Groundwater simulation studies – some examples

where, t_m is the time at which the derivative is being evaluated and t_m-1 is the proceeding time.

Therefore, the flow terms can be expressed in terms of h^m at time t_m and equation (2.34) can be rewritten in backward-difference form as:

   

Finally, equation (2.36) is a backward-difference equation, which can be used as the basis for a simulation of the partial differential equation of ground water flow, in equation (2.18).

2.4.2 Groundwater simulation studies – some examples

The finite difference formulation presented in equation (2.18) has been implemented in numerous commercial groundwater simulation software packages of which the most commonly used is the modular finite-difference groundwater flow (MODFLOW) (McDonald and Harbaugh, 1988). The MODFLOW model is probably the most frequently used groundwater modelling programme (Winston, 1999). MODFLOW is a computer program that numerically solves one-, two- or three-dimensional groundwater

flow equation for a porous medium by using a finite-difference method. The original computer program was developed by McDonald and Harbaugh (1996). MODFLOW-2000, is designed to accommodate the solution of equations in addition to the groundwater flow equation )Harbaugh et al., 2000). It can also simulate steady and non-steady flow in an irregularly shaped flow system in which aquifer layers can be confined, unconfined, or a combination of the two aquifers. The reputation of MODFLOW comes from its power and excellent documentation. It is also friendly to users because it works with many graphical interfaces, such as GMS (EMRL, 2004), MODMAN and GROUNDWATER VISTAS. GMS is a US Department of Defence Groundwater Modelling System. It is a comprehensive graphical user environment for performing groundwater simulations. The entire package consists of a graphical user interface and a number of analysis codes such as MODFLOW, MT3DMS, RT3D, SEAM3D, MODPATH, MODAEM, SEEPD2D, FEMWATER etc… (EMRL, 2004).

There are several solver packages in MODFLOW for solving the partial differential equations such as the Preconditioned Conjugate Gradient (PCG2) packages (Hill, 1990) which will be used in this study. It also incorporates automatic calibration to determine aquifer parameters for any degree of heterogeneity. PCG2 package was used in preference to other solvers because PCG2 includes two preconditioning options: the modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and the polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers (Hill, 1990). PCG2 has also been shown to perform better than other available solvers for many simulation problems (Hill, 1990).

A lot of studies and researchers have been using MODFLOW language in simulation models to solve and address several hydro-geological and groundwater-related problems.

Zhou and Li (2011) provided an excellent recent review of the historical development of regional groundwater flow modelling. They used Death Valley and Great Artesian Basin transient groundwater models as examples to show the application of large scale regional groundwater flow models. However, their models could only be used to give the general overview of regional groundwater flow and could not be used for proper management planning. This is because the basins were discretized with large uniform grid size of 5km x 5km, hence the spatial variations in both the hydrological and geological characteristics had not been taken in considerations especially for these basins with 600 springs and 2300 wells. Therefore, the computed hydraulic head in this model represents the average value over an area of several kilometres and can not be considered as a point value. Furthermore, this large scale model would be better if to be calibrated by automation calibration rather than by trial and error calibration approach adopted in the system.

Numerical simulation modelling by MODFLOW language was also used by the Ministry of Water Resources (MWR) to design and locate the existing two wellfields in the Ash Sharqiyah Sands Aquifer (MWR, 1997i). The study only located potential sites for the wellfields development but it did not simulate the potential effect of the two wellfields which were drilled later in the area during 2002 (GULFAR / SADE consortium, 2001).

This research therefore as one of its objective will assess and evaluate the impact of the existing two wellfields on the groundwater aquifer system for the Ash Sharqiyah Sands Aquifer.

Boronina et al. (2003) implemented the simulation model to study the groundwater resources in the Kouris catchment, Cyprus. The catchment has suffered from a scarcity of water resources due to the semi-arid climate. They conducted water balance using a steady state groundwater model in order to find acceptable solutions. While the

outcomes of this model have shown serious implications for groundwater in Cyprus, it can not be used to asses the future groundwater conditions as not enough data were available to develop the transient model. Therefore, the usefulness of the outcome of this study for long-term management decision making is limited.

Amsterdam Water Supply Utility has been using MODFLOW to design deep-well recharge systems and to position extraction wells for the groundwater supply in the dune area for many years (Olsthoorn, 1999). The study compared the results by using the analytic element method and the modular three-dimensional finite-difference groundwater flow model (MODFLOW). Each of the two modelling techniques has its own advantages.

However, the MODFLOW has extra rewards such as its ability to model transient flow in complex groundwater systems, something which most analytical methods are incapable.

In general, as noted ealier, analytical solution of the groundwater flow equation is only valid if the system is grossly over-simplified. The application of MODFOW gave useful information about the hydraulic impact on historical and future groundwater abstraction in Kuwait (Szekely et al., 2000). Many groundwater modelling studies in Oman were executed using MODFLOW software such as Modelling of Groundwater in the Nejd Region (Century Architects, 2007) and Drilling & Aquifer Testing Project in the Western Al Wusta Desert (Geo-Resources, 2005).

Don et al. (2005) used flow model to simulate the groundwater flow and test the environmental impacts of aquifer over-pumping in the south-western Kyushu, Japan. In the study, they coupled MODFLOW and the modular three-dimensional finite difference groundwater solute transport model, MT3D, to simulate groundwater flow hydraulics, land subsidence, and solute transport in the alluvial lowland plain. The simulated results show that subsidence rapidly occurs throughout the area with the central prone in the center part of the plain. Moreover, they concluded that seawater intrusion would be

expected along the coast if the current rates of groundwater exploitation continue. The study demonstrated the multi-faceted nature of groundwater investigations that can be achieved by simulation and especially the use of MODFLOW.

Shaki and Adeloye (2007) developed and applied a numerical simulation model of the Murzuq aquifer system in Libya to better understand its hydraulic behaviour and to assess the impact of the water abstractions for irrigating the Irawan irrigation project. Although the study relied on a number of assumptions because of the paucity of data in the Murzuq basin, it nonetheless demonstrated that current abstractions practice from the aquifer was wasteful of water and that effective irrigation of the fields could be achieved by operating a sub-set of the pumps, which will represent a significant saving in water and reverse the downward trend in the trajectory of the water table. The study made a number of recommendations for increasing the availability of data for the Murzuq and indeed other regional aquifer systems in Libya. Abdalla (2008) used a numerical groundwater flow simulation model using MODFLOW to examine groundwater recharge/discharge mechanisms in the regional Central Sudan Rift Basins (CSRB). The decline in groundwater level along a flow path was calculated using Darcy's law to estimate average recharge and evapotranspirative discharge. Steady-state 2D flow modeling used in the study has demonstrated its usefulness as a good tool to evaluate and to understand the hydraulic behaviour of such aquifers.

Seneviratne (2007) used groundwater simulation model within a Geographical Information System (GIS) environment to study the flow in lower part of Walaw Basin in Sri Lanka., Remotely sensed data were used to solve the problem of the lack of in-situ measurements which as remarked earlier was a major issue for the Libyan Murzuq basin reported by Shaki and Adeloye (2007). The study concluded that high recharge was observed in the agricultural area while the discharge most concentrated in the flat area in

the lower part of the basin. In this study, an integrated groundwater simulation model incorporating GIS and remote sensing techniques was successfully achieved to establish areas of recharge and discharge in the targeted basin.

Yuan et al. (2011) used a coupled model that simulates interacting surface water and groundwater flow and solute transport processes in these wetlands. The results suggest that the model represents well the interacting surface water and groundwater flow and solute transport processes in the lagoons.

A recent study by Pool et al. (2011) used a numerical flow model (MODFLOW) of the groundwater flow system in the primary aquifers in northern Arizona to simulate interactions between the aquifers, perennial streams, and springs for predevelopment and transient conditions during 1910 through 2005. Results from simulation modeling include the importance of variations in recharge rates throughout the study area and recharge along ephemeral and losing stream reaches in alluvial basins. Also, the groundwater-flow systems in individual basins include the hydrologic influence of geologic structures in some areas and that stream-aquifer interactions along the lower part of the Little Colorado River are an effective control on water level distributions throughout the Little Colorado River Plateau basin. This model is not unique and it needs better information on several aspects of the groundwater flow to reduce uncertainty of the simulated system. Many areas lack documentation of the response of the groundwater system to changes in withdrawals and recharge.

From the above review, it is clear that the MODFLOW model has the capability to simulate different conditions and scenarios in groundwater aquifers, which has clearly fuelled its popularity in groundwater planning and management studies. Therefore, the grid approach of MODFLOW in GMS graphical interfaces has been selected for the

simulation model for the Ash Sharqiyah Sands Aquifer in the study of Ash Sharqiyah domestic water supply in using desalinated water and groundwater.

The simulation models are an important management tool because they can be used to investigate different management scenarios. However, a weakness of the simulation models is their inability to determine the optimal aquifer management strategy. Thus, the application of simulation models is limited to the understanding of operation of the aquifer. Also they must be executed repeatedly for different logical guesses to get as close as possible to an optimal solution for a specified objective. Repeated simulation requires much time and money, especially when dealing with large-scale projects. Therefore, a mathematical management model can be achieved to solve the mentioned constraints by combing an optimization model and simulation model. Various optimization models, which have been applied in groundwater management, are described in the next section.