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Groundwater modelling for large-scale mine dewatering in Chile: MODFLOW or FEFLOW?

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  • Fresh Water Solutions Ltd.

Abstract and Figures

This paper reviews and compares the numerical features of MODFLOW and FEFLOW that are specifically relevant to the development of a groundwater flow model for open pit dewatering. Two dewatering models are presented, which were developed using respectively MODFLOW (McDonald and Harbaugh, 1996) and FEFLOW (Wasy Gmbh, 2002), and were used to improve the design of dewatering / depressurisation systems for two large open pit copper mines in Northern Chile. The comparison considers how the two modelling packages represent complex fault systems, dewatering wells, groundwater seepage into the pit and phreatic surface movements during dewatering. Practical considerations on the pre/post-processing facilities and the computational requirements of MODFLOW and FEFLOW in the two applications are also provided.
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Groundwater modelling for large-scale mine
dewatering in Chile: MODFLOW or FEFLOW?
SARAH ALLOISIO
Water Management Consultants Ltd., 23 Swan Hill, Shrewsbury, SY1 1NN, United Kingdom
e-mail: salloisio@watermc.com
BLAIR R. DOUGLAS, ROWAN MCKITTRICK, PHILIPPE
PRIGNEAU
Water Management Consultants Ltda., Alcantara 44, Piso 3, Las Condes, Santiago, Chile
Abstract This paper reviews and compares the numerical features of
MODFLOW and FEFLOW that are specifically relevant to the development
of a groundwater flow model for open pit dewatering. Two dewatering
models are presented, which were developed using respectively
MODFLOW (McDonald and Harbaugh, 1996) and FEFLOW (Wasy Gmbh,
2002), and were used to improve the design of dewatering / depressurisation
systems for two large open pit copper mines in Northern Chile. The
comparison considers how the two modelling packages represent complex
fault systems, dewatering wells, groundwater seepage into the pit and
phreatic surface movements during dewatering. Practical considerations on
the pre/post-processing facilities and the computational requirements of
MODFLOW and FEFLOW in the two applications are also provided.
Key words open pit mining; dewatering; finite-difference and finite-element grid; faults;
fractured media; phreatic surface; pit seepage.
INTRODUCTION
A fundamental requirement for the successful development of mining operations in
large open pits, where the excavation can extend several hundred metres below the
phreatic surface, is the design of an effective dewatering and depressurisation system.
Inadequate drainage of the floor and slopes of a pit during its excavation can lead to
hydraulic pore pressure build-up and eventually slope failure, which has serious safety
and operational implications. Dewatering and depressurisation activities have a
significant impact on the overall cost of mine production. Therefore, an effective
dewatering / depressurisation plan can reduce the cost of ore production by a
considerable amount.
Numerical groundwater flow models can be used to assist in the design of dewatering /
depressurisation schemes, by simulating the impact of alternative schemes on
piezometric heads and seepage flows reporting to the pit. This allows to identify the
optimal location and pumping schedule for dewatering wells and to assess the
performance of other dewatering methods, such as underground drainage tunnels. In
order to be a useful design and planning tool, a groundwater flow model for open pit
dewatering / depressurisation should be able to reproduce adequately the following:
Detailed representation of the phreatic surface along the pit slopes.
Highly heterogeneous media and geological structures, such as fractures and
faults dipping at an arbitrary angle, which can cause compartmentalisation and
hinder free drainage of the pit slopes.
Dewatering wells the can penetrate multiple hydrogeological units and where
yield decreases with increasing drawdowns.
Vertical, horizontal and inclined underground drains.
Groundwater seepage into the pit throughout the excavation.
Development of perched conditions, typically occurring where a high
permeability unit underlying a low permeability layer is being pumped.
The ability of the modelling packages MODFLOW (McDonald and Harbaugh, 1996)
and FEFLOW (Wasy Gmbh, 2002) to represent the above features has been reviewed
and compared. This has been done with reference to the dewatering / depressurisation
models developed for two large open pit copper mines in Northern Chile.
THE MODFLOW MODEL
The purpose of this model is to assess the efficiency of a system of drainage tunnels in
providing dry conditions during the northward extension of an open copper pit. The
domain of this model is shown in Figure 1. The domain is included in a rectangle of
area 3.7 × 6.8 km, which is divided by a uniform finite-difference grid with 40 m
spacing into 93 rows and 171 columns. A uniform grid was chosen after trying several
configurations based on different degrees of refinement of the pit expansion area,
which were found to cause instability and convergence problems. It is noted that the
use of a uniform grid is far from ideal, because it introduces an unnecessary level of
resolution outside the pit expansion area, where a simplistic representation of the
groundwater system is sufficient to reproduce the regional flow pattern. In this respect,
a finite-element grid would allow the local refinement of the pit area without
computational difficulties.
A NNE-SSW sub-vertical fault runs across the pit area and acts as a preferential flow
path.
Fig. 1 Domain and grid of the MODFLOW model
The inflow and outflow components to the model include:
Inflows: industrial recharge from mains leakage and leaching of tailings.
Natural recharge is negligible, as the pit is located in the extremely dry region
of the Atacama Desert, Northern Chile.
Outflows: evaporation from tailings; regional southeasterly groundwater flow;
discharge into drainage tunnels; groundwater abstraction from dewatering
wells; flow not captured by the drainage system, which reports to the pit as
seepage.
In order to assess the performance of the drainage system during the implementation of
the pit expansion plan, it is important to simulate adequately the following:
fault across the pit area
flow intercepted by the drainage tunnels
dewatering wells with drawdown-dependent yield (if present)
seepage into the pit.
Fault structure
The fault running across the pit area in NNE-SSW direction is a linear sub-vertical
structure associated with an alteration zone, which coincides with a paleochannel in
the gravel deposits and represents a zone of enhanced groundwater flow. It is
represented in the model three top layers as a zone of higher hydraulic conductivity.
Drainage Tunnels
Groundwater discharge into the tunnels is reproduced using MODFLOW drain cells,
whereby flow, Q, is calculated as:
Q = C × (h – h
drain
)
where:
h is the groundwater head
h
drain
is the drain elevation
C is the drain conductance. This parameter can be initially estimated using Goodman’s
formula (Freeze and Cherry, 1979), and subsequently modified during model
calibration, to reproduce historic flow data.
Dewatering wells
The dewatering plan for the pit under consideration comprises only drainage tunnels,
therefore no wells were represented in the model. However, in other pit-dewatering
models developed in MODFLOW, dewatering wells located in the pit area have been
represented using MODFLOW stream cells. The well mechanism is generally not used
since this requires flow rates to be specified a priori, which can lead to over or under
pumping. The head dependent mechanism employed by stream cells, as well as drain
and river cells, enables the pumping rate to decrease as groundwater heads decline, in a
similar way to real well yields. The elevation of the stream cells is set to the base
elevation for each layer penetrated by the well, except for the lowest layer, where it is
set at the well bottom elevation.
Pit Seepage
Inflow to the pit that is not intercepted by dewatering / depressurisation systems
discharges on the pit face as seepage. This can be represented by means of different
MODFLOW boundary conditions, namely rivers, drains or evaporation. If rivers or
drains are used to simulate seepage, a high conductance value is typically employed to
allow free drainage, and the reference elevation of the boundary cells within the pit,
h
riv(drain)
, is set equal to the pit topographic level. If the evaporation package is used,
then the maximum evaporation rate is set equal to the potential evaporation estimated
in the pit area and the extinction depth is typically set to 1 m. In the model under
consideration, pit seepage was reproduced by means of drain cells. Difficulties related
to the use of both types of boundary conditions arise when the extension of the pit
varies in time and the pit extends through multiple layers. In the MODFLOW model,
outflow mechanisms remain constant during each year. Between years, however, the
pit topography and the position of the evaporative surface change. Also, some of the
drainage tunnels are removed during the pit excavation and replaced by dewatering
wells. The main problems encountered when reproducing pit expansion through
multiple layers in MODFLOW are:
The preparation of the river, drain or EVT file representing seepage in a series
of pit expansion phases and in different model layers is complex and time-
consuming, even with the assistance of existing pre-processing software
packages.
The model grid is fixed in time. As a result, when large changes in pit
topography occur between one year and the next the model can leave isolated
blocks of saturated cells high above the pit topography. This is a numerical
problem of no consequence to the validity of model results but it causes
unrealistic spikes in cross-sections of phreatic water levels. One solution to the
isolated spikes on cross-sections through the model domain uses MODFLOW
river or drain mechanism to remove the small volumes of water left in the
isolated cells and convert them into ‘dry’ cells. It was also found that the use of
MODFLOW-Surfact reduces the development of these ‘perched’ cells.
Due to the fixed model grid, ‘dry’ cells develop when the phreatic surface drops
below the base of the top layer. When the water table fluctuates across multiple
layers, re-wetting of the dry cells is required. Although a re-wetting option is
available, MODFLOW often encounters stability and convergence problems in
such drying/re-wetting conditions. In this respect, MODFLOW-Surfact
provides a better handling of drying and rewetting of grid blocks, where vertical
flow components and delayed yield are accounted for.
THE FEFLOW MODEL
This model was developed for a large open pit copper mine in the far north of Chile,
which is at its initial stage of development. The objectives of the model are:
1. investigate drawdown and pore pressure profiles resulting from the currently
planned dewatering / depressurisation system
2. test alternative dewatering strategies to assist in future mine planning and
geotechnical optimisation of the pit slope angles.
Figure 2 shows the model domain and grid. The area of the modelled domain is
approximately 203 km
2
. The finite-element grid has a coarse resolution (average 200
m spacing) outside the pit area, where detailed information on the groundwater system
is not available and a broad representation of regional flow can provide adequate
boundary conditions for the pit area. The model mesh is refined within the pit, where
node separation is about 25 m, and around the existing dewatering wells, where node
spacing is about 10 m. Local mesh refinement in the pit area and around the dewatering
wells does not affect the model stability and provides a more accurate simulation of the
phreatic surface and cones of drawdown than would be achievable using a finite-
difference scheme.
Fig. 2 Domain and grid of the FEFLOW model
WELL 1
WELL 3
WELL 2
WELL 4
WELL 5
WELL 6
Blue lines: surface
water network
Blue circles:
constant head
boundaries
Red line: planned
final pit extension
The groundwater system can be divided into basic hydrostratigraphic units, depending
upon the degree of alteration of the rock mass, rock type, structure, groundwater yield
and hydraulic conductivity. These units are represented in the model by means of 8
layers, as shown in Figure 3. It is noted that strongly argillised rock, which forms a
low conductivity and yield zone, is located above weakly argillised rock, where
conductivity is estimated to be up to 100 times higher. Dewatering by means of deep
wells is therefore likely to induce perched conditions in the low-conductivity unit, with
residual pore pressures that will affect slope stability. Groundwater flow in the pit area
is also strongly influenced by alteration and geological structures. The lithologic
discontinuities, faults and fractures present in the pit form leaky flow barriers, which
act to compartmentalise the aquifer.
Fig. 3 Main hydrostratigraphic units and vertical discretisation of the FEFLOW model
The most important features that the FEFLOW model needs to reproduce accurately in
order to assess the performance of the current and alternative dewatering /
depressurisation plans include:
faults and fractures with arbitrary dip
development of perched conditions
seepage into the pit
dewatering wells with drawdown-dependent yield
Layer 1
E
W
Unit 1
Unit 2a
Unit 2b
Unit 3
Unit 3b
Unit 2a
Alluvium
Colluvium
Unit 1: strongly argillised rock (low conductivity and storage)
Unit 2a: weakly argillised rock (high conductivity and storage)
Unit 2b: weakly argillised rock (very low conductivity and storage)
Unit 3: moderately altered fresh rock (moderately high conductivity and storage)
Unit 3a: Deep fresh rock (low conductivity and storage)
Unit 3b: deep fresh rock (very low conductivity and storage)
Layer 2
Layer 3
Layer 4
Layer 5
Layer 6
Layer 7
Layer 8
Planned final pit extension
Inclined faults and fractures
The main faults associated with alteration zones are represented as distinct zones of
hydraulic conductivity and storage. As the faults have dips of around 45 degrees,
several layers are required to provide an accurate step-wise approximation of the fault
inclination and geometry. However, many layers would reduce significantly the model
computational efficiency. For the model under consideration, the use of eight layers
was thought to achieve a good compromise between vertical resolution and
computation demand.
Minor faults and fractures that act as preferential flow paths are mainly linear
structures. When zones of distinct hydraulic parameters are used to represent these
structures, their width can be considerably overestimated if the portion of the model
mesh where they are located is not highly refined. Alternatively, FEFLOW can use
discrete feature elements. These are 1-D and 2-D elements connecting two or more
nodes within the same ‘slice’ (surface separating two model layers) or corresponding
nodes at adjacent slices, where flow is simulated according to specified laws for flow
porous media and channels. Discrete feature elements permit a much more accurate
representation of linear structures. However, they cannot connect two arbitrary nodes
across different slices, so that inclined faults and fractures still have to be
approximated by a combination of horizontal and vertical elements.
Perched conditions
In the pit area under study, wells are designed to operate through the low-conductivity
strongly argillised rock and the underlying high-conductivity weakly argillised rock
units. Due to the contrast in hydraulic conductivity, dewatering is likely to take place at
a much faster rate in the lower unit, thus inducing the development of perched
conditions in the upper unit. Flow occurring in the unsaturated zone underlying the
perched aquifer can be reproduced in FEFLOW in two ways:
simulating groundwater flow using an equation for unsaturated or variably
saturated media based on a moveable model mesh
using a phreatic slice configuration, where the model mesh is fixed and
unsaturated flow is approximated by scaling conductivity according to the
saturated thickness in an element.
The former approach provides a rigorous treatment of the multiple free-surface
problem, but it is computationally demanding, can cause convergence difficulties and
requires the assignment of unsaturated characteristics for which data are seldom
available. The latter is considered a pseudo-unsaturated modelling approach (Diersch,
2002), which provides an approximate representation of unsaturated flow, but is simple
and computationally robust. The pseudo-unsaturated method was employed in the
model under consideration, but was subsequently discarded because it could not
integrate adequately with the use of a moveable mesh to simulate the top phreatic
surface, as described below.
Pit seepage
Groundwater seepage into the pit slopes and floor is represented in the FEFLOW
model by means of transfer boundary nodes. The flow mechanism of transfer nodes is
analogous to the river, drain and stream mechanisms in MODFLOW, as it depends on
the difference between the groundwater head and a reference elevation and on a
conductance term. In the FEFLOW model, the reference elevation of transfer nodes is
set equal to the pit topography and boundary constraints are applied to allow only
outflows. The vertical expansion of the pit through different hydrogeological units can
be reproduced much more easily in FEFLOW than in MODFLOW. This is because the
BASD (Best Adaptation to Stratigraphic Data) technique is available in FEFLOW,
whereby all model slices except the base move to reflect changes in the phreatic
surface during the pit excavation. Therefore, pit seepage can be simulated by assigning
transfer nodes only at the model top slice and by lowering their reference elevation as
the pit deepens. As the pit excavation and dewatering progress, the moveable model
slices collapse to mirror deepening of the pit and drop in the water table, as shown
schematically in Figure 4. The change in hydraulic properties as the slices move due to
the excavation into different formations is also accounted for.
Fig. 4 Schematic representation of BASD during the pit excavation
Whilst leading to a simpler and more accurate representation of pit seepage, the use of
time-variant transfer nodes on a moveable mesh could not be used to represent the pit
expansion through time, as it was found to increase simulation times dramatically. In
order to simulate the pit development, a series of models, each representing a pit phase,
was developed and run sequentially. This solution is obviously less practical than
running a single time-variant simulation.
4000
4100
4200
4300
4400
3900
Elevation [masl]
Year 1
Year 2
Year 3
Year 4
Year 5
Pit elevation
(h
drain
)
Model slice
Dewatering wells
During the model calibration, abstraction from dewatering wells was represented using
well boundary nodes. Wells penetrating multiple slices were reproduced using the bore
option in FEFLOW, whereby well nodes are connected by a high-conductivity and
storage element, so that no vertical head gradient develops between well nodes located
on different slices.
In order to assess the performance of alternative dewatering / depressurisation
schemes, the dewatering wells were represented using constant head boundary nodes
constrained by flow. Constant heads were set equal to 5 m above the bottom of the
screen of the dewatering wells. The upper flow constraint was set equal to the largest
pumping rate estimated for each well, and the lower constraint was set equal to zero, in
order to prevent injection of water.
Table 1 Comparison of approaches available in MODFLOW and FEFLOW to represent relevant
features of a groundwater flow model for open pit dewatering / depressurisation
Feature MODFLOW
approach Advantages (+) /
Disadvantages (-) of
MODFLOW
approach
FEFLOW
approach Advantages (+) /
Disadvantages (-)
of FEFLOW
approach
Linear
geological
structures
(faults,
fractures)
Zones of distinct
hydraulic
conductivity and
storage
+ Simple assignment
and modification
-
Overestimation of
structure width
without high mesh
refinement
-
Step-wise
approximation of
inclined structures
requiring several
layers
٠Zones of
distinct hydraulic
conductivity and
storage
٠
Discrete feature
elements
(Same as in
MODFLOW
approach)
+ Accurate
representation of
linear structures
- Step-wise
approximation of
inclined structures
requiring several
layers
Pit
expansion
٠Refinement of
finite-difference
grid
٠
Time-variant
head-dependent
boundary cells in
different layers
- Instability /
convergence problems
due to irregular grid
-
Laborious setup
+ Simulation of time-
variant pit expansion
is computationally
feasible
٠Local
refinement of
finite-element
grid
٠
Transfer cells
set on the top
moveable surface
+ Accurate and
computationally
robust simulation
of phreatic surface
+ Simple setup
- Simulation of
time-variant pit
expansion is highly
computationally
demanding
MODFLOW vs. FEFLOW
The summary of the advantages and limitations of the approaches available in
MODFLOW and FEFLOW to simulate the most critical features of a groundwater flow
model used in open pit dewatering / depressurisation are summarised in Table 1.
Other relevant issues that emerged during the development of the MODFLOW and
FEFLOW groundwater flow models for pit dewatering / depressurisation pertain the
following:
I/O data format. MODFLOW produces an ASCII output file that includes data on
the model settings and parameters, as well as on simulated groundwater heads and
flows. It is therefore possible to check the model setup and analyse the results outside
pre-post processing packages. This is not the case in FEFLOW, where input and output
files are prepared in binary format and cannot be analysed outside FEFLOW graphics
interface.
Pore pressure cross-sections. Easy extraction of pore-pressure profiles along
specified sections is of primary importance in a pit-dewatering model, because pore-
pressure profiles represent the input of geotechnical models employed to assess slope
stability. None of the MODFLOW post-processing packages currently available
provides pore pressure cross-sections as direct output. In the MODFLOW
implementation presented in this paper, cross-sections of pore pressure were
constructed by means of dedicated spreadsheets. FEFLOW can provide pore pressure
values along a section at all model layers, but performs no vertical interpolation, so
Table 1 (continue) Comparison of approaches available in MODFLOW and FEFLOW to represent
relevant features of a groundwater flow model for open pit dewatering / depressurisation
Feature MODFLOW
approach Advantages (+) /
Disadvantages (-) of
MODFLOW
approach
FEFLOW
approach Advantages (+) /
Disadvantages (-)
of FEFLOW
approach
Perched
conditions Not possible - ٠Unsaturated
flow equation
٠
Phreatic slice
configuration
+ Rigorous
solution
-
Computationally
demanding and
parameter
intensive
+ Simple and
computationally
robust
- Coarse
approximation of
unsaturated flow
Dewatering
wells with
drawdown-
dependent
yield
٠Head-dependent
boundary cells in
different layers
+ Simple assignment
- Inaccurate cone of
drawdown due to
limited grid refinement
- Not possible to
simulate in-well
drawdown
٠Flow
constrained-
constant head
boundary nodes
in different layers
+ Simple
assignment
+
Accurate cone of
drawdown due to
local grid
refinement
- Not possible to
simulate in-well
drawdown
that external processing is still required.
Time-variant simulations. These are performed in MODFLOW according to
stress periods and time steps specified a priori, so that inflows and outflows must be
averaged in time to reflect the time discretisation. Conversely, FEFLOW employs
adaptive time step refinement, where time steps are defined according to the time
resolution of input and output flows and the magnitude of changes in groundwater
heads and flows.
REFERENCES
Diersch H-J. G. (2002) Treatment of free surface in 2D and 3D groundwater modelling. White Papers Vol. I, Wasy
Software Feflow – Finite Element Subsurface Flow & Transport Simulation System, 67-100.
Freeze R. A., Cherry J. A.. (1979) Groundwater. Prentice Hall, Englewood Cliffs, NJ 07632.
McDonald M. G., Harbaugh A. W. (1996) A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model.
USGS.
Wasy Gmbh (2002) User’s Manual. Wasy Software Feflow Finite Element Subsurface Flow & Transport Simulation
System.
Article
Full-text available
Rock mass has force equilibrium which can be disturbed due to changes in rock mass conditions, both by naturally as well as human activities. In response, rock masses could have instability to reach new equilibrium and trigger landslides. Unstable slopes will affect the safety, economic and social factors. Groundwater has its own problems in mining management. Pore water pressure can cause uplift force and reduce the strength of the rock mass forming slopes and affect the slope stability. The study area has groundwater level relatively close to surface and causes the slope to be in nearly saturated condition. This research aims to study of the effect of groundwater levels on the stability of coal mine slopes in the study area. The research method includes collecting primary data through field observations to collect related technical data and secondary data collection through literature studies. Slope stability analysis was carried out to obtain recommendations with a minimum Safety Factor of 1.30. The results showed the ground water level has an inverse relationship to Safety Factor value. The recommendation is depressurisation using drain holes. The target of groundwater level reduction in the mine wall is RL+40 in the sidewall area and RL+65 in the highwall area. Another alternative is is by resloping the overall slope angle of the mine wall in the study area. The mine slope is recommended for layback with an overall slope angle of around 24 °.
Chapter
A computer program for simulating ground-water flow in three dimensions is presented. This report includes detailed explanations of physical and mathematical concepts on which the model is developed. Ground-water flow within the aquifer is simulated by using a block-centered finite-difference approach. The program is written in Fortran 77 and has a modular structure, which permits the addition of new packages to the program without modifying existing packages.
User's Manual. Wasy Software Feflow-Finite Element Subsurface Flow & Transport Simulation System
  • Wasy Gmbh
Wasy Gmbh (2002) User's Manual. Wasy Software Feflow-Finite Element Subsurface Flow & Transport Simulation System.
Treatment of free surface in 2D and 3D groundwater modelling
  • H-J G Diersch
Diersch H-J. G. (2002) Treatment of free surface in 2D and 3D groundwater modelling. White Papers Vol. I, Wasy Software Feflow -Finite Element Subsurface Flow & Transport Simulation System, 67-100.