Groundwater Quantity and Quality Management

Groundwater Quantity and Quality Management

Edited by

Mustafa M. &ral and StewartW. Taylor

ASCE

~ -. ~ w~

CHA PTER 10 DENSITY DEPENDENT FLOWS, SALTWATER INTRUSION AND MANAGEMENT Bithl n Datta l and An irban Dhar! Ij ames Cook Uni versity, Townsville, QLD 481 t, Australia 21ndian Institu te o(Technology Kharagpur, Khoragpur, W.e. 721302, India

10.1

Introduction

Intrusion of saltwater in coastal aquifer hinders its beneficial use as a source of water. The speci fic aim of coastal aquifer management may involve the design of a spatiotcmporal pumping strategy to meet demands. while controlling ,Ihe intrusion process, also through planned pumping. Many coastal aquifers, i.e., aquifers hydraulically connected with the ocean, can be used as major operational reservoirs in water resources systems. Development of such reservoirs for supply of water is very common in many parts of the world. The ex ploitation of these reservoirs is restricted in many cases, because of seawater intrusion in to the coastal aquifers. Saltwater intrusion in coastal aquifCT1i is global problem. Over the years differen t studies have been reported worldwide, e.g., Madras, India (Rouve and Stocssinger 1980), the ' Mediterranean coast of Israel (Shamir et a1. 1984), the Waialae aquifer of southern Oahu, Hawaii (Essaid 1986; Emch and Yeh 1998), in southern Oahu, Hawaii (Souza and Voss 1987), the Nile delta aquifer in Egypt (Shcrifet al. 1988), in Hallandale, Florida (Andersen ct al. 1988), the Yun Lin Basin in southwestern Taiwan (Willis and Finney 1988), the Northern Guam aquifer (Contractor and Srivastava J 990), the Soquel-Aptos Basin, Santa Cruz County, California (Essaid I 990a, 1990b), the Jakarta Basin (Finney et al. 1992), the southwest region of Bangladesh (Nobi and Gupta 1997). Hernando County, Florida (Guvanascn et a1. 2000), Island ofTexel, The Netherlands (Oude Essnik 2001), the Johe River Basin, Shandong Province, China (Cheng and Chen 200 1), the Lei-Qiong Depression Zone, near the Leizhou Peninsula in southern China (Zhou et aJ. 2(03), Savannah, Georgia (Kentel et al. 2(05), the Llobregat de lta, south of Barcelona, Spain (Abarca et a1. 2(06). and the coastal karstic aquifer in Crcre, Greece (Karterakis et aJ. 2007). A comprehensive review of saltwater intrusion modeling, management and mon itoring methods ean be found in Bear et al. ( 1999) and Cheng and Ouazar (2004). Some of the works focused on prediction, while others stressed management. Saltwater intrusion is a phenomenon that occurs due to movement of seawater towards freshwater aquifers and ereation of a brackish environment. Heavier saltwater tries to underlie freshwater due to differences in buoyancy. A brackish environment or mixing zone of varying density is created. In this transition zone (diffuse interface) a gradual increase in density of mixed fluid is observed from freshwater to seawater. Figure 10.la shows the transition zone in an unconfined

394

GROUNDWATER QUANTITY AND QUALITY MANAGEMENT

395

coastal aquifer. Variation in transi tion zone thickness is observed depending on the coastal aquifer environment. [n presence of thin transition zone, a coastal aquifer can be idealized by considering freshwater and saline water as immiscible fluids . The transition zone can be replaced by a sharp interface (Figure 10. [b). These idealizations can be used to facilitate modeling of the saltwater in trusion phenomenon in coastal aquifers. Although, sharp interface models are popular due to their simplicity, they inherit the possibility of oversimplifying the actua l situation. In reality, a transition zone should be considered in coastal aquifer modeling. Incorporation of a transition zone causes the saltwater intrusion model to be highly nonlinear.

(.)

Figure 10.1 :

(b)

(a) Diffuse interface in an unconfined coastal aquifer, and (b) sharp interface

in an unconfined coastal aquifer. Seawater is comprised of more than seventy elements, with six ions contributing greater than 99% of the total dissolved solids (TDS) concentration. Table 10.1 provides a typical seawater composition and corresponding concentrations (Younos 2005). The TDS of seawater varies largely between 500 mg/I to 50,000 mgll. Lower range values indicate brackish water while upper range represents seawater. The TDS level in brackish water system fluctuates spatiotemporally. Variations may be due to tide, freshwater inflow (rain or river flows), and evaporation rate (Younos 2005). Although TDS concentration of 500 mg/I is considered as Secondary Maximum Contaminant Level (SMel) by U.S . EPA ([992), a much lower value is desirable for drinking purpose. Table 10.[: Composition ofseawaler (Younos 2(05). [I emen l Chloride (Cll Sulfate (SO.) Calcium (Ca)

Sodium (Na) Magnesium (Mg) P01assium (Kl

Mass Fratlion

~*I·l 55.04 7.68 1.16 30.61 3.69 1.10

Conun lration ~mGLll 19.400

'" '"

10,800 1290 392

396


10.1.1 Density Dependent Flow Saltwater intrusion simulation modeling approoches available for dealing with the freshwater and saltwater in coastal aquifer are: (a) sharp interface approach, and (b) diffuse interface approach. Saltwater intrusion is generally modeled considering two immiscible fl uids with a sharp interface, or a single fluid approach with density dependence. Density-dependent models are highly nonlinea r due to the coupled nature of the flow and transpon equations. Variation of fluid density is the prominent feature of the density-dependent flow. Density dependence necessarily changes the flow pattern compared to common groundwater problems where variation of fluid density is not prominent. A historical perspective of saltwater-freshwater interaction is presented by Reilly and Goodman (1985). Segol (1994), Holzbecher (1998), and Bear et al. ( 1999) provide insight to the subject. Bobba (1993) provided a review of mathematical models for saltwater intrusion in coastal aquifer. Many approximate analytical and numerical models arc available for simulating the physical processes in coastal aquifers.

Analytical Models: Most analytical models arc based on Ghyben-Hcrzberg approach, which uses sharp interface assumption along with simple hydrostatic conditions to describe the saltwater intrusion phenomenon in a homogeneous, unconfi ned coastal aquifer. This approach underestimates depth to the saltwater interface and fails when there is freshwater flow towards sea (Freeze and Cherry 1979). The sharp interface assumption facilitates the derivation of analytical solutions. Different studies have , used the sharp interface approach, e.g., Henry (1959), Bear and Dagan {I 964), Hantush (1968), Schmorak and Mercado (1969), Strack (1976), van Dam and Sikkema (1982), Sikkema and van Dam (1982), Huppen and Woods (1995), Dagan and Zeitoun ( 1998), and Kacimov and Obnosov (200 I). Recently, Dentz ct al. (2006) derived analytical solutions for Henry's problem using a coupled density approach. A detailed review of analytical methods can be found in Cheng and Ouazar ( 1999). However, analytical solutions are available for only simplified field conditions. Numerical Models: Numerical models arc effective in representing physical processes irrespective of their complexity. A number of algorithms are available for obtai ning numerical solutions of the governing panial differential equations. Usually, stability criteria dictate the choice of spatial and temporal discretization. The approaches and challenges for modeli ng density-dcpendent flow are reviewed by Simmons et al. (2001), Diersch and Koditz (2002), POSt (2005), and Simmons (2005). Different numerical techniques have been applied for simulating the saltwater intrusion phenomenon, including the fi nite difference method (Mercer et aJ. 1980; Polo and Ramis 1983; Ledoux et aJ. 1990; Essaid 1mb; Das and Datta 2000), the finite element method (Lee and Cheng 1974; Segal et al. 1975; Voss 1984; Huyakom et aJ. 1987; Contractor and Srivastava 1990; Huyakorn et aJ. 1996; Lin et al. 1997; Cheng et al. 1998; Guvanasen et al. 2(00), the boundary element method (Volker and Rushton 1982; Taigbenu et al. 1984; Cabral and Wrobel 1993; Naji et al. 1998), the finite volume method (Liu et al. 2(01), the mixed finite element-finite volume


397

approach (Mazzia and Puni 2(06), Picard and Newton linearization approaches (Pulli and Paniconi 1995). and the network simulation method (Mcca et al. 2(07). Many standard models are available for simulating the saltwater intrusion process. A review of such codes can be found in Sorek and Pinder (J 999). Commonly used codes include SUTRA (Voss 1984; Voss and Provost 2002), FEMWATER (Lin et aJ. 1997), FEFLOW (Diersch 2(02), H$T3D (Kipp 1986, 1997), MOCDENS3 D (Oude Essnik 1998). SWIFT (HSI GeoTrans 2000), SEAWAT (Guo and Langevin 2002), MODHMS (HydroGeoLogic Inc 2002), and SWI (Bakker 2003; Bakker and Schaus 2005). 10. 1.2 Sallwater Int rusion a nd Ma nagement Management of saltwater intrusion in coastal aquifers is a cri tical issue of modem times. Simulation models can provide ncccssary future managcment guidclincs only if repetitively used in an exhaustive manner. Simulation models can only answer the question: what if a specific management strategy is implemented. Therefore, an effective mechanism is needed that can combine the optimization and physical processes simultaneously to efficiently evolve management stmtegies. Linking of the process simulation model with an optimal decision model can address this requirement. Objeclil'e.~ of MQlwgemellf Mode/: Identification of a proper Objective function is a challenging task in management modeling. Different methods can be utilized for controlling saltwater intrusion in coastal aquifer. In some of the methods, surrogate objectives are used to quan tify the management goals.

Different management objectives reponed in the litemture include maximizing the total pumping mte (Shami r et al. 1984; Hallaji and Yazicigill996; Cheng et al . 2000; Bhattacharjya 2003; Mantoglou 2003; Abarca et al. 2006; Kanemkis et al. 2007), minimizing the pumped water salinity (Das and Dalla 1999a, I 999b), minimizing the volume of saltwater intrusion into the aquifer (Finney ct a1. 1992; Emch and Yeh 1998), minimizing the dmwdown (Hallaji and Yazicigil 1996), minimizing the deviation from the target concentration, and pumping and recharge rate (Abarca et al. 2006), and minimizing the distance of the stagnation point (Stmek 1976) from coast (Park and Aral 2004). Pumping or injection costs are also included in different studies, e.g., Emch and Yeh (1998). Gordon et al. (2001 ). Reichard and Johnson (2005), and Ferrcia da Silva and Haie (2007). However, only a few works considered multiple objectives ofopcration at a time (Shami r et al. 1984; Emch and Yeh 1998; Das and Dana I 999a; Park and AraI2(04). Surrogate objectives are sometimes expressed as constraints. Constmints on maximum and minimum pumping rau:s (Hal1aji and Yazicigil 1996; Emch and Yeh 1998; Das and Dalla 1999a; Cheng et al. 2000; Zhou et al. 2003; Abarca et al. 2006). toe location (Cheng ct al. 2000; Mllntoglou 2003; Mantog]ou et Il\. 2004; Park Ilnd Aral 2004; Ferrciu da Silva and Haie 2007), interface elevation at a particular location

398


(Rao et al. 2003, 2004a), groundwater heads (Hal1aji and Yazicigil 1996; Emch and Yeh 1998; Zhou et al. 2003; Reichard and Johnson 2005; Abarca et al. 2006), flow potcntial (Mantoglou 2003; Mantoglou et a1. 2(04), and salt concentration of the pumped water (Gordon et al. 2000; Das and Datta 1999a, 1999b) are more common.

IIrcorporation of Physical Processes in Management Model: Accuracy of management strategy depends on the level of approximation and the way in whieh they are incorporated. In broader sense, physical processes can be incorporated using (a) an analytical model, (b) a numerical simulation model, (c) an embedding approach, or (d) a meta-model-based approach. The way physical processes are included vary, e.g., analytical solutions (Cheng et al. 2000; Mantoglou 2003; Cheng et al. 2004; Park and Aral 2(04) or numerical simulation using the sharp interface approach (Willis and Finney 1988; Finney et a!. 1992; Emch and Yeh 1998; Rao et 01. 2004a; Mantoglou et al. 2(04). Gordon et al. (2000) used a chloride transport model. Only a few studies have used density_ dependent flow and transport witbin the management framework, e.g., Das and Datta (l999a, 1999b) and Qahman et a!. (2005). Das and Datta (1999a. 1999b) used the embedding technique for this purpose. Computational complexity increases when density variations are taken into account, which results in a highl y nonlinear and non convex problem (Finney et a1. 1992). A good number of work used meta-models (approximation-based models) to reduce the computational complexity of physical process-based models. Thcse models are useful approximators of the highly nonlinear nature of the saltwater intrusion process. The most primitive version of a meta-model is the "Rcsponse Matrix," which is generally linear in nature. This linear nature has been exploited also while formulating optimization models. Response matrix-based studies are reported in Hallaji and Yazicigil (1996), Zhou et al. (2003), Reichard, and Johnson (2005), Abarea et a1. (2006), and Karterakis et a1. (2007). Sometimes Ihis approach yields incorrect results due to ovcrsimplification of expressions for nonlinear processes. In recen t years, a few studies concentrated on the use of complex meta-models, like Artificial Neural Network models, e.g., Bhattae harjya (2003), Rao et al. (2003, 2004b), and Bhattacharjya and Datta (2005).

Different Optimization Algorithms ill Management Models: In solving management problems, the choice of algorithm greatly influences the solution quality. Generally, complexity (linearity, nonlinearity and discontinuity) and nature of decision variables (discrete, continuous and integer) dictate the choice. Linearization of pbysical processes by response matrix approach is a widely used method, which fac ilitates the use of linear programming, e.g., Hal1aji and Yazicigil (1996), Mantoglou (2003), Reicbard and Johnson (2005), and Karterakis et aI. (2007). The saltwater intrusion problem is a necessarily nonlinear problem due to nonlinear physical processes involved. Applications of nonlinear algorithms include: sequential quadratic programming (Mantoglou 2003; Mantoglou et al. 2004) and the


399

geostatistical inversion technique (Abarea et al. 2006). A large number of studies have used different versions of MINOS (Munagh and Saunders 1993), which utilizes the reduced-gmdienl algorithm in conjunction with quasi-Newton algorithm, e.g., Willis and Finney (1988), Finney el al. (1992), Emch and Yeh ( 1998), and Das and Dalla ( 1999a, 1999b). However, MINOS is "designed to find solutions that arc locally optimal" (Munagh and Saunders 1993). Non-diffcrentiable ronnulalions are the most difficult ones to solve using classical algorithms. Gordon et al. (2001) used Bundle-Trust nonsmooth optimization procedure to opti mize discontinuous fannulation. Application of nontraditional algorithms (evolutionary algorithm, genetic algorithm, s imulated nnnealing) has gained popularity in recent years. These algorithms can easily handle highly nonlinear, even non-smooth problems. In addition these algorithms are well suited for linking optimization algorithms with numerical simulation models. Over the years different genetic algorithms have been used in saltwater intrusion management, e.g., structured messy gcnetic algorithm (Cheng et al. 2000), real coded genetic algorithm (Bhallacharjya and Datta 2005), simple genetic algorithm (Cheng et al. 2004; Katsifamkis and Petala 2006, Qahman et al. 2005), and real coded progressive genetic algorithm (Park and Ami 2004). Application or other algorithms include the evolutionary algorithm (Mantoglou et al. 2004), simulated annealing (Rao et al. 2003, 2004a, 2004b). and differential evolution (Kanemkis et al. 2007).

10.2 Density-Dependent Governing Equations To simulate the density-d.ependent saltwater intrusion processes in coastal aquifers, the governing equations that represent the three-dimensional, advective-dispcrsivc flow and \ranspon processes are to be solved simultaneously. The three-dimensional advective-dispersive flow equation for a heterogeneous, anisotropic and fully saturated aquifer may be written as proposed by Huyakom et al. (1987):

( 10.1)

The reference hydraulic head is defined as (10.2)

The densi ty coupling coefficient is defined as

c '1 "'-

'.

(10.3)

400


The density difference ratio (E) is expressed as ( 10.4)

The actual hydraulic conducti vit y is defined as

',,,. " The density of the mixed fluid is defined as K,

:=--

(IO.S)

(10.6)

The advcctive-dispersive equation can be wrillen as (Huyakorn et al. 1987) (l0.7)

The Darcy velocity vector is expressed as:

( 10.8)

The dcnsity of water primarily depends on concentration and tcmperature. It has been observed that chlorinity contributes a major portion of the seawater (Table 10.1 ). Figure 10.2 shows the variation of density with chlorinity and temperature. Coupling between flow and transport processes are described in tenns of Equation ( 10.6).

GROUNDWATER QUANTITY AN D QUA LITY MANAGEMENT

40 I

..

n. " ,c,~r-r-r-l r-,-,-,-,-";-r-r-r-r-" .... __ . __ , _.. __ . __ ..•. _....... . "

-:-~':-~-:-:--~-:-~-~-~-:j '~. ~~~.~.~~.~~'~~~:;: .. _.- ,---_ .. _. _,

,

•__________ . -0._ . - .•• __ - -._ ..... . ,__ ____ __ ________ ~

tI

'

,m

,

, _ fo-O-=A'·~·'-c-c-c·l-"-"-o-O-"-"-. .-i----~~"3,~, ~~-~-~-.~-4~-~.~-~-~-~t~-~-~-~-~-~-:.-:.-:-:-1':-:-:-~--~~::l ~ .. -.. --.. -,.- -----.--,--- --.---- ,"' o.~ 1l

.. ~ .. -'

-_.-.. _.. -

k;-;-~-·@-·~·-~·~-;-;-~}~-~-~-:-:-:-:-:-:-:-i::-::~:::::l '~.

r.:-~-~-~--~-~-~-~-~-~:~-~-~-~-~-~-~-~-;:;:1;~:=:=::-::~:~:~-~-~-] ,010

t~;-___ . • _C.. ___ . ___ ... __ . _ , Ol! ~-~-9:______ ,~-~-~-;-;-~,~-C-:-:-:-:-:-: -:i,::::::~~ G.nco

. __ .

l===:":':"-::'~'E,..,-~-~-~-~-:-:-i~~-:-~-:--:-~-~-~~ ~ -"" [r:-~-~-'~:,-~.-~"~-~-~-j:t:=:::~ , :~:~:~:~:~:~:i:~: , ;-~-,~,~'~-~-~-j ~- ."T.VIIV- • • • • • - -

~

Temperalure T

Accurate

Figure 10.2:

, . - _ . - - . - --

.0

101'

IS

rei

for T< 15 'C aNl for C¥1.1

'" "

%

Density of waler as a function of the chlorinity and temperature (Oude Essnik 2(01).

10.2. 1 Olffrrr ni Solution Allproachrs The flow and transport equations descri hcd by Equations ( 10. 1)-( 10.8) can only be solved numerically. There are two approaches in numerical solution, viz: (a) forward modeling using discretized equations, and (b) optimiza tion-based emhcdding tcchnique. Different forward models for simulaling the densily-dependent flow and transport are SUTRA (Voss 1984; Voss and Provost 2(02), FEMWATER (Lin et al. 1997), HST3D (Kipp 1986, 1997), SEAWAT (Guo and Langevin 2002 ), and FEFLOW (Diersch 2002 ). Optimization-based embedding approaches are relatively rare in the litel1lture. Das and Dalla (2000) proposed an approach fo r solving the diseretised fin ite difference fonn of the governing flow and transport equations for the transient saltwater intrusion process using nonlinear optimization. The resul ting model serves as a simulation model utilizing classical nonlinear optimization technique. Equations ( 10.1)-( 10.8) can be approximated by finite difference methods to fonn a set of discretized non-linear equa tions. They are no n-linear due to the densi ty coupling as represented in Equation ( 10.6). The discretizcd sct of equations can be expressed in a functional fonn as

402


!,(U J )= 0 • VI E {I, 2•.. .• N,},} E {I. 2•... , 2>< N,}

(10.9)

where II] is a vector consisting of values of II, c, q.. , and q" in the three-dimensional space and time domain of the problem. N, is the total number of equality constraints. This system of equations can be solved using an appropriate numerical method described in Das (J 995) and Das and Datta (2000). In the optimization-based embedded model, the diseretized version of flow and simulation equations given by Equation (1 0.9) constitutes the constraints of optimization; the objective is to minimize the total error &, given by

Minimize:

" :tlr,! ,-,

(10.10)

subject to

!,(U J )= r, ,VI E {I, 2, ...• N,}.} E {1. 2, ...• 2x N,}

(10.11)

Interestingly. solution of the above mentioned optimization problcm provides the spatiotcmporal distribution of head and concentration values. 10.2 .2 Verification of Numerical Codes Density-dependent numerical codes need to be veri fied against standard solutions such as the Henry problem (Henry 1964), the Elder problem (Elder 1967), the HYDROCOIN salt dome problem (Swedish Nuclear Power Inspectorate 1986), and the rota ting immiscible fluids problem (Bakker et al. 2003). Das and Datta (2000) used Henry's seawater intrusion problem (Henry 1964) to evaluate the perfonnance of the their non-linear, optimization-based simulation methodology. The two dimensional cases in the vertical plane were utilized in the evaluation. Henry's problem is used as a standard problem for the verification of steady-state, density-dependent flow and transport models of seawater intrusion in coastal aquifers. In this problem. freshwater discharges to the venieal open sea boundary over a diffuse wedge of seawater that has intruded the aquifer. Several investigators have used different represenlation of the problem with different parameter values. A number of numerical models based on significantly different methods of solution give nearl y identical results for Henry's problem. Henry's seawater intrusion problem in a coastal aquifer is described schematically in Figure 10.3. The representation of the Henry problem, the parameter values and other data specified in Ihe study are identical to the used by Huyakom et al. (1987). The problem specifications arc chosen so thaI Ihe cases analyzed correspond to numerically solved by other researchers. The hypothetical two-dimcnsional confined aquifer is 100 m thick and 200 m long. Freshwater enters the aquifer through the inland face with a unifonn velocity v~ and leaves the aquifer through the ocean face.


403

The heavier seawater enters the aquifer through the bollom portion of the aquifer and the lighter mixed fluid leaves the aquifer through a narrow outlet portion near the top end of the ocean face. The extent of the outlet portion was specified as identified by Huyakom et al. (1987). ldtn - O- Vn

lO"'~ b - tOO", 80n.

Figure 10.3 :

Schematic details of Henry problem in a coastal aquifer (Das 1995).

The resul ts pertaining to a steady-state constant dispcrsion case is described in the following. The parameter values used for the steady state constant dispersion case are: a~=ar=O

d

'" Q

6.6>< 10-) ml/d

U = 6.6xI0-J mid (; = 0.025 ¢ = 0.35

K:'

= K;~ =1 mid

K ~, =0 1::.x=lly=llz=IOm

where aL and aT are the longitudinal dispersivities, respectively; do is the molecular diffusion coefficient; U is the freshwater influx through the inland face; K:", K;" and

K;

are the freshwater hydraulic conductivities corresponding 10 x, y and z directions, respectively; and /lx, Ily, and llz are the elemental step lengths. The flow and transport boundary conditions used were identical to that of Huyakorn et al. (1987). The boundary conditions at the inland face allow freshwater influx. The coastal boundary conditions allows convective mass transport out of the system over the top outlet portion 80 m S y S 100 m. For th is region, the nOnTIal concentration gradient is sel equaito zero. Figure 10.4 compares the 0.5 isochlors for steady-state conditions and constant dispersion case computed using the embedded optimization methodology (Das 1995 ; Das and Dalla 2000) with those obtained by other researchers (Huyakorn et al. 1987; Lee and Cheng 1974; Henry 1964; and the sharp

404


interface solution of Henry 1959) as presented in Huyakom el al. (1987). II can be scen that resu lts by Das and Datta (2000) and Huyakorn et al. (1987) are in good agreement. The comparison is reasonably good with those of Lee and Cheng ( 1974) and Henry (1964). ' OO r-----------------------------~

,

0 _(1'")

i:

H~"'.f.:J.(I \If7)

~

J.n .... C..... (l97. ) Ho "", (lH-l)

. .

DISTAf'lCE. 1n

!-' igure 10.4 :

Comparison of 0.5 isochlors for steady·state conditions and constant dispersion (adapted from Oas 1995).

10.3 Sa ltwater Intru sion and Ma nagement Saltwater intrusion cnn be managed in combination with one or more than one of the following alternatives (Maimone 2002): • • • • • • • • • • • • •

Demand management - reduction in pumping by lowering the demand of water. Non-potable water reuse - reduction in demand by reuse of treated water. Injection barrier - creating hydraulic barriers by injecting wate r. Extraction barrier - extraction of saline water to protect wells funher inland. Tapping alternative aquifers - transferring pumping stress to aquifers below or above the impacted one. Well relocation - relocation of wells to an area where fresh water head is higher or less prone to saltwater intrusion. Plugging abandoned wells - reduces risk of intennixing of saltwater and fresh aquifer. Modified pumping rates - space-lime scheduling of pumping rates. Pumping caps - restricted pumping by imposing upper limits. Physical barriers - slurry walls or sheets pi les to prevent intrusion at a small scale. Scavenger wells - specially designed wells tha t extract fresh water under hydrodynamic stabilization of saltwater· fresh mixing zone. Controlled intrusion - in case of a depleted source wit h adequa te supply of substitute resource. Conjunctive use - use of surfaee waler to relieve extra load on coastal aquifer.


• •

•

405

Aquifer storage and recovery - storage of potable surface water in saline aquifer for future use. lntn/sion with treatment - desalination plant can be used to conven saline water to fresh water. However concentrate management is major issue in desa lination process. Sliring pit - passing freshwater with a certain velocity through pil.

Ideally, integrated management of saltwater intrusion in coastal aquifers should be able to incorporate any of these alternatives. The basic steps necessary for integrated management of saltwater intrusion is presented in Figure 10.5. Most common management strategies for coastal aquifers require careful planni ng of wi thdrawal strategies for control and remediation of saltwater intrusion in coastal aquifers. Such strategies can be evolved only if, the physical process involved in the coastal aquifers arc simulated reliably and studied. Numerical simulation is the 1110S\ direct way of identifying possible solutions of saltwater intrusion management problem, but sequential numerical solUlions do not generate sensitivity and/or tradeoff information. Moreover, simulation methodology can examine only a finite number of alternatives. Also, the obtained solutions are only optimal with respect to alternatives considered during the analysis. In linked Simulation-optimization, the optimization model performs the search process by iterating between the optimization and the simulation model. The simulation model provides the necessary information to the optimization model at every stage of iteration in order to reach the optimal solution. The advantage of this approach is that any type of simulation model can be incorporated in the search for optimal management strategies. The principal advantage of the linked simulation optimization is its applicability to highl y nonlinear systems. Management models are of three categories: (a) descriptive management model, decision is taken based on the simulation results; (b) prescriptive management model, optimization-based decision making; and (c) descriptive-prescripti ve management model, combined simulation optimization framework. Ideally, the third category of models is imponant from actual management point of view.

406


c.n..:,.... ON .\~o'ym.r .;,1,"0, Do.,

,.,,,,0
,' ''

!

.' Final.·.... ' Figure 10.6:

Linked simululion-oplimi:rotion mClllodology.

The pcrfonnancc of the developed model is evaluated by applying the mod el to an illustrative study area as shown in the Figure 10.7. The area ofthc aquifer is 2.52 kml (1.8 km in length by 1.4 km in width), and the thickness of the aquifer is 100 m. The unconfined aquifer system is subjccted 10 sal\waler inlrusion along the coastal side of Ihe study area. The right hand face of the aquifer is thc ocean face, which allows saltwater to enter into the aquifer through the bottom of the aquifer, and also allows the e}li t of the mi}led water from the lOp of lhe aquifer. It is assumed Iha1 mixed water can c:o;il the aquifer throu gh the top 20% of the aquifer at the ocean face. The left hand side o f the aquifers is inland face, which allows fresh water to cntcr in to the aquifer. The top of the aquifer is considered as phreatic. Unifonnly distributed vertical discharges occur though the phreatic su rface. The olher three faces, the front, back and the bol1om of the aquifer. arc considered as impenneable. The threedimensional unconfined hypothetical aquifer is assumed to be homogeneous and anisotropic with rcs~t to freshwa ler hydraulic conducti vity, mo lccular diffusion, and longitudinal and transverse dispersivity. Aquifer parameters val ues are specified in Table 10.2.

410


, t

,8 "•

.... ,

0

,m

,

I

~, i

"

~

j

'A

o.

0'

..

~_ 0

•

a

: 011'

,

0'

: 010:

06

: 09:

o.

. _-_ .. ......

No now bound", (oj PLAN

, ~I

~

0 '

0'

~i

•

...... ......

, ~

Inll..o,_11

.,

..

~.o

No r- bOIl"" •

8

'/ -"e;,;,;,",-&. , ..... A '

..

~_

a

, j

'"

"(~ •

• I

i

•

~

j ,ott

d_."'.... in ...1,.

(b) Sld;"n Ihrou~h ArA

Figure 10.7:

Illustrative study area.

The boundary condition in the aquifer (Figure 10.7) is considered as lime invariant. The now boundary condition on the ocean face is considered as hydrostatic in venica! direction. It is assumed to be constant throughout the ocean face. On the inland face, the reference hydraulic head is varying linearly along the length o f the inland face. In

this case, the value of hi and ll.h arc assigned 1.66 m and 0.08 m, respectively. The boundary condition for the phreatic surface is specified as follows (Galeati et at 1992):

K"By (Oh+cc) =v' T - sat oh

(10.24)

where Kxr is the actual hydraulic conducti vity in y direction; SJ. is the specific yield; v, is the vertical recharge; c is the salt concentration; and h is the reference hydraulic

GROUNDWATER QUANTITY AND QUA LITY MANAGEMENT

4 11

head. The three other faces of the aquifer are impcnneable. A zero-flux boundary condition is specified for these faces. Table 10.2: Values ofaquifer parameters for the study area. Para meter

K=, (mlday)

2S

Hydraulic Conductivity in ,. direction, K ~. (m/day)

0.25

K:' (mlday)

"

Hydraulic Conductivity inx direction,

Hydrautic Conductivity in z direction. Longitudinal di~ivity. as. (m) Lateral dispcn;v;ty. «r', (mlyur)

SO

"

0.69

oms

0.28 0.20

The advective mixed outflux can exit through the top 20"10 portion of the aquifer. [n this portion, the concentration gradient nonna[ to the ocean face is equal to zero. In the rest 80"/0 of the ocean face, the solute concentration is equal to one, as it allows influx of saltwater into the aquifer. Freshwater enters the aquifer through the inland face of the aquifer. Therefore, the solute concent!lltion is equal to z.ero on the inland face. It is considered that zero concentration mass influx occurs through the top phreatic surface, and the advective component of the solute mass influx is equal to ze ro. Therefore, concentration g!lldient nonnal to the phreatic surface becomes zero. The other three faces, front, back, and bottom of the aqu ifer arc impcnneablc. Hence the solute concentration gradient nonnal to these aquifer faces is set equal to zero. Steady state reference hydraulic head and concentration are assumed as the initial condition for transient flow and t!llnsport. Figure 10.7 shows the locations of lhe pumping wells. The water is pumped from the middle layer of the aquifer. The pumping from the aquifer is considered as transient. A time step of 180 days is considered in the case of pumping. The upper timi t of pumping rate is spedfied as 18,000 mJ/day and the lower limit is specified as 0 m1/day. The pumping !lite is considered constant for each time step of six months for a particular well. The pumping pattern is gene!llted randomly over a period o f three years, using a unifornl distribution. The concentration values used are the nonnaliz.ed saltwater concent!lltion with a range of (0, I), with a value of I corresponding to a concent!lltion of 35,000 mg/1. The t!llining and testing patterns for th is study area were generated using the embedded optimization-based numerical model developed by Das and Datta (2000). There are eight potential pumping locations to withdraw water for beneficial uses. Another three pumping locations are also considered near the coastal face. These pumping wells are used for controlling saltwater intrusion into the aqui rer. Therefore, the total number o f pumping wells for this study area is II. The simulat ion is done

412


over a period of 1.5 years with a time step of 0.5 years. The total number of inputs to the ANN model is 33. The input pumping patterns are randomly generated using a unifonn distribution function . The pumping patterns are then fed to the numerical simulation model to generate spatial and temporal distribution of concentrations over the aquifer. The salt concentration observation locations are the same as the pumping locations used to withdraw water for beneficial use. Therefore, the outputs from the ANN model is the salt concentrations of the pumped water at each time step. The number of output from the ANN model is, therefore, equal to 24. The training process involves find ing of an optimal set of weights for the synaptic connections between the artificial neurons of the network from sufficient sets of input patterns. It has been observed that the testing error decreases monotonically to a minimum but then starts to increase, even as the training error continues to decrease (Burian et al. 2001). When noisy data are used to train the ANN, the ANN would initially learn the actual patterns; therefore, the testing error decreases initially along with the training error. After learning the actual patterns, the ANN may try to learn the noise also; thus, the testing error starts increasing even if the training error continues to decrease. It has been reported that partially-trained neural networks beller approximate the unknown function (Hassoun 1999). In the present study, the testing error was carefully monitored du ring the training phase, and the training was stopped just before the testing error started to increase. The total set of generated patterns was divided into three sub sets, 10% of the total patterns were kept for testing, 10% of total patterns for validation or prediction, and remaining 80% were kept for training the neural network. The training pattern fixes the synaptic weights of the networks during the training phase. The testing set determines the stopping criteria for training. The training continues as long as the testing error goes on decreasing. The validation set determines the performance of the ANN on a new data set. The perfonnance of the developed ANN model was evaluated on the basis of relative error and coefficient of correlation criteria. The relative error, RE, shows the relative differences between actual and predicted salt concentration of the pumped water. The actual salt concentrations are those generated by the numerical simulation model. The predicted salt concentrations are those genCfllted by the developed ANN model. The Icsser the value of the relative error, the better the model performance. The relative errors ranged from 0.08% to 6.06%, with an average of 0.98%. These values are small and are in the acceptable range. Figure 10.8 shows the graphical representation of relative errors at different pumping locations. The coefficient of correlation between actual and predicted salt concentrntions in the pumped water varied between 99.77% to 97.81% respec tively, with an average of 99.41 %. These values show the potential utility of the proposed approach. The trnined ANN model took only 2 seconds CPU time to calculate the salt concentrntion of the pumped water on a P_IV (1.7 MHz), 128MB RAM personal computer. Therefore, linking the ANN model with the optimization algorithm is computationally very efficient.


I..

.... 0.005

0.010

g0.008

0

t:: 0.004

~ 0.003

W 0006

~ 0.002

~ O.OOI

a:: 0.000

4 13

,

2

In , •

~ 0:004

m 6

5

,,

-il 0.002 a::

0.000

,

I ~, 2

11 111

• ,,, 5

Pu~ingWeIl

Pumping Well

~(O '),-,FO ='C'='~ ==="='C p ='_ _ _ _ _ _ _-,(= b)C:F,or time step 2 0.000 , - - : : - - - - - - ,

~ 0.050 .

.ti 0.040 ~

0.030

~

0.020

a::

0.000

a; 0.010 ~

m

11

+-U-,""'...-.Ll_ _--r-l 12345618 PUlllling We ll (c:) For time step 3

f igure 10.8:

Relative error between actual and predicted salt concentrations.

Pa reto-optimal soilitiolls: The mul1iple-objective management models developed above were applied to a hypothetical coastal aquifer to evaluate their performance. The Non-dominating Sorting Genetic Algorithm 11 (NSGA II) is used here to obtain the Pareto-optimal solutions. NSGA II is an elitist non-dominating sorting algorithm used to solve muhiple-objeclive optimization problems. NSGA 11 seall:hes for the Pareto-optimal solutions by pllshing the non-dominating solutions in a panicular generation towards the Pareto-optimal solutions, while maintaining diversity among the solutions. The diversity of the solutions in the Parcto-optimal fron t is maintained by a crowding distance criterion. The efficiency of this algorithm is reponed to be beller than other multiple-objective evolutionary algorithms in maintaining diversity among the solutions of the Parclo-oplimal front; however, this capability of maintaining diversity amongst the individual solutions in the Pareto-optimal front is highly dependent on the scaling of the different objective functions. The real coded NSGA 11 (Deb 2(01) code was used in this study. The first muhiple-objective management model considers two conflicting objectives. These are: maximization of total pumping for beneficial use from wells at intcrior locations of the aquifer, and mi nimization of pumping from wells located along and in the vicinity of the ocean boundary. The second objective is applicable when pumping along the ocean boundary and in the vicinity of the ocean face is used to

414


alter the hydraulic gradients near to this boundary to eontrol saltwater intrusion. Therefore, in order to increase the extraction of water from the interior wells while maintaining the salinity wi th in permissible limits, it may be required to increase pumping rrom thc ocean race wells. The pumping from the wells located along, as well as in the vicinity of the ocean face, act as a hydraulic barrier. This barricr restricts the movement of saltwater into the aquifer. These two objectives are conflicting in nature, as the inerease in pumping from the interior wells would also increase pumping from the barrier wells, so as to maintain pre-specified upper limit on salt coneentration of the pumped water. This study considered eight interior potential pumping locations to wi thdraw of water for beneficial use. It also considered three pumping locations along and in the vicinity of the ocean boundary. All these wells are numbered I to II as shown in Figure 10.7. Locations Ito 8 are for the interior wells, and locations 9 to I I are for the barrier wells. Pareto-optimal solutions for the two objectives optimization model obtained using non-dominating sorting Genetic Algorithm II (NSGA II) are shown in Figures 10.10 and 10.11. The x-axis of the Pareto-optimal front represents the total withdrawal rate of water for beneficial use from the interior wells. The y-axis represen ts the total pumping rale from Ihe barrier wells. The solutions in Figure 10.9 correspond to a salt concentration upper limit of 0.2373. II can be observed from Figure 10.9 thai for any improvement in one of the objectives, the other objective has to bc sacrificed to a certain degree. The Pareto-optimal front touches the x-axis at a lotal pumping rate equal to 99,077 m1/day. Therefore, to withdraw water up to 99,077 ml/day from the inferior wells, there is no requirement of barrier pumping to maintain the prespeci fied salt concentration in the pumped water below the upper limit. The barrier pumping is necessary if the total withdrawal from the interior wells is more than 99,077 mJ/day. The amount of barrier pumping for different level of wi thd rawal from the interior wells can be obtained from the trade curve. For example, for withdrawal of 110,000 ml/day from the interior wells, about 5,000 ml/day of water has to be pumped from the barrier wells in order to maintain salt concentration in pumped water wi thin the permissible upper limit. E ~ 3i5\DJ ,

,g :g

- - - - - - - - - - -,

DDJ

Ee 2SDJ

a'