
<ul>
 +
  <li>Groundwater Vistas (Environmental  Simulations Inc., 2007)</li>
 +
  <li>Groundwater Modeling  System (GMS;Environmental Modeling Systems Inc., 2007)</li>
 +
  <li>Visual MODFLOW (Schlumberger  Water Services, 2007)</li>
 +
  <li>Processing MODFLOW for  Windows (PMWIN; Chiang, 2005)</li>
 +
  <li>Argus Open Numerical  Environments (ONE; Argus Holdings Ltd., 1997)</li>
 +
</ul>
 +
<p>Argus  ONE is an open environment for creating GUIs adapted to specific models. The  USGS and others have developed interfaces within Argus ONE for a number of  hydrogeological models. The other 4 GUIs are distributed as packages with their  respective models included in the distribution.</p>
 +
<p><em>Model  Calibration</em><br />
 +
  Calibration of a hydrogeological  model is an application of inverse modeling. Model calibration is the process  of selecting parameter values, inputs, and boundary conditions such that model  output matches related observed data with an acceptable degree of accuracy and  precision.</p>
 +
<p>Calibration can be a major portion  of the effort required to complete the modeling phase of a project. The level  of calibration required for a particular model depends on the type and amount  of data available in combination with project needs. Hill and Tiedemann (2007)  present suggested guidelines for effective model calibration along with a  description of the calibration process. Vrugt et al. (2008) review the state of  the science with respect to inverse modeling of subsurface flow and transport  properties.</p>
 +
<p>A number of computer programs have  been developed to automate the calibration process for particular  hydrogeological models. More recently, model-independent inverse-modeling  programs have been developed that can be applied to a broad range of forward  models. Two such programs that have been widely accepted are UCODE (Poeter et  al, 2005) and PEST (Doherty, 2004). Both UCODE and PEST have been incorporated  into several GUIs to speed the model-calibration process.</p>
 +
 
 +
[[#top|Top of this page]]
 +
 
 +
== Gas Transport Modeling ==
 +
 
 +
<p><em>Introduction</em><br />
 +
  Gas transport, particularly the  transport of oxygen into unsaturated waste-rock piles, can be an important  process affecting the generation of ARD. Principal modes of oxygen transport  include diffusion and advection. Wels et al. (2003) provide a comprehensive  overview of the role of gas transport in ARD generation and methods that can be  used to model gas transport.</p>
 +
<p><em>Data Needs</em><br />
 +
  Data required to model gas transport  are similar to the data needed for equivalent modeling of water flow and  transport in the subsurface. The permeability of the porous media is an  important consideration. Because permeability to gas is a function of the  degree of saturation of the pore space, moisture content is also important.</p>
 +
<p>Permeability and moisture-content  measurements can be made in the field or the laboratory. Measurements of  moisture content are reasonably straightforward using established  methodologies. Field measurements of air permeability using pneumatic pumping  tests are described by Baehr and Hult (1991) and are conceptually similar to  groundwater pumping tests used to determine aquifer characteristics. Stonestrom  and Rubin (1989) describe laboratory air-permeability measurements.</p>
 +
<p><em>Model  Selection</em><br />
 +
  Relatively few models have been  developed specifically to address gas transport in the subsurface and the  application to ARD-related problems. Modeling the complete set of physical and  chemical processes operating within a waste-rock pile requires a multi-phase  code capable of simulating gas and water flow in the unsaturated zone, chemical  interactions with the solid matrix, heat generation and transfer, and chemical  mass transfer in the liquid and gas phases.</p>
 +
<p>Several general-purpose, multi-phase  simulation programs have been developed that could be applied to these types of  problems. The TOUGH family of codes (Pruess et al., 2004) was developed at  Lawrence Berkeley National Laboratories and has been applied to a wide range of  complex, multi-phase problems. TOUGH-AMD (Lefebvre et al., 2001) is an  adaptation of TOUGH to address ARD‑related issues. TOUGHREACT (Xu et al., 2004)  was developed as a comprehensive non-isothermal multi-component reactive fluid  flow and geochemical transport simulator to investigate acid-mine drainage and  other problems.</p>
 +
<p>Groundwater flow models can be  adapted to simulate air flow using appropriate transformations of variables and  parameter formulations. Massman (1989) shows how groundwater solutions can be  modified for gas-flow problems. This type of adaptation would not be  appropriate to model the most complex multi-phase, reactive-transport problems,  but may be adequate to address many issues of importance to the prediction of  ARD generation.</p>
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== Considerations Regarding Predictive  Modeling of Effluent Quality ==
 +
 
 +
<p>As  discussed throughout Chapter 5 of the GARD Guide and this Appendix, the  principal objective of mine and process water quality prediction is to evaluate  the potential for geologic materials and mine and process wastes to generate  acid and contaminants and affect water resources. As an important corollary,  the need for and nature of mitigation measures is determined through  prediction.</p>
 +
<p>The nature and sophistication of the  prediction effort may vary depending on the desired outcome. A prediction  exercise aimed at merely answering a “yes/no” question (for instance: will the  water quality criterion for arsenic be exceeded?) requires less up-front  understanding of the system being evaluated, in which case while use of  relatively “crude” modeling tools may suffice. In contrast, when a more  quantitative answer is required (for instance: what is the expected arsenic  concentration?), the complexity of the modeling effort may be quite  significant, requiring both a detailed conceptualization of the system being  modeled as well as use of advanced modeling codes. <br />
 +
  It should be noted that use of more  sophisticated tools does not necessary equate to more accurate and precise  modeling outcomes. According to Oreskes (2000) and Nordstrom (2004), the  computational abilities of codes and advanced computers currently far exceed  the ability of hydrogeologists and geochemists to represent the physical,  chemical and biological properties of the system at hand or to verify the model  results. In light of these difficulties, the meaning of “accuracy” and  “precision” in the context of mine and process water quality modeling must be  re-assessed on a case-by-case basis, and numeric analysis needs to be conducted  to reflect the uncertainty inherent in predictive modeling. Accordingly, USEPA  (2003) recommends the following should be submitted at a minimum to  substantiate modeling used for regulatory purposes, regardless of the specific  model/code being used:</p>
 +
<ul>
 +
  <li>Description of the  model, its basis, and why it is appropriate for the particular use</li>
 +
  <li>Identification of all  input parameters and assumptions, including discussion of parameter derivation  (i.e., by measurement, calculation or assumption)</li>
 +
  <li>Discussion of  uncertainty</li>
 +
  <li>Sensitivity analysis of  important input parameters</li>
 +
</ul>
 +
<p>Having  said all that, despite the limitations identified throughout this chapter,  modeling and prediction have significant value as management tools and for  gaining an understanding of the geochemical, physical and biological systems at  mine and process sites (Oreskes, 2000). There is little doubt that the  understanding of geologic materials, mine and process wastes and the  hydrogeochemical factors that govern mine and process water quality will  continue to advance through the implementation of laboratory and field  experiments. In particular those experiments that isolate one variable at a  time to identify its effect on overall discharge water quality will prove of  great value. Similarly, ongoing characterization and monitoring of mine and  process facilities will allow development of improved scaling factors needed to  extrapolate results from smaller-scale tests to an operational level. Lastly,  the tools required for geochemical, hydrological and hydrogeological modeling  already largely exist. With an increased comprehension of the factors that  govern the generation of ARD, NMD or SD, modeling and prediction efforts will  become increasingly reliable.  </p>
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Latest revision as of 19:06, 31 May 2011

Back to Chapter 5.5.1 Introduction

Appendix 5-A

Introduction

Geochemical Modeling
This section describes the conceptual, thermodynamic, and kinetic fundamentals of geochemical modeling and its application to prediction of mine water quality in support of mine site characterization and remediation. The emphasis in this section is on the basic processes that models attempt to represent with discussions of the usefulness and the limitations of modeling.

In principle, geochemical modeling can be applied to all mine and process facilities, including mine portal effluent, subsurface waters (wells or underground workings), waste dumps, process tailings piles, surface waters, pit lakes, and open pits. The type of modeling used depends on both the objectives and the type of source or pathway. A wide variety of codes are available for these various environments but the critical factors are the quality of their databases, the inherent assumptions, and, most importantly, the knowledge and experience of the modeler.

Three basic approaches have been used with geochemical data: forward geochemical modeling, inverse geochemical modeling, and geostatistical analyses.

Forward modeling is also known as simulating (i.e. potential reactions between rock and water are simulated from initial conditions of a known rock type and composition). Reactions are allowed to proceed in equilibrium or kinetic or combined modes. Changes in temperature and pressure can be invoked, changes in water flow rate can be invoked, and minerals can be allowed to precipitate as they reach equilibrium solubility or dissolve as they become undersaturated. Potential reactions can be simulated to see what the consequences are. This type of modeling is the least constrained. A great many assumptions are either invoked as input data or invoked as dictated by the program that may not apply to the specific system being simulated. This approach assumes the modeler has a significant amount of information on the ability of minerals to maintain equilibrium solubility or their rates of reaction.

Inverse modeling assumes a water flow path is known and that water samples have been analyzed along that flow path. Such data can then be converted into amounts of minerals dissolved or precipitated along that flow path. Several assumptions are still made regarding the choice of minerals and their relative proportions contributing to the water chemistry, but the calculations are constrained with actual data. Inverse modeling can also be done without any recourse to kinetic or thermodynamic data, in which case it represents a relatively simple mass balance calculation. When speciation and thermodynamic and kinetic properties are included for additional constraints, the possible reactions become quite limited and the modeling is much more meaningful.

Modeling of any type does not lead to a unique solution but the possibilities are more limited with greater amounts of carefully collected field data.  Martin et al. (2005) summarized the benefits and limitations of geochemical modeling as follows:

Benefits

  • Provide insight into potential future conditions
  • Determine which variables are most important in determining future conditions
  • Assess the effects of alternative approaches to ARD management
  • Assess potential effects of uncertain parameters
  • Establish objectives and test conditions for field and laboratory studies
  • Integrate available information

Limitations

  • Insufficient input data
  • Modeling can be challenging and results misinterpreted
  • Uncertain and variability of the results
  • Difference between modeled and actual field conditions

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Approaches to Geochemical Modeling

Speciation
One of the most fundamental types of geochemical modeling is speciation modeling. “Speciation” refers to the distribution of chemical components or elements among the different possible forms or species. Aqueous speciation is the distribution of chemical components among dissolved free ions, ion pairs and triplets, and other complexes. This concept is important because research has shown that a number of processes, including mineral precipitation and dissolution, biological uptake and toxicology, and sorption are all affected by speciation.

Some species, such as redox species, have to be determined analytically. This is because most geochemical modeling codes erroneously assume that redox equilibrium is maintained while, in reality, disequilibrium among redox species is the rule, not the exception.  In particular, dissolved iron is usually present in high concentration in ARD and can exist as the reduced ferrous iron or as the oxidized ferric iron. For an accurate evaluation of iron speciation, chemical analysis rather than speciation modeling is required. In NMD and SD, dissolved iron is largely absent due to formation of sparingly-soluble ferrihydrite or similar iron oxyhydroxide minerals. Solid speciation is the distribution of chemical components among various solid phases. For example, iron can precipitate from ARD as goethite, jarosite, schwertmannite, or ferrihydrite. Identifying these phases would constitute solid speciation.

Aqueous speciation results are used in a variety of modeling objectives that include modeling of saturation-index calculations for mass-transfer, modeling of mineral precipitation and dissolution, modeling of adsorption and desorption, and reactive-transport modeling.

Mass Transfer (precipitation, dissolution, gas transfer)
Modeling of mineral precipitation and dissolution and gas-transfer reactions can take place conceptually in one of three possible systems: equilibrium state, steady-state, or transient state. The equilibrium state assumes the system under investigation is isolated from any external exchanges of energy or mass. Although an unrealistic concept, equilibrium state is actually quite practical because many reactions approximate equilibrium even though there are gradients in water pressure or temperature. For example, in many groundwaters, calcite and gypsum quickly reach their equilibrium solubility. Even with gradients in CO2 pressure or mixing with other sources of sulphate, these minerals adjust to maintain saturation and the assumption of equilibrium may be valid. In addition, even when geochemical reactions of interest do not reach equilibrium rapidly, such reactions may achieve equilibrium over the time scale of the modeling simulation (i.e. the life of a mine and beyond). Therefore, the majority of geochemical modeling can be conducted under the assumption of equilibrium conditions.

Reactive Transport (Coupled Models)
Reactive-transport models that can be applied to simulation of ARD, NMD, and SD are generally the subject of active research, although several have been applied with considerable success. The idea is to couple flow models with chemical reaction models to determine the effects of flow on reactions and vice versa, including the effects of dispersion. Such modeling is relatively straightforward for streams and rivers because the flow path is not only visible but measurable. Considerable effort has been made to develop quantitative reaction-transport models for streams affected by acid mine drainage (Kimball et al., 1994; Runkel et al., 1996). Progress in surface-water reactive-transport modeling has now advanced to the point where it can guide remediation decisions for complex mine sites (Runkel and Kimball, 2002; Kimball et al., 2003).

Reactive-transport modeling for groundwater has also progressed substantially over the last two decades and many of the recent codes have been applied to mine sites. Three general types of coupled models can be distinguished: those that model the groundwater only, those that model the unsaturated zone only, and those that model both. The most recent overview by Mayer et al. (2003) provides the theoretical foundations for groundwater reactive-transport modeling, methods of coupling flow with reaction, the various codes that have been used in mined environments, and case studies. An excellent example of combining laboratory testing of waste rock material with field measurements and modeling of small- to medium-scale test plots of actual mine wastes to predict the consequent water quality over the short term and the long term in a very sensitive environment is in progress at the Diavik mine site near Yellowknife, Northwest Territories, Canada (Blowes et al., 2007). This investigation may be one of the first to combine lab-scale tests, field tests, and modeling, supported by the detailed characterization of the rock and mineral composition and their weatherability.

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Role of Thermodynamic and Kinetic Data

Thermodynamic and, for some models, kinetic data are part of the basic input to codes that compute reactions and simulations for water-rock interactions. For some reactions, these data are known accurately and precisely; for others they are non-existent or poorly known. Thermodynamic measurements and evaluations are part of ongoing research. Sometimes the conclusions of a modeling study can be greatly affected by these databases and their uncertainties and sometimes not. Rarely are modeling results evaluated from the point of view of the basic data, which reflects a general lack of QA/QC common to many modeling efforts.

Scale-up Considerations

Drainage quality prediction is made challenging by a number of factors that range in scale from small to large. Small-scale factors that influence drainage quality are related to reactions at the water-rock interface in the aqueous, gas and solid phase. Information on reactive surface area and reaction rates generally is limited. On a large scale, geology, climate, mining method, mineral processing method, and waste management practices vary within and amongst operations. Variability of these large-scale factors implies that it may not always be feasible to apply information from one site to another. However, advances are being made in this respect, for instance, through the use of geo-environmental models that present unifying principles which link mine water quality to the nature of the ore deposit, climate, and type of mine waste.

Water quality prediction typically necessitates the extrapolation of laboratory-scale results to operational scale. This extrapolation must address factors such as differences in particle size, climate conditions, water and gas transport, and duration (i.e., how these variables affect drainage composition over decades, centuries or longer). Although the construction of instrumented, large-scale mine waste test cells has increased significantly in recent years and is expected to yield valuable data, little information is currently available describing the effects of these variables on well-characterized mine wastes over extended periods of time. Use of models therefore is required to bridge the gap between laboratory results and operational conditions (USEPA, 2003).

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Examples of Major Codes

Some of the more popular codes used primarily for groundwater geochemistry but also for mining-affected sites are shown in Table A-5-1 below. More detail on geochemical modeling, modeling codes and associated uses and limitations is presented in Alpers and Nordstrom (1999), Mayer et al. (2003), and Maest and Kuipers (2005).  Section XXX on hydrogeological models in this Appendix also provides additional information.

A-5-1: Summary of Geochemical Modeling Codes

Codes

Type

Reference

PHREEQC, PHAST

USGS codes: mass transfer and reactive-transport

Parkhurst and Appelo (1999), Parkhurst et al. (2004)

SOLMINEQ.GW

USGS code: mass transfer and high temperature

Perkins et al. (1990)

WATEQ4F

USGS code: speciation and low-temperature only

Ball and Nordstrom (1991)

MINTEQA2

EPA supported code: speciation and mass transfer

USEPA (1999)

MIN3P

Waterloo code: saturated and unsaturated flow

Mayer et al. (2002)

TOUGH-AMD

Quebec code: gas and energy transfer without reaction

Lefebvre et al. (2002)

RETRASO

Barcelona code: unsaturated and saturated flow and reaction

Saaltink et al. (2002)

SULFIDOX

ANSTO code: gas and energy transfer

Ritchie (2003)

CRUNCH

Bern/LBL code: unsaturated and saturated flow and reaction

Steefel (2000)

Geochemist’s Workbench

University of Illinois code: mass transfer, saturated flow

Bethke (1994, 1996)

EQ 3/6

Lawrence Livermore National Laboratory code: mass transfer and reactive transport

Wolery and Daveler (1992)

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Hydrological Modeling

Introduction
In a general sense, a hydrological model is an analog of a natural or human-modified hydrological system. This generic definition encompasses models of surface-water and groundwater systems. Scientists and engineers more commonly use the term hydrological model to refer to models of surface-water systems, and consider hydrogeological models for groundwater systems as a separate subject. This section follows the latter convention, describing hydrological models in the context of surface-water systems. Hydrogeological models and their applications are presented in Section XXX.

Hydrological models range from simple algebraic calculations to complex reactive-transport computer codes. Physical analogs, such as stream tables, can also be useful simulations of complex surface-water systems. Hydrological models can be used to predict the fate and transport of mine drainage through a surface-water system, providing important input to human-health or ecological risk assessments. Hydrological models can also be used to estimate the water-quality and water-quantity evolution of pit lakes over time. Hydrological models can be coupled with hydrogeological and geochemical models to incorporate the interaction between surface water and groundwater into the simulation and account for geochemical reactions.

Selection of an appropriate, quantitative hydrological model depends on the type of output that is required and, critically, on the conceptual model of the system being evaluated. A robust conceptual model will identify the important physical and geochemical characteristics of the field-scale system being evaluated. Based on that identification, an appropriate hydrological model can be selected that quantitatively represents those important processes. For complex systems or to assess a range of different types of processes, multiple hydrological models can be applied to predict the fate, transport, and potential impacts of mine discharges.

Data Needs
In common with all models, the output from a hydrological model is only as reliable as the data that are used to generate the model. Typical data requirements for many hydrological models include:

  • Precipitation, either local or distributed across a region
  • Evaporation from surface-water bodies such as lakes and rivers
  • Potential or actual evapotranspiration from vegetated areas and bare land
  • Surface slope and land cover
  • Channel slope, width, depth, and roughness for calculations of stream flow or conveyance capacity
  • Concentrations of chemical constituents. These may be determined from on-site monitoring programs, laboratory or field-scale testing programs, or estimated using geochemical models

Simple quantitative models of surface-water flow such as the United States Natural Resource Conservation Service (formerly known as the Soil Conservation Service [SCS]) curve-number method (SCS, 1972) may only require a few of before listed data elements. More detailed models, for instance those that incorporate reactive transport (e.g., Runkel and Kimball, 2002), may require additional information regarding the kinetics of reactions considered in the simulation.

Governmental agencies in many countries collect regional precipitation and evaporation data that may be used for hydrological models. Precipitation data are commonly collected with the greatest frequency through meteorological measuring stations. Evaporation data, such as pan evaporation measurements, generally are collected with less frequency. Some mine sites also collect these types of data on a local scale that can be used to refine the regional data sets.

Care must be taken if combining different types of data from different locations. The locations should be similar in terms of latitude, elevation, overall climatic zone, and cloud cover for the combined data set to be reliable. If this is not the case, statistical methods have been developed to estimate precipitation at a special site from a known precipitation network

Water-Balance and Mixing-Cell Models
Water-balance models apply the principle of conservation of mass to quantitatively track inflows and outflows from the various components of a conceptual model. Mass and concentration of ARD-related constituents can be incorporated into this approach through mixing-cell models. The hydrologic elements of a conceptual model, such as surface-water reservoirs, open pits, and groundwater basins, can be represented as a series of simulated reservoirs. The connections between the reservoirs, such as the creeks or groundwater flow paths, can be represented by quantitative estimates of capacity or flow. Concentrations of individual constituents can be tracked along with water quantity to calculate the transfer of chemical mass and mathematically mixed in the model to evaluate changes in concentration over time in the reservoirs.

Water-balance and mixing-cell models can be implemented in standard spreadsheets. More complex water-balance or mixing-cell models, incorporating additional physical or chemical processes, can be addressed by using dynamic system simulators such as GoldSimTM or STELLATM.

Rainfall Runoff Models
Appendix A of USEPA (2003) describes the basic approaches to modeling runoff processes based on precipitation inputs. Runoff can be thought of as the excess precipitation after processes such as infiltration and surface abstraction are evaluated. The most commonly applied model to estimate the volume of runoff is the SCS curve-number method (SCS, 1972). The SCS curve-number method involves estimating the vegetation and land-cover characteristics of a watershed or mine facility, looking up the resulting curve number, and then applying that number along with precipitation information to develop the runoff volume for a storm event.

The unit-hydrograph method of runoff determination may be more appropriate for many mine sites. The method is also described in SCS (1972). A hydrograph relating runoff to precipitation is developed for a unit precipitation volume over an area, for example 1 inch or 1 centimeter of rainfall. The unit hydrograph is then used to estimate runoff from storms of greater or lesser intensity.

Water quality in well-mixed rivers and streams can be predicted using a code such as QUAL2K developed by the USEPA (Chapra et al., 2007). QUAL2K represents a modernized version of QUAL2E (Brown and Barnwell, 1987). QUAL2K is programmed in the Visual Basic for Applications language and executed within the Microsoft Excel spreadsheet environment. The program can simulate 1-dimensional flow, changes in water quality along the flow path, and chemical interactions with bed sediments.

Distributed-parameter rainfall-runoff models are more appropriate for larger watersheds with heterogeneous flow characteristics. SWAT2000 (Neitsch et al., 2002) is a distributed-parameter model developed by the Agricultural Research Service of the U.S. Department of Agriculture to simulate runoff and water quality in large, complex watersheds. SWAT2000 and similar models break a complex watershed into hydrologic sub-units, each with a uniform set of characteristics. Flow and water quality are calculated for each sub-unit, then aggregated to provide predictions at a complex watershed scale.

Pit Lake Modeling
Pit lake formation and the evolution of water quality can be simulated using a water-balance approach or with complex numerical codes. Water balance models can be used to quantify the inflows to the pit lake as the pit fills after mining and dewatering ceases. Potential inflows include direct precipitation over the surface area of the lake, runoff entering the pit lake from the surrounding watershed, and groundwater inflow through the walls and floor of the pit. Outflows may include direct evaporation from the lake surface, groundwater outflow, and potentially surface-water discharges if a spill elevation is reached.

A chemical composition can be assigned to each inflow and outflow to extend the water-balance model to include ARD-related impacts. For example, wall-washing results can be used to estimate the mass input of chemical constituents from seepage or overland flow coming in contact with reactive portions of the pit wall. Geochemical speciation models can be used to predict the resulting chemical quality of water in the pit.

Rainfall-runoff models can be used to develop the surface-water inflow portions of the water balance. Groundwater inflow can be estimated using simple analytical equations (Marinelli and Niccoli, 2000). The solution to drawdown in a large-diameter pumping well presented by Papadopoulos and Cooper (1967) is often used to approximate the groundwater inflow to a mine pit, and can also be used to estimate recharge to the pit lake. Cimen (2001) and Aryafar (2007) present additional analytical solutions that can be useful in pit-lake studies.

Complex numerical models can also be used to estimate the groundwater inflow to a pit lake. SEEPW (Ref) and FEFLOW (WASY, XXXX) are finite-element, variably-saturated flow models that have been applied to this problem. MODFLOW2005 (Ref), including the LAK package, is a modular, 3-dimensional, finite-difference model that can be used to simulate the groundwater components of pit-lake evolution. Complex models such as these, however, require more data for parameterization and calibration than the simpler approaches. Selection of more complex simulation approaches should only be made if the conceptual model and project needs require the additional computational burden.

An alternative to geochemical models for the prediction of pit-lake quality is a code such as CE-QUAL-W2 developed by the U.S. Army Corps of Engineers Waterway Experiment Station (Cole and Buchak, 1995). CE-QUAL-W2 is suitable for applications to rivers, lakes, reservoirs, and estuaries.

Watershed Models
Watershed models are used to simulate the hydrologic cycle, including surface water, groundwater, and the interactions between the two, at the basin or watershed scale. Watershed models can be used to predict ARD impacts on downstream users and the evolution of ARD-related water quality through a flow system. Furman (2008) summarizes the mathematics and computational tools used to simulate coupled surface and subsurface flow processes.

Watershed models can be data-intense and numerically complex. The most widely used watershed models are:

  • MIKE SHE, developed by the Danish Hydraulic Institute (DHI) in Denmark
  • HEC-HMS, developed by the U.S. Army Corps of Engineers Hydrologic Engineering Center
  • WMS (Watershed Modeling System), a graphical interface developed by Environmental Modeling Systems, Inc. for a number of modules including HEC-HMS, CE-QUAL-W2 and other codes

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Hydrogeological Modeling

Introduction
Hydrogeological models address water flow and contaminant transport below the land surface. As with hydrological models, approaches to hydrogeological simulations range from simple to complex. The universe of hydrogeological models includes physical and electrical analogs. With the advent of powerful personal computers and high-level programming languages, these approaches are rarely used in current practice. Accordingly, this discussion of hydrogeological models will focus on quantitative, mathematical approaches to subsurface water flow and contaminant transport.

A large body of literature exists regarding hydrogeological modeling, as do a number of computer programs. Zheng and Bennett (2002) provide an excellent introduction to the topic of contaminant-transport modeling. Maest and Kuipers (2005) provide a review of hydrogeological models more directly focused on ARD prediction. Other references are provided in the discussion below.

Three basic types of hydrogeological models are available, in order from simple to more complex:

1.         Analytical models of flow and contaminant transport
2.         Analytic element models
3.         Numerical models

As a general rule, hydrogeological models should be as simple as possible while still representing the physical system with an adequate degree of precision and accuracy. More complex models should only be selected when project needs dictate, simpler models are demonstrably not adequate, and suitable data are available for model parameterization and calibration.

Hydrogeological models are useful tools for predicting the potential generation and resulting impacts of ARD. Models can be used to fill data gaps, either in space or in time. They can also be used to test alternative conceptual models in an iterative process designed to understand the complex natural or human-modified subsurface system.

Figure 5-19 in Chapter 5 of this GARD Guide presents a generalized approach to the development, calibration, and use of models, including hydrogeological models. The quantitative modeling process starts with a strong conceptual model, and the quantitative model can then be used to update the conceptual model as necessary. The majority of the effort for a hydrogeological model goes into the calibration phase of the process, sometimes also referred to as inverse modeling.

Data Needs for Model Parameterization
Basic Flow and Transport Models
As model complexity grows, the data requirements for model parameterization and calibration also increase. Basic data requirements for any groundwater flow and contaminant-transport model include:

  • Saturated hydraulic conductivity
  • Specific yield or storativity
  • Effective porosity (for calculations of contaminant transport)

Unsaturated-Zone Models
Simulating flow and transport in the unsaturated zone typically requires additional information regarding the flow characteristics of the unsaturated porous medium. Unsaturated hydraulic conductivity is a function of the saturated hydraulic conductivity and the degree of saturation of the porous medium. Additional data requirements for unsaturated-zone models include the parameters for the function describing the relationship between saturation, matric suction, and unsaturated hydraulic conductivity.

Sorption and Retardation Factors
Interaction between the aquifer matrix and dissolved constituents can be an important process for ARD-related hydrogeological models. Many contaminant-transport models simulate this interaction through the use of a retardation factor.

The retardation factor is the ratio between the apparent velocity of the contaminant front and the pore velocity of moving groundwater (Fetter, 1993). In its simplest form, the retardation factor is calculated using a distribution coefficient appropriate for a linear adsorption isotherm. More complex forms of the retardation factor can be derived using different adsorption isotherms and assumptions.

Models incorporating retardation thus require additional data, including:

  • Bulk density of the aquifer matrix
  • Distribution coefficient or other parameters defining the adsorption isotherm
  • Rate constants for non-equilibrium sorption models

Reactive-Transport Models
As discussed in Section XXXX under geochemical modeling, detailed evaluation of the evolution of ARD-related constituent concentrations over time and space in an aquifer may require the use of a reactive-transport model. These types of models allow the simulation of reactions between the dissolved constituents and the aquifer matrix and reactions between the dissolved species themselves. Relative to the more basic hydrogeological models, additional data are necessary to apply these models, including:

  • Non-equilibrium rate constants describing the reactions between dissolved constituents
  • Proportionality constants or functions describing the solubility controls on individual species under consideration

Steefel et al. (2005) and Mayer et al. (2003) provide overviews of reactive-transport models and their associated data requirements.
Data Collection
The field data most commonly obtained in support of hydrogeological modeling are the saturated hydraulic conductivity and storage coefficients (specific yield or storativity). Saturated hydraulic conductivity can be measured on core samples in the laboratory, by using single-well slug tests, or by using multiple-well, long-term pumping tests.

Slug tests and pumping tests provide better estimates of saturated hydraulic conductivity at the field scale than laboratory tests. Pumping tests conducted with one or more pumping wells in combination with at least one additional observation well can also provide data regarding the storage coefficients. Butler (1998) provides an extensive description of the design and performance of slug tests. Kruseman and de Ridder (2000) describe the design and performance of pumping tests.

The relationship of unsaturated hydraulic conductivity to moisture content can be measured in the field or laboratory, and the resulting data can be fitted to a number of equations. Stephens (1995) provides a detailed description of data collection and analysis related to unsaturated-zone hydrology.

Other Data Sources
Unsaturated hydraulic conductivity characteristic curves can be estimated by several methods. RETC (van Genuchten et al., 1991) and ROSETTA (Schaap, 2003?) are programs that can be used to estimate unsaturated flow characteristics from more commonly available data. SoilVision (SoilVision Systems, XXXX) contains a database of measured unsaturated hydraulic conductivity characteristic curves in addition to a number of algorithms to calculate unsaturated flow characteristics.

Adsorption-isotherm distribution coefficients for a number of metals are tabulated in Stenge and Peterson (1989). Values are included for three different pH ranges and a range of sorbent (organics, oxides, clays) contents.

Analytical Models
Analytical models are relatively simple methods for simulating groundwater flow and contaminant transport. These models are formulated as closed-form equations that can be solved directly without the use of numerical methods. Transient or steady-state solutions for groundwater flow and contaminant transport with simple retardation factors in one, two or three dimensions are available.
Because of their simplicity, data needs are relatively minor for analytical models. Homogeneous, isotropic flow conditions are typically assumed. Analytical models can be useful for screening-level evaluations. They can also be used for more definitive assessments of groundwater flow and contaminant transport if the assumptions are judged to be valid or insufficient data are available to warrant a more complex approach.

One useful analytical model for the prediction of ARD-related transport is the Ogata and Banks (1961) solution to the advection-dispersion equation. Domenico and Schwartz (1990) extended that solution to include a retardation factor based on a linear adsorption isotherm. The Domenico and Schwartz (1990) model can be implemented in a spreadsheet format and adapted to a wide variety of problems.

STANMOD (Simunek et al, 2003) is a public domain set of analytical solutions to the advection-dispersion equation in one, two or three dimensions. A variety of previously published solutions, already in the public domain, are included in STANMOD.

Analytic Element Models
Analytic element modeling takes advantage of the principle of linear superposition to solve groundwater flow and contaminant transport problems in more complex systems than can be addressed by analytical models. Haitjema (1995) provides the basic theoretical framework for the analytic element method and describes its use.

GFLOW (Haitjema Software, 2007) is a groundwater flow model that implements the analytic-element method. PhreFlow (Jankovic and Barnes, 2001) is a public domain analytic-element model of 3-dimensional groundwater flow and contaminant transport. WhAEM2000 (Kreamer et al., 2007) is a public domain and open source general purpose ground-water flow modeling system, with strengths in representing regional flow systems, and ground water/surface water interactions. It was initially designed to facilitate capture zone delineation.

Numerical Models
Numerical models use iterative processes to solve the equations of groundwater flow and contaminant transport in complex domains. Flow and transport under saturated, unsaturated, or variably-saturated conditions in heterogeneous, anisotropic systems with various boundary conditions can be simulated using these methods. Numerical models can also require a substantial amount of data regarding parameters and for input to the simulation.

Two numerical solution schemes, finite-difference and finite-element, are widely used in hydrogeological models (Wang and Anderson, 1982). Finite-difference models employ a rectangular discretization scheme to divide the model domain into individual cells, within which flow characteristics such as hydraulic conductivity are assumed to be uniform. Finite-element models employ either a triangular or rectangular discretization scheme to divide the model domain into individual elements of uniform characteristics.

As a general rule, finite-difference models are more computationally efficient for a given problem compared to finite-element models. Finite-element models can be fitted more closely to irregular boundaries and can handle internal boundaries such as mine pits, underground workings, or faults with less numerical instability than finite-difference models. The choice of numerical solution scheme and computer code should be driven by the conceptual model, project requirements, and available computer resources.

The MODFLOW family of computer codes (e.g., MODFLOW2005, Ref) contains examples of finite-difference models. MODFLOW, originally released by the USGS in 1988 and upgraded periodically since then, is probably the most widely used hydrogeological model in the world.

Finite-element models are exemplified by FEFLOW (WASY, XXXX). FEFLOW is a commercially available code that can be applied to a broad range of variably-saturated flow and transport problems. Compared to MODFLOW it has more capabilities for modeling mine water problems because the original program code was derived from a mining background.

Many other finite-difference and finite-element models suitable for application to ARD-prediction problems are available. Maest and Kuipers (2005) tabulate the capabilities for a range of models.

Commonly Available Models
Table A-5-2 summarizes the characteristics of several numerical model computer codes that are widely used and can be applied to problems of ARD-related contaminant transport. Some models are freely available in the public domain, while others are proprietary products distributed by commercial companies. Table A-5-2 is organized by computer program and by graphical user interface (GUI). More information on GUI use and characteristics is presented below.

Unsaturated-Zone Models
Unsaturated-zone models are often used to assist with predicting the formation and transport of ARD within and through waste-rock dumps and unsaturated process tailings impoundments. Commonly used unsaturated-zone models include HELP (Schroeder et al., 1994), HYDRUS (Simunek et al., 2007), UNSATH (Fayer, 2000), and VADOSE/W (GeoSlope International, 2002). HELP and UNSATH are available in the public domain, as is the 1-dimensional version of HYDRUS.

Fracture-Flow Models
The majority of hydrogeological models are strictly valid for simulating flow and transport through continuous porous media only. However, some ARD problems occur in subsurface systems dominated by flow and transport through discrete fractures or fracture networks. Even if flow and transport are primarily through fractures, porous-medium models may be adequate if the fracture density is great and the fracture aperture is small. Some models allow a dual-porosity formulation that can represent the flow through a fracture network as well as flow through the porous media between fractures.

If the assumption of flow through continuous porous media is not valid, models that represent the physics of fracture flow should be considered. Two such models are FRACMAN (Golder, 2007) and FRACTRAN/FRAC3DVS (University of Waterloo, 2004).

Density-Dependent Flow and Transport
Most contaminant-transport models are based on the assumption that concentrations are relatively dilute and the density of groundwater is not significantly different from fresh water. Groundwater that is heavily impacted by ARD, however, can have sufficiently large concentrations of metals, sulfate, and other species that the density effects are significant. If the conceptual site model indicates that density effects are important, a model capable of accounting for variability in density should be selected.

SEAWAT2000 (Guo and Langevin, 2002) is one such model, developed by the USGS to simulate 3-dimensional, variable-density groundwater flow in porous media. It was developed by combining MODFLOW and MT3DMS into a single program that solves the coupled flow and solute-transport equations.

Reactive-Transport Models
Most contaminant-transport models incorporate relatively simple reactions describing interaction between dissolved constituents and the aquifer matrix. These reactions are implemented in the form of retardation factors using one of several adsorption isotherms. Interactions between dissolved constituents are typically not considered.

Table A-5-2: Hydrogeological Models and Graphical User Interfaces for those models


GUI

Groundwater Vistas

Groundwater Modeling Systems

Visual MODFLOW

Argus ONE

PMWIN

Description

FLOW

SEEP2D

 

x

     

A 2D finite-element groundwater model designed to be used on profile models such as cross-sections of earth dams or levees

MODAEM

 

x

     

Analytic element model for simple flow and transport computations

MODFLOW 88

x

     

xXx

MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS

MODFLOW 96

x

   

x

xXx

MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS

MODFLOW 2000

x

x

x

x

xXx

MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS

MODFLOW 2005

x

 

x

   

MODFLOW is a 3D, cell-centered, finite difference, saturated flow model developed by the USGS

FEMWATER

 

x

     

3D finite-element model used to simulate density-driven coupled flow and contaminant transport in saturated and unsaturated zones

SOLUTE
TRANSPORT

ART3D

 

x

     

A three-dimensional analytic reactive transport model

MODPATH

x

x

x

x

 

A particle tracking code used with MODFLOW assuming particles are transported by advection

PATH3D

x

       

General particle tracking program for calculating ground-water paths and travel times in steady-state or transient, 2 or 3D flow fields

PMPATH

       

xXx

Particle tracking

MOC3D

     

x

xXx

3D method-of-characteristics ground-water flow and transport model integrated with MODFLOW-96

MT3D

x

x

x

x

xXx

Simulation of single-species transport via advection, dispersion and simple chemical reactions

MT3DMS

x

x

x

x

xXx

Simulation of multi-species transport by advection, dispersion, and limited chemical reactions of dissolved constituents

PHT3D

   

x

 

x

A reactive transport model coupling MT3DMS and PHREEQC

RT3D

x

x

x

 

x

An advanced multi-species reactive transport model developed by the Battelle Pacific Northwest National Laboratory

SEAM3D

 

x

     

Reactive transport model to simulate complex biodegradation problems involving multiple substrates and multiple electron acceptors

SEAWAT 2000

x

 

x

x

 

Simulation of 3D, transient, variable-density ground water flow

MODFLOW-
SURFACT

x

 

x

   

Enhanced simulation capabilities and robust solution methods for handling complex saturated/unsaturated flow and transport

MODFLOWT

x

       

Version of MODFLOW that includes modules for simulating 3D contaminant transport

SWIFT

x

       

3D model to simulate groundwater flow, heat, brine and radionuclide transport

UTCHEM

 

x

     

A multi-phase flow and transport model ideally suited for pump and treat simulations

CALIBRATION

MODFLOW 2000

x

x

     

Parameter inversion option built into MODFLOW 2000

UCODE

x

x

   

x

Developed by the USGS, UCODE is a universal inverse modeling code to solve parameter estimation problems

PEST

x

x

x

 

x

A model-independent, non-linear parameter estimator to assist in data interpretation, model calibration, and predictive analysis

Stochastic

x

x

     

Parameter inversion using Monte Carlo or Latin Hypercube

Modac

x

       

An inverse model that calculates a K for every cell in the model (or in selected layers) using starting heads as the calibration target

Automated
Sensitivity

x

       

Automated sensitivity analysis that can be used for initial calibration or to test parameter sensitivity

OPTIMIZE

Somos

x

       

Optimization modules to aid in optimally managing water resources

Brute Force

x

       

Optimization based on plume containment

MODOFC

x

       

MODOFC is designed to allow the user to create and solve optimization problems for hydraulic control in groundwater systems

MGO

x

 

x

   

Optimizes groundwater management and remedial strategy based on various physical, environmental and budgetary constraints

GRAPHICS

GIS

Import, export

Import, export

Import, export

Import, export

   

AutoCAD

Import, export

Import

Import, export

     

Registered
images

Import

Import

Import

 

Import

 

Surfer

Import, export

 

Import

 

Import, export

 

EQuIS

Import

         

Slicer

Export

         

Earth Vision

Import, export

         

EVS

Import, export

         

Tecplot

Export

         

Prop. 3D
Visualization

 

yes

yes

     

Local Mesh Refinement?

yes

yes

no

no

yes

 


If reactions between dissolved constituents, or precipitation and re-dissolution of individual constituents are important processes, reactive-transport models may be necessary to adequately represent the hydrogeological system. PHAST and PHT3D are two potential choices for this type of model.

PHAST (Parkhurst et al, 2004) simulates multi-component, reactive solute transport in three-dimensional saturated ground-water flow systems. The flow and transport calculations are based on a modified version of HST3D (Kipp, 1997) that is restricted to constant fluid density and constant temperature. The geochemical reactions are simulated with the geochemical model PHREEQC, which is embedded in PHAST.

The publicly-available code PHT3D (Prommer, 2002) couples MT3DMS and PHREEQC and therefore works within the MODFLOW scheme. PHT3D provides the highest level of coupling between constant density flow and fully reactive-transport codes. Because PHT3D couples MT3DMS with PHREEQC, it cannot be used simultaneously with SEAWAT2000, which also uses MT3DMS to couple MODFLOW.
Models available for fully coupled reactive flow and transport with density effects are severely limited. PHWAT (Mao et al., 2006) incorporates PHREEQC-2 into SEAWAT and provides the necessary capabilities. However, the model is still in development and not available commercially. It can simulate multi-component reactive transport with variable density groundwater flow.

Graphical User Interfaces
The raw input files for many hydrogeological models, including MODFLOW, are quite user-unfriendly. Model inputs are typically via multiple text files using line-entry and array format. Large models can be quite difficult to manage. Fortunately, several GUIs have been developed that are user-friendly and simplify the process of developing, calibrating, and using hydrogeological models.

In general, GUIs provide Windows-based interfaces that simplify pre- and post-processing for MODFLOW and other hydrogeological models. Several GUIs provide interfaces with AutoCAD, Geographic Information Systems (GIS), SURFER (Golden Software, 2002) or other graphical programs to directly input material properties and boundary conditions as well as visualize model outputs.

GUIs also provide interfaces with add-on modules such as calibration and optimization routines, including UCODE and PEST. Some GUIs provide interfaces with these codes in addition to the inverse-modeling routines contained within MODFLOW. Further, a suite of optimization codes can be used to evaluate a variety of hydrologic issues related to groundwater pumping, plume management, cost effectiveness, and receptor management for contaminated areas.

Local Mesh Refinement (LMR) provides the ability to create submodels within a regional model. While submodels cannot be used simultaneously with a regional model, they can be used to refine calibration or predictions within a smaller area after solving the regional model. Some GUIs provide this function while others do not

Table A-5-3 provides a comparison of capabilities of five widely used GUIs:

  • Groundwater Vistas (Environmental Simulations Inc., 2007)
  • Groundwater Modeling System (GMS;Environmental Modeling Systems Inc., 2007)
  • Visual MODFLOW (Schlumberger Water Services, 2007)
  • Processing MODFLOW for Windows (PMWIN; Chiang, 2005)
  • Argus Open Numerical Environments (ONE; Argus Holdings Ltd., 1997)

Argus ONE is an open environment for creating GUIs adapted to specific models. The USGS and others have developed interfaces within Argus ONE for a number of hydrogeological models. The other 4 GUIs are distributed as packages with their respective models included in the distribution.

Model Calibration
Calibration of a hydrogeological model is an application of inverse modeling. Model calibration is the process of selecting parameter values, inputs, and boundary conditions such that model output matches related observed data with an acceptable degree of accuracy and precision.

Calibration can be a major portion of the effort required to complete the modeling phase of a project. The level of calibration required for a particular model depends on the type and amount of data available in combination with project needs. Hill and Tiedemann (2007) present suggested guidelines for effective model calibration along with a description of the calibration process. Vrugt et al. (2008) review the state of the science with respect to inverse modeling of subsurface flow and transport properties.

A number of computer programs have been developed to automate the calibration process for particular hydrogeological models. More recently, model-independent inverse-modeling programs have been developed that can be applied to a broad range of forward models. Two such programs that have been widely accepted are UCODE (Poeter et al, 2005) and PEST (Doherty, 2004). Both UCODE and PEST have been incorporated into several GUIs to speed the model-calibration process.

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Gas Transport Modeling

Introduction
Gas transport, particularly the transport of oxygen into unsaturated waste-rock piles, can be an important process affecting the generation of ARD. Principal modes of oxygen transport include diffusion and advection. Wels et al. (2003) provide a comprehensive overview of the role of gas transport in ARD generation and methods that can be used to model gas transport.

Data Needs
Data required to model gas transport are similar to the data needed for equivalent modeling of water flow and transport in the subsurface. The permeability of the porous media is an important consideration. Because permeability to gas is a function of the degree of saturation of the pore space, moisture content is also important.

Permeability and moisture-content measurements can be made in the field or the laboratory. Measurements of moisture content are reasonably straightforward using established methodologies. Field measurements of air permeability using pneumatic pumping tests are described by Baehr and Hult (1991) and are conceptually similar to groundwater pumping tests used to determine aquifer characteristics. Stonestrom and Rubin (1989) describe laboratory air-permeability measurements.

Model Selection
Relatively few models have been developed specifically to address gas transport in the subsurface and the application to ARD-related problems. Modeling the complete set of physical and chemical processes operating within a waste-rock pile requires a multi-phase code capable of simulating gas and water flow in the unsaturated zone, chemical interactions with the solid matrix, heat generation and transfer, and chemical mass transfer in the liquid and gas phases.

Several general-purpose, multi-phase simulation programs have been developed that could be applied to these types of problems. The TOUGH family of codes (Pruess et al., 2004) was developed at Lawrence Berkeley National Laboratories and has been applied to a wide range of complex, multi-phase problems. TOUGH-AMD (Lefebvre et al., 2001) is an adaptation of TOUGH to address ARD‑related issues. TOUGHREACT (Xu et al., 2004) was developed as a comprehensive non-isothermal multi-component reactive fluid flow and geochemical transport simulator to investigate acid-mine drainage and other problems.

Groundwater flow models can be adapted to simulate air flow using appropriate transformations of variables and parameter formulations. Massman (1989) shows how groundwater solutions can be modified for gas-flow problems. This type of adaptation would not be appropriate to model the most complex multi-phase, reactive-transport problems, but may be adequate to address many issues of importance to the prediction of ARD generation.

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Considerations Regarding Predictive Modeling of Effluent Quality

As discussed throughout Chapter 5 of the GARD Guide and this Appendix, the principal objective of mine and process water quality prediction is to evaluate the potential for geologic materials and mine and process wastes to generate acid and contaminants and affect water resources. As an important corollary, the need for and nature of mitigation measures is determined through prediction.

The nature and sophistication of the prediction effort may vary depending on the desired outcome. A prediction exercise aimed at merely answering a “yes/no” question (for instance: will the water quality criterion for arsenic be exceeded?) requires less up-front understanding of the system being evaluated, in which case while use of relatively “crude” modeling tools may suffice. In contrast, when a more quantitative answer is required (for instance: what is the expected arsenic concentration?), the complexity of the modeling effort may be quite significant, requiring both a detailed conceptualization of the system being modeled as well as use of advanced modeling codes.
It should be noted that use of more sophisticated tools does not necessary equate to more accurate and precise modeling outcomes. According to Oreskes (2000) and Nordstrom (2004), the computational abilities of codes and advanced computers currently far exceed the ability of hydrogeologists and geochemists to represent the physical, chemical and biological properties of the system at hand or to verify the model results. In light of these difficulties, the meaning of “accuracy” and “precision” in the context of mine and process water quality modeling must be re-assessed on a case-by-case basis, and numeric analysis needs to be conducted to reflect the uncertainty inherent in predictive modeling. Accordingly, USEPA (2003) recommends the following should be submitted at a minimum to substantiate modeling used for regulatory purposes, regardless of the specific model/code being used:

  • Description of the model, its basis, and why it is appropriate for the particular use
  • Identification of all input parameters and assumptions, including discussion of parameter derivation (i.e., by measurement, calculation or assumption)
  • Discussion of uncertainty
  • Sensitivity analysis of important input parameters

Having said all that, despite the limitations identified throughout this chapter, modeling and prediction have significant value as management tools and for gaining an understanding of the geochemical, physical and biological systems at mine and process sites (Oreskes, 2000). There is little doubt that the understanding of geologic materials, mine and process wastes and the hydrogeochemical factors that govern mine and process water quality will continue to advance through the implementation of laboratory and field experiments. In particular those experiments that isolate one variable at a time to identify its effect on overall discharge water quality will prove of great value. Similarly, ongoing characterization and monitoring of mine and process facilities will allow development of improved scaling factors needed to extrapolate results from smaller-scale tests to an operational level. Lastly, the tools required for geochemical, hydrological and hydrogeological modeling already largely exist. With an increased comprehension of the factors that govern the generation of ARD, NMD or SD, modeling and prediction efforts will become increasingly reliable. 

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