numerical simulation of groundwater flow in shendi sub ... · rocks (figure 2) at sabaloka area on...

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

mailto:[email protected]

Volume 2, 2019 ISSN: 2664-0848

DOI: 10.31058/j.water.2019.11004


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

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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.

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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


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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DOI: 10.31058/j.water.2019.11004


© 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

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