Where:
Kxx: Hydraulic conductivity along X axis
Kyy: Hydraulic conductivity along Y axis
Kzz: Hydraulic conductivity along Z axis
H: Potentiometric head
W: Volumetric flux
Ss: Specific storage of the material
T: Time step
For the current study, the ‘Visual MODFLOW Premium 2011.1 was used to
develop a model for simulation of the groundwater regime of the study
area. Two layers’ groundwater Visual MODFLOW model was developed with
transient flow condition having a 650 m x 650 m grid size. The data of
191 pumping wells for the period 2011- 2020 and 03 observation wells
were assigned to the model.
Flow Properties
A groundwater flow model requires different hydrogeological properties
like hydraulic conductivity, specific storage, porosity, and specific
yield to simulate the hydrogeological
process.
The lithology/geology of the study area was observed from borehole logs
& reports of the Geological Survey of Pakistan (Dr. Firdous, Geological
Survey of Pakistan, “Preliminary Report on the Geology of Sri
Katas Raj and Adjoining Areas” , 2020). Some more literature
(Subramanya, 2007),
(Maidment, 1993),
(Batu, 1998) was also reviewed for
reference values of soil properties. The values of hydraulic
conductivity of the soils were determined by performing slug tests that
lie within the referenced values. The different values of soil flow
properties were assigned to the model to calibrate the model by hit &
trail method to get the calibrated values within permissible limits as
shown in Table 1 .
Boundary Conditions
The boundary conditions represent the flow exchange between the model
and the external hydrological system
(Hariharan & Shankar, 2017). Boundary
conditions are critical in groundwater modelling to get a close result
to the field situation (Kumar, 2013). The
accuracy of the results depends on field testing especially borehole
data and pumping test. The accuracy of the results directly correlates
with the accuracy of the boundary condition. Following boundary
conditions were assigned to the model based on field conditions.
Aquifer
Recharge
The aquifer recharge depends on
hydraulic conductivity and storage of the upper layer. Surface water
enters the groundwater system from the ground surface. Therefore, Visual
MODFLOW allows to assign recharge values to the uppermost layer only in
layer view mode (Hydrogeologic, 2015).
For the current study, 15% of annual rainfall was assigned to the model
(Dr. A.D Khan, Oriental Engineering Services, Lahore, Pakistan,Impact Assessment of Groundwater Pumping on Kahoon Valley
Aquifer , unpublished report, 2012).
General Head Boundary Condition
(GHBC)
The purpose of GHBC is to avoid unnecessary outspreading of the model
domain (Hydrogeologic, 2015). It is used
to contain the model domain within the boundary of the area under
consideration. Kallar Kahar Lake is present at a distance of 05 km from
the western boundary of the study area, therefore, it was assigned as
GHBC on the respective side of the model.
No Flow Boundary
Condition
The study area is a semi-closed valley bounded with deep impermeable
rocks on three sides restricting subsurface flow to the aquifer from
outside the valley or vice versa. The source of the sacred pond may be
the fractured limestone a confined/artesian aquifer containing
groundwater under positive pressure (Dr. A.D Khan, Oriental Engineering
Services, Lahore, Pakistan, Impact Assessment of Groundwater Pumping on
Kahoon Valley Aquifer, unpublished report, 2012). The recharge in this
area, therefore, is mainly from precipitation. Since there is no
subsurface inflow/outflow from these sides hence “No Flow
Boundary Condition” was assigned to the model on respective sides as
shown in Figure. 3 . The Lake boundary condition was assigned in
the MAR scenario only.
Model Calibration & Sensitivity
Analysis
The model was calibrated for three observation wells for the years 2012,
2013, 2016, and 2020. Various parameters were adjusted such as hydraulic
conductivity, specific yield, porosity, and specific storage to
calibrate the model by hit & trail method. The simulated values of
observation wells lie within the 95% confidence interval as shown inFigure. 4 and simulated results of observation wells are shown
in Figure. 5 . The standard error of the mean is 0.275 m whereas
the correlation coefficient is 0.998.
A sensitivity analysis is a process in which the input parameters are
varied within the allowable range to observe a relative change in the
model response. For the current study, different input parameters were
varied to observe the model calibration response. Hydraulic conductivity
was varied within allowable limits to observe its impact on the
calibrated results of the model. It was observed that by varying
hydraulic conductivity, the calibrated results of the model were
disturbed manifold as shown in Table
2 .