The procedures of this work are based on applying and integrating two techniques, the Visual MODFLOW groundwater model and Multi-Criteria Decision Analysis (MCDA) model. The operational steps and modeling processes are illustrated in a flow chart (Fig. 7).
3.1. Numerical modeling for groundwater system
3.1.1 Designing the conceptual model
Groundwater flow models are used to calculate the rate and direction of groundwater movement through aquifers and confining units in the subsurface; these calculations are referred to as simulations (Mandle, 2002). The model is also used to simulate possible future changes in hydraulic head or groundwater flows due to future changes in aquifer system constraints. MODFLOW 2005 is used as a numerical model. It is a standard USGS software developed by McDonald & Harbaugh (1988) and Harbaugh (2005). The integral finite difference method is employed to resolve the transient flux equation. There are virtually no hydrological studies specifically focused on the study area. Currently, the drilling of test wells is being carried out under the Ministry of Water Resources and Irrigation (MRWI) supervision. Available and updated field data from wells in the Eocene aquifer are collected and organized by integrating the attributes and spatial databases with GIS tools. GIS is used to manage the model's spatially distributed input parameters and outputs. The database constructed in the GIS technique is imported into the conceptual model, including the SRTM (Dem) 1-ARC resolution with 30 m, potentiometric water levels, hydraulic properties, and recharge and discharge components.
3.1.2. Grid system and boundary conditions
The model domain’s dimensions in the study area are discretized with a uniform, regular 500x500 m grid, the number of rows and columns is 200 and 150, respectively. To obtain results that reflect the hydrological conditions of the aquifer, it is essential to describe its hydraulic boundaries with known hydraulic heads. Boundary conditions are based on the hydraulic head map and hydrological conditions. Due to the absence of major branches or banks in or near the area at the northern, southern, and western boundaries, the initial hydraulic conditions were used to identify the sources of recharge of the study area. It is assumed that the aquifer is extended and represented by constant hydraulic pressure limits. The flow through these boundaries is determined as constant head boundaries (Dirichlet Conditions), where the derivatives of the groundwater head are constant and do not change with time. The eastern boundary of the model is a specified head boundary to represent the Nile River. For other areas, the no-flow boundary was specified (Neumann conditions) in which the derivatives of the head (flux) are set to zero. All boundaries were set distance from the area of main interest and simulated pumping wells to avoid the impact of uncertainty in subsurface boundary inflows and outflows and drawdown effect during transient simulation (Fig. 8).
3.1.3. Initial conditions
When studying the dynamic behavior of the aquifer to determine the amount of change in groundwater levels, it is necessary to decide on the initial conditions of the groundwater levels. Due to lack of available data for the study area, current static groundwater levels of the investigated wells have been used as the initial distribution head for the model (Fig. 9)
3.1.4. Aquifer hydraulic parameters
The present estimation of aquifer characteristics, including transmissivity, hydraulic conductivity, and storativity, is based on step-drawdown, constant discharge, and recovery tests for the investigated wells in the modeled area. Six wells were selected to represent field measurement data; their locations are shown in Fig. (4). The data of step drawdown tests are plotted on a linear scale (Fig. 10) to estimate the general well equation using Jacob (1947) and Rorabaugh (1953) techniques.
$${S}_{w }=BQ+C{Q}^{2}$$………………… 1
Where:
\({S}_{w:}\)is the total drawdown in the pumping well (m)
\(BQ\): is the formation loss (m) caused by laminar flow through the aquifer.
\(C{Q}^{2}\) is the well loss (m) caused by turbulent flow inside the well and its filter and damage zones. From this equation, the specific capacity curve is drawn. The initial Specific Capacity value is used to estimate the transmissivity (T) of the aquifer by using Driscoll (1986) equation:
$$T=2000\times \frac{Q}{S}$$…………………2
Where: \(T\) = Transmissivity (gpd/ft) and \(\frac{Q}{S}\) = Specific Capacity (gpm/ft). By using Formula/Conversion Table for Water Treatment and Water Distribution (FDEP, 2020), equivalent units for transmissivity (m2/day) and specific capacity (m2/hr.) values are obtained.
The records of pumping and recovery tests were represented graphically to estimate the transmissivity (T), storativity (S), and hydraulic conductivity(k) values by using Jacob’s straight-line method (Cooper and Jacob, 1946) and Theis’s recovery methods (Theis, 1935). (Fig. 11)
Table (1): Hydraulic parameters of the Eocene aquifer, West-West Minia, Egypt.
Well No.
|
Step drawdown test
|
Jacob straight-line method
|
Theis recovery method
|
Specific capacity
(m2/hr.)
|
T
(m2/d)
|
T
(m2/d)
|
S
|
K
(m/d)
|
T
(m2/d)
|
K
(m/d)
|
44
|
71.43
|
5952
|
7000
|
5.8×104−
|
3.88
|
|
|
247
|
17.14
|
1428.6
|
2900
|
6.1×104−
|
2.41
|
|
|
182
|
11.26
|
938.3
|
|
|
|
1100
|
0.916
|
43
|
42.2
|
3516.6
|
|
|
|
5000
|
4.166
|
42
|
13.2
|
1100
|
|
|
|
1500
|
1.25
|
53
|
26.5
|
2208.33
|
|
|
|
3200
|
2.13
|
3.1.5. Steady-State calibration
The objective of model calibration is to assure that it can produce field-measured heads, which are calibration values. The calibration process has been carried out for the boundary conditions and the hydraulic conductivity spatial distribution modification to match between the observed and simulated groundwater heads (Figs. 12&13).
3.1.6. Transient simulation
Transient simulation is needed to solve time-dependent groundwater problems. The calibrated steady-state model is run under transient calibration for one year to adjust the storativity values (Fig. 14). The model is subjected to sensitivity analysis to quantify the uncertainty in the calibrated parameters. It revealed the high sensitivity of the model toward the boundary conditions, hydraulic conductivity, and storativity, respectively. The new agricultural development project in the study area covers 4000 acres. Proposed pumping wells were distributed with a spacing of 1000 meters to decrease the pressure on the aquifer and reduce the interference between the wells. Virtual observation wells were distributed among the extraction wells to monitor the groundwater levels under the impact of each development plan.
3.2. Model results
Based on the future governmental development plan in the West-West Minia area, model scenarios have been proposed to support the decision-makers with the results and recommendations. The first scenario has been assumed to interpolate the sustainability of the groundwater aquifer in the newly reclaimed area under the current operation scheme by applying the proposed pumping wells with pumping rates of 150 m3/d for irrigation of 3953.68 acres. In the second proposed scenario, the sustainability of the groundwater aquifer in the newly reclaimed area is interpolated by considering the water meter consumption in the newly reclaimed area with a value of 6 m3/d for each acre (MALR 2007). The transient simulations have been carried out for 100 years divided into 10-time steps. Boundary conditions and wells pumping rates were constant during transient simulation.
3.2.1. Impact of the first proposed scenario
By applying the first proposed scenario, a significant depletion in hydraulic heads results from the end of each time step. The cone of depression is formed gradually at the center of the modeled area, reaching a maximum drawdown of about 100 m. The dynamic groundwater level got steady-state conditions after an estimated period of 5000 days (Fig. 15). Negative values of groundwater levels are recorded; it reached -80 m.b.s.l.
3.2.2. Impact of the second proposed scenario
This scenario results show a smaller decrease in groundwater level than the first proposed scenario. The lowest groundwater level is recorded at -20 m.b.m.s.l. The cone of depression with a maximum drawdown of about 60 m is formed. The dynamic groundwater level reached steady-state conditions after an estimated period of 9700 days (Fig. 16)
3.3. Multi-criteria Decision modeling
Based on the obtained results of the optimal scenario for groundwater sustainability of the applied Visual MODFLOW model, Multi-Criteria Decision Analysis (MCDA) model technique (Malczewski, 1999&2000) is used to assess the impact of groundwater consumption by detecting the groundwater suitability zones after long run reclamation in the concerned development area. The (MCDA) model is not a substitute for cost-benefit analysis; it is a complement analysis it gives ranges of decisions. In this work, the MCDA model integrates geospatial data of the most effective parameters in the groundwater potentials both for aquifer hydraulic characteristics and groundwater quality by merging all multicriteria layers into one prospective layer for groundwater exploitation. The contributing criteria are groundwater levels (GWL) which are obtained from the outputs of the optimal simulated scenario (second scenario) of groundwater flow model, groundwater salinity (TDS), aquifer transmissivity (T), and aquifer storativity (S). Arc-GIS is used to generate a thematic map for each criterion. All-controlling criteria thematic maps are reclassified in ARC-GIS to use in the model as a layer (Fig. 17). Each criterion is ranked according to its priority in the groundwater assessment and integrated into a GIS database model using the weighted overlay method. Weighted-Sum Overlay analysis provides the ability to obtain weight for each ranked criterion. It combines all inputs by overlaying all rasters, multiplying each by its given weight, and summing them together to calculate the overall suitably of each cell and create one output raster layer that defines the appropriate groundwater zones. The ranks, rates, and attributes of input criteria are indicated in the table (2). The equation used in this method is defined as the following:

………………… 3
Where,
-
WI: is the Relative weight of the I criterion
-
n: is the number of criteria
-
Wi: is the rank of the criterion
Table (2): Categorizing the contributing criteria and their rank, weight, and rate affecting the groundwater assessment.
Thematic layer
|
Rank
|
Weight
|
Relative weight
|
Attribute
|
Rate
|
Groundwater salinity
|
1
|
4
|
0.4
|
< 500
2000-3200
|
1
2
|
Groundwater levels
|
2
|
3
|
0.3
|
< 0
7-0
7-15
|
3
2
1
|
Transmissivity
|
3
|
2
|
0.2
|
<1000
1,000-3000
3,000-6000
6,000-10,000
10,000-23,300
|
5
4
3
2
1
|
Storativity
|
4
|
1
|
0.1
|
< 0.00552
0.00552 - 0.02443
0.02443 - 0.05911
0.05911 - 0.11980
0.11980 - 0.200991
|
5
4
3
2
1
|
3.4. Assessing groundwater prospects in the new development area
The raster layer generated from Multi-Criteria Decision Analysis (MCDA) is shown in Fig. (18). It defines the prospective groundwater zones which categorized into Most suitable (1584 sq km, 9.9%), Suitable (4592 sq km, 28.7%), Good (4784 sq Km, 29.9%), Moderate (1488 sq Km, 9.3%), and Unsuitable (3552 sq Km, 22.2%). It is observed that nearly 80% of the study area has moderate to good potential for groundwater prospecting. There is a matching between the Unsuitable zone of groundwater and the higher salinity zone of groundwater, which indicates the first rank and the highest weight of the salinity factor in groundwater development. In the rest of the area, where the salinity is almost constant, the Most suitable and Suitable groundwater zones match with high groundwater level zones, indicating the second rank and the high weight of the groundwater level factor in groundwater development.