model-aided design and optimization of artificial recharge-pumping

Hydrological Sciences-Journal-des Sciences Hydrologiques, 42(6) December 1997 937

Model-aided design and optimization of artificial recharge-pumping systems

ANDREJA JONOSKI, YANGXIAO ZHOU & JAN NONNER International Institute for Infrastructure, Hydraulic and Environmental Engineering, PO Box 3015, 2601 DA Delft, The Netherlands

SYLVIE MEIJER Water Supply Company of Eastern Gelderland WOG, PO Box 15, 7000 AA Doetinchem, The Netherlands

Abstract This paper presents a methodology for the design and optimization of artificial recharge-pumping systems (ARPS). The objective of ARPS is to provide a maximum abstraction rate through artificial recharge, while meeting two operational constraints: (a) the influences of the system operation on groundwater levels should be no more than 25 mm in the vicinity of the system; and (b) the travel time of the infiltrated water from the recharge pond to the pumping wells should be more than 60 days. The combined use of a 3-dimensional generic groundwater simulation model with particle tracking analyses has identified the two best ARPS systems: the circular pond system and the island system. By coupling the simulation model with linear and mixed integer programming optimization, the optimal pumping scheme (number, locations and rates of the pumping wells) has been determined. An unsteady state model has been used to simulate the response of the operation of the two systems under natural seasonal variations. The implementation aspects of the two systems are compared.

Utilisation de modèles pour la conception et l'optimisation de systèmes de recharge artificielle et de pompage Résumé L'article présente une méthodologie pour la conception et l'optimisation de systèmes de recharge artificielle et de pompage (ARPS). L'objectif des ARPS est de fournir un débit maximal de pompage grâce à la recharge artificielle tout en satisfaisant deux contraintes opérationnelles: (a) les influences de l'exploitation du système sur les niveaux de l'eau souterraine ne doivent pas dépasser 25 mm au voisinage du système; et (b) le temps de parcours de l'eau infiltrée à partir de l'étang de réalimentation jusqu'aux puits de pompage doit être supérieur a 60 jours. L'utilisation d'un modèle générique tridimensionnel d'écoulement souterrain combiné avec des analyses de traçage de particules a permis d'identifier les deux meilleurs systèmes ARPS: le système de l'étang circulaire et le système insulaire. Le schéma de pompage optimal (nombre, localisations et débit des puits de pompage) a été déterminé en couplant le modèle de simulation avec une optimisation utilisant la programmation linéaire mixte (Mixed Integer Programming). Un modèle d'écoulement souterrain en régime transitoire a été utilisé pour simuler la réponse du système aux variations saisonnières. Les aspects liés à la mise en oeuvre des deux systèmes ont été comparés.

INTRODUCTION

In the last few decades, artificial recharge-pumping systems (ARPS) have been widely implemented in various fields of groundwater resources management. Different methods are used, depending on the specific characteristics of the site and

Open for discussion until 1 June 1998

938 Andreja Jonoski et al.

the project objectives. The methods of artificial recharge are either spreading basins, ditches and ponds, when the aquifer is shallow, or injection wells when the aquifer is deep. The most common objectives are provision of storage of water, improvement of water quality, restoration of overexploited aquifers, prevention of negative impacts of lowered groundwater levels and disposal of polluted water (Huisman & Olsthorn, 1983).

In The Netherlands, ARPS have already been implemented in the field of water supply. Recently, restrictions on the use of natural groundwater have been introduced due to the negative impacts of the lowered groundwater levels on the environment. At the same time the demand for water supply is constantly increasing. To overcome this conflict ARPS are expected to be implemented more in the future. In the area of Eastern Gelderland there are plans to develop ARPS using existing sand excavation pits as ponds for artificial recharge. The objective of these systems is to provide a target abstraction rate of 5 x 106 m3 year1, while meeting two constraints: (a) the changes of the natural groundwater levels induced by the system operation should be less than 25 mm; and (b) the minimum travel time of the infiltrated water from the pond to the abstraction wells should be at least 60 days.

The restriction on the change of natural groundwater levels is imposed due to its influence on agricultural production and the natural environment. The Netherlands is a very flat country with artificially controlled shallow water tables. A small change of water table depth would result in the decrease of agricultural production and the alteration of natural vegetation. The water supply companies are liable to pay compensations to farmers if the operation of ARPS would cause a change of water table more than 25 mm. The second constraint is related to the quality of the abstracted water. In The Netherlands, the minimum travel time of 60 days is considered to be sufficient for the removal of all pathogenic organisms.

Research has been carried out to determine the optimal design solutions of ARPS that will meet the implementation objective under the two operational constraints. The study concentrates on a system consisting of a recharge pond and a number of abstraction wells superimposed on the natural groundwater system. The best configuration of the system, optimal number and locations of pumping wells, and maximum pumping and recharge rates are determined with the combined use of several modelling tools. This paper presents the methodology and the results obtained.

METHODOLOGY

Literature review

Coupled groundwater simulation-optimization models, called groundwater management models, have already been widely used in solving groundwater management problems. A thorough overview of groundwater management models has been presented by Gorelick (1983). The nature of the optimization problem in the case of ARPS falls into the group of so-called groundwater hydraulic management models.

Model-aided design and optimization of artificial recharge-pumping systems 939

The coupled simulation-optimization model is used to maximize pumping rates under constraints on drawdown and travel time.

There are two different methods of coupling a groundwater simulation model with an optimization technique: The embedding method and the response matrix method. In the embedding method the numerical discretizations of the partial differential equations are included as constraints in an optimization algorithm. For large problems related to real cases the embedding method is not suitable because the constraint matrix may become too large (Gorelick,1983; Willis & Yeh, 1987; Yeh, 1992). The response matrix method is based on the principle of linear superposition. The matrix of responses (drawdowns) from the unit stresses (pumping rates) are generated only for the desired control locations. The response matrix can then be used in the optimization model as the constraint matrix. It has much smaller dimensions and solutions for larger problems are possible.

In the case of ARPS, the objective function can be formulated as the maximization of the total pumping rate. The constraints on drawdown can be imposed easily with the response matrix technique. However, it is difficult to include directly the limits on the travel time of the infiltrated water as constraints. Placing limits directly on the travel time will lead to the incorporation of the method of particle tracking in the coupled simulation-optimization model. The nature of the problem is such that the travel time of a traced particle is nonlinearly dependent on the stresses (pumping or injection rates). In general the travel time can be expressed with the following integral (Greenwald & Gorelick, 1989):

r ( q ) = h ^ 5 (1) .; v(q)

where q is the vector of pumping and injection rates (stresses); T(q) is the travel time of a water particle; v(q) is the groundwater flow velocity in the flow direction; ds is the incremental distance along the pathline in the flow direction; and s = s(q) is the length of the particle pathline.

There are two reasons for the nonlinearity of equation (1). Firstly, the travel time depends on the groundwater flow velocity, which is a function of the pumping and injection rates. Secondly, the travel time is dependent on the velocity distribution along the whole particle pathline and the integral is over the total pathline length, s, which is also a function of the pumping and injection rates.

In the work of Greenwald & Gorelick (1989) the problems of contamination plume removal were solved with schemes that included only one pumping well. It has been shown that for those cases the particle travel time can be incorporated in the simulation-optimization procedure. It is clear that if only one pumping well is operating the particle travel time will always decrease with the increase of the pumping rate. In cases where the scheme includes more than one well, global optimization cannot be guaranteed. The increase of pumping rate at one well may cause increase of travel time of particles flowing to other wells. There are many combinations of pumping rates that would lead to many local minima for the particle travel time. Because of these problems it is not possible to incorporate directly the particle tracking method in the optimization model. Greenwald & Gorelick (1989)


gave recommendations to solve the problems for only single well cases and then to use these solutions as starting points for multiple well cases.

In the case of the optimization of ARPS, the system will involve more than one pumping well. Placing constraints directly on the particle travel time will lead to similar difficulties. In order to avoid these problems, the so-called head difference (velocity) constraint is used as a substitute for travel time limits since the travel time depends on the velocity distribution. The optimization problem is, therefore, greatly simplified because the head difference constraints are linear. The approach may not guarantee a real optimal solution with respect to the travel time constraints because the travel times are limited indirectly by the head difference constraints. However, the solution is acceptable for the engineering design of an ARPS.

Framework for analysis of ARPS

The methodology for the optimization of ARPS is presented in Fig. 1. Three phases can be distinguished. In the first phase, a generic groundwater simulation model in combination with particle tracking analysis is used to identify the possible ARPS. The generic groundwater model is designed to incorporate most possible hydro-geological and hydrological features representative for the area of Eastern Gelderland. The well known model codes MODFLOW (McDonald & Harbaugh, 1988) and MODPATH (Pollock, 1994) are adequate for this purpose.

GENERIC GW SIMULATION MODEL M O D F L O W

PARTICLE TRACKING ANALYSES M O D P A T H

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GENERIC GW SIMULATION MODEL, M O D F L O W

OPTIMISATION MODEL M O D M A N . L I N D O

PARTICLE TRACKING! ANALYSES MODPATH

UNSTEADY STATE SIMULATION MODEL M O D F L O W

PARTICLE TRACKING ANALYSES MODPATH

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S* STEM KKSI'O.NSK i ()

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V A R I A T I O N S

Fig. 1 Methodology for the analysis and optimization of ARPS.


In the second phase, the groundwater simulation model is coupled with an optimization model in order to obtain optimal system design. The software package MODMAN (Greenwald, 1994) has been chosen for this task. MODMAN generates the response matrix through a series of MODFLOW simulations, and defines the optimization problem. The actual optimization problem is solved by LINDO (Schrage, 1991) which is a mathematical optimization code. The optimization includes linear and mixed integer programming formulations. As indicated in Fig. 1, the particle tracking code is invoked again to check the travel time constraints once the optimal pumping scheme is found.

In the third phase, an unsteady model is built to simulate the response of the optimally designed ARPS to natural seasonal variations. These analyses provide vital information on the operation and the behaviour of the system under transient conditions.

Set-up of a generic simulation model

The hydrogeology of the area of Eastern Gelderland is simple (Fig. 2). The main aquifer consists of two sandy layers underlain by an impermeable base consisting of clay deposits. A study area of around 6 x 6 km2 was chosen for the development of a generic model where the ARPS was to be implemented.

Gridlines measuring 70 by 70 were used to discretize the modelling area (Fig. 3). A fine grid with a cell dimension of 20 m x 20 m was used in the central part of the area where the future ARPS will be located. The grid size was gradually increased

River i:

Fine sand Modelling layer

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~9> Fig. 2 Conceptual model and vertical discretization (east-west cross-section).


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Grid: x and y direction: 6x300; 1x225; 1x150; Ixl00;lx70; 2x45;2x30; 42x20; 2x30; 2x45; 1x70; 1x100; 1x150; 1x225; 6x300

Fig. 3 Spatial discretization in plan.

| River

~"J] Head dependent flux boundary

H No flow boundary

towards the boundaries. In the vertical direction the aquifer was subdivided into 10 modelling layers in order to have accurate calculation of the vertical flow velocities close to the recharge pond where the flow has a distinct three-dimensional nature.

The western boundary of the model followed the Ijssel River which was simulated with the MODFLOW River Package. The boundary below the river is hydraulically impermeable since the river is a regional drainage base of the natural groundwater. The eastern boundary was an artificial boundary defined as a head-dependent flux boundary. It was basically an inflow boundary where the flux was dependent of the groundwater head in the aquifer outside the boundary. This type of boundary can be simulated with the MODFLOW General Head Boundary package. The northern and the southern boundaries were delineated along two streamlines as impermeable boundaries (Fig. 3).

The main hydrological stress was the natural groundwater recharge from precipitation with an average value of 0.8 mm day4. In order to simulate the drainage of groundwater by numerous natural and manmade surface streams and ditches, lines of drains were included in the model using the MODFLOW Drainage


package. These drains were located at 2.0 m below the land surface and were equally distributed at a distance of 500 m. The model parameters (hydraulic conductivity, porosity) were taken as average values in the area.

One of the interesting features in the generic model was the inclusion of a pond which was an abandoned sand excavation pit. The pond will be developed in the future into an artificial recharge pond. Under natural conditions, the water level in the pond is the result of the interaction between the pond and the aquifer. Therefore the water level in the pond had to be determined by the model. This could be done by assigning an infinite hydraulic conductivity value (in this case a value of 10 000 m day'1) to model cells representing the pond.

The generic model created produced the spatial distribution of groundwater levels under natural conditions similar to the "observed head distribution" in the area. These groundwater levels were the reference levels for the analysis of the impact of ARPS on the natural groundwater flow.

The generic model was used to identify suitable ARPS through simulation of a lot of different configurations of the recharge pond and the pumping schemes. Under the situation of artificial recharge, the pond acted as an external source. The water level in the pond was artificially controlled by supplying water to the pond. The pond was therefore simulated in the model as a specified head boundary. During the operation of ARPS, the pumping wells would induce water from the pond as the specified head boundary. The amount of actual artificial recharge could be read from the water balance of the model as the net inflow from the specified head boundary. This approach had the advantage that the amount of artificial recharge was automatically adjusted in correspondence to any pumping scheme. The other advantage was that the artificial recharge was controlled by changing the water levels in the pond, easily measurable from a practical point of view.

The analyses showed that there were two possible configurations of the ARPS that could meet the implementation objective and satisfy the two operational constraints. They are called the circular pond system and the island system. These two systems are analysed further in the next two sections.

THE CIRCULAR POND SYSTEM

System design

In the circular pond system the pumping wells were located outside a circular recharge pond. The recharge pond was designed with a diameter of 560 m and a depth of 15 m, which extended to the fifth modelling layer. All pumping wells were located near the bottom of the aquifer at a depth of about 30 m, which is in the tenth modelling layer. The water level in the pond was artificially controlled in order to provide a sufficient amount of artificial recharge. The major design aspects of this system were the pumping scheme (number, locations and rates of the pumping wells), as well as the water level in the pond. The trial and error analyses showed that in order to meet the target pumping rate the water level in the pond had to be


raised 400 mm above the natural level. However, it was impossible to find the optimal pumping scheme using only the simulation model due to the following reasons: - A compromise for the well locations was necessary to satisfy both operational

constraints. The drawdown constraints required the pumping wells being located as close as possible to the pond. On the other hand it might be necessary to place the wells further away from the pond in order to create a longer travel time.

- The minimum travel time was influenced by the natural groundwater flow which caused an unfavourable gradient on the downstream side of the pond. The pumping wells located on that side either had to be placed further away from the pond boundary, or operated with smaller pumping rates. Therefore, the coupling of the simulation model with an optimization procedure

was necessary.

System optimization

The optimization problem was formulated with the response matrix approach. The objective was to maximize the total pumping rate, i.e.

n

Maximize Z = YuQ, (2) ;=1

subject to:

s, < 2.5 cm j =1, 2, ..., m (3)

Tk > 60 days k = 1,2, ..., n (4)

sj = £p , y a j = l,2,...,m (5)

Q, > 0 / = 1, 2, ..., n (6)

where Qt is the pumping rate of pumping well i; Sj is the drawdown at control location j at 500 m from the pond; ptj is the response coefficient in terms of drawdown at control location j by a unit rate of pumping at pumping well i. A matrix consisting of all coefficients ptj{i = 1,2, ..., n;j = 1,2, ..., m) is called a response matrix; Tk is the travel time of the fastest particle arriving at each pumping well; n is the total number of pumping wells; and m is the total number of control locations.

The drawdown constraint in equation (3) limited the drawdown at locations of 500 m from the pond to be smaller than 25 mm. Equation (4) imposed a travel time constraint of at least 60 days. Equation (5) defines the relation between the drawdowns at the control locations and the pumping rates of the pumping wells. The last constraint of equation (6) is the so-called non-negativity constraint of the decision variables.

The optimization problem as defined above cannot be solved directly as a linear programming problem since the travel time is a nonlinear function of pumping rates.


To overcome this problem, the optimization procedure proceeded in two stages. In the first stage the travel time constraints were left out, and the problem was formulated as a linear programming optimization, using only the drawdown constraints. The solution from the first stage was further improved in the second stage, when mixed integer programming optimization was used and the travel time constraints were indirectly imposed through the head difference constraints.

Linear programming optimization with only drawdown constraints

The purpose of the linear programming optimization was to determine the optimal number of wells and their locations, if only the drawdown constraints were used. For

100 400 METERS • D r a w d o w n c o n t r a i n t l o c a t i o n s

1 1 * P o t e n t i a l w e l l l o c a t i o n s

• A c t i v e w e l l s

Fig. 4 Optimal pumping scheme and travel times of fastest particles from linear optimization with drawdown constraints only.


that purpose, 108 potential well locations were selected around the recharge pond. All the potential well locations were placed further than 110 m from the pond, since the initial analyses showed that placing the wells closer than 100 m from the pond would give unacceptable travel times. The drawdown constraints were specified at 198 control locations. The results from the optimal solution are presented in Fig. 4. The solution gave only 12 wells to be active. As expected, they were all located at the closest ring around the pond. The solution was symmetrical with respect to the x-axis. The total pumping rate was very high (gmax = 17 974 m3 day"1).

In order to check the travel time of the optimal pumping scheme, backward particle tracking was performed, tracing 45 water particles from each well backwards towards the recharge pond. The travel time of the fastest particle from each well to the pond was recorded. The results are also presented in Fig. 4. As can be seen, the travel times were satisfactory only at the two wells placed upstream from the pond. For all other wells the travel time was less than 60 days. On the downstream side of the pond the fastest particle travel time was only about 30 days.

The travel time calculation indicated that placing the pumping wells further from the pond on the downstream side, and closer to the pond on the upstream side might provide satisfactory results with respect to the travel time. Therefore, the possibility for varying the well locations was included in the second stage of the optimization procedure.

Mixed integer optimization with drawdown and head difference constraints

Head difference constraints are in fact flow velocity constraints. If one limits the difference in head between two locations in the flow field, the flow velocity between these two locations is also limited. The advantage of using head difference constraints for placing limits on particle travel times is that the calculated heads, and therefore the head differences as well, are linearly dependent on the pumping rates of the wells.

It can be expected that the highest flow velocities occur around pumping wells. There are two directions of the flow velocity that are critical for the minimum particle travel time: the velocities directed towards the pond in the horizontal and vertical directions. The velocities in these two directions can be controlled by limiting the differences in heads between the pumping well cell and the two adjacent cells respectively. These two head differences are accordingly named: top head difference and lateral head difference (Fig. 5).

Since the distance between the well and the pond was the most influential factor on travel time, the relationship between the distance from the pond to the well, and the top and the lateral head differences had to be established in order to use the head difference constraint as a substitute for the travel time constraint. This relationship was established by a set of runs of the simulation model while placing only one pumping well at different distances from the pond. The pumping rate of the well was adjusted such that the travel time of the fastest particle was a little more than 60 days in order to account for the influence of other wells since the system would consist of


Top

Head difference

X

Lateral Head difference

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Cell with a pumping well Fig. 5 Schematic presentation of the top head and the lateral differences.

more than one well. Then for each distance between the pond and the well the values for the top and the lateral head difference could be recorded.

The head difference-distance relationships are established for five directions: west, northwest, north, northeast and east (Figs 6(a) and 6(b)). Since the system was symmetric with respect to the x-axis, the established relationship of the head difference and distance in the northwest, north and northeast directions could be applied to the southwest, south and southeast directions, respectively.

The optimization problem was formulated as follows. Three potential well locations were specified at different distances from the pond along each direction

(a) o-5o

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0.30

0.20

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0.60

0.40

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0.00 70 90 110 130 150 170 190 70 90 110 130 150 170 190

Distance from the pond (m) Distance from the pond (m)

Fig. 6 (a) Top head and (b) lateral head difference-distance relationships for 5 directions.


(Fig. 7). In total there were 36 potential well locations. The top and lateral head difference constraints were imposed on each potential well location with values taken from the established relationships. The drawdown constraints remained the same as in the previous case. The optimization problem was defined as a mixed-integer problem, where only 12 wells were to be chosen as active out of the 36 potential well locations. Furthermore, these 12 active wells were to be chosen in such a way that there was one active well in each direction. In total, there were 198 drawdown constraints, 96 head difference constraints and 8 integer constraints.

The results from the mixed integer programming optimization are presented in Fig. 7. It can be seen that the travel time of the fastest particle to each well was above 60 days. The total pumping rate was 14 426 m3 day"1 which was higher than the target pumping rate of 13 700 m3 day"1.

• D r a w d o w n c o n t r a i n t l o c a t i o n s 0 100 400 METERS 1 I | ! I * P o t e n t i a l w e l l l o c a t i o n s

• A c t i v e w e l l s

Fig. 7 Optimal pumping scheme and travel times of fastest particles from mixed integer optimization with drawdown and head difference constraints.


Response of the system to seasonal variations

In the previous section, the circular pond system was designed and optimized with the steady state model. It was necessary to check whether the ARPS would satisfy the drawdown and travel time criteria under seasonal variations of hydrological stresses. For this purpose an unsteady state model was developed on the basis of the steady model. The unsteady model consisted of an average hydrological year divided into 12 monthly stress periods. The hydrological stresses, such as recharge and inflow from the eastern boundary, varied from the one stress period to the next stress period, but were constant within a stress period. The groundwater heads calculated by the steady model were taken as the initial conditions for the unsteady model. Under natural conditions, the pond was simulated with infinite hydraulic conductivity values and with a unit storage coefficient since there is no resistance of flow in a pond and the changes of storage in the pond are equal to the changes of the volume of water in the pond. In this way, the natural fluctuations of the water levels in the pond as well as the groundwater levels in the aquifer were generated, serving as reference levels for the analysis of the impacts of the ARPS. The circular pond system was then superposed on the natural model by defining the pond as a specified head boundary and including the optimal pumping scheme. The water level in the pond was raised 400 mm again above the natural level, the same as in the steady model. The model then simulated the groundwater head variations in the aquifer under the operation of the ARPS.

A comparison of the calculated groundwater heads under natural conditions with those of the circular pond system indicated that the influence of the operation of the circular pond on the natural groundwater was still within the limits of 25 mm. The travel time was checked by particle tracking under unsteady state conditions with a varying velocity field in time. Particle tracking was carried out for the dry and wet periods. The results showed that in the dry period the calculated travel time was 58 days, only slightly smaller than the travel time constraint.

The amount of artificial recharge, AR, from the pond for the unsteady state case

2 00 00

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- 1 2 0 0 0

- 1 6 0 0 0

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Apr. May Jim. Jul. Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar.

Fig. 8 Monthly artificial recharge and total abstraction rate for the circular pond system.

X Total pumping rate ° Artificial recharge


could be calculated as:

AR = Q* pond G, pond (7)

where <2*pond is the total flow from the pond to the aquifer with the operation of the circular pond system; Qpoad is the total flow from the pond to the aquifer under natural conditions. The results are plotted in Fig. 8 which shows that the artificial recharge was practically equal to the total abstraction rate. The artificial recharge meant also that the same amount of water had to be supplied to the recharge pond.

ISLAND SYSTEM

System design

In the island system, pumping wells were placed on an island encircled by the recharge pond (Fig. 9). The design of the system included the outer diameter, depth and water level of the recharge pond, the diameter of the island, and the pumping scheme. According to the geometry of the existing excavation pit, the most likely outer diameter of the recharge pond was 560 m, and its depth 15 m. The water level in the pond had to be maintained at the same level as under the natural condition since a change of water level in the pond would certainly influence groundwater levels outside the pond. The analyses showed that abstraction in the island caused a decrease of groundwater head only within the island, not outside the pond. Therefore

4 wells on an island; Tt = 60 d Relationship Q total - D island

Qtotal (m3/day)

\ / * » \

mm

D,

Dp<ma=560m

E S

160 200 240 280 320 360 400 440

D island (m)

Fig. 9 Island system: relationship between the total abstraction rate and the island diameter.


the pumping scheme was determined only by the minimum travel time constraint. Since the distance between the well and the pond was the most influential factor on the travel time, the pumping wells needed to be located as close as possible to the centre of the island. The maximum total abstraction rate could be determined while the minimum travel time was adjusted to the required value of 60 days. The number of pumping wells depended on the transmissivity of the aquifer and the capacity of the well.

The only possibility to increase the total abstraction rate in the island system was to increase the island diameter. In order to investigate the influence of the island diameter on the total abstraction rate a set of simulations was made with the same pumping scheme (four wells in the centre of the island) for different island diameters. In each simulation the travel time of the fastest particle was adjusted to be 60 days. Then the relationship between the maximum total abstraction rate and the island diameter was established (Fig. 9). It was shown that, in order to provide the target pumping rate, the island diameter had to be larger than 400 m. Further analysis indicated that when the island diameter was 480 m and eight wells were located in the middle of the island, the total pumping rate could be 14 400 m3 day"1. It can be concluded that the island system could be successfully implemented in cases where the creation of a large island is possible.

Response of the system to seasonal variations

The response of the island system to seasonal variations was simulated with the same procedure as for the circular pond system. The natural seasonal groundwater heads in the aquifer (including the island) and the water level in the pond were calculated with the unsteady state model when the pond was simulated with infinite K values and unit storage coefficient. Afterwards, the pond was converted into a specified head boundary and eight wells were placed in the centre of the island with a total abstraction rate of 14 400 m3 day"1 for all stress periods. The seasonal groundwater flow under the operation of the island system was then simulated.

The drawdown constraints were checked at several control locations just outside

20000 -

16000 ~

- 12000 -

0000 ••

- 4 000

0 -

-4000 -

• -H000-

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Total pumping rate Artificial recharge

0 1 2 3 4 5 e 7 a 9 10 11 12 Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Jan. Feb. Mar.

Fig. 10 Monthly artificial recharge and total abstraction rate for the island system.


the outer pond boundary. The results show that the drawdowns were close to zero. The minimum travel time both in the dry and the wet period was 59 days. The artificial recharge was calculated to be 14 350 m3 day"1 which is a little smaller than the abstraction since there was a contribution of the natural recharge on the island itself (Fig. 10). The artificial recharge is also the amount of water to be supplied to the recharge pond.

COMPARISON OF THE TWO SYSTEMS

The circular pond system and the island system were compared from the point of view of their practical implementation (Table 1).

The advantages of the island system over the circular pond system are: (1) the zone of influence of the island system was small and limited in the island itself; (2) the island system had practically no influence on groundwater levels in the surrounding environment; and (3) it was easier to protect the island system.

In practice, the creation of an island system may be more difficult than that of the circular pond system since many existing sand pits can be more easily converted into a circular pond system. Furthermore, if there is a need to increase the total abstraction, this can be easily achieved in a circular pond system by simply increasing the water level in the pond. However, in the island system, the dimensions of the pond have to be enlarged.

Sensitivity analysis indicated that the hydraulic conductivity influences the operation of both systems. In a circular pond system, the influence of the hydraulic conductivity on the travel time is small, but large on the drawdowns. The K value determines the appropriate rise of the water level in the pond in order to maintain the required artificial recharge. The smaller the K value, the higher the water level in the pond has to be. In an island system, the hydraulic conductivity does not influence the travel time at all, but determines the amount of artificial recharge. Since the water

Table 1 Comparison of the two systems.

Circular pond system Island system

Dimensions of the system Influence on environment Amount of AR Water level in the pond

Response to seasonal variations

Protection of the system Influence of hydraulic conductivity, K

Favourable locations for implementation

Large Small, but present AR = Ctotal Higher than under natural conditions Small violations of the drawdown and travel time constraints in the dry period Difficult Small influence on travel time; large influence on drawdowns; K value determines the water level in the pond High K value

Small Absent AR = eM, Same as under natural conditions No violations of drawdowns; small violations of travel time

Easy No influence on travel time; large influence on drawdowns; K value determines the minimum pond dimensions High K value


level of the pond in the island system cannot be raised, the only way to supply the required artificial recharge is to increase the pond dimension. In view of these influences, favourable areas for the implementation of both systems are locations with high hydraulic conductivity.

Since the amount of artificial recharge was practically the same as the total abstraction rate for both systems, and should be maintained constant over time, it is important to secure an adequate source of water for artificial recharge. The successful operation of both systems, after all, depends on the availability of sufficient good quality water for artificial recharge.

REFERENCES

Gorelick, S. M. (1983) A review of distributed parameter groundwater management modelling methods. Wat. Resour. Res. 19(2), 305-319.

Greenwald, R. M. & Gorelick, S. M. (1989) Particle travel times of contaminants incorporated into a planning model for groundwater plume capture. J. Hydrol. 107, 73-98.

Greenwald, R. M. (1994) MODMAN, MODflow MANagement: An optimization module for MODFLOW, Version 3.0. Geotrans Inc. Sterling, Virginia.

Huisman, L. & Olsthoorn, T. N. (1983) Artificial Groundwater Recharge. Pitman Books, London. McDonald, M. G. & Harbaugh, A. W. (1988) A Modular Three-Dimensional Finite-Difference Ground-Water Flow

Model (MODFLOW). USGS, Scientific Software Group, Washington DC. Pollock, D. W. (1994) User's Guide for MODPATH/MODPATH Plot, Version 3: A particle tracking postprocessing

package for MODFLOW, the USGS finite-difference ground-water flow model. USGS, Reston, Virginia. Schrage, L. (1991) User's Manual for Linear, Integer and Quadratic Programming with LINDO, Release 5.0. The

Scientific Press, San Francisco. Willis R. & Yen W. W-G. (1987) Groundwater Systems Planning & Management. Prentice-Hall, New Jersey. Yeh, W. W-G. (1992) Systems analysis in ground-water planning. / . Wat. Resour. Plan. Manag. Div. ASCE 118(3),

224-235.

Received 15 August 1996; accepted 14 May 1997

model-aided design and optimization of artificial recharge-pumping

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