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Aquatic Procedia 4 ( 2015 ) 87 – 94

INTERNATIONAL CONFERENCE ON WATER RESOURCES, COASTAL AND OCEAN ENGINEERING (ICWRCOE 2015) Stochastic Simulation of Seawater Intrusion into Freshwater Aquifers

S.K.Pramadaa,* and S.Mohanb

aDepartment of Civil Engineering, National Institute of Technology, Calicut-673601,Kerala,. bDepartment of Civil Engineering, Indian Institute of Technology, Madras, -600 036,,India.

Abstract

Groundwater flow and transport in aquifers are strongly influenced by the geological heterogeneity at various scales. The erratic nature of the hydro geological parameters and the insufficient information about the spatial distribution suggests, a description of these parameters in a probabilistic context rather than a deterministic one. Theories based on homogeneous assumption can lead to serious errors. This paper presents a methodology for the effect of heterogeneity on seawater intrusion modelling based on stochastic simulation of the system. The heterogeneity has been modelled by coupling Monte-Carlo simulation to a seawater intrusion model. SEAWAT was used as a simulation model. This study leads to a better understanding of the transport mechanism in heterogeneous formation in coastal aquifers. The applicability of the developed methodology is illustrated by a case study.

© 20152015 The The Authors. Authors. Published Published by byElsevier Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (Peerhttp://creativecommons.org/licenses/by-nc-nd/4.0/-review under responsibility of organizing committee). of ICWRCOE 2015. Peer-review under responsibility of organizing committee of ICWRCOE 2015 Keywords: Coastal aquifer;seawater intrusion;heterogeneity;stochastic simulation; Monte-Carlo simulation

1. Introduction

The coastal aquifers are very vulnerable to seawater intrusion because of the overexploitation of the coastal aquifers. Seawater intrusion models are very efficient tool for coastal aquifer management and protection. There are mainly two general approaches used to analyze saltwater intrusion in coastal aquifers, the sharp interface (Mahesha, 1996) and the disperse interface approach. The sharp interface approach is based on the simplification of the thin transition zone relative to the dimension of the aquifer.

* Corresponding author. E-mail address: [email protected]

2214-241X © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of ICWRCOE 2015 doi: 10.1016/j.aqpro.2015.02.013 88 S.K. Pramada and S. Mohan / Aquatic Procedia 4 ( 2015 ) 87 – 94

The disperse interface approach explicitly represents a transition zone or a mixing zone of the freshwater and saltwater within an aquifer due to the effects of hydrodynamic dispersion (Huyakorn et al., 1987; Cheng and Chen, 2001; Tejeda et al., 2003; Park et al., 2012). In the transition zone there is a gradual change in density. The mathematical modeling of density-dependent problems is quite complex in case of disperse interface approach. They are generally formulated as a coupled system of two partial differential equations, one describing continuity equation for fluid (the flow equation), and the other continuity equation for the salt concentration (the transport equation). While studying the problem involving mass transport, it is necessary to solve both the equations simultaneously, as the solution to one depends on the solution of the other. There are a large number of modeling codes that have been designed to simulate variable density groundwater flow.

The groundwater models have not been enjoying great success as predictive tools (Konikow and Bredehoeft, 1992; Anderson and Woessner, 1992). To obtain reliable results from modelling, accurate data should be the input to the model, and it is difficult to obtain reliable information regarding hydrogeological properties. It is widely recognized that hydraulic conductivity vary significantly over a wide range of spatial scales [Gelhar, 1994]. Transport process are generally more complicated, because the process is influenced by the complicated paths taken by fluid moving through a heterogeneous medium. Heterogeneity in hydraulic conductivity can cause the difference in length of intrusion in case of seawater intrusion. Penetration can be longest at the more conductive path. Hydro dynamic dispersion, which is the cause of dispersed interface in seawater intrusion is the combined effect of molecular diffusion and mechanical dispersion. Molecular diffusion slowly occurs over long periods of time and generally is considered negligible compared to mechanical dispersion. Mechanical dispersion depends on variations in the fluid velocity and from Darcy law it is obvious that hydraulic conductivity play a role. Mechanical dispersion refers to the spreading of a plume or solute as a result of heterogeneities in the aquifer. These heterogeneities occur at microscopic and macroscopic scales. Field scale dispersivities may be many orders of magnitude larger than those observed in the laboratory. If microscale variations of water flux due to heterogeneity could be precisely described, there would be no need to simulate dispersion, which would emerge naturally from a solution considering only advection and molecular diffusion. Thus the heterogeneity of the hydraulic conductivity is indeed a central problem in modeling coastal aquifers. To deal with heterogeneity stochastic approach can be adopted. In the past two decades, research efforts have been directed to describe the spatial heterogeneity of porous media. These can be considered in the stochastic framework while modelling the systems. In the stochastic approach uncertainty is represented by probability or by related quantities like statistical moments. The solution can be obtained by Moment Equation (ME) approach (Aguirre and Haghighi, 2003; Morales-Casique et al., 2006) or Monte Carlo simulation (Woldt et al., 1992; Copty et al., 2000). Many stochastic methods have been developed and used in contaminant transport modelling. However, the literature dealing with saltwater intrusion models which is based on disperse interface approach , under uncertainty is limited.

2. Methodology

The computer code that was used in the present study is SEAWAT (Langevin et al., 2004), which is based on disperse interface approach. Argus ONE 4.2w was used a pre and post processor for the numerical model. After developing the numerical model. a program is developed to link the Monte Carlo Simulation with the SEAWAT dispersed interface model. Monte-Carlo simulation is a statistical technique by which a quantity is calculated repeatedly using randomly selected parameter values for each calculation. A simplified flow chart that illustrates the linking of the Monte-Carlo method to the SEAWAT simulation is presented in Figure 1. After developing the SEAWAT model, the model is exported first to create the input data format, which is necessary to run the model, followed by reading the input data which consists of uncertain parameter(s). But for parametric uncertainty analysis for hydraulic conductivity, the only input that is required to change is hydraulic conductivity. All the other input parameters are not subjected to change.

S.K. Pramada and S. Mohan / Aquatic Procedia 4 ( 2015 ) 87 – 94 89

Start

Develop SEAWAT model

Export the model

Read the input data which consists of uncertain parameter

Number of realization=N

N=1

Write the input as the same format except the uncertain parameter

Generate random number based on a probability distribution

Update the input based on the distribution of uncertain parameter

Perform SEAWAT simulation runs N=N+1

Print head and concentration

Is N=Number No of realization

Stop

Fig.1 Flow chart –Linking Monte Carlo simulation with SEAWAT 90 S.K. Pramada and S. Mohan / Aquatic Procedia 4 ( 2015 ) 87 – 94

Generate random number based on a probability distribution. Multiple realization of hydraulic conductivity field is generated through a pseudo-random procedure. The generated random parameter values are then assigned to the model variables. Following this, the SEWAT model run is performed. The result is given in terms of the length of intrusion. The generation of random parameter values and SEAWAT simulation is repeated as many times as necessary to accurately determine the probability distribution length of intrusion. Individual results are compiled, and eventually analyzed statistically to give an overall assessment of the uncertainty the length of intrusion in heterogeneous soils.

3. Description of the study area

The coastal aquifer of interest in this study is the - Injambakkam aquifer, which is part of the aquifer system adjacent to the city of Chennai. The South Chennai aquifer that holds substantial quantity of groundwater, meets 20% of city’s water requirement. The South Chennai aquifer system covers an areal extent of about 55.2 sq. km. The area is bounded by the on the eastern side. The confluences with the Bay of Bengal on the Northern boundary of the area. The along the western margin runs almost parallel to the Bay of Bengal in the north-south direction and contains stagnant water. The study area has a terrain elevation ranging between 3 and 10 m and experiences a sub-tropical climate, the annual temperature ranging between 24º C and 41º C. The annual rainfall is about 1200 mm. The aquifer receives around 60% of its recharge from northeast monsoon during the months of October, November and December. Both the Besant nagar and the Thiruvanmiyur-Injambakkam belt comprise coastal alluvium deposits. The alluvium comprises of sand (medium to coarse grained) silt, clay and shells. The coastal alluvium is followed by basement of Charnockite of Archaean age.

4. Numerical Model Development

A regularly spaced, finite-difference model grid of size 100x100 m. was developed to study the seawater-freshwater interface. The top of and bottom of the single layer model is based on borehole details from nine boreholes. The top elevation varies from 0 to 9m above MSL and bottom elevation varies from 1 to 16m below MSL. Temporal discretization was done by dividing the simulation time into 72 monthly stress periods from January 2000 to December 2005. The stress period is again divided into transport steps. The transport step is automatically selected by the program to meet various stability constraints that are solution dependent. Boundary conditions were established to represent as closely as possible the conceptual model of the flow system. The seaside is represented with constant head of zero meter and constant TDS concentration of 35000 mg/lit. The large water body nearby is represented with a flux boundary. The Adyar river is represented as the river boundary condition and the top boundary is represented as a recharge boundary. The western and southern boundaries are represented as time varying head boundaries based on the observed head values. The water level and TDS concentration data for January 2000 was specified as the initial head and initial concentration The initial aquifer parameters were obtained from the earlier study (Mohan, 2003). During calibration the aquifer parameters were slightly modified to match the observed head and concentration to that of simulated values. SEAWAT simulation model was run for 72 monthly stress periods from January 2000 to December 2005. Specifications on observation wells were given in the control points specified, and used for calibration. Fig.2 shows the control wells used for calibration. The hydraulic heads and concentration values calculated at nine control points were compared with the respective monthly head and concentration values for years 2000 to 2005. The model was calibrated to observed field conditions by adjusting the hydraulic conductivity and dispersivity parameters. Dispersivity was varied to match the simulated and observed TDS values. Fig.3 and Fig.4 show the comparison of simulated head and concentration in an observation well at Besant Nagar. It can be seen that there is reasonable agreement between the observed and computed values of head and concentration values. The calibrated hydraulic conductivity at nine control locations are given in Table 1. The hydraulic conductivity varies from 50.2 m/day to 65 m/day for this aquifer. The initially and final calibrated values of aquifer parameters in the model are given in Table 2. The longitudinal dispersivity varies from 50m to 35m and transverse dispersivity is assumed as 1/10 of longitudinal dispersivity.

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Table 1.hydraulic conductivity values. Observation well Assumed Value of K Calibrated Value of K (m/day) (m/day Besant nagar 65 61.24 Thiruvanmiyur 65 64 65 63.8 Pallavakkam 65 62.1 65 61.9 Injambakkam 65 65 Velachery 65 53.5 65 50.2

Table 2.The Initial and finally adopted parameter values Parameter initial value Final calibrated value Hydraulic conductivity (K in m/day) 65 50.2-65 Specific yield 0.15 0.15 Effective porosity (T) 0.2 0.2

Longitudinal dispersion (DL in m) 50 35

Transverse dispersion (DT in m) 5 3.5 3 1000 1000 Density of freshwater(Uf in kg/m ) 3 1025 1025 Density of source(Usin kg/m Concentration of source (Csmg/l) 35000 35000

9000

Besant Nagar 8000 Thiruvanmiyur

7000 Vellachery

6000 Kottivakkam

5000 Perungudi

4000

Neelankarai 3000

Bay of Bengal

Y in meters 2000

1000

Injambakkam 0 0 1000 2000 3000 4000 5000

Fig.2 Observation wells used for calibration

X in meters 92 S.K. Pramada and S. Mohan / Aquatic Procedia 4 ( 2015 ) 87 – 94

Fig.4 Comparison of observed and computed concentration at Besant Nagar

5. Application of the linked model

The basic idea here is to characterize quantitatively, the uncertainty in estimates the length of intrusion due to heterogeneity of the aquifer. The linked model with Monte Carlo and SEAWAT was used to quantify the uncertainty on the length of intrusion. The SEAWAT model consists of 4876 cells (92 rows 53 columns). The 100 m x 100 m finite difference block of varying thickness, the hydraulic conductivity of each cell should be different. This is achieved through the probability distribution function of hydraulic conductivity value. Hydraulic conductivity is normally assumed to be log normally distributed (Gelhar, 1994), which shows that the hydraulic conductivity varies over many orders of magnitude. The mean and standard deviation of the hydraulic conductivity were arrived at based on the calibration results and are found to be 60 m/day and 5m/day respectively. For the case study the hydraulic conductivity variation is found to be very less and hence a normal distribution is assumed for hydraulic conductivity. Based on these, hydraulic conductivity field is randomly generated and assigned to each cell, and each iteration results in new realization of hydraulic conductivity. The hydraulic conductivity field is generated based on S.K. Pramada and S. Mohan / Aquatic Procedia 4 ( 2015 ) 87 – 94 93

Eqn.1 2 1 ª 1 § x'P · º xf )'( exp« ¨ x' ¸ » 2SV 2 ¨ V ¸ 1 x' ¬« © x' ¹ ¼» where x’ is the random variable, f(x’) is probability density function of x’, Vx’ and Px’ are standard deviation and mean respectively. Fig.5 shows the distribution of hydraulic conductivity for the first realization. New realizations of the head and concentration values for each realization of the hydraulic conductivity are obtained by running SEAWAT for the same boundary and initial conditions. The number of required realizations depends mainly on the model, the assumed input parameter distribution, and the desired accuracy of output and variance in output. It is necessary to ensure that Monte Carlo simulation is slowly getting converged. This is done by carrying out different set of simulations with increased number of realizations. The statistical parameters can be compared with those of the previous set, and if significant difference in the result occurs then it is an indication that the Monte Carlo simulation has not converged. The procedure can be repeated with increased realizations until convergence of the Monte Carlo is confirmed. First, 20 realization has been done and the number of realizations is increased for each set of simulation. For this particular problem the Monte Carlo Simulation is converged for a realization of 30. For this particular problem the degree of heterogeneity is very less and the simulation is converged within 30 realizations.. For more complex problems, several hundred or more number of realization may be required. But the number of realization can be reduced by latin hypercube sampling or stratified sampling.. Simulation results are analyzed in terms of the probability distribution of interface length. The derived cumulative distribution function (CDF) for the length of intrusion is shown in Fig.6. Standard deviation was found to be 14 m.

Fig.5 The distribution of hydraulic Fig.6 Cumulative distribution function for conductivity for the first realization length of intrusion 94 S.K. Pramada and S. Mohan / Aquatic Procedia 4 ( 2015 ) 87 – 94

6. Conclusions

In all the coastal aquifers, an interface exists between groundwater flowing towards the sea and the saline water. Under undisturbed conditions this interface will be stationary. But due to over exploitation of coastal aquifers the interface starts moving towards landward. In order to prevent/control this landward movement, better and efficient management of coastal aquifers is very much necessary. Saltwater intrusion models can be used to evolve efficient management strategies. Due to uncertainties in model input parameters, in particular those describing heterogeneity, model predictions may not represent the exact behaviour. In order to study the effect of heterogeneity on seawater intrusion length, an interface is developed to link Monte Carlo simulation with SEAWAT by treating hydraulic conductivity as an uncertain random variable. The uncertainty on the interface length due to heterogeneity was examined by conducting several realizations. In very complex system where the hydraulic conductivity varies from place to place, it is very much necessary to determine the uncertainty in the length of intrusion due to the heterogeneity. Even for a small variation of hydraulic conductivity it was found that the error in the prediction of length of intrusion is 14 m. In this study the system is homogeneous at the grid scale of 100 m.

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