Real-Time Management of an Urban Groundwater Well Field

Aug 9, 2010 - We present an optimal real-time control approach for the management of drinking water well fields. The methodology is applied to the Har...
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Environ. Sci. Technol. 2010, 44, 6802–6807

Real-Time Management of an Urban Groundwater Well Field Threatened by Pollution G E R O B A U S E R , * ,† H A R R I E - J A N H E N D R I C K S F R A N S S E N , †,‡ HANS-PETER KAISER,§ ULRICH KUHLMANN,| FRITZ STAUFFER,† AND WOLFGANG KINZELBACH† Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland, Agrosphere ICG-IV, Forschungszentrum Jülich GmbH, 52425 Ju ¨ lich, Germany, Waterworks Zurich, Hardhof 32, 8064 Zurich, Switzerland, and TK Consult, Seefeldstrasse 285, 8008 Zurich, Switzerland

Received February 28, 2010. Revised manuscript received July 2, 2010. Accepted July 13, 2010.

We present an optimal real-time control approach for the management of drinking water well fields. The methodology is applied to the Hardhof field in the city of Zurich, Switzerland, which is threatened by diffuse pollution. The risk of attracting pollutants is higher if the pumping rate is increased and can be reduced by increasing artificial recharge (AR) or by adaptive allocation of the AR. The method was first tested in offline simulations with a three-dimensional finite element variably saturated subsurface flow model for the period January 2004August 2005. The simulations revealed that (1) optimal control results were more effective than the historical control results and (2) the spatial distribution of AR should be different from the historical one. Next, the methodology was extended to a real-time control method based on the Ensemble Kalman Filter method, using 87 online groundwater head measurements, and tested at the site. The real-time control of the well field resulted in a decrease of the electrical conductivity of the water at critical measurement points which indicates a reduced inflow of water originating from contaminated sites. It can be concluded that the simulation and the application confirm the feasibility of the real-time control concept.

1. Introduction The management of well fields in urban areas or coastal areas often faces the challenge of polluted or saline groundwater reaching the wells (1). Management under these circumstances is not trivial as the prediction of pollutant inflow is affected by the uncertainty of aquifer properties and forcings like river leakage, recharge rate, and lateral inflow as well as unknown point sources in the form of sewer leakage. Recently, the concept of a stochastic well capture zone, which takes into account one or multiple sources of uncertainty (such as the spatial heterogeneity of hydraulic conductivity) * Corresponding author phone: 0041 44 633 3074; e-mail: [email protected]. † Institute of Environmental Engineering, ETH Zurich. ‡ Forschungszentrum Ju ¨ lich GmbH. § Waterworks Zurich. | TK Consult. 6802

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has been proposed in the literature (2). With our study we suggest a novel concept for the management of drinking water well fields which relies on real-time hierarchical control. So far, successful applications of optimal real-time control concepts for environmental and/or resources exploitation systems can be found in the field of oil reservoir management (3) and surface water supply networks (4). Hierarchical control concepts for an optimal allocation of water resources or the control of water quality by chlorination have been introduced since the 1970s, yet a renaissance in recent years can be observed (5). These concepts were mainly used to control large scale water resources systems under optimality criteria and calculation time constraints. Gorelick et al. (6, 7) were using hydraulic head differences as control states for the management of aquifer remediation processes. Hydraulic head differences indicate whether the flow of contaminants points toward the pumping wells or away from it. State-ofthe-art optimal well field management uses groundwater flow models. One of the first approaches coupling simulations with a finite element groundwater model with real-time control algorithms was introduced in 1990 (8). However, realtime measurement data were not integrated in this case study. In such studies model runs are combined with optimization techniques to determine the optimal pumping schedules or optimal well placements under the assumption that all future conditions stay either constant or follow some predefined scenarios, such as in refs 9, 10, and 11. Recent publications show real-time control concepts for water resources systems, such as real-time denitrification processes (12) and the dynamic management of optimal pumping schemes (13) using artificial neural network techniques. Recently, a synthetic case study was presented minimizing the pumping energy of a well field in real-time (14). None of the cited approaches above meets the requirements of a real-time control concept applied to the optimal management of a groundwater well field. A real-time control concept has to contain a real-time system model (15, 16), real-time measurements which are used for model updating in real-time (17, 18), and a real-time control algorithm (3-5) which are all coupled together and deliver control decisions at a rate in accordance with the response time of the system. Such an approach was applied in a real-world case and the real-time operational control of the water works Zurich, Switzerland. To our knowledge this is the first groundwater well field where the management is automatically controlled on the basis of a real-time simulation model and a real-time control strategy.

2. Field Site The study area is the Limmat valley aquifer in the city of Zurich (Switzerland), with a special focus on the well field Hardhof. The aquifer is mainly fed by infiltration from the rivers Limmat and Sihl but also recharged by excess precipitation (precipitation minus actual evapotranspiration). The aquifer receives also some lateral inflow from the hills South and North of Zurich. Details on the calculation of net recharge and lateral inflow for the aquifer can be found in ref 15. The well field is situated near a former industrial zone of the city, which could affect the pumping wells with contaminated groundwater. This problem is addressed by the particular design of the well field. Figure 1 schematically illustrates the well field system, including the city domain (green area). It consists of four horizontal wells (A, B, C, and D), three recharge basins (I, II, III), 12 additional infiltration wells (S1-S12), and 19 bank filtration wells, which are all situated in a well head protection zone. Filtrated river water is abstracted in the bank filtration wells and infiltrated in the 10.1021/es100648j

 2010 American Chemical Society

Published on Web 08/09/2010

FIGURE 1. Scheme of the Hardhof waterworks: Four horizontal wells A, B, C, and D deliver daily amounts of drinking water by abstraction. Bank filtration water is pumped in vertical wells diverted to recharge the basins I-III and the four groups of infiltration wells S1-6, S7, S8-10, and S11-12 as well. The artificial recharge creates a hydraulic barrier protecting the well field. Three pairs of piezometric head measurements ∆h1, ∆h2, and ∆h3 are used as control criterion for automatic optimal control. recharge basins and infiltration wells. The horizontal wells supply the daily amount of drinking water demand. For technical details, see Table S1, Supporting Information. A study carried out in 2001 (19) showed a typical spatial distribution of electrical conductivity (EC) with elevated values in the city domain (above 500 µS/cm (EC is always reported for a reference temperature of 20 °C)) and low values for the river Limmat (between 200 and 270 µS/cm, showing an annual cycle). For the bank filtration water EC values between 250 µS/cm and 300 µS/cm were measured (19). The EC values measured in the different wells give an indication of the percentage of city water pumped. Measured EC in wells A and B are relative low, indicating infiltration of river water. The measured EC in wells C and D is larger, which is indicative of a more elevated fraction of city water. Measured EC values in piezometer 3407 (Figure 1) were around 400 µS/cm in the years 1996-2000. This study led to the assumption that the actual artificial recharge (AR) did not fully detain the attraction of city water and needed to be improved. The need for its improvement was the main motivation to develop a three-dimensional (3D) finite element groundwater flow and transport model, combined with real-time modeling (using the Ensemble Kalman Filter (EnKF)) and real-time control of the well field operation. In simulations the flow field produced over time by the calibrated groundwater flow model is considered as reality and used to test the real-time control of the well field. Based on the groundwater flow model, the optimal AR for the basins and infiltration wells are calculated such that the hydraulic barrier function is fulfilled with a minimal total infiltration rate. For the online-application, real-time piezometric head data are used to update the groundwater flow model in realtime regarding head. In total 87 continuously monitored piezometers are available in the study area, some of them directly located south of the basins, which is our main area of interest.

3. General Methodology 3.1. The Groundwater Model and the Ensemble Kalman Filter. The groundwater flow is simulated by a threedimensional finite element groundwater model consisting

of 173,599 prismatic elements and up to 26 layers using the code SPRING (20). The hydraulic conductivity K and the leakage coefficient L of the rivers Limmat and Sihl were adjusted by transient inverse modeling taking into account 87 head time series. Details can be found in refs 15 and 21. Model calibration was based on a modified pilot point method introduced by ref 22. Although the groundwater flow model fits well the measured head data, deviations between measured and simulated heads are not negligible. Moreover, if the calibrated model is applied in prediction mode deviations tend to be larger, which is common when applying any calibrated model for predictions. Updating the model in real-time with the help of EnKF (16, 21), assimilating measurement data, reduces the discrepancies between measured and simulated hydraulic heads (17, 18). EnKF uses measurement data to update model predictions by optimally weighting measurement data and model predictions. For choosing the optimal weights it is essential to characterize the model prediction uncertainty. Details can be found in ref 23, among others. In this study, uncertainty was dominated by the spatial variability of K and L and was described with the help of geostatistical methods (see ref 15 for more details). For online applications with the real-time control method, uncertainty of river stage values could be reduced by making use of existing predictions on the basis of a coupled regional climate-surface hydrological model (24). The EnKF used 100 stochastic realizations to characterize the model prediction uncertainty. Using 200 stochastic realizations only gave a small additional improvement in terms of head prediction. Given the CPU-intensity of the calculations, only 100 realizations were used. 3.2. Multilevel Control Method. In order to prevent polluted city water from flowing into the domain of the horizontal wells, the heads near the basins have to be higher compared to the heads closer to the city domain. Three pairs of measurement points, located in the transition zone between the wells and the city center (Figure 1), were selected in order to calculate three head differences (∆h1, ∆h2, ∆h3) which are used as inputs for the control algorithm. They are regarded as representative values for three relevant regions of influence of three well groups (well A&B, well C, and well VOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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∼

D). All pairs are located on a straight north-south axis. If ∆h for each of the pairs is larger than zero, the groundwater flow direction points away from the wells, avoiding the abstraction of city water. The requirement ∆hi ) ∆href (i ) 1,2,3) for all three ∆h is imposed in the control strategy. ∆href is a user specified reference value for the head differences. The desirable state (i.e., ∆hi ) ∆href) is achieved by optimal recharge rates in basins and infiltration wells. In the case study, the daily drinking water demand is given, and therefore the daily historical water abstraction rates have been used as model input. The AR rates u are obtained from the nonlinear fuzzy logic controller’s (FLC) transfer function (Figure S1, Supporting Information)

uI(t + 1) ) puI*fuI(∆h1(t), c1(t)), ∼

uII(t + 1) ) puII*fuII(∆h2(t), c2(t)) ∼

uIII(t + 1) ) puIII* f uIII(∆h3(t), c3(t)), ∼

uS1-6(t + 1) ) puS1-6* f uS1-6(∆h3(t), c3(t)) ∼

uS7(t + 1) ) puS7* f uS7(∆h3(t), c3(t)), ∼

uS8-10(t + 1) ) puS8-10* f uS8-10(∆h2(t), c2(t)) ∼

and uS11-12(t + 1) ) puS11-12* f uS11-12(∆h1(t), c1(t))

∼

uj(t + 1) ) puj* f (∆hi(t), ci(t))

(1)

where uj indicates the controller (artificial recharge basin or a group of infiltration wells, j ) 1, 2, .., 7) that uses the head difference ∆hi(t)as first input, obtained by the head of the groundwater model and its time derivative ci(t) ) ∆hi(t)/∆t as second input. The function gain parameter (FGP)puj can be scheduled for every controller individually with the help of a genetic search algorithm typically presented by ref 27. The controllers’ functions yield the necessary recharge rate of the jth basin or injection well uj(t + 1) for the next time step t+1. The calculation of optimal AR rates by separate controllers and the optimization of the control parameters for each time step can be regarded as a multilevel, hierarchical control approach which is related to the concepts introduced by refs 5, 25, and 26 and consists of the following steps (“O” is Optimization step and “F” Feedback control step): O1. Select random numbers for function gain parameters puj. F1. For the time step t the piezometric heads h(t) are calculated with the groundwater flow model. The head differences at the pairs of observation wells ∆hi(t) are inputs for the FLCs as are their time derivatives ci(t) ) ∆hi(t)/∆t. F2a. The rule base of the FLC transfer functions were defined a priori on the basis of information provided by the control staff and the maximal capacity of recharge per day in basins and infiltration wells and are defined such as: “IF ∆h1 , THEN uI ”; “IF ∆h1 , THEN uI ”. These rules help also to constrain the optimization problem so that less iterations are needed in the subsequent minimization of the objective function (O2). The membership functions of input and output variables and their inference are implicitly shown with the transfer function curve in Figure S2 (Supporting Information) and are programmed in C according to methods presented by ref 28. F2b. All recharge rates for the basins and groups of infiltration wells for the next time step t+1 are determined by the nonlinear FLC transfer functions according to

F3. After the calculation of the AR rate for the next time step uj(t+1), j ) 1,2... 7; these amounts of recharge are used as input for the next model run and the calculation of h(t+1). O2. In this optimization step, the FGP puj of the FLC function are again randomly set between 0 and 1, and the control of the time step t+1 is again simulated with the alternated gain parameter. The new output of the controllers is used to calculate the objective function value of iteration step 2 with following equation m

Q ) w1

∑ 1

n

uj(t + 1) + w2

∑ (∆h (t + 1) - ∆h i

2

ref)

f min !

1

(2) where m is equal to 7 (i.e., four groups of infiltration wells and the three basins), n is equal to 3 (i.e., three pairs of head observations), and w1 and w2 are weighting factors. The function values form a set of trade-offs between AR and head differences and therefore the optima form a Pareto front. The objective function values of the iteration steps 1 and 2 are compared, and the FGP of the better iteration is used as starting value for a new randomization. This iterative stochastic search is performed for a predefined number of iterations, i.e. 5. Each of the optimization iterations requires one model run. The optimization needs between 5 to 10 iteration steps to converge, with up to 55 s CPU-time per iteration.

4. Results and Discussion 4.1. Testing with Historical Data in Offline Simulation Experiments. In order to test the control concept offline, several numerical experiments were carried out in order to allow a comparison with historical management. The most important question was whether the AR could be reduced or had to be increased instead to meet the ∆h-criterion. Historical data of the period between the 1st of January 2004 and the 23rd of August 2005 (daily values for river stage, lateral inflow, natural recharge, and pumping) were used to simulate offline the optimal control of artificial recharge. Simulation scenario I optimized the AR such that all three head differences were positive on all days. Simulation

TABLE 1. Comparison of Historical Management and Optimal Management Using the ∆h-Criterion for Simulation Scenarios I and II (with ∆href = 0.01 m) over 600 Days measurement

simulation I

simulation II

16,500,000 13,000,000 1.3 84 100 100

22,000,000 13,000,000 1.69 0 0 0

16,500,000 13,000,000 1.3 40 15 40

3

overall recharge for 600 days in m overall abstraction for 600 days in m3 ratio percentage of days when ∆h1 negative percentage of days when ∆h2 negative percentage of days when ∆h3 negative

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FIGURE 2. Pareto front of optimal control simulations including simulation scenarios I and II. Plotted are the minimized amounts of artificial recharge as function of the average head difference, calculated over three pairs of piezometric heads. In the figure also the measured average head difference for the traditional management and the simulated average head difference for the traditional management are indicated. scenario II optimized the spatial distribution of recharge, under the additional constraint that the total amount of applied AR was the same as the one applied historically. Simulation scenario III consisted of an additional number of model runs in order to calculate a Pareto front solution. In these calculations, the amount of required artificial recharge is minimized for a given reference ∆href. The result forms a functional relationship between the amount of AR and ∆hi, for a broad spectrum of ∆hi values. For scenario I, it is found that positive head differences during the complete simulation period of 600 days can only be achieved by an increased amount of AR in the basins and infiltration wells. See Table 1. The implication of the increased AR is an increase of the groundwater level of about 0.5 m, which does not have any negative side effects. Historical head differences both obtained by measurement and recalculated with the flow model were negative at almost all days of the considered simulation period (i.e., 100% of the days ∆h2 and ∆h3 were negative, whereas ∆h1 was negative 85% of the days). Modeled and calculated head differences differ, yet this difference does not matter as the analysis focuses on the comparison of the modeled heads for the historical management with the modeled heads for the optimized management. With the optimal control approach described in chapter 3, better results were produced. However, the overall AR is 1.7 times higher than the overall abstraction, in order to achieve permanently positive head differences (i.e., 0% of the days with negative ∆h). In simulation scenario II the amount of artificially recharged water is fixed (the optimal search algorithm was enhanced by a constraint of a maximum daily AR rate of 29,000 m3 not to be exceeded by the sum of the AR calculated by the controllers), while the spatial distribution of this recharge is optimized over the different basins and infiltration wells. In this case a better operation scheme of basins and infiltration wells still can be achieved as compared with the historical simulations. The spatial distribution of AR of the real-time control simulation is quite different from the historical one, see Table S2, Supporting Information. On average, ∆h is positive although the same average artificial recharge rate was applied as in the past (Table 1). The average artificial recharge rate of about 28,000 m3 per day yielded a ∆h, averaged over the three observation pairs, of -0.046 m in history (Figure 2). While the historical management comprised ca. 16% of AR in S1-6 and 26% in S8-10 and basin II, the focus of the optimized artificial recharge shifts upstream with almost 50% AR being now recharged in S8-10 and basin II.

In simulation scenario III (Figure 2), the management was optimized for different given reference values of ∆href, and a comparison was made with the historical (simulated) management. The results of simulation scenarios I and II are part of the Pareto optimal set of solutions together with the results of scenario III. The values are trade-offs between the two criteria: achieving positive head values and minimizing the amount of AR. Acceptable values regarding the control criterion (i.e., its desirable state ∆h ) ∆href) are average values of ∆h above the zero line (Figure 3, dashed line). 4.2. Results of Field Tests (Online-Application). The control-concept was also implemented online at the control center of the waterworks together with the model and the EnKF. EnKF updated the model predictions with the 87 measured head data each day. The updated model output, the head, is used to calculate the head differences ∆h1, ∆h2, and ∆h3 which are inputs for the controllers to determine the artificial recharge rates for the next day. With several iterations of the flow model optimal values for the controllers’ parameters can be determined, as outlined in section 3.2. During the night, the control center’s dispatchers use the proposed values of artificial recharge and switch pumps on or off for the supply of basins and infiltration wells. The next day the procedure of updating the model and adaptation of AR amounts is repeated. The measured value of the EC σ3407 at the piezometer 3407 (which is one of the measurement points for the calculation of ∆h2) is of interest regarding the performance of the real-time control in online mode. Horizontal well C is the most likely one to abstract water with high EC originating from the city area. In this particular case, we would expect a negative correlation between ∆h and EC at the measurement points. In order to avoid “city water” a positive head difference should generate a decreasing value of EC. Head data and measured EC at the same locations were analyzed for the period over which the optimal control strategy was applied in online-mode between the 1st of March 2009 and the 5th of May 2009. Only during this time period a full operation schedule was possible (∆href ) 0.05 m). After the 5th of May, construction work made the onlineapplication impossible. When the signal of ∆h2 converged to ∆href (still with some oscillations) and became positive in March 2009, the signal of the electrical conductivity σ3407 decreased over time. After the control went offline, the head difference became negative in June 2009, and the electrical conductivity σ3407 rose again after a delay time (Figure 3). We use the discrete cross-correlation function R(∆h2, σ3407, T) ) l

∑ [(∆h (k) - µ 2

∆h2)(σ3407(k

- T) - µσ3407)]

k

∑ l

k

∑

(3)

l

(∆h2(k) - µ∆h2)2

(σ3407(k - T) - µσ3407)2

k

in order to calculate the correlation coefficients between the two signals ∆h2(k) and σ3407(k) as a function of time. T is the time delay, k is the discrete time index (in days) of the two signal values, and l is the total number of days. A negative and high correlation coefficient R(∆h2, σ3407) between the two signals was found with a minimum of -0.75 for a time delay T of 20 days. This shows the influence of the controlled positive head difference on a decreasing EC. 4.3. Discussion of ∆h-Criterion. The proposed real-time control method possesses the important advantage of a favorable CPU-time required to calculate the optimal allocation of the artificial recharge. However, the three-dimensional groundwater flow model is associated with uncertainty and does not represent well small-scale heterogeneities and connected structures. ThereVOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Signal of ∆h2 during the time period between February 15th and June 30th, 2009. The signal shows the head difference ∆h2 between the measurement points 3224 and 3407. The head difference ∆h2 complying with the reference value ∆href is plotted on the left scale against time. The electrical conductivity σ3407 in piezometer 3407 is drawn against time, with the scale provided by the axis on the right.

FIGURE 4. Path lines produced by particle tracking with boundary conditions of April 30th, 2004. The computation uses the historical artificial recharge in the basins and wells. The dashed line indicates the boundary of the contaminated city area which is located south of the line. The yellow lines indicate the path lines with real-time control, and the red lines indicate the path lines for the historic management. fore, in spite of a positive head difference in the model, it cannot be excluded that city water would reach the pumping wells. On the other hand, small negative head differences do not automatically imply that city water reaches the wells. As an alternative, path lines of the instantaneous flow field can be calculated using particle backtracking from the pumping wells. The path lines indicate from where the pumped water originates. The percentage of city water that is pumped at a given well is calculated by the percentage of path lines weighted with the corresponding flux that originates from the city domain. For each and every model time step all boundary conditions, forcings, and calculated groundwater flow velocities are kept constant assuming quasi-steady state conditions while 5400 virtual particles are tracked backward until 200 days in the past. The starting positions of 1350 virtual particles are placed symmetrically on the surface of a cuboid with dimensions 2 m × 30 m × 30 m containing the well in its center. In order to check whether the back 6806

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tracking yields the correct flux over the surface of the control volume, the volume flow rates of all particles in x-direction, in y-direction, and in z-direction (depending on the face on which they start) are calculated and summed up and balanced with the abstraction rates of the four horizontal wells. After calculation of the weighted flux over the surface of the control volume, the next step is to calculate the percentage of city water. The term “city water” (CW) is used for the counting of path lines (weighted with their fluxes) which cross the defined boundary (dashed line) south of the infiltration basins and infiltration wells (Figure 4). For additional information, see Figure S2, Supporting Information. As an example, Figure 4 shows the path lines (red) for the model simulation step of April 30th in the year 2004 with historical pumping rates and recharge rates. The calculated city water percentage is 20% in well C and almost 12% in well D at this day. The path lines in yellow show the situation under optimal control conditions.

FIGURE 5. City water (CW) percentages for the period January 2004-August 2005 in the horizontal wells C and D. The CW is calculated for three scenarios: historical management, and optimization with real-time control according to simulation scenarios I and II. Figure 5 shows time series of the percentage of city water that reaches the pumping wells C and D (for January 2004August 2005). These percentages are shown for the historical management and the simulation scenarios I and II with optimization according to the ∆h-criterion. Real-time control with the ∆h-criterion yields better results than according to the historical management; in simulation scenario I city water is completely avoided, and in simulation scenario II the percentage of city water in both wells C and D is in general clearly lower than for the historical management.

Acknowledgments The study was performed within the project “Real-time control of a well-field using a groundwater model”, a cooperation between ETH Zurich, Zurich Water Supply, and TK Consult Zurich. This project was funded by the Swiss Commission for Technical Innovation CTI under Contract No. 7608.2 EPRP-IW. The author gratefully acknowledges the doctoral scholarship granted by the German National Academic Foundation.

Supporting Information Available Table S1 (technical data), Table S2 (i.e., comparison of historical mean artificial recharge and optimized artificial recharge), Figure S1 (i.e., the nonlinear transfer function curve of a fuzzy logic controller), and Figure S2 (i.e., path line map). This material is available free of charge via the Internet at http://pubs.acs.org.

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