POLYMIN - University of Waterloo

POLYMIN
Version 3.0
2D REACTIVE MASS TRANSPORT MODEL WITH
OXYGEN DIFFUSION, SULPHIDE OXIDATION &
GEOCHEMICAL SPECIATION
USER GUIDE
Designed by
J.W. Molson 1,2 and E.O. Frind 1 , M. Aubertin 2 , D. Blowes 1
With contributions from Andrea Walter and Horst Gerke
1 Department of Earth Sciences, University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
2 Ecole Polytechnique, Montreal
NSERC POLY/UQAT Chair: Environment and Mine Waste Management
john.molson@polymtl.ca
(c) March 2005

POLYMIN 2005
License Agreement
I. Copyright Notice
This software is protected by both Canadian copyright law and international treaty
provisions. Therefore, you must treat this software just like a book, with the following single
exception. The University of Waterloo (UW) and Ecole Polytechnique (EP) authorize you to make
archive copies of the software for the sole purpose of backing-up our software and protecting your
investment from loss.
By saying "just like a book", it is meant for example, that this software may be used by any
number of people and may be freely moved from one computer location to another, so long as there
is no possibility of it being used at one location while it is being used at another. This restriction is
similar to that in publishing where a book for example, can't be read by two different people in two
different places at the same time.
II. Warranty
UW and EP warrant the physical disks and documentation enclosed herein to be free of
defects in materials and workmanship for a period of 30 days from the date of purchase. In the event
of notification of defects in material or workmanship, UW or EP will replace the defective disks or
documentation. The remedy for breach of this warranty shall be limited to replacement and shall not
encompass any other damages, including but not limited to loss of profit, and special, incidental,
consequential, or other similar claims.
III. Disclaimer
Neither the developers of this software, nor any person or organization acting on behalf of
them makes any warranty, express or implied, with respect to this software; or assumes any
liabilities with respect to the use, or misuse, of this software, or the interpretation, or
misinterpretation, of any results obtained from this software, or for damages resulting from the use
of this software.
IV. Governing Law
This license agreement shall be construed, interpreted, and governed by the laws of the
Province of Ontario, Canada.
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POLYMIN 2005
TABLE OF CONTENTS
page
LIST OF FIGURES....................................................................................................................... 4
LIST OF TABLES ......................................................................................................................... 4
1. INTRODUCTION...................................................................................................................... 5
1.1 Overview............................................................................................................................................5
1.2 Capabilities, Assumptions and Limitations....................................................................................6
1.3 Software Support..............................................................................................................................7
2. THEORETICAL DEVELOPMENT ......................................................................................... 8
2.1 Background .......................................................................................................................................8
2.2 Mass Transport.................................................................................................................................8
2.3 Primary Variables and their Dimensions .....................................................................................19
2.4 Geochemical Database ...................................................................................................................20
2.5 Input/Output File Definition..........................................................................................................21
3. DESIGNING A MODEL ......................................................................................................... 22
Grid Definition & Boundary Conditions.......................................................................................................22
4. SAMPLE DATA SET............................................................................................................... 25
Input options .................................................................................................................................................27
Grid parameters.............................................................................................................................................28
Data Block 1..................................................................................................................................................29
Print output of components ...........................................................................................................................30
Tolerance and relative values........................................................................................................................31
Oxidation Parameters ....................................................................................................................................31
Breakthrough points......................................................................................................................................32
Time Step Data..............................................................................................................................................32
Background aqueous chemistry ....................................................................................................................33
Background solid chemistry..........................................................................................................................34
5. STEP BY STEP INSTRUCTIONS.......................................................................................... 37
6. TIPS AND TECHNIQUES ..................................................................................................... 39
7. PROBLEM DIAGNOSIS AND SOLUTIONS........................................................................ 40
8. REFERENCES ........................................................................................................................ 41
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POLYMIN 2005
LIST OF FIGURES
Figure
page
1. Conceptual domain for POLYMIN model applications ................................ 6
2. Simplified POLYMIN flowchart .............................................. 16
3. Typical boundary condition configuration. .............................................. 24
4. Typical node and element numbering convention .............................................................. 24
LIST OF TABLES
Table
page
1. Capabilities, assumptions and limitations ................................................... 5
2. Input/Output file definition ........................................................ 21
3. Boundary condition identification ............................................................... 23
4. Problem Diagnosis ...................................................................... 40
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POLYMIN 2005
1. INTRODUCTION
1.1 Overview
POLYMIN is an advanced numerical model for solving reactive mass transport problems. The
model can be used to solve one or two-dimensional mass transport problems within a variety of
hydrogeological systems. POLYMIN was originally developed as a research tool to study the
behaviour of acid mine drainage or reactive contaminant plumes within porous media (see Figure 1).
recharge
waste lagoon
monitor well
flow
2000 ppm Cl
shrinking core model
R
r c
C L
recharge
q=0.365m/yr
O 2
Diffusion
sulphurcontining
grain
sand (SBL)
gravel (GRV)
10m
free drainage
Figure 1. Conceptual model domains for the POLYMIN model; top: contaminant plume, bottom:
oxidizing rock waste pile (after Molson et al., 2005).
POLYMIN will run on any computer although it is recommended that the model be run on at least a
Pentium III/500 MHz machine. The memory requirements depend on your application. 2D
simulations may require on the order of 64-128 Mbytes.
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POLYMIN 2005
POLYMIN has been developed with some of the most efficient and powerful numerical algorithms
available. Finite elements are employed for high accuracy and to allow deformable domain
geometry, and the Leismann time-weighting scheme (Leismann and Frind, 1989) has been
incorporated to maintain matrix symmetry which saves memory and execution time. The model
includes one of the most efficient preconditioned conjugate gradient solvers available to solve the
matrix equations.
Custom versions, and executables are available to suit individual needs. Please contact the authors
for available updates. A more recent model, BIONAPL/3D, can also simulate density flow along
with multiple-component NAPL dissolution and reactive transport (Molson, 2001). The POLYMIN
model has most recently been applied by Molson et al. (2005) to waste rock piles, based on flow
systems developed by Fala et al. (2005).
1.2 Capabilities, Assumptions and Limitations
The capabilities of POLYMIN, and its major assumptions and limitations are summarized in Table
1.
Table 1. Summary of the capabilities, assumptions and limitations of POLYMIN.
Capabilities
- 2D or 1D domains.
- fully coupled oxygen diffusion, geochemical
speciation and advective-dispersive mass
transport.
- domain can be heterogeneous and
anisotropic.
- deformable elements can conform to
complex geometry.
- versatile boundary condition options.
- computes concentration breakthrough data
(conc. vs time) at selected points.
Assumptions and Limitations
- non-deforming, isothermal aquifer
- fluid is incompressible.
- chemical reactions are assumed at equilibrium
- flow system read separately
- non-fractured or equivalent porous media (2)
(2)
Research versions also available with 1D and 2D fractures (Yang et al, 1996a,b).
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POLYMIN 2005
1.3 Software Support
If you have questions or comments concerning POLYMIN, or this manual, please contact the
authors at the following address:
John Molson / Dr. E.O. Frind
Department of Earth Sciences
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1
phone: (519) 888-4567 x3959
fax: (519) 746-7484
email: molson@uwaterloo.ca
www: http://sciborg.uwaterloo.ca/~molson/
Montreal address:
J.W. Molson Ph.D. P.Eng.
Dept. of Civil, Geological and Mining Engineering
Ecole Polytechnique, Montreal
john.molson@polymtl.ca
http://www.enviro-geremi.polymtl.ca/
Office: (514) 340-4711 x5189
Home: (514) 935-0610
Adjunct Professor, University of Waterloo
molson@uwaterloo.ca
http://sciborg.uwaterloo.ca/~molson/
John.Molson@polymtl.ca
We would also appreciate hearing about your particular model application and suggestions for
improvement.
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POLYMIN 2005
2. THEORETICAL DEVELOPMENT
2.1 Background
POLYMIN is based on the solutions to the 2D advective-dispersive mass transport equation.
The flow field must be generated by a separate program such as FLONET (Molson & Frind,
2004), however other codes can be used as well, provided the grid is compatible. This version of
the POLYMIN model can read the flow system from either the 2D flow model HYDRUS
(Simunek et al., 1999), or from the 2D saturated flow model FLONET (Molson & Frind, 2004).
(see section 4 for a step-by-step list of how to run the code)
2.2 Mass Transport
Mass transport is governed by the advection-dispersion equation which includes a source/sink
term for equilibrium reactions. The transport equation in POLYMIN for aqueous component k (k
= 1, ..., N c , where N c is the number of components) is of the form:
∂ θ w C
∂ t
k
∂ ⎛
= ⎜
w D
x
θ
∂ i ⎝
ij
∂ C
∂ x
k
j
⎞
⎟
⎠
-
∂
∂ x
i
( q Ck) + R
i
k
(1)
where C k is the concentration of the k th component in the pore water [ML -3 ], q i is the i th
component of the volumetric water flux [LT -1 ], D ij is the dispersion coefficient tensor [L 2 T -1 ],
and R k is the source/sink term for the k th component resulting from geochemical equilibrium
reactions [ML -3 T -1 ]. The components of the dispersion tensor, D ij , are given by:
θ w Dij
= αT
|q| δ ij + ( α L -α
T
q
j
qi
) + θ Dd
τ δ ij
|q|
(2)
where D d is the molecular diffusion coefficient in water [L 2 T -1 ], ⏐q⏐ is the absolute value of the
Darcy fluid flux [LT -1 ], δ ij is the Kronecker delta function, α L is the longitudinal and α T the
transverse dispersivity [L], and τ = θ 7/3 /θ s 2 is a tortuosity factor according to Millington and
Quirk (1961). The tortuosity factor was incorporated into the transport equation to account for
solute diffusion with a spatially variable water content.
Changes to the solid phase due to precipitation-dissolution and sorption-desorption reactions are
represented in POLYMIN by the mass conservation equation:
∂ S
∂t
k
= R
S
k
(3)
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POLYMIN 2005
where S k is the solid phase concentration of the k th solid component, [ML -3 ], and R k S represents
the change in the k th solid component concentration [ML -3 T -1 ]. Further details are provided by
Walter et al. (1994a).
Oxygen Diffusion
Assuming an immobile air phase (convection is neglected), oxygen transport through the
unsaturated porous medium is governed by the 2D equation for oxygen diffusion, expressed as:
θ
eq
2 2
∂ [ O2 ]
a
⎛ ∂ [ O2 ]
a ∂ [ O2
]
a
⎞
= D e ⎜ + - Q
2 2 ⎟
∂t ⎝ ∂ x ∂ z ⎠
O 2
(4)
where θ eq (x,z,t) is the spatially and temporally-variable water phase corrected volumetric air
content [-], D e (x,z,t) is the effective oxygen diffusion coefficient [L 2 T -1 ], and Q O2 (x,z,t) is the
sink term for oxygen consumption due to sulphide mineral oxidation (M O2 /L 3 /T) (see below).
The equivalent air content θ eq in Equation (4) is defined here as θ eq = θ a + Hθ w where θ a is the
air-filled porosity and H is Henry’s Law coefficient for equilibrium oxygen partitioning between
air and water (-). The oxygen diffusion coefficient D e is represented in POLYMIN by the Aachib
et al. (2002) model:
D
e
1 ⎡ p D
a w pw
= ⎢Daθ
a
+ θ
w
θ 2
⎣ H
s
⎤
⎥
⎦
(5)
where D a and D w are the diffusion coefficients in air and water, respectively, and p a and p w are
fitting coefficients; here p a = p w = 3.3 is assumed, as suggested by Aachib et al. (2002).
The coefficient D e , representing diffusion within the air-filled porosity of the unsaturated spoil,
can be represented using models presented by Elberling & Nicholson (1993), Millington &
Quirk (1961), or Aachib et al. (2002).
Sulphide Oxidation
Acid mine drainage is controlled by the oxidation of sulphide minerals, mostly pyrite and
pyrrhotite, within the waste rock. The oxidation of pyrite, for example, can be described in
simplified form by the following stoichiometric equations (Wunderly et al, 1996):
2+
2- +
Fe S 2 + H 2 O +7/2 O2
⇒ Fe + 2 SO4
+ 2 H
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POLYMIN 2005
2+
+ 3+
Fe +1/4 O2
+ H ⇒ Fe +1/2 H 2 O
3+ 2- +
Fe S 2 +1/2 H 2 O +15/4 O2
⇒ Fe + 2 SO4
+ H
The rate of these oxidation reactions, however, is controlled by the availability of oxygen at, and
within the mineral grains. A common approach for modeling this process, and that adopted here,
is the shrinking core model (Levenspiel, 1972) which assumes the sulphide mineral is
uniformally distributed within each spherical grain. Derivations for this model have been
presented by Davis and Ritchie (1986; 1987), Wunderly et al. (1996), and Gerke et al. (1998),
and are not repeated here.
The shrinking core model provides the oxygen sink term Q o in equation (4), defined by
3 ( 1 - θ ) ⎛ r ⎞ [ O 2 ]
R ⎝ r ⎠ H
c
o
= 2 2 ⎜
R -
⎟
c
Q D
a
(6)
where D 2 is the effective diffusion coefficient incorporating the characteristic diffusion
properties of both the water film and the oxidized shell of the pyrite particle, R is the average
radius of the soil particles, r c is the average radius of the unreacted core, and [O 2 ] a is the oxygen
concentration in the air phase in contact with the particle.
From the computed change in the oxidized grain radius (r c ), and knowing the fraction of sulfide
minerals in the grain f s , (M Su /M solids ), the bulk density ρ b [ML -3 ], and ε, the mass ratio of oxygen
to sulphur consumed on the basis of the reaction stoichiometry, the mass of each oxidation
product can be determined for each oxidation time step ∆t oxid (Gerke et al., 1998).
Geochemical Equilibrium Equations
The chemical equilibrium reactions are those provided in the geochemical equilibrium model
MINTEQA2 (Felmy et al., 1983; Allison et al., 1990). MINTEQA2 was derived from combining
the geochemical equilibrium model MINEQL (Westall et al., 1976) with the data base of the
WATEQ2 model (Ball et al., 1979).
The reactions considered are chemical speciation, acid-base reactions, mineral precipitationdissolution,
oxidation-reduction, and adsorption. The chemical model uses the general
transformation-of-the-bases mathematical approach to solve the chemical equilibrium problem
for all of the chemical reaction types (Felmy et al., 1983). The ion-association equilibriumconstant
approach is used to represent the geochemical reactions. The ion-association aqueous
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POLYMIN 2005
model involves three separate constituents; the masses of aqueous species and complexes,
equilibrium constants which relate these complexes in solution, and the individual ion-activity
coefficients for each species. These constituents are related through a system of algebraic
equations that solve for the individual ion activities in a solution, which are in turn used to
predict chemical reaction equilibrium.
Chemical Speciation, Acid-Base Reactions and Redox Reactions
In a solution, there exists a set of chemical components and species. The set of chemical
components is the minimum number of species that uniquely describe a solution and that is
required to be reaction invariant (Mangold and Tsang, 1991). The component mass remains
constant, regardless of the distribution between chemical species in both the aqueous and solid
phases. This mass conservation principle yields a set of linear algebraic equations, with one
equation for each component (Cederberg, 1985).
The total component concentration T k (moles/1000g H 2 O) is the sum of the aqueous-phase
concentration C k and the solid-phase concentration S k , of component k:
T k = Ck
+ S k
(7)
where
C
S
k
k
naq
alk
∑ cl
(8)
l=1
= k = 1, ... N
=
naq
blk
∑ s
k = 1,...
l
N
(9)
l=1
and where c l is the concentration of species l in the aqueous phase (moles/1000g H 2 0), s l is the
concentration of species l in the solid phase (moles/1000g H 2 O), a lk is the stoichiometric
coefficient of component k in species c l , b lk is the stoichiometric coefficient of component k in
species s l , n aq is the number of species in the aqueous phase, and n s is the number of species in
the solid phase.
The total mass of each chemical component must be known to describe a solution. The
distribution of the species included in the component concentrations is estimated by mass-action
equations that form a set of nonlinear algebraic equations, with one equation for each chemical
species. For the aqueous-phase species, these equations are:
N c
alk
χ = K ∏ χ
naq
(10)
l
cl
k=1
k
while for the solid-phase species, they are:
l = 1,...
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POLYMIN 2005
sl
= K
N
c
blk
∏ χ k
ns
(11)
sl
k=1
l = 1,...
where K cl is the equilibrium formation constant for species c l , K sl is the equilibrium formation
constant for species s l in the solid phase, χ k is the activity of component k (moles/1000g H 2 0),
and χ l is the activity of species l (moles/1000g H 2 0).
The stoichiometric mass-balance equations for the components are written in terms of
component concentrations, while the mass action equations are expressed in terms of activities.
The activities, χ l , are related to concentrations, c l , through the individual ionic activity
coefficients, γ l , using the approximation
χ = cl
(12)
l
γ l
The activity coefficients are calculated using the WATEQ, extended Debye-Hückel or Davies
equations (Felmy et al. 1983). The specific equation used is dependent on the availability of
specific solute parameters.
These equations form a set of algebraic equations which are used in the ion-association model to
solve for the individual ion activities given the total component concentrations in solution. The
interrelationships between the species concentrations and activities and the ionic strength cannot
be solved for explicitly but require an iterative solution. MINTEQ uses the Newton-Raphson
iterative technique.
Chemical reactions involving the hydrogen and hydroxide ion are simulated in the chemical
model using the proton condition (Westall et al., 1976; Felmy et al., 1983; Allison et al., 1990).
The proton condition, representing the total analytical component concentration of H + , is the
primary variable used in the transport solution. The H + -value may theoretically be negative
because it does not have the physical interpretation of a total mass of hydrogen but is the change
in H + activity from the reference condition. Similarly, the total calculated mass of H 2 O can also
be negative.
Oxidation-reduction reactions are calculated with MINTEQ using the external redox couple
approach. This approach requires that the initial distribution of the specified redox couples is
known before the chemical equilibrium problem can be solved. This distribution can be
determined from the initial solution component chemistry and the solution pe. MINTEQ permits
selection of redox couples that are set in equilibrium with the solution pe. Other electroactive
species may be considered independent of the pe. Thus, the multivalent species can be reacted
with their respective solid mineral phases without requiring interactions with other multivalent
species. In the present transport model, the total dissolved concentration of each redox state is
transported separately, and the new solution pe is calculated using the activities calculated for
the specified redox couples at the new location. The electron activity, therefore, is not transported
independently.
Sorption
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POLYMIN 2005
The three basic mathematical forms of sorption reaction models, namely isothermal, massaction/ion-exchange,
and surface complexation/electrostatic models, have been incorporated into
MINTEQ (Allison et al., 1990). The isothermal models included are the activity K d adsorption
model, the activity Langmuir adsorption model, and the Freundlich model. The electrostatic
adsorption models available are the constant-capacitance model, the diffuse-layer model, and the
triple-layer model. To date only the ion-exchange model has been verified in the combined
mass-transport chemical-equilibrium model.
Ion-exchange sorption reactions are simulated using the Gaines and Thomas model for ion
exchange (Allison et al., 1990). This model assumes that the surface site is initially occupied by
an exchangeable ion that is released into solution during the exchange process, that the charge on
the surface of the solid remains constant, and that the number of surface sites available for
sorption, expressed as the cation exchange capacity (C.E.C.), is fixed. The ion-exchange
reaction is written as:
vA
vB
B + AB(ad) ⇔ B A(ad) + A
(13)
v A v v v
B
where v A and v B are the change on components A and B respectively, A(ad) and B(ad) are the
adsorbed mass of components A and B. The mass action equation for the above expression is
K
AB
⎛ A(ad)
= ⎜
vA
⎝ [A ]
⎞
⎟
⎠
vB
vB
⎛ [B ]
⎜
⎝ B(ad)
⎞
⎟
⎠
vA
(14)
where the square brackets represent solution activity, and K AB is the selectivity coefficient of
species A with respect to species B.
Mineral Precipitation and Dissolution
Mass-action equations, which relate ion activities and a solid specific solubility product, describe
mineral precipitation and dissolution reactions. These reactions can be written as follows (Walter
et al., 1994a):
A a
B b(s)
⇔ aA (aq)
+ bB (aq)
(15)
The subscripts (s) and (aq) refer to solid and aqueous phases respectively. The thermodynamic
solubility product for a given solid is described by:
K
sp
a
A B
= [ ] [ ]
[ AB]
a
b
b
(16)
where K sp
is the solubility product for the solid.
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POLYMIN 2005
⎛ I.A.P. ⎞
S.I.= log ⎜ ⎟
(17)
⎝ K sp ⎠
If the saturation index is greater than zero, representing supersaturation, there is a tendency for
the mineral to precipitate. When the S.I. is zero, the mineral and the solution are in equilibrium.
If the S.I. is less than zero the mineral is undersaturated, and the tendency is for the mineral to
dissolve. In real geochemical situations, minerals which are super-saturated or undersaturated
may not precipitate or dissolve due to kinetic limitations. These limitations are not addressed in
the current model.
The solid phases incorporated in the data base may be designated as one of three types:
1. A solid which is in infinite supply (reacted to equilibrium),
2. A solid with a finite supply where the initial amount of solid must be specified (moles of
solid per litre of pore water), and
3. A dissolved solid which may precipitate if it becomes supersaturated.
Within an individual chemical simulation, the designation may switch between the last two solid
types. This occurs when a finite-mass solid is completely dissolved, becoming a dissolved solid.
The solid type change is accounted for in the combined chemical-transport model to allow
complete mineral dissolution at an individual node within the spatial domain at any point in time.
Switching solid types is well suited to the coupled geochemical-reaction, solute-transport
problems where sharp changes in solid-phase concentrations may be observed.
The determination of solids that are thermodynamically stable from the array of solids allowed to
precipitate or dissolve is calculated by treating the S.I. (eq. 14) as an inequality. Each solid is
ranked for its tendency to precipitate by dividing the S.I. by the number of ions in the solid
formation reaction. After ranking, the solid with the highest value is allowed to precipitate. All
of the remaining solids are then ranked again and sequentially precipitated or dissolved until all
of the solids considered are undersaturated. A provision is made to insure that if the mass of the
previously precipitated solid becomes negative, that solid will redissolve and the solution
procedure will continue.
Limitations of Geochemical Model
The ion-association model used in MINTEQ to account from deviations from chemical ideality
is valid only for low ionic strengths of 0 - 0.5. The previously-described chemical reactions are
all based on the L.E.A. This assumption means that the reactions modelled are sufficiently rapid
relative to the contaminant travel times through the reacting medium, or that a reaction will go to
equilibrium before a component is transported to another point in space. On a purely
geochemical basis, the majority of the reactions considered in this study adhere to the L.E.A.,
with the possible exception of some solid and redox reactions which are often rate-dependent.
The field results presented by Morin (1983) suggest that both the use of the ion-association
model and the L.E.A. are reasonable at the Nordic Site.
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POLYMIN 2005
Solution Strategy
POLYMIN uses two-step sequential physical-chemical coupling (Walter et al, 1994a) to solve
the reactive transport equations. In this approach, the transport equation is split into a physical
step, and a chemical step:
Step 1 (physical)
n+1 phys
equil
( C k - Ck
) δ(t + ∆t)= Rk
δ(t + ∆t)
k = 1,...,N c
(18)
Step 2 (chemical)
( C
- C
∆t
phys
k
n
k
)
= L( C
k
)
n+1/2
k = 1,...,N
c
(19)
where C k phys is the concentration of component k at the end of the physical step, L represents the
transport operator, δ is the Dirac delta, and n, n+1/2, n+1 relate to the beginning, midpoint, and
end of the time step ∆t, respectively.
The transport model is coupled to the oxygen diffusion and pyrite oxidation modules following
the sequence shown in Figure 1. The simulation over a transport time step ∆t begins with an
iterative solution to the oxygen diffusion and reactive core equations which liberates H + , SO 4 2+ ,
Fe 2+ and Fe 3+ . Because of the nonlinearity for these coupled reactions, the solution is performed
over a smaller sub-time step ∆t oxid , typically 1/10 th - 1/50 th of the transport time step ∆t. These
calculations are very rapid and do not significantly affect the total execution time. The reactive
products are accumulated over each sub-time interval and are added to the existing nodal
concentrations just before the chemical equilibration step.
Following convergence of the diffusion and reactive core equations, a second iterative sequence
begins for the physical/chemical steps. The accumulated oxidation products are added to C k
phys
following the transport step. The equilibrium chemical step is completed independently for each
grid node. An option is available for automatically bypassing this step if the changes in
concentration from the transport and oxidation steps are below a threshold. Typically, the
transport and chemical steps account for approximately 1/3 rd and 2/3 rd of the total execution
time, respectively. Execution times for a 50-year, 13,657-node simulation using a Pentium IV,
3.3Ghz machine were on the order of 40 hours.
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POLYMIN 2005
Transport/Reaction time step ∆t
Oxidation time step (∆t oxid =∆t/20)
Solve oxygen diffusion (O 2
)
Solve core oxidation (r c
)
[O 2
] Converged?
no
yes
Accumulate reaction products (SO 4 2+ , Fe 2+ , Fe 3+ , H + )
Solve physical transport step
Solve chemical step
Components Converged?
no
yes
Figure 2. Flowchart of the Polymin model.
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POLYMIN 2005
Discretization Criteria
Accuracy and stability criteria for the numerical solution of multi-component reactive
transport problems are not yet well defined. The basic requirements, which apply to linear
transport of nonreactive solutes with linear retardation are the Peclet and Courant criteria (Daus
et al., 1985):
Pe=
Co=
v ∆L
≤ 2
D
v ∆t
≤
∆x
Pe
2
(20)
(21)
where v and D are the velocity and dispersion coefficient in the principal (flow) direction,
respectively, ∆L is the effective element length in the flow direction, and ∆t is the time step. In
order to control numerical dispersion and oscillations, eq. (18) is used to constrain the spatial
discretization, while eq. (19) is used to constrain the time step.
In nonreactive transport applications, the Peclet and Courant constraints are often exceeded by a
factor of 2 to 4 since the resulting small oscillations are generally harmless. In reactive
transport, on the other hand, numerical oscillations are more problematic since negative concentrations
can be fatal for the chemical equilibrium model. Some authors eliminate oscillations at
the cost of smearing by using upwinding; we do not recommend this procedure because the
smearing causes fictitious reactions ahead of the actual concentration front. Instead, we seek to
maintain second-order accuracy (or equivalent) in time through time-centred weighting throughout.
Numerical oscillations are controlled by satisfying criteria (19) and (20) everywhere.
For reactive transport, constraints arise out of the basic requirement that the mass reacted per
time step should be in some reasonable relationship to the mass present. In the case of decay or
biodegradation, this requirement leads to a relationship between the time step and the decay
coefficient (Luckner and Schestakov, 1991). For general reactive transport, a useful quantity is
the elemental Damköhler number, defined by Zysset and Stauffer (1992) as the ratio of the
advective time t a = ∆L/v to the reactive time t r = C k B /S k , with C k B being some representative
concentration such as the boundary input or the background concentration of k, and S k being the
reaction rate.
In the case of equilibrium reactions, the reaction rate has no theoretical meaning. We therefore
define the reactive time as:
t
r
=
t+ ∆t
∫
t
t+ ∆t
R
∫ C k dt
t
=
k δ(t+
∆t)
C
k
R
∆t
k
(22)
where C k represents the elemental average concentration over the time step. The Damköhler
17

POLYMIN 2005
number is then defined as:
ta
Dak
=
tr
∆L
Rk
=
v C k
∆t
(23)
The product of the Courant number and the Damköhler number is used by Zysset and
Stauffer (1992) to express the relationship between the reaction rate and the characteristic
concentration of a component. In the case of equilibrium reactions, the equivalent quantity is the
reactive mass ratio ρ k , which can be defined relative to the characteristic (background or input)
concentration C k B , as:
B
B
= Co =
Rk
ρ
k
• Dak
(24)
B
C k
Alternatively, the reactive mass ratio can be defined relative to the actual point concentration
at the end of the physical step C k phys , as:
C
=
Rk
ρ
k
= Co • Dak
(25)
phys
Ck
Since the reactive mass depends on the time step ∆t, either of these relationships can be
used to define a time step constraint. The value of such a constraint will depend on the nature of
the chemical reactions as well as the characteristics of the particular chemical reaction routine
used. For fast reversible reactions, Zysset and Stauffer (1992) recommend ρ k B ≤ 0.01. The
MINTEQ-based model generally reached much higher values (see applications below), for the
scenarios investigated.
The reactive mass ratio ρ k C defined by eq. (23) represents the mass generated or consumed
relative to the mass present at the end of the physical step. Since the mass consumed (R k ≤ 0)
cannot exceed the mass present, ρ k C ≥ - 1. Upper limits on ρ k B and ρ k C have not yet been defined;
it is to be expected that any such limits will depend on the ability of the geochemical model to
equilibrate a perturbed system. By monitoring the performance of the model for various
scenarios under different chemical environments, we expect eventually to be able to define
appropriate constraints.
18

POLYMIN 2005
2.3 Primary Variables and their Dimensions
The following variables must be dimensioned large enough to accommodate the chosen grid size.
These values are set in the PARAMETER statement within the main program.
Array dimension limits: (see parm.inc, parmt.inc, mintran.inc, minteq.inc)
maxne ....
maxnn ....
maxn ....
maxna ....
laa ....
Nxdim …
Nydim …
Nrdim …
maxbt ....
maxtim ....
maxpt …
Maximum number of elements in the transport grid.
Maximum number of nodes in the transport grid.
Maximum number of degrees of freedom (= maxnn - # of fixed nodes).
Total number of non-zero matrix entries in condensed matrix.
(As a conservative approximation, use maxna = 14 * maxn).
PCG solver matrix dimension.
(As a conservative approximation, use laa = 3*maxn+maxna).
maximum number of components
maximum number of aqueous species
maximum number of solid species
Maximum number of "wells" at which breakthrough curves are generated
Maximum number of time steps
maximum number of print times
Note these values all represent maximum limits, they can be equal to, or greater than, the actual
number required.
A conservative estimate for maxna is 14 x maxn, and since this parameter reserves memory for one
of the largest real arrays, it should be minimized if available computer RAM is limited. POLYMIN
computes the minimum vector length (maxna) required by the flow and transport problems and
writes this information to the listing file (look for "vector length"). For more efficient memory use,
these values can be substituted into the PARAMETER statement. To do this, the model must first be
run using an initial estimate for maxna (and hence laa), at least until the correct vector lengths are
computed. The minimum vector length and new value for laa is then entered into the program,
which is then recompiled and rerun for the full simulation. The code will detect if the given array
limits are too small, in which case the execution will terminate with an error message.
19

POLYMIN 2005
Other important variables:
nn
ne
x,y,z
vx,vy,vz
u0,u1,u2
in
........... total number of nodes in the finite element grid
........... total number of elements in finite element grid
........... nodal grid coordinates
........... elemental average linear groundwater flow velocities
........... nodal concentration arrays (at last time step, most recent iteration, and new
solution respectively)
........... element incidence array
2.4 Geochemical Database
The database files used by POLYMIN and their analogous MINTEQA2 files are:
POLYMIN
alk.dbm
analy.dbm
error.dbm
compcp.dbm
type6cp.dbm
thermcp.dbm
MINTEQA2
alk.dbs
analyt.dbs
error.dbs
comp.dbs
type6.dbs
thermo.dbs
Redox and gas reactions can be included in type6cp.dbm and thermcp.dbm database files
within MINTOX and thus do not have their own database files. Modifications to these database
files can be made relatively easily. They are in ascii format and the format/unformat routine
necessary when modifying MINTEQA2 database files is not needed.
To add a component to the databases edit the compcp.dbm file and insert the new
component in the same format as in the comp.dbs MINTEQA2 file. To add reactions, add the
reaction to both the type6cp.dbm and the thermcp.dbm files in the same format as the reaction
occurs in the MINTEQA2 database files. The POLYMIN program does not need to be
recompiled when changes are made to the database files.
20

POLYMIN 2005
2.5 Input/Output File Definition
Table 2. Input/Output files used in POLYMIN.
Unit # Filename: I/O Contents:
5 polymin.dat I primary input data
5 Polymin.in I name of input data file
16 Polymin0.gen O Echoes the input data, prints info while running
various Polymino.aq_ O 2D concentration data for all aqueous components
various Polymino.so_ O 2D concentration data for all solid components
various Brkaq_.out O Breakthrough data (time, concentration) - aqueous
various Brks_.out O Breakthrough data (time, concentration) - aqueous
88 Debug.out O Debug information
2 Thermcp.dbm I Thermodynamic database
3 Compcp.dbm I database
4 Type6cp.dbm I database
10 Alk.dbm I database
7 Analy.dbm I database
13 Error.dbm I database
99 Bckgrndpoly,min I Background concentration data
100 Meshtria.txt I Finite element triangular mesh coordinates, incidences
110 th.txt I Water content
120 Bdy.txt I Boundary nodes
99 Nodeprop.txt I Initial nodal properties (grain radius, porosity, sulphur fraction)
99 v.txt I Element velocities
50 Polymin.ur1 O 2D plotting file for Tecplot (x,z,c k ) – aqueous components
51 Polymin.ur2 O 2D plotting file for Tecplot (x,z,c k ) – solid components
21

POLYMIN 2005
3. DESIGNING A MODEL
Grid Definition & Boundary Conditions
POLYMIN currently supports a 1D or 2D domain discretized using triangular elements. With
triangular elements, the grid can be unstructured, the connectivity (incidence) information is
provided in the meshtria.txt file.
The grid is generated either with the Flonet (Fnpcg) model, or by Hydrus. In either case, the grid is
imported into POLYMIN using the meshtria.txt file.
The element incidence array, which defines the global node numbers connected to each element, is
stored in the array in(l,i) where l is the global element number, and i (=1,2,3) is the local element
node number.
Two examples are provided here to clarify the grid generation procedure. Note these examples are
for demonstration purposes only, and would not be of sufficient resolution for a practical application
since the Peclet and Courant criteria would be violated under most situations.
Transport boundary conditions can be 1 st , 2 nd or 3 rd type (Table 3, Fig. 3.). The default is 2 nd type,
zero-gradient. The bdy.txt file is divided into 2 sections: top and bottom boundary nodes. Currently,
the model is restricted to a fixed oxygen concentration across the top, and a zero-gradient oxygen
boundary at the bottom (the O2 conc. Can also be fixed to zero across the bottom boundary nodes
using lo2fix=.true.. For the aqueous components, the top boundary nodes can be either first or thirdtype,
depending on the value of kcauchy.
The grid numbering is shown in Fig. 4 (for the case of a rectangular grid subdivided into triangles, as
created by FLONET).
22

POLYMIN 2005
Table 3.
Summary of transport boundary conditions available in POLYMIN.
Boundary
Type
Definition
First / Dirichlet c = c 0
Fixed concentration boundary (e.g. a large, wellmixed
source)
Second /
Neumann
∂c = 0
∂n
Zero-concentration gradient (e.g. outflow or
impermeable boundary).
Third / Cauchy q0
0 ∂c
= vc - D
θc
∂ x i
Dispersive flux boundary
(e.g. source with known influx q 0 and
concentration c 0 ).
23

POLYMIN 2005
C=1 0
C=0
or
dc/dx=0
C=0 0
dc/dx=0
Dc/dz=0
Z
X
Figure 3. Typical boundary condition configuration.
4
8
12
3
2
1
18
17
2
1
3
4
16
1
1
Element number
Node number
Figure 4. Typical node and element numbering convention for rectangular-based triangle grid.
24

POLYMIN 2005
4. SAMPLE DATA SET
The example below is used to illustrate the format of the input files polymin.dat and
bckgrndpoly.min. The example is a source of low pH water at the watertable of an unconfined
aquifer.
We begin with the data file for the FLONET model, which is explained further in the FLONET
manual. The polymin.dat file is explained line-by-line below.
FLONET model datafile:
(refer to Molson & Frind (2004) for the FLONET User Guide.
FLONET: HEAD / STREAM FUNCTION MODEL:
FLOW.DATA - SAMPLE DATA FILE -
November, 2000
0 0 -999. ;SSINK
1 1 0 0 1 0 ;kp,kv,kg,kread,ksolv,khk
101 21 200. 10. 1 1 ;NX,NY,XL,YL,NGX,NGY
0 20 0.01 0. ;maxit,nwtl,tol,datum
0 ;WATERTABLE CODE(KW)
1. 0.0 .00 0.0 -0.05 ;watertable shape
1 1 999 1 10.7 ;BOUNDARY CONDITIONS - left side
2 1 999 0 1.000e-8 ;boundary conditions - top
3 1 999 1 10.0 ;boundary conditions - right side
4 1 999 0 0. ;boundary conditions - bottom
-1 ;END BOUNDARY CONDITIONS
-1 ;END INTERNAL DIR NODES
1 4000 0.5e-4 0.5e-4 0.0 0.35 -1 ;hydraulic K triangle elements!
100. 150. 2. 5. 1.e-3 1.e-3 0. .35 -1 ;high-K lense
0 0 0 0 0.e-4 0.e-4 0. 0.35 -1 ;indexed
25

POLYMIN 2005
Sample POLYMIN Input Data File (polymin.dat)
Poly triangle version
1.0 0.5 0.0 ;WP,WA,WB,Leissman terms
0 50.0 0 0 1 0 0 ;KMAS,PTIME,KTS,kiter,kbypass,kint,kdim=1 axisymmetric
0 7 2 0 0 ;KPRT,NPRT,LPRT,N1,N2
0.1 0.5 1. 5. 10. 20. 50. ;(PRNTT(I),I=1,NPRT)
200 20 2 9 ;NEX,NEZ,NVTYP,NGTYP
40. 50. 1000. ;XL,ZL,CONF
0.06 0.35 10. 1836. .0003 0.9 ;core: fs2i,por2i,temp2i,rhob2i,ox1i,uradius1i
0 0 0 ;IS1,IS2,NCHS
0. 0. false ;vx,vz,lnoflx(t: zero water velocity)
0.5 0.05 0.005046 ;Al,At,DD
10.0 0.0 14 8 0 ;TEMP,FIONS,NNN,NR,NAS
0 0 3 0 4 0 0 0 0 0 0 ;IFL(11)
0 0 0 ;IADS,NUMADS,IABG
0 ;ntsn
1 1 2 2 3 3 4 4 5 5 6 6 7 0 0 0 ;KPLT(I),I=1,NNN
0 1 2 3 4 5 6 7 0 0 0 0 ;KPLTS(I),I=1,NR
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 ;KPNT(I),I=1,NNN
1 1 1 1 1 1 1 1 1 1 1 0 ;KPNTS(I),I=1,NR
2.000E-03 1.375E-02 ;CA TOLERANCE AND RELATIVE VALUES
2.000E-03 2.490E-02 ;MG FROM NICKEL3
2.000E-03 1.093E-02 ;NA "
2.000E-03 5.140E-03 ;K "
2.000E-03 4.252E-04 ;CL "
2.000E-03 1.380E-02 ;CO3 "
2.000E-03 3.390E-02 ;SO4 "
2.000e-03 1.000e-06
;MN
2.000E-03 2.468E-05 ;FE2 "
2.000E-03 1.249e-04 ;FE3 "
2.000e-03 1.000e-04 ;h4sio4 new 03/09
2.000E-03 5.711E-03 ;AL new 03/09
2.000E-03 1.309E-02 ;H "
2.000E-03 1.000E+00 ;E "
t f 2
;loxy(t=oxidation), ldonly(t=diff.only), 2=Aachib
f
;lo2fix(t=o2-conc,bottom=0)
0.050 50 0.001 30 1.e-6 0.265 ;gradius,no2step,oxtol,maxo2it,d2,o2atm
4970 5746 4993 3902 2948 ;breakthrough node numbers
5032 5903 3255 1377 5280 ; "
0.0 5.0 .005 5 50 -1 ;t0,t1,dt,maxit(trans,chem),kprint
0.265 ;O2 atm conc.
26

POLYMIN 2005
Input options
1.0 0.5 0.0 ;WP,WA,WB,Leissman terms
0 50.0 0 0 1 0 0 ;KMAS,PTIME,KTS,kiter,kbypass,kint,kdim
0 7 2 0 0 ;KPRT,NPRT,LPRT,N1,N2
0.1 0.5 1. 5. 10. 20. 50. ;(PRNTT(I),I=1,NPRT)
where:
wp,wa,wb are the Leisman weighting terms (leave these as is)
kmas - mass weighting
= 0 for lumped mass matrix
= 1 for consistent mass matrix
ptime - time to save solution to restart file
kts - restart option
= 0 for normal start
= to use restart option, read initial conditions from file
kiter = 0 for sequential physical-chemical coupling,
= 1 for iterative coupling
kbypass= 0 for minteq solution everywhere,
= 1 for minteq bypass when calculated changes from transport solution are small
kint = 0 for direct integration
= 1 for numerical integration (added 1995 by jwhm)
kdim = 0 for 2D
= 1 for axisymmetric
kprt - flag to print intermediate solutions
nprt - number of print times
lprt - flag for printout type for plotting
= 1 for id simulations, conc vs time at exit boundary
= 2 for 2d simulation
= 3 for 1d conc vs distance profiles
= 4 for 1d simulations,conc vs time at two distance ( nodes n1 and n2)
= 5 for 1d vertical simulations conc. vs depth
n1,n2 - nodes on 1d simulation distance profiles to print out
prntt - print/plot flag, print out at nprt times
27

POLYMIN 2005
Grid parameters
200 20 2 9 ;NEX,NEZ,NVTYP,NGTYP
40. 50. 1000. ;XL,ZL,CONF
c
c
c
c
c
c
c
c
c
c
c
c
nex,nez = number of elements in respective directions
nx,nz = number of nodes in respective directions
nvtyp = type of velocity field
1 - unidirectional flow
2 - velocities read from flonet
ngtyp = type of grid
1 - constant element length and/or widths
2 - variable element length and/or widths
3 - read in grid coordinates
xl,zl = x and z lengths of rectangular grid
conf = conversion factor to account for the unit
conversion between concentrations and flux rates
Note: the grid parameters nex,nez,xl,zl are read but not used (they originated from a previous
version using rectangles). The grid information is instead provided in the input file of
meshtria.txt.
Default material properties
(some of these parameters are over-written by data in nodeprop.txt)
0.06 0.35 10. 1836. .0003 0.9 ;core: fs2i,por2i,temp2i,rhob2i,ox1i,uradius1i
fs2i = fraction of sulphur
por2i = porosity
temp2i = temperature
rhob2 = bulk density
ox1i = initial oxygen concentration
uradius1i = initial fraction of unoxidized code
28

POLYMIN 2005
Data Block 1
0 0 0 ;IS1,IS2,NCHS
0. 0. false ;vx,vz,lnoflx(t: zero water velocity)
0.5 0.05 0.005046 ;Al,At,DD
10.0 0.0 14 8 0 ;TEMP,FIONS,NNN,NR,NAS
0 0 3 0 4 0 0 0 0 0 0 ;IFL(11)
0 0 0 ;IADS,NUMADS,IABQ
0 ;ntsn
is1, is2 = source nodes (only used if ntsn>0)
nchs = skip factor for source nodes
vz, vz = fixed velocities (only used if nvtyp=1)
lnoflx … not used
al, at,dd = longitudinal, transverse dispersivities (m), dd = coefficient of diffusion (m 2 /day)
c temp = solution temperature, isothermal
c fions = ionic strength variation flag
c nnn = number of components (original number does not include
c water or sulphur, but is added after minteq call)
c nns = value to keep track of the original value for nnn
c nr = number of chemical reactions
c nas = number of adsorbing components (not used in minteq)
c
c
c
c
c
c
c
c
c
c
c
c
ifl(11) = list of minteq chemistry flags
1 = coralk
2 = idebug
3 = icharge
4 = iprint
5 = niter
6 = iphvry
7 = isorp
8 = iprdct
9 = kkdav
10 = kkthr
11 = iact
ntsn = number of source nodes
temp [R], temperature in o C, fions [R], the ionic strength variation option (see Felmy et al.
1984),nnn [R], number of chemical components not including water or elemental sulphur, nr [R],
number of chemical reactions, nas [R], number of adsorbed components (these are also included
29

POLYMIN 2005
in the nnn value).
ifl(11) [I], an array of 11 values which are equal to the MINTEQA2 input options. A thorough
description of these options (except for ifl(11)) is given in Felmy et al. 1984. ifl(11) = IACT,
activity correction option, =0 use activity corrections, =1 don’t use any activity corrections (i.e.
γ‘s =1).
iads [I], adsorption model flag, =0 for no adsorption, =1 for ion exchange (the only adsorption
model tested in MINTRAN), numads [I], number of adsorbing surfaces, iabq [I] a number (1-7)
indicating the type of adsorption model used in MINTEQA2 (use 4 = ion exchange).
Print output of components
1 1 2 2 3 3 4 4 5 5 6 6 7 0 0 0 ;KPLT(I),I=1,NNN
0 1 2 3 4 5 6 7 0 0 0 0 ;KPLTS(I),I=1,NR
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 ;KPNT(I),I=1,NNN
1 1 1 1 1 1 1 1 1 1 1 0 ;KPNTS(I),I=1,NR
c plot options
c
c kplt = plot counter,for aqueous phases
c greater than 0 - plot to file o.aq* 0 - no plot
c kplts = plot counter for solid phases
c greater than 0 - plot to file o.so* 0 - no plot
c print options
c
c kpnt = print counter,for aqueous phases
c greater than 0 - plot to file o.gen 0 - no plot
c kpnts = print counter for solid phases
c greater than 0 - plot to file o.gen 0 - no plot
c similarly for printing kpnt, kpnts
30

POLYMIN 2005
Tolerance and relative values
2.000E-03 1.375E-02 ;CA TOLERANCE AND RELATIVE VALUES
2.000E-03 2.490E-02 ;MG FROM NICKEL3
2.000E-03 1.093E-02 ;NA "
2.000E-03 5.140E-03 ;K "
2.000E-03 4.252E-04 ;CL "
2.000E-03 1.380E-02 ;CO3 "
2.000E-03 3.390E-02 ;SO4 "
2.000e-03 1.000e-06
;MN
2.000E-03 2.468E-05 ;FE2 "
2.000E-03 1.249e-04 ;FE3 "
2.000e-03 1.000e-04 ;h4sio4 new 03/09
2.000E-03 5.711E-03 ;AL new 03/09
2.000E-03 1.309E-02 ;H "
2.000E-03 1.000E+00 ;E "
tol - component tolerance values as a fraction of the representative component concentration
relative value - the component representative concentration, either the component background
value of the cauchy source concentration, whichever is highest
Oxidation Parameters
t f 2
;loxy(t=oxidation), ldonly(t=diff.only), 2=Aachib
f
;lo2fix(t=o2-conc,bottom=0)
0.050 50 0.001 30 1.e-6 0.265 ;gradius,no2step,oxtol,maxo2it,d2,o2atm
where
loxy = true to include pyrite oxidation
ldonly = true to simulate oxygen diffusion only
idmodel : diffusion model =0 Millington & Quirk; =1 for Elberling =2 for Aachib
lo2fix = true if O2 concentration at bottom boundary is to be fixed at zero
= false to leave O2 conc free
gradius = initial grain radius (m)
no2step = number of oxidation time steps within each transport time step
oxtol = oxygen concentration tolerance
maxo2it = maximum iterations for oxygen convergence
d2 = diffusion coefficient within grains (m2/year)
o2atm = oxygen concentration at boundary
31

POLYMIN 2005
Breakthrough points
4970 5746 4993 3902 2948 ;breakthrough node numbers
5032 5903 3255 1377 5280 ; "
each number represents a node at which breakthrough curves will be assembled (time vs.
concentration – into files brkaq_.out and brks_.out)
Time Step Data
0.0 5.0 .005 5 50 -1 ;t0,t1,dt,maxit(trans,chem),kprint
0.265 ;O2 atm conc.
T0 = initial time (years)
T1 = final time (years)
Dt = time step (years)
Maxit = maximum iterations for oxidation/reaction/transport
Kprint = print frequency (output files polymin.ur1, polymin.ur2 updated every kprint th time step)
32

POLYMIN 2005
Background aqueous chemistry
The background (initial) aqueous chemistry data for POLYMIN is contained in the file
bckgrndpoly.min. An example of this file is included at the end of this section.
There is one line for the each of the background component values. The first variable on these
lines is idx(nnn) [I] , the component I.D. number (see the comp.dbm data file or Felmy et al.
1984), the second variable is T(nnn) [R], the total analytical component concentration in
moles/kg, or for the case of an adsorbed component the concentration of the surface sites in eq/l.
The third variable is gx(nnn) [R], the guess for the log of the activity for the component , use
zero if a good initial guess is not known and for H + and e - components use the pH and pe values
respectively. The final variable of these lines is stad(nnn) [R], the reaction stoichiometry for the
adsorbed phase components (i.e. Na-S); for dissolved components, enter zero.
The total component concentrations (T(nnn)) are determined from the chemical analysis of the
solutions of interest. Often the chemistry will have to be modified to be used in MINTRAN or
POLYMIN by MINTEQA2. This would have to be done for one of the following reasons: for a
solution of known pH, the initial proton condition must be determined by fixing the pH to give
the initial value for the total analytical concentration of H + component, for the simulation of
redox reactions, the distribution of the multi-valence elements must be predetermined from the
solution pe (same procedure as fixing the pH) and e- (idx=1) must be included as a component
(T=0.0), and a type 6 reaction, and for ion-exchange reactions the dissolved and adsorbed phases
must both be included as components with the initial surface site concentration of the adsorbed
phase determined from the cation exchange capacity (CEC) and the individual selectivity
coefficients of the ion-exchange reactions (K s ). For ion-exchange reactions, the thermodynamic
data base (file thermo.dbm) must be modified. Finally, chemical analyses are generally not
perfectly charge balanced and it is advised that the initial background chemistry be charge
balanced with a non reactive anion or cation. In summary, run the chemical data through
MINTEQA2 and use the equilibrated results as input into MINTRAN or POLYMIN.
33

POLYMIN 2005
Background solid chemistry
The background (initial) solid chemistry data for POLYMIN is also contained in the file
bckgrndpoly.min. An example of this file is included at the end of this section.
The following lines are for the background reaction values, three lines for each reaction.
lty(nr) [I], MINTEQA2 designated reaction type 2-6 (see Felmy, 1984). lrx(nr) [I], is the
MINTEQA2 reaction type, = 1 for gas, = 2 for solid, =3 for redox reaction.
idys(nr) [I], reaction identification number (see type6.dbm file), gks(nr) [R], the new log K of
the reaction, dhs(nr) [R], the new enthalpy of the reaction (use 0.0 for the last two values and
they will default to the value in the thermodynamic data base), cons(nr) [R], the initial total
mass of a type 4 solid (use 0.0 for all other reaction types in moles of solid per litre of pore
water.
nc [I], number of components in the reaction , (idd(nc) [I], stoc(nc) [R])×nc. where idd is the
identification number (as in idx) and stoc is the stoichiometry of the component in the reaction
(+ or -)
idnrx [I], is the reaction identification number for a reaction which will be taken out of the
reaction sequence once the background chemistry has been equilibrated. This option has been
used to initially set the CO 2 for an open system then remove this reaction to represent a closed
system. This option has not been well used and it is recommended to leave this value as 0.
ntsn [I], is the number of source nodes which have a chemical composition different then the
background nodes. If this value is zero then the subroutine SRCHEM is not called and the
following Source Chemistry Section inputs are not required.
34

POLYMIN 2005
Input File: Bkgrndpoly.min
(refer to MINTEQ User Guide for further information, see Felmy et al., 1983; Allison et al.,
1990)
This file defines the initial background aqueous and solid chemistry. The chemistry is applied
from nodes ix1-ix2 in the x-direction, and from iy1-iy2 in the y-direction. The values urmin and
urmax were used in a previous version to restrict application of the background chemistry to
only certain ranges of grain radii (see Gerke et al., 1998). This feature is no longer supported but
these values must still be entered. The initial chemistry is assumed uniform throughout the
domain.
1 101 1 21 0.0 1.0 -1 ;ix1,ix2,iy1,iy2, urmin,urmax background,-1 to end
150 4.000E-03 -1.86 0.0 ;CA b/g main tailings IDX,T,GX,STAD
460 3.200E-03 -1.68 0.0 ;MG "
500 1.100E-03 -1.96 0.0 ;NA "
410 5.140E-04 -2.29 0.0 ;K "
180 0.500E-03 -3.37 0.0 ;CL "
140 0.200E-03 -1.93 0.0 ;CO3 "
732 1.000E-02 -1.53 0.0 ;SO4 "
470 3.000E-04 0.0 0.0 ;MN "
280 2.468E-05 -3.61 0.0 ;FE2 "
281 1.000e-04 -7.90 0.0 ;FE3 "
770 1.000e-04 0.0 0.0 ;H4SIO4 "
030 1.000E-03 -8.24 0.0 ;AL "
330 1.000E-03 0.0 0.0 ;H "
001 0.000E+00 0.0 0.0 ;E "
3 3 ;LTY,LRX SOLID & REACTION VALUES
2812800 0.0 0.0 0.0 ;FE2/FE3 IDYS,GKS,DHS,CONS
0 ;NC,(IDD,STOC)*NC
4 2 ;LTY,LRX
5015001 0.0 0.0 .1 ;CALCITE IDYS,GKS,DHS,CONS [mol/l(solid)]
2 150 1.00 140 0.0 ;NC,(IDD,STOC)*NC
4 2 ;
2077004 0.0 0.0 1.0 ;AMORPHous SILICATE
1 770 1.00 ;
4 2 ;
2003003 0.0 0.0 1.0 ;GIBBSITE
2 30 1.00 330 -3.00 ;
5 2 ;
5028000 0.0 0.0 0.0 ;SIDERITE
2 280 1.00 140 1.00 ;
5 2 ;
2028100 0.0 0.0 0.0 ;FERRIHYDRITE
2 281 1.00 330 -3.00 ;
4 2 ;
6015001 0.0 0.0 1.0 ;GYPSUM
2 150 1.00 732 1.00 ;
6 4 ;
001 0.0 0.0 0.0 ;e-
0 ;
0 ;idnrx
35

POLYMIN 2005
y y
10
5
0
10
5
0
10
flow system
O 2
pH
y
5
y
y
0
10 SO 4
5
0
10 Fe(III)
5
0
0 50 100 150 200
Distance (m)
POLYMIN simulation results for example data set (provided in previous section), after 10 years.
36

POLYMIN 2005
5. STEP BY STEP INSTRUCTIONS
POLYMIN is a mass transport model which assumes a steady state velocity field. The velocity
field can be obtained either from the FLONET model for saturated systems (Molson & Frind,
2004), or from the HYDRUS2D model (Simunek et al., 1999). In either case, the output files
must converted to POLYMIN input format by running a “processing” code (process_flonetpoly.exe,
or process_hydrus-poly.exe).
Steps 1 & 2 below assume the flow field will be derived from the FLONET model. If running
directly from a HYDRUS flow simulation, steps 1 & 2 can be skipped and replaced with steps 1b
& 2b which follow.
1. Simulate the flow system (refer to the FLONET user guide)
• edit the fnpcg.data file
• make sure kp=1 to get required output files
• run fnpcg.exe
• transfer these file to your transport directory: flow.vxyst, flow.incid, flow.nodes
2. Convert flow system file formats for transport:
• edit process_flonet-poly.in to adjust gradius, fs2, and source nodes for oxidation
• run process_flonet-poly.exe
• you should now have these files for input to POLYMIN:
meshtria.txt, bdy.txt, v.txt, nodeprop.txt, th.txt
(mesh, boundary nodes, velocities, nodal properties & water content)
3. Prepare transport input files
• edit polymin.in (must contain the name of your input file; e.g. polymin.dat)
• edit polymin.dat (primary input file), check path to data base
• edit bkgrndpoly.min (contains background chemistry data)
• check database files:
alk.dbm, analy.dbm, compcp.dbm, error.dbm, thermcp.dbm, type6cp.dbm
4. Run polymin5.exe
5. Interpret results:
• Check if job ran completely: check polymino.gen
• Aqueous component output: polymin.ur1
(Tecplot-compatible file of x,z,O2, ph, aqueous components, etc)
• Solid species (minerals) output: polymin.ur2 (x,z, solid species)
• Edit polyminbrkaq_nn.out and polyminbrks_nn.out files – replace “999” in the
third line with the number of data lines (= number of time levels)
• Use Tecplot to visualize the above files
37

POLYMIN 2005
Option for running POLYMIN with HYDRUS2D:
If running POLYMIN from a HYDRUS flow simulation, Steps 1 & 2 above are replaced
with the following steps as shown below:
1: Run HYDRUS2D to get these files: meshtria.txt, th.txt, v.txt
which contain, respectively, the grid, moisture content and velocities
The files th.txt and v.txt may contain data for several time levels. The number of time
levels should be kept less than or equal to 13 as POLYMIN will only read a maximum of
13, and will only use the data from the last time level.
2: Edit the file process_hydrus-polymin.in to set default host and secondary material
properties, and to set the nodes for the breakthrough points:
host material: dgrav,porgrav,fsgrav (diameter, porosity, sulphide fraction)
secondary: dsable,porsable,fssable
breakthrough nodes: ipoint(i), i=1,10
The host material is the default material, initially assigned to all elements. The secondary
material properties are assigned to elements that lie within quadrilaterals defined in the file:
geofile.dat – which is created in the next step.
3: Create the file: "geofile.dat" which contains the coordinates of at least one quadrilateral
which defines the locations of the secondary material
Note: you can create "geofile.dat" manually, or by using Tecplot.
If using Tecplot:
(a) follow steps 1-2, then run the processing code to get a Tecplot file of the grid.
(b) use the Tecplot file to plot the mesh, then define the quadrilaterals using the
mouse and export them to a geometry file, and rename this file to geofile.dat
(c) edit the geofile.dat file to remove unecessary text
Here is a sample format for the file geofile.dat:
gs112dH
; title
GEOMETRY
0.00, 20.00 ;origin of quadrilateral 1 – vertex 1
0.000 -0.5 ;vertex 2 (dx,dz)
6. -0.5 ;vertex 3
5.000 0.00 ;vertex 4
0.0 0.0 ;vertex 1 (dx=0, dz=0)
GEOMETRY ;origin of quadrilateral 2 – vertex 1
0.00, 10.01
0.000 -0.5
31. -0.5
30. 0.00
0.0 0.0 ;vertex 1 (dx=0, dz=0)
Up to 100 quadrilaterals can be defined. Note that the coordinates for the quadrilateral vertices
are relative to each origin, i.e. the coordinates are given as dx, dz relative to vertex.
38

POLYMIN 2005
6. TIPS AND TECHNIQUES
1. Design your flow system correctly
Many problems in simulating mass transport are derived from a poor definition of the flow field. A
little more time spent on generating a realistic flow field will save a great deal of time in unnecessary
transport simulations.
Also check the grid Peclet and Courant criteria before running your transport problem.
2. Other tips:
- review the output listing file polymino.gen, if possible while the model is running. This will help
you identify errors in your input data before wasting valuable simulation time. Early detection of
convergence problems may also be made.
- to speed execution, use kint = kintv = 0 (direct integration) for all regular grids generated by
POLYMIN. The small grid deformations produced as the model grid conforms to the free watertable
are usually not sufficient to warrant use of the numerical integration options.
- if you are uncertain about an input data entry, check the source code; many comments are included
to describe the input data.
39

POLYMIN 2005
7. PROBLEM DIAGNOSIS AND SOLUTIONS
Table 4. Problem Diagnosis: POLYMIN Model
Problem: Cause: Solution:
PCG Matrix solver error message and
program termination
- Array dimensions are too small for
your grid
- fault in grid definition or time
intervals
- increase array dimensions in
parameter statement and recompile
- check input data file for grid
definition, and time interval data
solution not converging
- time step too large
- check tolerance, and maximum
iteration limit
- decrease time step
bandwidth insufficient error - array limits are too small - increase array limits in parameter
statement, and recompile
I/O error on unit 5
- fault in data file
- check all input data lines, line
continuation flags (more = +/- 1)
40

POLYMIN 2005
8. REFERENCES
Aachib, M., M. Aubertin, and M. Mbonimpa, 2002. Laboratory measurements and predictive
equations for gas diffusion coefficient of unsaturated soils. Proceedings of the 55 th Canadian
Geotechnical and Joint IAH-CNC and CGS Groundwater Speciality Conferences, Niagara Falls,
October 2002, pp. 163-171.
Aachib, M., M. Aubertin, and R.P. Chapuis, 1998a, ‘Essais en colonne sur des couvertures avec
effets de barrière capillaire’, 51st Canadian Geotechnical Conference, Edmonton, Alberta,
Canada, vol. 2, 837-844 (in French).
Allison, J.D., D.S. Brown, and K.J. Novo-Gradac, 1991. MINTEQA2/PRODEFA2, a
geochemical assessment model for environmental systems: Version 3.0 User's Manual.
EPA/600/3-91/021, Environmental Research Laboratory, Office of Research and Development,
U. S. Environmental Protection Agency, Athens, Georgia 30613, U.S.A.
Bain, J., D.W. Blowes, W.D. Robertson, E.O. Frind, Modelling of sulfide oxidation with reactive
transport at a mine drainage site, Jour. Contam. Hydrol., 41(1-2), 23-47, 2000.
Bain, J.G., K.U. Mayer, D.W. Blowes, E.O. Frind, J.W. Molson, R. Kahnt, and U. Jenk,
Modeling the closure-related geochemical evolution of groundwater at a former uranium mine,
Jour. Contam. Hydrol., Vol. 52 (1-4), 109-135, 2001.
Blowes, D.W., & C.J. Ptacek, Acid neutralization mechanisms in inactive mine tailings, In: The
Environmental Geochemistry of Sulfide Mine-Wastes, Short Course Handbook 22 (eds. D.W.
Blowes and J.L. Jambor), pp. 271-292, Mineralogical Association of Canada, Waterloo, Ontario,
1994.
Davis, G.B. and A.I.M. Ritchie, A model of oxidation in pyritic mine waste: Part 3: Importance
of particle size distribution. Appl. Math. Model. 11: 417-422, 1987.
Elberling, B., R. V. Nicholson, and D. J. David, Field evaluation of sulphide oxidation rates,
Nordic Hydrology, 24, 323-338, 1993.
Fala, O, Étude des écoulements non saturés dans les haldes à stériles à l’aide de simulations
numériques, Mémoire de maîtrise (M.Sc.A., unpublished), Génie Minéral, Dépt. CGM, École
Polytechnique de Montréal, Canada, 2002.
Fala, O., Aubertin, M., Molson, J.W., Bussière, B., Numerical Modelling of Flow and Capillary
Barrier Effects in Unsaturated Waste Rock Piles, accepted in Mine Water & the Environment,
2005.
41

POLYMIN 2005
Fala, O., M. Aubertin, J.W. Molson, B. Bussière, G. W. Wilson, R. Chapuis, V. Martin,
Numerical modelling of unsaturated flow in uniform and heterogeneous waste rock piles, In:
Proceedings Sixth International Conference on Acid Rock Drainage (ICARD), Australia, July
2003.
Felmy, A.R., D.C. Girvin, and E.A. Jenne. 1983. MINTEQ: A Computer Program for
Calculating Aqueous Geochemical Equilibria. Report, U.S. Environmental Protection Agency,
Washington D.C., 62 p..
Fredlund, D.G. and R. Rahardjo, Soil Mechanics for Unsaturated Soils, John Wiley & Sons, Inc.
New-York, 1993.
Gerke, H.H., J.W. Molson, and E.O. Frind, Modelling the effect of chemical heterogeneity on
acidification and solute leaching in overburden mine spoils, Journal of Hydrology, Special Issue:
Reactive Transport Modelling, vol. 209, 166-185, 1998.
Hurst, S., P. Schneider & G. Meinrath, Remediating 700 years of mining in Saxony: A heritage
from ore mining, Mine Water and the Environment, 21: 3-6, 2002.
Jambor, J.L., Mineralogy of sulfide-rich tailings and their oxidation products, Chapter 3:
Mineralogical Association of Canada Short Course Handbook on Environmental Geochemistry
of Sulfide Mine Wastes (J.L. Jambor & D.W. Blowes Eds.), Waterloo, May, 1994.
Johnson, R.H., D.W. Blowes, W.D. Robertson and J.L. Jambor, The hydrogeochemistry of the
Nickel Rim mine tailings impoundment, Sudbury, Ontario, J. Contam. Hydrol. 41, 49-80, 2000.
Jurjovec, J., C. Ptacek, and D. Blowes, Acid neutralization mechanisms and metal release in
mine tailings: A laboratory column experiment, Geochimica et Cosmochimica Acta, 66(9),
p.1511-1523, 2002.
Lefebvre, R., D. Hockley, J. Smolensky, A. Lamontagne, Multiphase transfer processes in a
waste rock pile producing acid mine drainage, 2. Applications of numerical simulation, J.
Contam. Hydrol., 52, 165-186, 2001.
Levenspiel, O., Chemical Reaction Engineering. 2 nd Edition, J. Wiley & Sons, New York, 1972.
Mayer, K.U., E.O. Frind, and D.W. Blowes, Multicomponent reactive transport modeling in
variably saturated porous media using a generalized formulation for kinetically controlled
reactions, Water Resour. Res. 38(9), 13:1-21, 2002.
Mbonimpa, M., M. Aubertin, M. Aachib and B. Bussiere, Diffusion and consumption of oxygen
in unsaturated cover materials, in submission to: Canadian Geotechnical Journal, 2003.
Millington, R. J., J.M. Quirk, Permeability of porous solids. Trans. Faraday Soc. 57: 1200-1207,
1961.
42

POLYMIN 2005
Molson, J.W., Fala, O., Aubertin, M., Bussière, B., Numerical simulations of sulphide oxidation,
geochemical speciation and acid mine drainage in unsaturated waste rock piles, Journal of
Contaminant Hydrology, Volume 78, Issue 4, Pages 343-371, August 2005.
Molson, J.W., Frind, E.O., FLONET v5.0 User Guide, Dept. of Earth Sciences, University of
Waterloo, 2004.
Newman, L.L., G.M. Herasymiuk, S.L. Barbour, D.G. Fredlund, T. Smith, The hydrogeology of
waste rock dumps and a mechanism for unsaturated preferential flow, Proceedings: 4 th ICARD
Vancouver 1997. pp. 551 – 564, 1997.
Poirier, P., M. Roy, Acid mine drainage characterization and treatment at La Mine Doyon,
Proceedings: Fourth International Conference on Acid Rock Drainage (ICARD, Vancouver),
1487-1497, Nat. Res. Canada., Ottawa, 1997.
Ritchie, A.I.M., Sulfide oxidation mechanisms: controls and rates of oxygen transport, Chapter
8: Mineralogical Association of Canada Short Course Handbook on Environmental
Geochemistry of Sulfide Mine Wastes (J.L. Jambor & D.W. Blowes Eds.), Waterloo, May, 1994.
Ritchie, A.I.M., Oxidation and gas transport in piles of sulfidic material, Mineralogical
Association of Canada, 2003.
Romano, C. G., K.U. Mayer, D.R. Jones, D.A. Ellerbroek, and D.W. Blowes, Effectiveness of
various cover scenarios on the rate of sulphide oxidation of mine tailings, Jour. Hydrology 271,
p.171-187, 2003.
Schneider, P., K. Osenbrueck, P.L. Neitzel, and K. Nindel, In-situ mitigation of effluents from
acid waste rock dumps using reactive surface barriers – a feasibility study, Mine Water and the
Environment, 21: 36-44, 2002.
Simunek, J, Sejna, M and van Genuchten, Th M, The HYDRUS-2D software package for
simulating the two-dimensional movements of water, heat, and multiple solutes in variablysaturated
media, Version 2.0, U.S. Salinity Laboratory, 1999.
Sracek, O., M. Choquette, P. Gelinas, R. Lefebvre, and R.V. Nicholson, Geochemical
characterization of acid mine drainage from a waste rock pile, Mine Doyon, Quebec, Canada,
Jour. Cont. Hydrol., in submission, 2003.
Steefel, C.I., and K.T.B. MacQuarrie, Approaches to modeling of reactive transport in porous
media, In: Reviews in Mineralogy (P. Lichtner, C. Steefel & E. Oelkers, Eds.), Volume 34,
Mineralogical Society of America, p. 83-129, 1996.
Walter, A.L., E.O. Frind, D.W. Blowes, C.J. Ptacek, and J.W. Molson, Modeling of
multicomponent reactive transport in groundwater 1. Model development and evaluation, Water
Resour. Res. 30(11): 3137-3148, 1994a.
43

POLYMIN 2005
Walter, A.L., E.O. Frind, D.W. Blowes, C.J. Ptacek, and J.W. Molson, Modeling of
multicomponent reactive transport in groundwater 2. Metal mobility in aquifers impacted by acid
mine tailings discharge. Water Resour. Res. 30(11): 3149-3158, 1994b.
Wunderly, M.D., D.W. Blowes, E.O. Frind, and C.J. Ptacek, Sulfide mineral oxidation and
subsequent reactive transport of oxidation products in mine tailings impoundments: A numerical
model. Water Resour. Res. 32(10): 3173-3187, 1996.
44

POLYMIN 2005
Example 1: Geochemical modelling of AMD from a waste rock pile
From base case in Molson et al. (2005)
Elev. (m)
20
15
10
(a) Oxygen, 2 years
[O 2
]g/L
0.25
0.2
0.15
0.1
0.05
0
10
9.5
9
24 25
5
0
Elev. (m)
20
15
10
(b) pH, 2 years
pH
7
6
5
4
3
10
9.5
9
24 25
5
0
0 10 20 30 40 50
Distance (m)
Top: Oxygen concentrations at 2 years, bottom: pH at 2 years.
45

POLYMIN 2005
Polymin.dat for Example 1:
Poly Waste Rock Pile.
1.0 0.5 0.0 ;WP,WA,WB,Leissman terms
0 50.0 0 0 1 0 0 1 ;KMAS,PTIME,KTS,kiter,kbypass,kint,kdim=0 2d, =1 axisymmetric,kcauchy
0 7 2 0 0 ;KPRT,NPRT,LPRT,N1,N2
0.1 0.5 1. 5. 10. 20. 50. ;(PRNTT(I),I=1,NPRT)
100 129 2 9 ;NEX,NEZ,NVTYP,NGTYP
40. 50. 1000. ;XL,ZL,CONF
0.06 0.35 10. 1836. .0003 0.9 ;core: fs2i,por2i,temp2i,rhob2i,ox1i,uradius1i
0 0 0 ;IS1,IS2,NCHS
0. 0. false ;vx,vz,lnoflx(t: zero water velocity)
0.5 0.05 0.005046 ;Al,At,DD
10.0 0.0 14 8 0 ;TEMP,FIONS,NNN,NR,NAS
0 0 3 0 4 0 0 0 0 0 0 ;IFL(11)
0 0 0 ;IADS,NUMADS,IABG
0 ;ntsn
1 1 2 2 3 3 4 4 5 5 6 6 7 0 0 0 ;KPLT(I),I=1,NNN
0 1 2 3 4 5 6 7 0 0 0 0 ;KPLTS(I),I=1,NR
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 ;KPNT(I),I=1,NNN
1 1 1 1 1 1 1 1 1 1 1 0 ;KPNTS(I),I=1,NR
2.000E-03 1.375E-02 ;CA TOLERANCE AND RELATIVE VALUES
2.000E-03 2.490E-02 ;MG FROM NICKEL3
2.000E-03 1.093E-02 ;NA "
2.000E-03 5.140E-03 ;K "
2.000E-03 4.252E-04 ;CL "
2.000E-03 1.380E-02 ;CO3 "
2.000E-03 3.390E-02 ;SO4 "
2.000e-03 1.000e-06 ;MN
2.000E-03 2.468E-05 ;FE2 "
2.000E-03 1.249e-04 ;FE3 "
2.000e-03 1.000e-04 ;h4sio4 new 03/09
2.000E-03 5.711E-03 ;AL new 03/09
2.000E-03 1.309E-02 ;H "
2.000E-03 1.000E+00 ;E "
t f 2 ;loxy(t=oxidation), ldonly(t=diff.only), 2=Aachib
f
;lo2fix(t=o2-conc,bottom=0)
0.050 50 0.001 30 1.e-6 0.265 ;gradius,no2step,oxtol,maxo2it,d2,o2atm
927 5247 6226 3559 696 ;breakthrough node numbers
796 1007 633 904 4538 ; "
0.0 20. .005 5 100 -1 ;t0,t1,dt,maxit(trans,chem),kprint
0.265 ;o2bdy
150 2.00E-05 ;CA influx to aquifer IDX,UIN CAUCHY BDRY
460 2.00E-05 ;MG " new rainwater - Mayer+Appelo
500 7.000E-05 ;NA "
410 5.000E-06 ;K "
180 2.0E-05 ;CL "
140 2.0e-05 ;C03 "
732 7.400e-05 ;SO4 "
470 1.0E-06 ;Mn
280 2.200E-16 ;FE2 "
281 1.000E-08 ;FE3 "
770 1.000e-08 ;h4sio4
030 1.000E-10 ;AL "
330 0.35E-04 ;H "
001 0.000E-01 ;E
46

POLYMIN 2005
Bkgrndpoly.min (from Example 1)
1 101 1 130 0.0 1.0 -1 ;ix1,ix2,iy1,iy2, urmin,urmax background
150 4.000E-03 -1.86 0.0 ;CA b/g main tailings IDX,T,GX,STAD
460 3.200E-03 -1.68 0.0 ;MG "
500 1.100E-03 -1.96 0.0 ;NA "
410 5.140E-04 -2.29 0.0 ;K "
180 0.500E-03 -3.37 0.0 ;CL "
140 0.200E-03 -1.93 0.0 ;CO3 "
732 1.000E-02 -1.53 0.0 ;SO4 "
470 3.000E-04 0.0 0.0 ;MN "
280 2.468E-05 -3.61 0.0 ;FE2 "
281 1.000e-04 -7.90 0.0 ;FE3 "
770 1.000e-04 0.0 0.0 ;H4SIO4 "
030 1.000E-03 -8.24 0.0 ;AL "
330 1.000E-03 0.0 0.0 ;H "
001 0.000E+00 0.0 0.0 ;E "
3 3 ;LTY,LRX SOLID & REACTION VALUES
2812800 0.0 0.0 0.0 ;FE2/FE3 IDYS,GKS,DHS,CONS
0 ;NC,(IDD,STOC)*NC
4 2 ;LTY,LRX
5015001 0.0 0.0 .1 ;CALCITE IDYS,GKS,DHS,CONS [mol/l(solid)]
2 150 1.00 140 0.0 ;NC,(IDD,STOC)*NC
4 2 ;
2077004 0.0 0.0 1.0 ;AMORPHous SILICATE
1 770 1.00 ;
4 2 ;
2003003 0.0 0.0 1.0 ;GIBBSITE
2 30 1.00 330 -3.00 ;
5 2 ;
5028000 0.0 0.0 0.0 ;SIDERITE
2 280 1.00 140 1.00 ;
5 2 ;
2028100 0.0 0.0 0.0 ;FERRIHYDRITE
2 281 1.00 330 -3.00 ;
4 2 ;
6015001 0.0 0.0 1.0 ;GYPSUM
2 150 1.00 732 1.00 ;
6 4 ;
001 0.0 0.0 0.0 ;e-
0 ;
0 ;idnrx
47

POLYMIN 2005
Example 2: Geochemical evolution of a low-pH plume
Steady State Flow System from FLONET:
15
z(m)
10
5
0
0 20 40 60 80 100
Distance (m)
pH and Selected mineral buffers after 24 years:
z(m) z(m) z(m) z(m)
pH
15
10
5
0
15 CaCO 3
4 5 6 7 pH
10
5
Calcite
0
15 FeCO 3
0 0.01 0.02 CaCO 3
10
5
Siderite
0
15 AL(OH) 3
10
0 0.02 FeCO 3
5
Gibbsite
0
0 20 40 60 80 1000 0.02 Al(OH) 3
Distance (m)
48

POLYMIN 2005
Input Data file for Example 2:
(Note: This example uses the original input format of the MINTRAN model)
2D Elliot Lake simulation .. Jan 1993 ;Problem Title (A32)
1.0 0.5 0.0 ;WP,WA,WB,Leissman terms
0 8.0 0 0 1 ;KMAS,PTIME,KTS,kiter,kbypass
0 4 2 0 0 ;KPRT,NPRT,LPRT,N1,N2
8.0 16.0 24.0 48 ;PPRTT(I)
200 56 2 3 ;NEX,NEZ,NVTYP,NGTYP
1.000e+02 1.400E+01 1.000e+03 ;XL,ZL,CONF
0 0 0 ;IS1,IS2,NCHS
0 0 0 3 ;KB(4),BOUNDARY CODES
0. 0. ;vx,vz
3.000e+00 3.000E-02 5.046e-03 3.000e-01 1.250e-01 ;AT,AL,DD,POR,DT
25.0 0.0 16 12 00 ;TEMP,FIONS,NNN,NR,NAS
0 0 3 0 4 0 0 0 0 0 0 ;IFL(11)
0 0 0 ;IADS,NUMADS,IABG
1 201 1 57 -1 ;xstart,xend, zstart,zend, more ... for background chemistry
150 5.390E-03 0.0 0.0 ;CA BACKGROUND CHEMISTRY IDX,T,GX,STAD (mol/L)
460 1.935E-03 0.0 0.0 ;MG "
500 1.305E-03 0.0 0.0 ;NA "
410 6.651E-05 0.0 0.0 ;K "
180 1.033E-03 0.0 0.0 ;CL "
140 3.376E-03 0.0 0.0 ;CO3 "
732 7.479E-03 0.0 0.0 ;SO4 "
470 4.731E-05 0.0 0.0 ;MN "
770 3.350E-04 0.0 0.0 ;H2SIO4 "
280 1.021E-03 0.0 0.0 ;FE2 "
281 1.405e-14 0.0 0.0 ;FE3 "
030 1.100E-05 0.0 0.0 ;AL "
211 1.000e-08 0.0 0.0 ;CR "
600 1.000e-08 0.0 0.0 ;PB "
330 4.552E-03 -6.59 0. ;H "
001 0.000E+00 -2.65 0. ;E "
3 3 ;LTY,LRX SOLID & REACTION VALUES
2812800 0.0 0.0 0.0 ;FE2/FE3 IDYS,GKS,DHS,CONS
0 ;NC,(IDD,STOC)*NC
4 2 ;LTY,LRX
5015001 0.000E+00 000.00 01.954E-02 ;CALCITE IDYS,GKS,DHS,CONS (conc in moles solid /L water)
2 0000150 001.00 0000140 001.00 ;NC,(IDD,STOC)*NC
4 2 ;LTY,LRX
2003003 0.000E+00 000.00 02.507E-03 ;GIBSITE
2 30 1.00 330 -3.00 ;
4 2 ;
2077004 0.000E+00 000.00 04.069e+01 ;AMORPHOUS SILICA
1 770 1.00 ;
4 2 ;
5028000 0.0 0.0 4.222e-03 ;SIDERITE
2 280 1.00 140 1.00 ;
4 2 ;
2028100 0.0 0.0 1.865e-03 ;FERRIHYDRITE
2 281 1.00 330 -3.00 ;
5 2 ;
6015001 0.0 0.0 0.0 ;GYPSUM
2 150 1.00 732 1.00 ;
5 2 ;
49

POLYMIN 2005
6060003 0.0 0.0 0.0 ;ANGLESITE
2 600 1.00 732 1.00 ;
5 2 ;
5060000 0.0 0.0 0.0 ;CERRUSITE
2 600 1.00 140 1.00 ;
5 2 ;
5047000 0.0 0.0 0.0 ;RHODOCHROSIT
2 470 1.00 140 1.00 ;
5 2 ;
2021102 0.0 0.0 0.0 ;CR(OH)3 (A)
2 211 1.00 330 -1.00 ;
6 4 ;
001 0.0 0.0 0.0 ;e-
0 ;
0 ;idnrx
0 ;NTSN
1 0 0 0 2 3 4 5 0 6 7 8 8 8 0 0 ;KPLT(I),I=1,NNN
0 1 2 0 3 4 5 6 7 8 8 0 ;KPLTS(I),I=1,NR
1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 ;KPNT(I),I=1,NNN
0 1 1 0 1 1 1 1 1 1 1 0 ;KPNTS(I),I=1,NR
1.000E-03 1.625E-02 ;CA TOLERANCE AND RELATIVE VALUES
1.000E-03 1.935E-03 ;MG "
1.000E-03 1.386E-03 ;NA "
1.000E-03 8.136E-04 ;K "
1.000E-03 1.578E-02 ;CL "
1.000E-03 7.353E-03 ;CO3 "
1.000E-03 4.997E-02 ;SO4 "
1.000E-03 7.837e-03 ;MN "
1.000E-03 2.080E-03 ;H2SIO4 "
1.000E-03 3.131E-02 ;FE2 "
1.000E-03 3.512E-05 ;FE3 "
1.000E-03 4.298E-03 ;AL "
1.000E-03 1.332E-04 ;CR "
1.000E-03 1.520E-05 ;PB "
1.000E-04 1.394E-02 ;H "
1.000E-03 1.000E-00 ;E "
1 ;NTSC #OF CONSTANT TIME STEPS
3 ;FBF,NTB,CAUCHY BDRY FLUX,#BDY SEG
.1419 20 ;recharge flux, #elements across top for this group
150 6.917E-03 ;CA CAUCHY INFLUX IDX,UIN
460 1.935E-03 ;MG "
500 1.305E-03 ;NA "
410 6.651E-05 ;K "
180 1.033E-03 ;CL "
140 3.936e-03 ;C03 "
732 7.479e-03 ;SO4 "
470 4.731E-05 ;MN "
770 1.938E-03 ;H4SIO2 "
280 5.358E-05 ;FE2 "
281 2.317E-08 ;FE3 "
030 1.275E-07 ;AL "
211 1.000e-08 ;CR "
600 1.000e-08 ;PB "
330 4.585E-03 ;H "
001 0.000e-00 ;E "
.1419 40 ;recharge flux, #elements across top
150 1.078E-02 ;CA CAUCHY INFLUX IDX,UIN
460 9.686E-04 ;MG "
50

POLYMIN 2005
500 1.386E-03 ;NA "
410 8.136E-04 ;K "
180 1.578E-02 ;CL "
140 4.920e-04 ;CO3 "
732 4.997e-02 ;SO4 "
470 7.837E-03 ;MN "
770 2.080E-03 ;H4SIO2 "
280 3.061E-02 ;FE2 "
281 1.987E-07 ;FE3 "
030 4.298E-03 ;AL "
211 1.332e-04 ;CR "
600 1.520e-05 ;PB "
330 1.055E-03 ;H "
001 0.000e-00 ;E "
.1419 140 ;recharge flux, #elements across top
150 6.917E-03 ;CA CAUCHY INFLUX IDX,UIN
460 1.935E-03 ;MG "
500 1.305E-03 ;NA "
410 6.651E-05 ;K "
180 1.033E-03 ;CL "
140 3.936e-03 ;C03 "
732 7.479e-03 ;SO4 "
470 4.731E-05 ;MN "
770 1.938E-03 ;H4SIO2 "
280 5.358E-05 ;FE2 "
281 2.317E-08 ;FE3 "
030 1.275E-07 ;AL "
211 1.000e-08 ;CR "
600 1.000e-08 ;PB "
330 4.585E-03 ;H "
001 0.000e-00 ;E "
1 2 3 4 5 ;breakthrough nodes
0.000E+00 48.00E+00 1.250e-01 30 ;T0,T1,DT,MAXIT (time step data)
51