Transport Modelling

9.1 Introduction

A solute transport model describes the movement of solutes dissolved in groundwater. Solutes dissolved in groundwater may include major ions (e.g. calcium or sulphate), metals (e.g. iron, copper, cadmium) and miscible organic constituents (e.g. BTEX, LEPH). In the context of environmental assessments, "solutes" are also referred to as "contaminant of concern (CoC)" or simply "contaminants".

In these guidelines the term "solute" is used in the general discussion of "solute transport" and the term "CoC" is used in the context of solute transport modelling for environmental assessments (also referred to as "contaminant transport"). The use of the terms "contaminant" or "contaminant transport" in these guidelines does not necessarily imply a demonstrated impact (or risk of impact) to the environment.

This section will provide an overview of the concepts of solute transport modelling and provide guidance on its application to natural resource projects.

9.2 Concepts of Solute Transport Modelling

Solute transport in groundwater is controlled by physical and geochemical mass transport processes (e.g. Domenico and Schwartz, 1990).

All solutes are influenced by the same physical transport processes, namely advection and dispersion. In contrast, geochemical transport parameters depend on the solute of interest as well as geochemical conditions in the aquifer. Solutes which are not influenced by geochemical transport processes are defined as "non-reactive" or "conservative" solutes and can be simulated using a "conservative" solute transport model.

Solutes which are influenced by chemical transport processes are defined as "reactive" solutes and require the use of a "reactive" solute transport model.

9.3 Physical Transport Processes

9.3.1 Advection

Advection describes the movement of groundwater under a hydraulic or pressure gradient. Advective transport describes the movement of dissolved solutes carried along with flowing groundwater. The direction and rate of advective transport coincide with that of the groundwater flow (Domenico and Schwartz, 1990).

The rate of advective transport is described by a modified version of Darcy's Law:

v = Ki/n

where

v = average linear velocity of water movement (in L/T)

K = hydraulic conductivity (in L/T),

i = hydraulic gradient (L/L) and

n = effective porosity (L³ /L³ )

In words, the average linear velocity (or simply "transport velocity") is directly proportional to the hydraulic conductivity and the hydraulic gradient and inversely proportional to the effective porosity. The above transport equation is very useful in estimating travel time of groundwater and/or solutes dissolved in groundwater.

The effective porosity of an unconsolidated homogeneous material may be as high as its total porosity. However, most aquifers contain dead-end fissures, unconnected pore-space and lower permeability than average material, and therefore the effective porosity of such materials is generally lower than their total porosity (NGCLC, 2001).

In highly fractured aquifers, the effective porosity may be as high as the porosity of the fractures. In dual porosity aquifers (i.e. fractured porous materials), the relevant porosity may be somewhere between that of the fissure and matrix porosity and may change with average flow velocity (NGCLC, 2001).

Advective transport can be simulated very efficiently using particle tracking codes (see Section 5.2.5). Particle tracking codes can be used to determine the flow path ("path-line") and the average travel time of a solute. An analysis of advective transport (using particle tracking) should always be carried out prior to considering other transport processes using a full solute transport model (see Section 5.2.5).

9.3.2 Dispersion

As water and solutes migrate through the subsurface via advection, they will tend to spread out, parallel to and normal to the flow path. The result will be dilution of the solute by a process known as dispersion. The mixing that is known along the streamline of fluid flow is called longitudinal dispersion. Dispersion which occurs normal to the pathway is called lateral (or transverse) dispersion (Fetter, 2001).

Dispersion occurs at the pore-scale and at the macroscopic (field) scale.

9.3.2.1 Mechanical Dispersion

Longitudinal dispersion at the pore scale is caused by the following factors (see Figure 9-1a):

• Pore size - some pores are larger than others and allow fluid to move faster;
• Path length - some particles travel along longer flow paths to go the same linear distance;
• Friction in pores - fluid moves faster through the center of pores than along the edges.

Lateral dispersion is caused by the fact that as a fluid containing a solute flows through a porous medium, the flow paths can split and branch out to the side (or in the vertical) (see Figure 9-1b). This lateral spreading will occur even in the laminar flow conditions that are prevalent in groundwater flow (Fetter, 2001).

The mechanical dispersion caused by the factors described above is equal to the product of the average linear velocity and a factor called the dynamic dispersivity (a_L ). The dynamic dispersivity has units of length and is a function of the subsurface material (porous medium or fractured bedrock). At the field scale, the dispersivity is also influenced by the heterogeneity of the aquifer unit and is therefore scale-dependent (see Section 9.3.2.3).

Figure 9-1a

Figure 9-1b

Figure 9-1: (a) Factors causing pore-scale longitudinal dispersion and (b) flow paths in a porous medium that cause lateral hydrodynamic dispersion (from Fetter, 2001).

9.3.2.2 Hydrodynamic Dispersion

Dispersion of the solutes dissolved in groundwater also occurs by diffusion, i.e. movement of solutes from a region of high concentration to a region of low concentration. The processes of molecular diffusion and mechanical dispersion cannot be separated in flowing groundwater. Instead, a factor termed the coefficient of hydrodynamic dispersion (D_L ) is introduced. It takes into account both the mechanical mixing and diffusion (Fetter, 2001). For one-dimensional flow it is represented by the following equation:

D_L = a_L x v + D*

Where:

D_L = longitudinal coefficient of hydrodynamic dispersion (in L² /T)

a_L = longitudinal dispersivity (L)

D* = the effective molecular diffusion coefficient (L² /T)

At the field scale, hydrodynamic dispersion also occurs in the direction normal to flow which requires definition of the coefficient of hydrodynamic dispersion in the transverse and vertical direction.

In most groundwater flow systems, mechanical dispersion dominates dispersion and diffusion is insignificant. However, diffusion can be an important process in low permeability environments and/or in heterogeneous systems where diffusion facilitates exchange between active and stagnant flow zones (e.g. in dual porosity systems).

The relative contribution of diffusion and dispersion processes should be established as part of the conceptual model development.

9.3.2.3 Dispersion at the Field Scale (Macrodispersion)

Mechanical dispersion is also caused by the heterogeneities in the aquifer. As groundwater flow proceeds in an aquifer, regions of greater than average hydraulic conductivity, and regions of lesser than average hydraulic conductivity are encountered. The resulting variation in linear groundwater velocity results in much greater hydrodynamic dispersion than that caused by the pore-scale effects (Fetter, 2001). This macro-scale dispersion effect is also known as "macro-dispersion".

Macro-dispersion is influenced by the type and degree of heterogeneity and is difficult to quantify in a simple mathematical formulation commonly used in solute transport models (such as the dispersion equation shown above).

Figure 9-2 illustrates macro-dispersion in a heterogeneous porous medium. In this hypothetical (numerical) example, advective transport through a heterogeneous porous medium was simulated (using particle tracking). Pore-scale dispersion was ignored in this simulation. This example illustrates that the solute plume moves preferentially through high permeability zones resulting in significant localized channeling. Transport velocities and solute concentrations in those preferential flow channels can be significantly higher than would be predicted if a homogeneous aquifer and a standard dispersion model (with average properties) would be assumed for solute transport predictions.

Figure 9-2: Macro-dispersion in a heterogeneous, porous medium. The upper panel shows the explicit representation of aquifer heterogeneity. The lower panel shows the resulting macro-dispersion simulated using particle tracking (dispersion at the pore-scale was not modeled).

Macrodispersion in fractured bedrock depends on the hydraulic properties of the fracture network (i.e. fracture density and connectivity, fracture aperture) and the matrix porosity (Beth et al., 2011). In densely fractured bedrock, solute transport occurs in a large number of fractures and transverse dispersion (i.e., plume spreading orthogonal to groundwater flow) is strong, similar to what is observed in a uniform porous medium (see Figure 9-3a). In sparsely fractured bedrock, the solute plume is channeled or funneled into narrow zones due to the dominance of flow in one or a few large, major fractures or fracture zones extending over long distances (Beth et al., 2001). In this case, the plumes would become long and narrow or 'snake-like' in shape rather than fan shaped (see Figure 9-3b). These plumes could extend for significant distances from the source locations with limited dispersion and hence dilution.

Figure 9-3: Macrodispersion in a heterogeneous porous medium (reproduced from Beth et al., 2011).

Figure 9-4 shows an example of macro-dispersion in fractured bedrock in which advective transport occurs in discrete fractures (e.g. bedding planes) but the rock porosity supports diffusion-driven solute mass transfer between the fractures (typical for sedimentary rocks). In this scenario, diffusion could significantly retard the advance of the solute plume (similar to a porous medium) but spreading of the solute plume would still not be random but instead follow the main orientation of the fracture network.

The influence of aquifer type (bedrock versus porous medium) and degree of heterogeneity (and/or degree of fracturing) on macro-dispersion should be considered when selecting the appropriate dispersion model and numerical values of dispersivity. For example, the presence of a few discrete fractures may require an explicit representation of these discrete features and advective transport only (no hydrodynamic dispersion). Alternatively, densely fractured bedrock may be adequately represented using the equivalent porous medium approach and using the hydrodynamic dispersion equation.

Figure 9-4: Macrodispersion in a fractured network (reproduced from Beth et al., 2011).

9.3.2.4 Scale Dependency of Dispersion

A review of a large number of transport studies indicated that dispersion is scale dependent, i.e. dispersivity increases with transport distance (see Figure 9-5a and 9-5b reproduced from Gelhar et al., 1992). Dispersivity values obtained from laboratory experiments (column tests) were typically one to two order of magnitudes lower than dispersivity values obtained from field tests (tracer tests, contaminated sites). However, a detailed assessment of the field studies indicated that the majority of the larger-scale field studies are unreliable.

The observed scale dependency of dispersivity values introduces uncertainty into solute transport predictions. For example, modelling of solute transport at the regional scale may justify the use of a larger dispersivity value. However, the use of a large-scale dispersivity value may overpredict the effects of dispersion at the local scale.

The measurement of dispersion is difficult and expensive in the field and consequently empirical expressions are almost always used. Gelhar et al. (1992) point out that the use of a large dispersivity value (in the upper end of a given scale) could result in the prediction of excessively large dilution which could result in non-conservative predictions of contaminant concentrations. They therefore recommend the use of dispersivity values from the lower third of a given scale shown in Figures 9-5a and 9-5b).

Note also that scale dependency of dispersion is strongly influenced by the influence of heterogeneity on dispersion (see above). It follows that the appropriate value of dispersivity for a numerical model will depend on the degree of heterogeneity explicitly included in the model. For example, if the local heterogeneity is well-represented in the numerical model (see Figure 9-2) then a smaller dispersivity value should be selected that matches the scale of the heterogeneity represented in the model.

Figure 9-5a

Figure 9-5b

Figure 9-5: (a) Longitudinal dispersivity versus scale with data classified by reliability and (b) horizontal transverse dispersivity as a function of observation scale (from Gelhar et al., 1992).

These guidelines recommend the use of dispersivity values at the lower end of the reported range of values for a given scale (see Figures 9-5a/b). For typical basin-scale transport problems, longitudinal dispersivity values are usually in the range of 2 to 10 metres. Lateral transverse dispersivity values should be about one order of magnitude lower and vertical transverse dispersivity values should be about one to two order of magnitudes lower than longitudinal dispersivity.

The scale dependency of solute dispersion and the degree of heterogeneity represented in the numerical model is an important consideration in selecting an appropriate numerical value for dispersivity in the mathematical model and should be discussed in the conceptual model.

9.3.2.5 Influence of Dispersion on Solute Transport

Dispersion influences solute transport in three ways (see Figure 9-6):

• Longitudinal dispersion tends to spread out the breakthrough of a solute, resulting in earlier breakthrough of a solute (typically at low concentrations) than predicted based on the (average) advective velocity (Figure 9-6a)
• Transverse dispersion tends to spread out the lateral (and vertical) extent of the solute plume, resulting in greater spatial impacts than would be predicted using advection only (Figure 9-6b)
• Longitudinal and transverse dispersion tend to dilute the solute concentrations; this dilution effect is most pronounced in the case of a source term of short duration (e.g. a contaminant spill) (Figure 9-6c).

The consideration of dispersion tends to provide conservative water quality predictions with respect to first arrival times and maximum spatial extent of impact but tends to be non-conservative with respect to predicting actual contaminant concentrations at specific locations.

The effects of dispersion on solute transport require careful consideration by the modeller during model conceptualization and numerical modelling. To this end the following general guidelines should be followed:

• The nature and magnitude of solute dispersion and its potential effect on solute transport for the specific project should be discussed in the conceptual model
• The numerical value used for longitudinal and transverse dispersivity should be justified (default values by the model code are not acceptable without justification)
• If dispersivity values cannot be calibrated, a sensitivity analysis should be completed to determine the sensitivity of solute transport predictions to the uncertainty of this important transport parameter
• The influence of large-scale heterogeneity on dispersion and solute transport predictions should be discussed in the modelling report
• The limitations of the dispersion model used for simulating solute transport in the specific subsurface environment should be discussed in the modelling report.

Figure 9-6a

Figure 9-6b

Figure 9-6c

Figure 9-6: (a) Influence of dispersion and diffusion on "breakthrough" of a solute, (b) development of contaminant plume from a continuous point source, and (c) travel of a contaminant slug from a one-time point source. Density of dots indicates solute concentration (after Fetter, 2001).

9.4 Geochemical Transport Processes

The most common geochemical transport processes include:

• Sorption/desorption
• Precipitation/dissolution
• Degradation

Other chemical processes such as speciation, redox reactions, acid-base reactions, and volatilization may also influence solute concentrations but are not discussed further in these guidelines (see for example Appello and Postma, 2009 for more details on those processes).

The following sections provide a very brief overview of these three chemical transport processes. A more detailed discussion is provided in textbooks on aqueous geochemistry (e.g. Domenico and Schwartz, 1990; Appello and Postma, 2009).

9.4.1 Sorption/Desorption

Sorption processes include adsorption, absorption, chemisorption and cation exchange. These processes are complex and are dependent on the geochemical environment, the rate of groundwater flow, the surface area in contact with groundwater and the concentration of contaminants present in groundwater (NGCLC, 2001).

Different conceptual models have been developed to quantify sorption and desorption. Most sorption models are defined by a sorption isotherm, which describes the relationship of the solute concentration dissolved in groundwater and the solute concentration sorbed on the solid phase (i.e. soil particles or bedrock surface).

The following three sorption models are common (e.g. Appello and Postma, 2009):

• Linear isotherm
• Freundlich isotherm
• Langmuir isotherm.

The linear isotherm is the most common sorption model used in solute transport modelling. This model assumes that the quantity sorbed is directly proportional to the concentration in the groundwater and that sorption is instantaneous and reversible. Under those assumptions the travel velocity of a sorbing solute is reduced (relative to the average linear velocity of water) by a factor known as the retardation factor. The slope of the linear isotherm is known as the partition coefficient (k_D ) and can be used to estimate the retardation factor (R_f ).

This "retardation approach" does not apply to situations where the amount of sorption sites is limited (e.g. for major ions limited by the cation exchange capacity) and/or where sorption is not fully reversible (e.g. for sorption of some trace metals such as cobalt which exhibit "ageing"). In the first situation a non-linear isothern (e.g. Freundlich or Langmuir isotherm) can be used. The second situation may require the use of a kinetic sorption model (with different rates for sorption and desorption).

The selection of an appropriate sorption model will require an in-depth review of the site-specific geochemical conditions, including the CoC, ambient groundwater quality (e.g. pH, redox conditions) and the solid substrate. The use of sorption and selection of a particular sorption model for solute transport modelling should be justified based on site-specific monitoring and/or testing. Sorption parameters should be determined using field and/or laboratory testing which replicate in-situ geochemical conditions (i.e. local soils and in-situ pH and redox conditions).

9.4.2 Precipitation/Dissolution

Transport of selected solutes may also be influenced by precipitation/dissolution reactions. The solid phase of the aquifer (soil or bedrock) comprises minerals which in turn consist of an assemblage of major ions and trace metals. When the groundwater is in contact with these minerals, the mineral (e.g. calcite) will dissolve into its mineral components (in this example calcium and bicarbonate). The dissolution of natural minerals may also release trace metals. For example, elevated concentrations of trace metals are commonly found in mineralized areas where mining takes place.

Mineral precipitation is the reverse process of mineral dissolution. In mineral precipitation, the mineral constituents dissolved in groundwater bond together to form a mineral, i.e. they will precipitate out of solution. Precipitation and dissolution are controlled by the "solubility product" (or K_sp ). A smaller solubility product indicates that the mineral is less soluble and that the concentrations of the mineral constituents dissolved in groundwater will be smaller.

The most common precipitation/dissolution reactions in groundwater in the context of natural resource projects include

• Precipitation/dissolution of common minerals such as calcite, dolomite and gypsum
• Precipitation/dissolution of iron-oxi-hydroxides and
• Co-precipitation of trace metals.

The precipitation of iron-oxi-hydroxides is of particular importance because they often result in co-precipitation of trace metals which can be of environmental significance. Precipitation of these oxi-hydroxides typically occur where reducing groundwater with elevated iron discharges and comes in contact with oxygen (e.g. in pumping wells, drains and/or at springs).

A significant body of research is available on the subject and the reader is referred to geochemical textbooks (e.g. Appello and Postma, 2009) and the scientific literature for more details.

Sophisticated multi-species solute transport models are available to simulate the influence of precipitation/dissolution reactions on solute transport (e.g., PHREEQC). However, such geochemical models are not routinely used for assessment of solute transport at the field scale.

The conceptual model of solute transport should discuss the potential influence of precipitation/dissolution reactions on solute transport. If justified, the potential influence of such geochemical controls on solute transport may be demonstrated using a simplified transport model (e.g. along a 1D flow path). However, the incorporation of precipitation/dissolution reactions into a basin-wide solute transport model is not recommended.

9.4.3 Degradation

Degradation can be a significant process in decreasing the contaminant mass of organic compounds in which case the process is called biodegradation. This process is complicated and the actual rate of biodegradation varies according to a range of factors including contaminant type, microbe type, redox, temperature and chemical composition of groundwater.

Radioactive materials will also experience degradation due to radioactive decay.

This process is usually represented mathematically either as a first order reaction (exponential decay), or by a rate limited reaction. Exponential degradation implies that the rate of decrease in concentration of the substance is proportional to the amount of substance and can be characterized by a half-life (i.e. it is assumed to be a first order reaction) (NGCLC, 2001). This behaviour is commonly observed in biodegradation (since the activity of a microbial population is proportional to the availability of its food), radioactive decay, and in other non-biological processes where the contaminant is present in trace amounts relative to other reactants.

The use of degradation in a solute transport model will require an in-depth review of the properties of the CoC and site-specific geochemical conditions potentially favoring degradation. The use of degradation and selection of a particular degradation model for solute transport modelling should be justified based on site-specific monitoring and/or testing.

9.4.4 Use of Geochemical Transport Processes for Natural Resource Projects

The use of geochemical transport processes for solute transport modelling tends be non-conservative, i.e. typically result in predictions of delayed and/or or reduced contaminant concentrations at potential receptors (e.g. stream or lakes).

For this reason, geochemical processes should only be included in the solute transport model if the presence of such processes can be demonstrated using site-specific observations and the geochemical model can be parameterized (e.g. using site-specific field data and/or lab testing).

If geochemical processes are included in solute transport modelling, a detailed sensitivity analysis should be included to demonstrate the influence of uncertainty in reactive transport parameters (e.g. k_D value) on the water quality predictions. This sensitivity analysis should always include a simulation of conservative solute transport (i.e. without geochemical controls) to allow an assessment of the influence of the assumed geochemical reactions on water quality predictions.

9.5 Numerical Methods of Solute Transport

9.5.1 Solution Methods

Several numerical methods are available to solve the advection-dispersion equation for solute transport (NGCLC, 2001):

• Eulerian method
• Lagrangian method
• Mixed Eulerian-Lagrangian method

9.5.1.1 Eulerian Methods

Eulerian methods involve approximate solutions to the equations governing contaminant transport by advection and dispersion. These methods can be subject to numerical instability, artificial oscillations and numerical dispersion when compared to exact analytical solutions (see Section 9.5.2 for more details).

The numerical problems associated with the Eulerian method makes this method less attractive for solute transport problems (see Section 9.5.2).

9.5.1.2 Lagrangian Method

The Lagrangian methods represent solute transport by a large number of moving particles to avoid solving the advection transport equation. The method is free of numerical dispersion, although numerical problems may be associated with irregular grids or contaminant sources or sinks. The method is most suited to problems where advection dominates contaminant transport.

9.5.1.3 Mixed Eulerian - Lagrangian Approach

The Mixed Eulerian - Lagrangian approach combines the advantages of these two techniques and uses the Lagrangian approach to solve the advection term and the Eulerian approach to solve the dispersion term. The Method of Characteristics ("MOC"), the Modified Method of Characteristics ("MMOC"), and the Hybrid Method of Characteristics ("HMOC") are examples of this approach.

The mixed Eulerian-Lagrangian approach is often the preferred solution method for solute transport problems, in particular when both advection and dispersion are important transport processes.

9.5.2 Numerical Problems with Solute Transport Models

The two most common numerical problems with solute transport models are:

• Numerical dispersion
• Numerical instability

The following sections describe these numerical issues and provide guidance on how to avoid them.

9.5.2.1 Numerical Dispersion

A common problem in running numerical models of solute transport is numerical dispersion. Numerical dispersion results in artificial spreading of the solute plume due to inaccuracies in the numerical solution. Figure 9-7a illustrates the effect of numerical dispersion. Numerical dispersion is usually caused by insufficient discretization in space and/or time.

Numerical dispersion occurs in all three principal directions but is often most pronounced in the vertical direction because the vertical discretization in 3D models tends to be less than in the x-y plane.

Numerical dispersion can be minimized by a number of methods:

• Decreasing the model grid spacing and time step to minimize dispersion particularly for models that are solved by Eulerian methods (Appendix E); however, this will increase model run times;
• Choice of the solution method; for example, Lagrangian methods are less susceptible to numerical dispersion;
• Choice of initial or starting conditions;
• Choice of convergence criteria for the model.

The degree of numerical dispersion should always be checked by gradually reducing the dispersivity until the numerical solution does not change any longer. The remaining dispersion (deviation from advective transport) is due to numerical dispersion. Numerical dispersion is acceptable if it is much smaller than the dispersion due to the dispersivity of the natural aquifer system.

9.5.2.2 Numerical Instability

The advection-dispersion equation is difficult to solve by numerical methods and may result in model instability, in particular if standard finite-element or finite difference schemes are used.

Figure 9-7a

Figure 9-7b

Figure 9-7c

Figure 9-7: Illustrative examples of numerical problems in solute transport modelling (Reproduced from NGCLC, 2001).

Numerical instability in the transport model can lead to numerical oscillations in space and/or time (see Figure 9-7b/c).The modeller (or reviewer) should always check the transport solutions for such oscillations which indicate the presence of numerical instability.

In general, the likelihood of model instability increases with a coarser discretization in space and time. These guidelines recommend that the maximum grid size and time step for solute transport be estimated using common criteria known as the grid Peclet number and Courant number (see Appendix E). In addition, the effect of grid spacing and time stepping on the solute transport solution should be evaluated using sensitivity analyses.

9.5.2.3 Review of Numerical Problems

The following checks should be performed by the modeller (or reviewer) to determine whether there are problems with the numerical solution of the solute transport problem (NGCLC, 2001):

• Mass Balance: Errors in the mass balance provide evidence of numerical instability
• Time Series: Oscillations in predicted contaminant concentrations with time may indicate instability
• Contaminant Distribution: Anomalies in contaminant distributions may also indicate instability.

9.6 Common Transport Problems in Natural Resource Projects

Solute transport modelling is usually required to assess potential water quality impacts by a proposed natural resource project, typically to nearby valued ecosystem components (VECs) such as a drinking water well, fish-bearing creeks or lakes. Solute transport modelling is more commonly required for mining projects which can produce seepage from mine waste units (TSFs, WRDs) with poor water quality (elevated TDS and/or metals). Most aggregate mining and groundwater extraction projects do not impact water quality and therefore do not require solute transport modelling.

Typical modelling objectives requiring solute transport include:

• Predict pathway and travel time of a solute in a steady-state (or transient) groundwater flow field
• Predict spatial and temporal evolution of a solute plume in the aquifer (from source to receptor)
• Predict "breakthrough" of a solute (i.e. concentration versus time) at a receptor (e.g. private well, reach of lake or stream)
• Predict solute loading to surface water (lake /stream)
• Design of mitigation measures such as
• Natural attenuation
• Seepage interception system (SIS)
• Pump & treat
• Reactive barriers
• Predict recovery of solute load in seepage interception system.

Particle tracking is usually adequate to determine pathways and average travel times. Figure 9-8a/b shows an example of the use of particle tracking to determine the efficacy of a deep drain to intercept seepage from a tailings dam. In this example, the depth of the drain was varied until all particles are captured in the drain, demonstrating that full hydraulic capture is achieved. For this design, the water quality (contaminant concentrations) in the intercepted seepage was not important (all intercepted water is recycled to the tailings impoundment). Hence, a solute transport model was not required.

Figure 9-8a

Figure 9-8b

Figure 9-8: Example of particle tracking for design of seepage interception system. The upper panel shows the pathlines of seepage (advective transport) prior to seepage interception. The lower panel shows the pathlines of seepage after installation of a partially penetrating drain (arrow = 100 days). In this example, the design depth of the drain was not sufficient allowing underflow beneath the drain in the northern portion.

In some cases, particle tracking may even be sufficient to estimate solute loads to a VEC. Figure 9-9 illustrates an example where the average solute load from a waste rock dump to a nearby creek had to be estimated. Particle tracking was completed to estimate the reach of the creek impacted by seepage from the waste rock pile. The average travel time from the waste rock dump to the creek was estimated to be only a few years. Since the waste rock dump had been placed several decades ago it could be assumed that that the seepage plume had reached a pseudo steady-state. Therefore, the solute load reaching this particular reach of the creek could be (conservatively) assumed to be equal to the net infiltration into the waste rock dump times the average solute concentration (known from piezometers installed in the waste rock dump).

Figure 9-9: Example of particle tracking used to estimate contaminant load from a waste rock dump (right) and backfilled open pit (left) to a near-by creek. The blue lines illustrate the pathlines of seepage from the two mine waste units and the reach of the creek.

Note that particle tracking does not provide any insight into the degree of dispersion (in the aquifer) and dilution (by local recharge) along the flow path and hence the solute concentration in groundwater emerging into the creek. However, these processes did not need to be simulated in this example because solute loads (not actual solute concentrations) were required for this impact assessment.

In general, solute transport models are used when a prediction of solute concentrations (in space and/or time) is required. In the context of an EA, solute transport models are often used to predict solute concentrations in groundwater or surface water which are then compared to numerical water quality standards (e.g. BC Water Quality Guidelines or site-specific water quality objectives). Figure 9-10 shows the predicted evolution of a sulphate plume due to seepage from a tailings dam. This model was first calibrated using observed sulphate concentrations in a series of monitoring wells. Once calibrated, the solute transport model was then used to design seepage mitigation measures required to meet applicable water quality guidelines at the downgradient boundary.

Figure 9-10: Example of solute transport modelling used to predict movement of a sulphate plume. The upper panels show the simulated spatial extent of the sulphate plume after 30 years. The lower inset plot shows the simulated breakthrough of sulphate at different monitoring locations.

It should be recognized that predictions of solute concentrations for specific locations (e.g. a compliance point) carry significantly greater uncertainty than predictions of solute loads to a general area (e.g. to a stream reach). This applies in particular for heterogeneous porous media and fractured media, where preferential flow paths exist but are usually not well understood.

For this reason, the modeller should always discuss the limitations in predicting solute concentrations at specific locations (or receptors) and should provide recommendations as to the appropriate use of such solute transport predictions in the regulatory context.

9.7 Calibration of Solute Transport Models

Solute transport modelling requires knowledge about the groundwater flow field. In most cases a groundwater flow model is first calibrated (using observed groundwater levels (or hydraulic heads) and/or observed flows (see Section 7). In a subsequent step, the solute transport model is then calibrated using observed solute concentrations (e.g. spatial distribution and/or time trends). It is emphasized that the use of a calibrated groundwater flow model is a requirement for solute transport modelling. However, the use of a calibrated flow model does not imply that the solute transport model is calibrated. The transport parameters (such as effective porosity, dispersivity and reactive transport parameters) can only be calibrated by matching simulated and observed spatial and/or temporal distributions of a solute.

A common problem in applying solute transport models to natural resource projects is the lack of suitable monitoring data available for model calibration. Significant changes to the groundwater quality (such as seepage from a mine waste unit resulting in a solute plume) usually do not occur until after start of the project. For example, seepage from a proposed tailings impoundment clearly does not occur until after the project is permitted and operation has started. In fact, it may take many years to decades before a solute plume has migrated into the aquifer and can be used for model calibration.

It follows that most solute transport models used for EA submissions or permitting are not calibrated. Instead, transport parameters such as effective porosity and dispersivity have to be selected based on analogue sites and/or experience by the modeller. This lack of model calibration introduces uncertainty in solute transport predictions. The modeller should clearly state in the model documentation whether the solute transport model is calibrated. If the model is not calibrated, the model documentation should justify the selection of the solute transport parameters.

If the solute transport model is not calibrated, a detailed sensitivity analysis should be completed to evaluate the influence of uncertainty in solute transport parameters on transport predictions.

Calibration of a solute transport model may be possible at later stages of the project life, in particular at closure or post-closure, when a solute plume might have developed. During model conceptualization, the modeller should review current and historic groundwater quality data to determine whether suitable groundwater quality data are available to calibrate the solute transport model (see Section 4).

Calibration of a solute transport model provides significant insight not only into solute transport but also into groundwater flow. For example, the spatial distribution of a solute may indicate the presence of a high-permeability channel(s) (or a barrier to flow) that was not included in the groundwater flow model. In many cases, calibration of the solute transport model requires recalibration of the flow model and sometimes even a change in the conceptual model.

The combined calibration of a flow model (against heads and flow) and solute transport model (against concentrations and loads) significantly increases the confidence in model predictions of both flow and transport.

9.8 Uncertainty in Solute Transport Modelling

In general, predictions of solute transport carry significantly more uncertainty than prediction of groundwater flow for the following reasons:

• Solute transport parameters (effective porosity, dispersivity and reactive transport parameters) cannot be measured directly at the field scale; yet, measurements of these transport parameters at the laboratory scale (e.g. using column experiments) may not be directly applicable to the field scale due to scale effects (effective porosity, dispersivity) and/or different geochemical conditions (reactive transport parameters)
• The only reliable method to determine transport parameters is through calibration of a solute transport model; however, model calibration is often not possible because of a lack of calibration data, in particular during early stages of EA and project permitting
• Solute transport is strongly influenced by heterogeneity (macro-dispersion), in particular in fractured bedrock environments; even with implementation of a comprehensive drilling and hydraulic testing program, uncertainty about preferential flow paths will always remain (in particular in fractured bedrock)
• Most solutes are influenced by geochemical reactions which can be complex and difficult to represent by a simple mathematical model to be included in the solute transport model
• The transport of a solute is strongly influenced by the "source term", i.e. the strength and timing of contaminant release from a contaminant source; however, the source term is often controlled by geochemical processes (such as sulphide oxidation and precipitation/dissolution reactions in sulphidic mine waste) which need to be estimated using geochemical models and carry their own uncertainty
• Solute transport is a slow process, with predictions for mining projects often covering decades to centuries; this large time frame adds additional uncertainty with respect to future conditions (e.g. future groundwater use, climate change).

The above uncertainties in solute transport modelling should be evaluated in a detailed uncertainty analysis (see also Section 8). Such an uncertainty analysis should include a qualitative discussion of all uncertainties in solute transport predictions and a quantitative assessment of key uncertainties, including the sensitivity of water quality predictions to uncertainty in macro-dispersion and uncertainty in geochemical controls.

Considering the uncertainty in solute transport modelling, conservative assumptions should be used as much as possible, in particular during the early stages of project life (EA application and/or permitting). Non-conservative assumptions (such as high dispersivity, sorption) should only be used if there is evidence from the project site (or a suitable analogue site) to support these non-conservative assumptions.

9.9 Case Study Example

9.9.1 Case Study 2: Underground Mine

Case Study 2 illustrates the application of a solute transport model to a mining project. In this project, total organic carbon (TOC) had been identified as a potential CoC and the transport of this CoC to nearby receptors (lakes and streams) was simulated (see Appendix C2).

Initially, particle tracking was used to estimate the advective path and travel times of seepage from the new adit, the underground stopes, and beneath the load-out facility post-flooding. Particle tracking confirmed that mine-related CoCs may reach groundwater discharge points several decades after closure (see Figure 9-11). The particle tracking exercise helped to identify potential receptors, but was not able to provide estimates of CoC concentration (see Section 5.6.2.2).

Figure 9-11: Pathline Endpoints from Particle Tracking Simulations, Calibration Runs and Worst-Case Hydraulic Parameters (GD4).

Subsequently, conservative and reactive solute transport modelling was undertaken to simulate the transport of total organic carbon (TOC) to the receiving environment. A single value representing the initial TOC concentration was assumed based on a consultant's report. The transport simulation was conducted as two separate scenarios: (i) where TOC does not react or degrade with time; and (ii) where TOC is reactive and decays with time.

Three observation wells were created in the model domain to track the break-through of TOC over time (Figure 9-12). These wells were located upstream of the sensitive receiving environments and distributed spatially (across the domain as well as with depth). The predicted break-through curves for TOC in these monitoring wells are shown in Figure 9-13.

Figure 9-12: Location of simulated observation wells (purple) along with existing residential and monitoring wells (green).

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Figure 9-13: Predicted break-through curves for TOC assuming (a) biodegradation and (b) no biodegradation.

The transport model predicted a breakthrough of the TOC at two of the three observation points, with average arrival times ranging from about 20 to 30 years. The model predictions further indicated that the use of a first-order reaction rate (to simulate biodegradation) did not significantly influence the timing and peak concentrations of TOC (considering all other uncertainties).

At this point, an additional sensitivity analysis was performed to assess the effect of the shallow till hydraulic conductivity. The effect was to deflect particles towards different areas of the receiving environment (e.g. away from a lake and towards a river) which could have significant implications regarding receptor sensitivity and dilution capacity.

The transport module MT3D was used to simulate non-reactive transport of a non-specific mine-related CoC from the mine workings (representing 100% concentration). The default values for dispersivity were adopted (a_L =10m, a_TH =1m and a_TV =0.1m). Simulations of post-closure transport indicate that supply wells and surface water will not receive a significant percentage of the solute in the 100 year timeframe simulated (see Figures 9-14 and 9-15).

Figure 9-14: Predicted concentration contours (blue) at 100 years after mine closure for depths represented by Layers 2 and 5 of the model. Contours at 50, 10, 1, and 0.1% of mine concentration.

Figure 9-15: Vertical distribution of mine solute at 30 and 100 years after mine closure. Contours at 50, 10, 1, and 0.1% of mine concentration.

Additional analyses were performed with a subsequent model to show that the downstream supply wells would receive only 1% more groundwater from the mine area compared to pre-mining conditions. On the basis of transport simulations and the predicted path of the mine-affected plume, additional groundwater monitoring well locations were recommended by the modeller

This case study is typical for solute transport modelling completed for EA submissions in that (i) site-specific information on solute transport parameters was not available and (ii) the solute transport model was not calibrated. It follows that the uncertainty in these solute predictions is very high. The model study addressed the uncertainty in the groundwater flow predictions by simulating different conceptual flow models and performing additional sensitivity analyses (see Section 8). However, the study did not address all uncertainties in the solute transport predictions. For example, the uncertainty in macro-dispersion in this bedrock aquifer was not discussed nor quantified. The potential for numerical dispersion (in combination with use of the default dispersivity value) was also not evaluated.

Considering the remaining uncertainties, the solute transport predictions presented in this case study should be viewed as illustrative, describing the general pathway and general trends in solute plume behavior. However, the predictions of specific breakthrough curves at specific locations (such as wells) carry significant uncertainty. These model limitations should be considered when interpreting the solute transport predictions.

Review Questions

1. The use of a calibrated flow model does not imply that the solute transport model is calibrated.
   1. True.
   2. False.
2. Macrodispersion in fractured bedrock is primarily dependent on four characteristics of the bedrock. These are:
   1. Fracture connectivity, aperture, infilling, and surface roughness.
   2. Fracture density, vertical extent, surface alteration, and matrix density.
   3. Fracture density, connectivity, aperture, and matrix porosity.
   4. Fracture density, connectivity, aperture, and confining stress.
   5. Fracture connectivity, horizontal spacing, orientation, and aperture.
3. The three most common geochemical transport processes are:
   1. Sorption/desorption, precipitation/dissolution, and denitrification.
   2. Precipitation/dissolution, hydrolysis, and degradation.
   3. Sorption/desorption, precipitation/dissolution, and degradation.
   4. Precipitation/dissolution, oxidation, and degradation.
   5. Sorption/desorption, ionization, and precipitation.
4. Under which circumstances is it appropriate to use reactive solute transport modelling for an EA submission?
   1. If there is evidence from the project site (or a suitable analogue site) to support these non-conservative assumptions.
   2. If adequate field and/or laboratory data is available to parameterize the reactive transport model.
   3. If a detailed sensitivity analysis is completed to demonstrate the influence of uncertainty in reactive transport parameters on the water quality predictions.
   4. A and C.
   5. A, B, and C.
5. Solute transport models submitted at the Environmental Assessment (EA) or Permitting stages are generally:
   1. Not calibrated because calibration is not necessary at the EA or Permitting stages.
   2. Well calibrated to field observations and measurements.
   3. Well calibrated, but should include extensive sensitivity analyses.
   4. Not calibrated due to lack of data and should include extensive sensitivity analyses and discussion of model limitations.
   5. Solute transport modelling should not be undertaken at the EA or permitting stages.
6. Three examples of transport assumptions that yield conservative water quality predictions are:
   1. Low dispersivity, no solute precipitation, no sorption.
   2. High dispersivity, dissolution, sorption.
   3. Degradation, solute precipitation, desorption.
   4. High dispersivity, solute precipitation, sorption.
   5. Low dispersivity, no solute precipitation, high sorption.

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Proceed to Section 10: Model Documentation