A Computational Model for the Optimal Management of Coastal Aquifers

A computational model for the optimal management of coastal aquifers

S.K. Arvanitidou, C.G. Koutitas, K.L. Katsifarakis Division of Hydraulics and Environmental Engineering, Department of Civil Engineering Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece G.H. Pechlivanidis Division of hydraulic structures and Environmental Engineering, Department of civil infrastructure Engineering, Technological Educational Institute of Thessaloniki, 57400, Thessaloniki, Greece

ABSTRACT: A generic computational model describing the evolution in the 3D space and time of the fresh and salt water movement (two layers 2DH) and the intrusion of salt water in coastal aquifers is formulated and solved. The model has been validated and compared with analytical solutions produced by Strack and with experimental results, for specific flow conditions, produced in the flume of the Hydraulics laboratory of Thessaloniki TEI. A sensitivity analysis to the model parameters is conducted. Two interesting tests refer to the issue of increased seawater intrusion due to the forecasted sea level rise for almost 1m during the 21st century and due to the negative trend of precipitation on the Mediterranean coast. Two alternative methods to increase the aquifer’s sustainable productivity by artificial means are preliminarily tested, namely: a) use of recharge canals and b) use of distributed scavenger wells placed between the productive wells and the coastline

1 INTRODUCTION

Overexploitation of groundwater in coastal aquifers has upset the balance between freshwater and seawater potentials, causing landward movement of seawater into freshwater aquifers. In- tensive pumping of coastal aquifers, especially during summer months, results in saltwater intrusion which decreases aquifers’ efficiency below sustainability levels. Since the famous works of Badon-Ghyben and Herzberg, extensive research has been carried out, and much progress has been made in understanding the various mechanisms that govern seawater intrusion e.g. Bear, (1999), Oude Essink and Boekelman (2000). Models of salt and fresh water flow in coastal aquifers serve as important tools for assessing the extent of saltwater intrusion and for planning rational development of water resources e.g. Dagan & Zeitoun (1998). Two general approaches have been used to analyze saltwater intrusion in coastal aquifers: the disperse interface and the sharp interface. In the first approach, the disperse interface explicitly represents the presence of a transition zone, where mixing of fresh water and salt water is taking place, due to the effects of hydrodynamic dispersion (Essaid, 1990). Some numerical solutions of the transition zone problem have been presented in the works of Pinder and Cooper (1970), Segol et al. (1975), Voss and Souza (1987), Das and Datta (1995, 2000), Bear (1999). In the second category, the sharp interface approach simplifies the analysis by assuming that the transition zone is thin relative to the dimensions of the aquifer (Essaid, 1990). Numerical solution based on the sharp interface approximation include Mercel et al. (1980), Essaid (1990), Nazi et al. (1998a, 1998b, 1999), Khalid et al. (2005). The present paper presents a two-layer numerical model and a generic solution algorithm, based on the second approach. The model is compared with the analytical solution of Stack’s potential (Strack, 1976; Cheng & Quazar, 1999) and laboratory observations. The influence of the sea level rise and reduction in freshwater flow towards the sea are examined and two hydraulic techniques for the protection of coastal aquifers are proposed. 2 FORMULATION OF THE MATHEMATICAL MODEL

The formulation of the mathematical model is based on the equilibrium equation and the mass balance, subject to two simplifying assumptions. a) The assumption of two immiscible layers of salt and fresh water and the formation of a sharp interface between the two layers, which has been used extensively for coastal stratified flows and for porous flows. This assumption allows the separate consideration of the hydrodynamics (continuity and equilibrium) of the two layers, and their interaction through the pressure terms. b) The well known “Dupuit” assumption, referring to the hydrostatic pressure distribution in the two layers (assumption of nearly horizontal flow) and the consideration of the depth- mean seepage velocities in each of them. Hydrostatic pressure distribution in case of quasi-horizontal flows is assumed, the pressure distribution is estimated according to the notation of fig.1 and the following relation for the upper layer (fresh water) holds (Koutitas, 1988):

1 p f (h f  hs  zb ) p f   f gh f  hs  zb    g (1)  f x x

For the lower layer (seawater) it can be easily proved that:

ps   f gh f  hs  zb  (hs  zb )  s g(hs  zb ) 

1 p  h f (h  z ) s  (1 )g  g s b (2)  s x  s x x

Where, ρf and ρs are the density of the upper and the lower layer respectively, and Δρ/ρs = (ρs- ρf)/ρs is the density gradient.

Figure 1. Two–layer model, basic notations, where hf is the freshwater piezometric head, hs is the seawater Vf f hf Uf depth, u & v are seepage velocities, zb the distance from reference level, ρf and ρs the density of fresh and

Vs s hs. seawater respectively. Us

z y Zb x

The seepage velocities are estimated using the Darcy law and the governing equations can be written for the two layers separately. Thus for the upper layer the mass balance equation, taking in consideration the Dupuit assumption, is expressed by the Boussinesq equation which for an unconfined aquifer is written as:

1 h f 1     p f     p f     K h    K h   q (3) n t  g x  x  f x  y  y  f y  f        The same approach for the lower layer leads to the equation: 1 h 1     p     p  s   K h s    K h s   q   x  s   y  s  (4) n t  s g x   x  y   y 

Where n is the porosity and the q describes the local sinks or sources distributed along the aquifer. The numerical solution is achieved by an explicit Finite Differences 1st order scheme on a staggered grid, giving to the user the ability to follow the time-space evolution of the free surface and of the salt-fresh water interface, from an initial state to any transitional or steady one, for any field geometry, any transmissivity distribution, and any local or distributed flow perturbations like production or recharge wells, underground diaphragms, etc. (Koutitas, 1983). The model in its 1DH and 2DH form is applied under several management scenarios, com- prising production wells as well as various technical means offering protection to the aquifer from salt water and ensuring the safe operation of the production wells.

3 APPLICATIONS AND COMPARISON TO NUMERICAL SIMULATION

Analytical solutions based on simplifying physical assumptions and geometry, though they do not solve ‘real world’ problems, they can be used as a tool for first-cut engineering analysis in a feasibility study (Cheng & Ouazar, 1999). Another contribution of analytical solutions is to serve as bench-mark problems for testing numerical algorithms. The numerical model, in its 1DH and 2DH form, is compared to the analytical solution pro- vided by Strack (1976) and Cheng & Ouazar (1999). Strack in1976 proposed a single potential for all over the flow domain. In the formulation, the Dupuit assumption is applied to the fresh water flow, and the Ghyben-Herzberg relation is utilized to define the interface depth. More de- tails about Strack’s single potential solution can be found in Mantoglou et al. (2004) and Cheng & Ouazar (1999). Figures 2 and 3 indicate that the predictions of the analytical model are very close to numerical simulations. An unconfined aquifer has been considered, with the following features: K=100m/d, n=0.2, Δρ/ρ=0.0025, the aquifer’s horizontal impermeable bottom lies 10 m below the sea level and the fresh water upstream head is 10.5m.

Two dimensional geometry one dimensional geometry 7 saltwater toe location shape of freshwater surface & analytical solution interface between the 2 layers numerical solution 8 ) 6

numerical solution m K

analytical solution ( e ) n i m

l 5 ( t d s a a e o h

C 4

4 3

1 0

0 2000 4000 6000 8000 10000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 i: location of seawater toe(Xtoe), i: position of saltwater toe (Xtoe) Figure 2. where Xtoe=i x dx, and dx=50m One di- Figure 3. Two dimensional wheregeometry. Xtoe=i*dx Salt water [m] and dx=200m mensional geometry. Salt water intrusion due to intrusion with a single pumping well (bold dot) fresh water outflow of coastline. Comparison of with pumping rate equal to Qw=100m3/d. Com- analytical solution to numerical simulation parison of analytical solution to numerical simulation A sensitivity analysis to the model parameters is undertaken. An interesting test refers to the issue of the forecasted sea level rise for almost 1m during the 21st century. (Figure 4) The rate of freshwater flow from the upstream part of the aquifer to the sea (above the interface) determines the length of seawater wedge intruding into the aquifer. Decrease in the rate of seaward flow of fresh water moves the seawater wedge landward, increasing the possibility of saline water pumping from wells. Figures 4 & 5 show the influence of the change in the fresh water flow to the sea, combined with a simultaneous sea level rise, upon the upstream movement of seawater toe. Decrease of the outflow rate can be considered as the result of the ob- served negative trend of annual precipitation heights over the Mediterranean basin.

12 12

q:seaward freshwater flow q:seaward freshwater flow q=0.0414m^2/s q=0.0257m^2/s d=10m d=10m d=11m d=11m )

) d=12m 8 d=12m m 8 m ( ( d d

l l e e v v e e l l

r r e e t t a a w w

a a e 4 e 4 s s

0 0

0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 i : saltwater toe location, where Xtoe=i*dx, dx=100m i : saltwater toe location, where Xtoe=i*dx, dx=100m Figure 4. saltwater wedge movement due to sea Figure 5. saltwater wedge movement due to sea level rise when q=0.0414(m3/d/m), K=100m/d, level rise when q=0.0257(m3/d/m), K=100m/d , Δρ/ρ=0.0025 Δρ/ρ=0.0025

A number of experiments have been conducted in the flume of the Hydraulics laboratory of Thessaloniki TEI, to test the model. A two layer flow at low Re numbers (resembling the creep- ing flow in a porous medium) is established. Figure 6 depicts the comparison of the experimental results with the model solution (for the respective flow conditions), in terms of the slope of the fresh-salt water interface along the channel, under steady flow conditions.

surface e e q=166cc/s q=166cc/s l l fresh water layer b b a a y y e r e r A B a H a H=190mm m m sharp interface d d r r n n e e saltwater layer u u p p o o m m impermeable i b i b boundary L=4400mm

Canal width=75mm

Figure 6. Comparison of numerical solution with experimental results and sketch of experimental canal. Two techniques for controlling the length of seawater wedge were checked. The first is use of recharge canals, as proposed by Cheng and Ouazar in 1999, aiming at the formation of a freshwater barrier in order to prevent saltwater intrusion. For an unconfined aquifer with the aforementioned features, figure 7 shows the location of saltwater toe due to a pumping well with 3 Qw=100m /d, located at (4000m, 2000m) and a recharge canal. The amount of recharged water is directly proportional to the length of the canal. So the canal should be long enough to protect the well. As shown in fig.7 when the length of the canal is L2=1Km and the discharge rate equal to 0.6QW the toe location retreats seaward and the pumping well is protected. Indeed, a recharge canal of L1=600m is not adequate. The second technique for the control of the salinity intrusion refers to saltwater pumping, re- sulting in the decrease of the hydraulic head of saline water. For the same aquifer and under the same data as before, figure 8 shows the effect of a salt water pumping well at (2000m, 2000m) and the influence of the pumping rate to the length of seawater wedge. As salt water pumping rate increases the encroachment of the salt wedge eventually stops and the fresh water pumping well becomes more productive, especially when Qs is close to Qw/5.

Qw=0 & Qc=0 Qw=100m^3/d & Qc=1.08Qw Qw=100m^3/d & Qc=0.60Qw Qw=100m^3/d & Qc=0.36Qw Qw=100m^3/d & Qc=0

Figure 7 Saltwater intrusion due to pumping well at (4000m, 2000m) with Qw=100m3/d & canal recharge

Qc, where Li is the length of the canal.

Qw=0 Qw=100m^3/d & Qs=Qw/5 Qw=100m^3/d & Qs=Qw/10 Qw=100m^3/d

Figure 8 Saltwater intrusion due to pumping well at (4000m, 2000m) and to saltwater pumping well at

(2000,2000), where Li is the length of the canal.

The disposal of the pumped saline groundwater may be a problem. Transport by pipelines and then discharge into the sea adds to the cost, and injection of the brine into deep aquifers-if feasible and acceptable from the hydrologic point of view-adds also to the cost. This means that such solution can only be realistic when pumping the saline groundwater near the coastline or estuaries (van Dam, 1999). Both of the aforementioned methods belong to the class of the hydraulic techniques and aim to restrain the intrusion of the salt wedge towards the production well.

4 SUMMARY AND CONCLUSIONS

A generic computational model describing the movement of the seawater wedge under certain flow conditions is formulated, solved and tested. The model is simple and operational, simple because it does not require a lot of hydrological and hydrogeological information and computational time and operational because it can be applied for any field geometry and boundary conditions. The model was initially applied for certain conditions and the comparison of the numerical results with the analytical solution of Strack’s potentional and laboratory experiments proved the efficiency and the reliability of the two-layer model. The sensitivity analysis that followed emphasized the influence of the sea level rise and the rate of seaward flow of fresh water decrease to the location of the saltwater toe. Under such conditions, it is essential to control of seawater intrusion. Two methods have been applied to control the encroachment of seawater into coastal aquifers, use of a recharge canal and use of a scavenger well. The length of the canal and its discharge rate, as well as the location and the pumping rate of the scavenger well are crucial fac- tors that determine the capacity of a coastal aquifer. As stated before the disposal of the pumped seawater maybe a problem. Thus, saltwater pumping wells should be located near the shoreline. Flow perturbations like production or recharge wells and canal, scavenger wells, underground diaphragms etc pose interesting optimization problems. In conclusion it is documented that the presented model is simple, effective, generally appli- cable for any field geometry; it requires limited computer resources (CPU time and memory) and can be used in combination with heuristic and stochastic optimization methods, like the method of genetic algorithms or the method of “annealing” for an ultimate synthesis of an operational tool supporting the integrated management of coastal aquifers under the contemporary demand pressures and the forecasted climatic changes.

REFERENCES

Bear, J. 1999. Conceptual and mathematical modeling, in Seawater intrusion in coastal aquifers: concepts, methods and practices, edited by J. Bear et al., pp.127-161. Cheng, A. & Ouazar, D. 1999. Analytical Solutions. Conceptual and mathematical modeling, in Seawater intrusion in coastal aquifers: concepts, methods and practices, edited by J. Bear et al., pp.163-191. Dagan, G. & Zeitoun, D.G. 1998. Seawater-freshwater interface in a stratified aquifer of random perme- ability distribution. Journal of Contaminant Hydrology 29:185-203. Dam, J., 1999. Exploitation, Restoration and Management, in Seawater intrusion in coastal aquifers: concepts, methods and practices, edited by J. Bear et al., pp.73-161. Essaid, H.I. 1990. A multilayered sharp interface model of coupled freshwater and seawater flow in coastal systems: model development and application. Water Resources Research 26(7):1431–1454 Koutitas, C. 1988. Density currents-stratified flows. Mathematical models in Coastal engineering: 89- 104. London: Pentech Press. Koutitas, C. 1983. Groundwater flow. Elements of computational hydraulics: 88-98 London: Pentech Press. Mantoglou, A., Papantoniou, M., Giannoulopoulos, P. 2004. Management of coastal aquifers based on nonlinear optimization and evolutionary algorithms. Journal of Hydrology 297 (1-4): 209-228. Oude Essink, G.H.P.& Boekelman, R.H. 2000. Saltwater intrusion in coastal aquifers. in: Groundwater Pollution Control, edited by K.L. Katsifarakis, WIT Press, Southampton, pp. 145-201 Qahman, K., Abdelkader, L., Ouazar, D., Naji, A. & Cheng, A. 2005. Optimal and sustainable extraction of groundwater in coastal aquifers. Stoch. Environ. Res. Risk Assess 19: 99–110. Strack, O. D. L., 1976. A single-potential solution for regional interface problems in coastal aquifers, Wa- ter Resour. Res. 12(6): 1165–1174