# Mathematical modelling of the Germasogeia aquifer

Figure 1. Aerial view of the Germasogeia aquifer

Water is a scarce, precious commodity in Cyprus and in the wider Mediterranean region. While seeking suitable challenges for the 1st Study Group with Industry in Cyprus (125th European Study Group with Industry), Dr Katerina Kaouri approached the Cyprus Water Development Department (WDD), the governmental organization responsible for the management of water resources in Cyprus, and two challenges were identified. These challenges were about the Germasogeia aquifer which supplies drinking and irrigation water to a large part of Limassol, the 2nd largest town of Cyprus.The Germasogeia aquifer is 5.5km long and approximately 0.2 km wide, it starts at the Germasogeia dam (underground) and ends at the sea (Fig.1). The water flows into the aquifer from the dam and it is also supplied by the WDD artificially at designated points through a recharge process.

The two challenges are as follows:

(i) Which is the optimal recharge strategy for the aquifer that leads to water savings, while ensuring that seawater does not enter the aquifer?

(ii) If the aquifer is contaminated at a certain point how fast and where will the pollution spread?

During the Study Group week a team of about 10 mathematical modellers from several universities worked intensively on the above challenges, in close collaboration with the WDD, and preliminary mathematical models of the aquifer flow were developed. The work was summarized in a detailed report which was delivered to the WDD in early 2017. As there were still many unresolved questions at the end of the Study Group three members of the team from the University of Oxford (Raka Mondal, Sourav Mondal, Graham Benham) returned to Cyprus, in June 2017, to collaborate further with the WDD and with researchers at the Cyprus University of Technology.

Regarding challenge (i), we modelled the flow in the aquifer using the well-known ansatz of Darcy flow for porous media. In this way we determined the water height and the water velocity in the aquifer as a function of the incoming dam flow rate, and the recharge and extraction rates. For the Germasogeia aquifer, the variation of the width is not large and hence we were able to work with two-dimensional geometries which led to faster simulations. The model agrees well with data provided by WDD (see Fig.2) and can be used to predict the water height in following years. Subsequently, based on the above model we developed an optimization protocol for improving the recharge strategy for various scenarios (summer/winter, more/fewer recharge points, more/fewer extraction points). Our preliminary results indicate that WDD could achieve considerable water savings by switching from the current empirical/intuitive strategy to an optimized, model-driven, recharge strategy.

Figure 2

Regarding challenge (ii), in order to investigate the hypothetical scenario of contamination of the aquifer by pollutants (chemicals, sewage etc.) we modelled the evolution of the pollutant in the aquifer using an advection-diffusion equation. The advection speed of the contaminant was predicted to be about 2m/day. As an example, for a continuous contamination source, if no remedial measures are taken, we predict that the whole aquifer will be polluted within 10 years. Additionally, the model can be used to tackle the “inverse” problem: if WDD detects contamination in the extracted water they can infer where the contamination source is and take remedial actions.

Additionally, in a third modelling direction, we studied the effect of the sea water intrusion which was not taken into account in our first model. (Seawater intrusion is highly undesirable as it makes the extracted water unusable.) We thus developed a more detailed model of the flow in the aquifer, which is again based on Darcy flow but with the water density varying due to the varying salt concentration. We found that the freshwater-seawater interface in the aquifer is sharp (just a couple meters compared to the 5.5 km long aquifer) and approximately determined the position of this interface. This knowledge can be used by the WDD as a guidance for extracting water from regions that have not affected by the seawater intrusion. Since the interface is sharp, the model was simplified to a two-fluid model where the first fluid is the freshwater and the second fluid is the seawater. This simplification led to less numerically intensive simulations and enabled us to determine the water table height in the case of seawater intrusion.

We presented the results and recommendations to the WDD in June (Fig. 3) and we are currently writing them up for submission to a journal on water resources research. We have also identified appropriate grants to apply for in order to further develop our modelling framework to other aquifers in Cyprus and in other countries.

Fig. 3 The mathematical modelling team with officers of the Water Development Department, after the presentation of the results, outside the WDD building.

Acknowledgements: The Mathematics for Industry Network (MI-NET, COST Action TD1409) provided financial and logistics support to the 1st Study Group with Industry through an ESGI grant. The Annual Meeting of MI-NET took place in Cyprus just before the Study Group and senior experts from MI-NET and ECMI provided (pro bono) advice and mentoring to the Study Group Organising Committee. The subsequent visits to Cyprus for the aquifer work were funded by MI-NET (STSM for Dr Raka Mondal), the University of Oxford (Dr Sourav Mondal) and the WDD (Graham Benham).