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Volume 2, 2019 ISSN: 2664-0848
DOI: 10.31058/j.water.2019.11004
Submitted to Waters, page 55-66 www.itspoa.com/journal/water
Numerical Simulation of Groundwater
Flow in Shendi Sub-Basin, Sudan
Adil Balla Elkrail1*
, Amin Dafaalla2, Mohamed Adlan
3
1 Department of Hydrogeology, Faculty of Petroleum and Minerals, Al-Neelain University,
Khartoum, Sudan 2 Department of Geology, Faculty of Science, Nahr Anneel University, Sudan
3 Department of Hydrogeology, Faculty of Petroleum and Minerals, Al-Neelain University,
Khartoum, Sudan
Email Address [email protected] (Adil Balla Elkrail), [email protected] (Amin Dafaalla),
[email protected] (Mohamed Adlan)
*Correspondence: [email protected]
Received: 8 November 2019; Accepted: 28 November 2019; Published: 9 December 2019
Abstract: This study investigated the groundwater regime of the porous medium of Cretaceous
sedimentary formation in Shendi sub-basin. The aims of this study are to
determine the aquifer characteristics, groundwater flow dynamic, and groundwater
balance and storage capacity of the aquifer, using groundwater model techniques. A
three dimensional numerical model was developed for two aquifer system to simulate
groundwater flow through variably saturated porous medium. Visual MODFLOW,
Geographical Information System (GIS) and Aquifer Test techniques were used for
model conceptualization, data processing and obtained results manipulation. Model
simulation was optimized by using a trial and error method. Acceptable model
calibration was obtained with root mean square error (RMS) of 0.313 m and absolute
residual mean (ARM) of 0.124 m, normalized root mean square (NRMS%) of 0.6 %
and mass balance discrepancy of 0.01% with water reserve of 14.36 m3/d after all
prevailing abstraction activities. The general groundwater flow direction, as depicted
from model results, is towards east and northeast with a cone of depression at the
center of the area, which attributed to heavy abstraction for agricultural activities. The
annual groundwater supply from well fields in both aquifers was estimated to be
37×106 m
3. Aquifers storage capacities of covering area of 8325 km
2 were calculated
to be 60×106 m
3 and 63×10
6 m
3 for upper and lower aquifer respectively. The
sensitivity analyses reflected that the model was more sensitive to hydraulic
conductivity and least sensitive to specific storage. The model was validated after
sufficient testing had been performed to ensure an acceptable level of predictive
accuracy.
Keywords: Groundwater Modeling, Simulation, Aquifers, Visual MODFLOW, Hydrogeological
Parameters, Specific Coefficient, Water Budget
Volume 2, 2019 ISSN: 2664-0848
DOI: 10.31058/j.water.2019.11004
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1. Introduction
Increasing demands on the groundwater resources are creating a need for improved
scientific information and analysis techniques to better understand and manage
groundwater systems in Shendi basin. Identifying flow patterns is important in
understanding and classifying groundwater flow [1]. The present state of social and
economic development throughout the world is characterized by a sharp increase in
groundwater exploitation [2]. Groundwater models have become a major part of many
researches dealing with groundwater assessment, management, exploitation,
protection and remediation development strategies and predictive tools available for
managing water resources in aquifers [3]. These models can be used to test or refine
different conceptual models, estimate hydraulic parameters, and, most importantly for
water-resource management, predict how the aquifer might respond to changes in
pumping and climate effects [3]. Model is a physical system or mathematical
description of several properties and characteristics relating to the selected modeled
object. Moreover, mathematical models for groundwater contamination with varying
velocity field were recently resented [4,5]. Modeling is an experimental method of
research based on constructed models. The aim of the models is to assist in the
solution of practical problems, simulating processes in subsurface fluids and
improving the understanding of hydrogeological systems in porous media.
Forecasting and studying the response due to different scenarios is the goal of
modeling [6,7]. In many aquifers, groundwater models have proved to be adequate
for simulating regional groundwater flow [8,9,10,11,12,13,14]. The finite difference
technique was one of the first methods used for various types of flow problems and its
applications had been widely developed. Other numerical solution techniques for
similar governing equations have continuously emerged, such as the finite element
(FE), integrated finite difference (IFD), boundary element (BE) and finite volume (FV)
methods. These techniques have been increasingly introduced into groundwater
modeling studies. All of these widely used methods have already discussed in
groundwater applications, and some of the corresponding codes have been developed
and applied successfully. Any groundwater model should be interpreted and used
properly, and its technical limitations should be well understood such as accuracy of
computations, assumptions regarding the real natural system, approximation of
parameters being used by the model and the replacement of theoretical differential
equations describing groundwater flow system with algebraic equations [15,16].
MODFLOW was originally developed to simulate saturated flow in a porous media
with uniform temperature and density. Visual MODFLOW is the latest version of
MODFLOW and currently the most widely used numerical model for groundwater
flow problems. It is a three-dimensional, block-centered finite difference groundwater
flow model. It is capable of simulating subsurface conditions such as steady state,
transient flow, confined and unconfined aquifers. The study area is subjected to severe
agricultural and industrial activities and population settlements expansion. So
considerable efforts should be exerted for the groundwater evaluation to achieve the
requirements of the people to offset the overdraft resulted from these activities. The
objectives of this study are to evaluate the groundwater flow system in the study area
based on determination of the aquifer characteristics, groundwater flow dynamic, and
storage capacity of the aquifers and groundwater balance of the area using
groundwater model techniques (Visual MODFLOW code).
2. Materials and Methods
Volume 2, 2019 ISSN: 2664-0848
DOI: 10.31058/j.water.2019.11004
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2.1. The Study Area
The study area lies at River Nile state around Shendi Town between latitudes
16˚30.618′ &17˚ 17.244′ N and longitudes 33˚ 25.200′ & 34˚02.920′ E covering
an area of 8325 km2 (Figure 1). It is characterized by low relief, marked with isolated
hills of sedimentary outcrops at the southeast and the north.
Figure 1. Location map of the study area.
The area is dominated by arid to semi-arid climate condition with hot summer, cold
winter and rainy autumn. The rainfall intensity varies from 50 to 100 mm/y. The
drainage pattern is dominated by parallel to dendritic seasonal streams flow through
sedimentary provinces to the west and northwest, which drain the water to the River
Nile.
From geological view point, Shendi sub-basin is an outlier composed of Cretaceous
sedimentary formation surrounded by the pre-Cambrian and Paleozoic crystalline
rocks (Figure 2) at Sabaloka area on the south; Bayuda desert to the northwest and
Butana terrain to the east and southeast [17,18,19]. The main rock types of these
terrains are gneisses, schists, migmatites, granites, micro granites, syanite, gabbro,
basalts, rhyolite, and agglomerates. The Cretaceous sedimentary formations are
characterized by vertical rapid facies changes from more fine-grained to more coarse-
grained fluvial deposits and influenced by a shift from a more humid to a more arid
paleoclimate. It is composed of continental fluvial and lacustrine facies including
conglomerate, sandstones and mudstones and unconformably overlain by Hudi Chert.
Conglomerates composed of rounded to sub rounded pebbles and rock fragments. The
sandstone is mainly made up of poorly cemented detrital quartz (fine to very coarse
grain-size), poorly sorted, interbedded with mudstones layers. The thickness of
sandstone layers varies from 5 to 100 m. Mudstone layers are composed of clay and
silt particles, moderately to well cement by silica or iron oxides, reflecting different
colors. They vary in thickness from 5 to 125 m. Hudi Chert formation consists of
fragments of boulders and cobbles of irregular ellipsoidal and sub-rounded shapes,
with cavities and pitted surface (Figure 2). It is of Oligocene age overlying Cretaceous
sedimentary formation and ranges in size from 5 to 20 cm. It has been regarded as
lacustrine deposits that have been silicified into Chert [20]. The superficial sediments
include alluvial and eolian deposits of gravel, sand, silt and clay materials. Alluvial
deposits of unconsolidated coarse sand and fine gravels were found at the upper part
whereas fined to medium-grained sands were encountered at the middle and lower
part of the succession. Most of the study area was covered with eolian wind-blown
sands.
Volume 2, 2019 ISSN: 2664-0848
DOI: 10.31058/j.water.2019.11004
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Figure 2. Geological map of the study area.
From hydrogeological view point, the Cretaceous Sedimentary Formation and
superficial deposits represent the main water-bearing formations. Mudstones and
clays intercalations form more than one aquifer in the sedimentary formation. In the
study area four layers with two aquifers were considered namely upper and lower
aquifers separated by impermeable mudstones and clay layers. The lower aquifer was
assumed to be confined, with thickness varies from 27 to 74 m. The upper aquifer
thickness (second layer) varies from 24 to 96 m. The depth to water level varies from
15 to 81 m below the surface. The River Nile and seasonal streams are the main
source of recharge to the aquifers in the area, whereas the direct precipitation and
natural subsurface flow represent additional source of recharge. Thies’s, Cooper and
Jacob methods [21] were applied for the unsteady- state flow in confined aquifer for
estimating the aquifer hydraulic parameters in the study area. Accordingly, the
hydraulic conductivity (K) ranges between 2.5 and 5.58 m/d, the transmissivity ranges
between 50 and 390 m2/d, whereas the storage coefficient (S) ranges between 0.12-
0.15.
2.2. Model Input Data
The main input data for model design in the study area that collected and observed
from the field work and calculated with relevant methods include: aquifer types,
observation wells, pumping wells, recharge sources, aquifer hydraulic properties,
initial and boundary conditions which were discussed in the following paragraphs:
Observation wells were used for monitoring groundwater heads during model
simulations to reveal the water level distributions in the model area. Seventeen (17)
observation wells were used in the model area, where the water level measurements
were taken in 2014.
Groundwater abstraction through pumping wells and evapotranspiration are the
main source of discharge. The main sources of recharge to the aquifers are assumed to
be from the River Nile and seasonal streams, whereas the direct precipitation and
natural subsurface flow represent additional source of recharge. For aquifer hydraulic
properties, the hydraulic conductivity, specific coefficient, storage coefficient,
effective porosity and total porosity were measured with relevant methods for upper
and lower aquifer in the model domain. The initial conditions are simply the values
of the dependent variable (water head) specified everywhere inside the model domain
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or along the boundaries before the start time of measurements. The measured heads in
the observation wells from 2014 were used as initial head distribution for the model
simulation. Based on the boundary conditions, the bottom of the aquifers and the
western side of the model area were considered as no-flow boundaries. The top of the
aquifers is considered as the variable head boundary. The southern, eastern and
northern sides of the model domain were taken as general head boundary (GHB),
whereas, the northwestern part was taken as river boundary.
2.3. Model Design
Three-dimensions, finite difference, block-centered, steady state groundwater flow
model was used on the conceptual model of the study area. For model discretization
an initial grid network of 90 rows, 80 columns, 4 layers and 28800 cells were used to
cover the model area. A total of 76 pumping wells were used to discharge water from
the aquifer in the model area (Figure 1). There were seventeen (17) observation wells
used in the model area, where the water level measurement was taken in 2014.
The hydraulic conductivity of 2.5, the specific coefficient of 0.000124, storage
coefficient of 0.12, effective porosity of 0.17 and total porosity of 0.22 were assigned
to the upper aquifer. On the other hand, hydraulic conductivity of 5.58 m\d, the
specific storage of 0.00131, storage coefficient of 0.15, effective porosity of 0.23 and
total porosity of 0.28 were assigned to the lower aquifer for model simulation.
The measured heads in the observation wells were used as initial head distribution
for the model simulation. The bottom of the aquifer and the western side of the model
area were considered as no-flow boundaries. The top of the aquifer is considered as
the variable head boundary, where flow may enter the model as a recharge from the
River Nile (Figure 4) seasonal stream and direct precipitations. The southern, eastern
and northern sides of the model were taken as General Head Boundary (GHB) of 331,
328 and 322 m, above sea level ( a.m. ) respectively for upper aquifer, whereas GHB
of 328, 322 and 321 m, a.s.l were assigned to the southern, eastern and northern sides
of lower aquifer respectively. The western side of the model area was assigned as
river boundary, along the River Nile course.
2.4. Model Calibration and Validation
Steady-state assumption was appropriately given that the system is not heavily
stressed by municipal, agricultural and industrial pumping and drawdown, and it is
assumed flow conditions have not substantially changed. Calibration was performed
by adjusting the initial horizontal (Kh) and vertical (Kv) hydraulic conductivities and
recharge values and model boundary conditions until the model approximates field-
measured values of head and flow [16]. Since steady-state conditions were simulated,
the calibration values were time-averaged field measurements when such data were
available. The 95% confidence intervals, estimated by Kriging [15], were used for
conservative calibration targets for the water table elevations in model cells with
monitoring wells. During model calibration, model parameter values were adjusted so
that simulated heads, gradients and fluxes would fall within the calibration targets
[15].
In the model parameterization, the available field data are used to define the spatial
patterns of the parameter values to describe the most significant variations. This is
done by defining a conceptual model with appropriate parameter classes of geological
units, soil and vegetation types [22]. For each class, some parameters are then
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assessed directly from field data and modeling experience while other parameters are
subjected to calibration. The challenge is to formulate a relatively simple model
parameterization in order to provide a well-posed calibration problem but at the same
time keep it sufficiently distributed in order to capture the spatial variability of the key
model parameters [22]. Model validation is a process carried out by comparing the
model predictions with independent field or experimental observations. A model
cannot be considered validated until sufficient testing has been performed to ensure an
acceptable level of predictive accuracy [23].
The calibration of the three dimensional, finite difference, steady state flow model
of the study area was undertaken using the Root Mean Squired Error (RMS), Absolute
Residual Mean (ARM), Normalized (RMS %) and mass balance percent discrepancy
using trial-and-error procedure.
3. Model Results and Discussion
The scatter plot of simulated versus measured heads indicates that there is very little
bias in the simulation results (Figure 3). RMS error reflects uncertainties in both
measured and simulated hydraulic heads. The model calibration criteria such as
absolute residual mean (ARM), root mean square error (RMS) and mass balance error
of water into and out of the system were adjusted through hundreds of model runs.
Figure 3. Scatter plot of simulated versus observed water level.
The final calibration has RMS value of 0.313 m and average absolute residual mean
(ARM) of 0.124 m and average normalized root mean square (NRMS %) of 0.6 %,
and mass balance discrepancy of 0.01%. The steady state model generally reproduced
the potentiometric surface developed from water level measurements in 2014. The
piezometric surface of the simulated heads was drawn using visual MODFLOW post-
processing tool (Figure 4). From the piezometric surface map, the general flow
direction is from the west to the east and northeast, confirming the natural aquifer
recharge from the River Nile which is one of the model credibility (Figure 4). A cone
of depression was observed at the center of the area due to heavy pumping for
agricultural activities at these areas. The model shows that the contour lines shape and
spacing is proportional to the pumping. Hence an acceptable calibration was obtained
and the model can be used for future prediction.
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Figure 4. Piezometric Surface and Flow direction map.
3.1. Groundwater Balance
Based on general hydrogeological principles, a groundwater budget was prepared to
estimate the amount of groundwater inflow, out flow and change in storage. The field
– estimated inflows may include groundwater recharge from direct precipitation,
overland flow, subsurface baseflow along the boundaries, or recharge from surface
water bodies. Outflows may include spring flow, base flow, evapotranspiration and
pumping. A water budget should be prepared from the field data to summarize the
magnitudes of these flows and changes in storage.
Generally, the visual MODFLOW computes flow-rate and cumulative budget
balance from each type of inflow and outflow for each time step for the whole area.
The zone budget was calculated for steady state model simulation for the whole model
domain (Table 1). The volume of water in cubic meter per day (m3/d) and its
percentage was calculated for each component of the hydrologic budget. Recharge is
the most important hydrologic component of inflow to the aquifer, which is able to
offset the groundwater extraction from the aquifer. The total volume of the aquifer
inflow is 200490.58 m3/d, while the total volume of the aquifer outflow is 200476.22
m3/d (Table 1). Groundwater pumping volume through production wells in the entire
area computed by the model represents 50.38 % of the total outflow from the aquifer
(Table 1). The subsurface inflow through the GHB represents 20.5% from the total
inflow. The river recharge to the aquifer as subsurface inflow represents 79.53% of
the total inflow. The recharge water volume from direct precipitation represents 5.0%
of the total inflow. The subsurface outflow from the river represents 49.62% from the
total outflow. Finally, the discrepancy between inflow and outflow amount to 14.36
m3/day as daily water reserve (Table 1). The annual groundwater supply from well
fields in both aquifers was estimated to be 37×106 m
3. Aquifers storage capacities
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were calculated to be 60×106 m
3 and 63×10
6 m
3 for upper and lower aquifer
respectively.
Table 1. Cumulative budget for the model area.
Component Inflow
(m3/day)
% of total
inflow
Outflow
(m3/day)
% of total
outflow
Discrepancy
(m3/day)
Wells’
Discharges - 101007.34 50.38
Recharge 9981.90 5.0 -
River
Leakages 159487.16 79.53 -
GHB 31021.54 15.47 99468.88 49.62
Total 200490.58 100 200476.22 100 14.36
3.2. Sensitivity Analyses
Sensitivity analysis is a procedure for quantifying the impact on an aquifer’s
simulated response due to an incremental and decremental variation in a model
parameters or a model stresses. In most entry hydrogeological parameters for
numerical modeling, there is uncertainty in the boundary conditions, in measurement
of abstractions and the estimation of recharge, in representation of natural processes
within algorithms in standard software packages and in conceptualization of the real
system. Therefore, sensitivity analysis becomes important as the uncertainty in the
key input parameters increases. Model sensitivity can be expressed as the relative rate
of change of selected output caused by unit change in the input [24]. If the change in
the input causes a large change in the output, the model is sensitive to that input. The
most influential factor yielded parabolic-shaped sensitivity curves having deep
troughs and steeply dipping sides [25]. The sensitivity analyses were performed for
changes in hydraulic conductivity (K), specific yield (Sy) and specific storage (Ss)
with respect to root mean square error (RMS). The model was executed four times for
each parameter increment of 10 and 20 percent and decrement of 10 and 20 percent
(Table 2).
Table 2. Parameters used for different sensitivity analyses.
Control parameters K Sy Ss RMS
5.58 0.15 0.000131 0.313
K×1.2
K×1.1
K×0.9
K×0.8
6.696
6.138
5.022
4.464
0.15
0.15
0.15
0.15
0.000131
0.000131
0.000131
0.000131
1.657
0.992
0.897
2.1
Sy×1.2
Sy×1.1
Sy×0.9
Sy×0.8
5.58
5.58
5.58
5.58
0.18
0.165
0.135
0.12
0.000131
0.000131
0.000131
0.000131
0.313
0.313
0.313
0.313
Ss×1.2
Ss×1.1
Ss×0.9
Ss×0.8
5.58
5.58
5.58
5.58
0.15
0.15
0.15
0.15
0.0001572
0.0001441
0.0001179
0.0001048
.313
0.313
0.313
0.313
The corresponding percentage changes in root mean squared error (RMS) values
were plotted versus percentage changes of parameter values. Accordingly, sensitivity
analyses reflected that the model is more sensitive to hydraulic conductivity and least
sensitive to specific storage (Figure 5). Hence for prediction purpose, precaution
should be taken to hydraulic conductivity (K) measurements and its distribution.
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Considering accurate hydraulic conductivity measurements the model can be used for
future prediction, although some technical limitations were encountered; such as
accuracy of computations (hardware and software), model dependability on the
various simplifying assumptions of the natural modeled system and approximations of
the actual measurements and distributions of hydrologic and hydrogeological
properties (vertical hydraulic conductivity).
Figure 5. Parameters used for sensitivity analyses.
4. Conclusions
Three-dimensions, finite difference, block-centered, steady state groundwater flow
model was used on conceptual model for the study area. The model was simulated to
evaluate the groundwater flow regime based on determination of the aquifer
characteristics, groundwater flow dynamic, and groundwater balance and storage
capacity of the aquifers. Visual MODFLOW, geographical information system (GIS),
relevant aquifer test techniques were used for model conceptualization, data
processing and obtained results manipulation. Model calibration was performed using
a trial and error technique. Acceptable results was obtained with root mean square
error (RMS) of 0.313 m and absolute residual mean (ARM) of 0.124 m, normalized
root mean square (NRMS%) of 0.6 % and mass balance discrepancy of 0.01%. The
scatter plot of simulated versus measured heads indicates that there is very little bias
in the simulation results. From the piezometric surface map, the general flow direction
is from the west to the east, confirming that the natural aquifer recharge is mainly
from the River Nile. A cone of depression was appeared at the center of the area due
to heavy pumping for agricultural activities. Aquifers storage capacities were
calculated to be 60×106 m
3 and 63×10
6 m
3 for upper and lower aquifer respectively.
The annual groundwater supply from well fields was estimated to be 37×106 m
3.
Finally, the discrepancy between total inflow and total outflow amount to 14.36
m3/day as daily water reserve after all abstraction activities. The sensitivity analyses
reflected that the model is more sensitive to hydraulic conductivity and least sensitive
to specific storage. The model was validated after sufficient testing has been
performed to ensure an acceptable level of predictive accuracy.
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of
this article.
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DOI: 10.31058/j.water.2019.11004
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Acknowledgments
The authors would like to acknowledge the Non-Nile water corporation, Atbara
Branch for providing most of hydrogeological data and direct support during field
work in the study area. Thanks to Al Neelain University for generous support and help
to improve the manuscript.
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Volume 2, 2019 ISSN: 2664-0848
DOI: 10.31058/j.water.2019.11004
Submitted to Waters, page 66-66 www.itspoa.com/journal/water
© 2019 by the author(s); licensee International Technology and
Science Publications (ITS), this work for open access publication is
under the Creative Commons Attribution International License (CC
BY 4.0). (http://creativecommons.org/licenses/by/4.0/)