## Novel Method for Selection of Ranney Wells for Regeneration Based on Hydraulic Modeling

David Mitrinović^{1}, Milenko Pušić^{1}, Oliver Anđelković^{1}, Jelena Zarić^{1}, Milan Dimkić^{1}

^{1} Institute for the Development of Water Resources ˝Jaroslav Černi˝, Jaroslava Černog 80, 11226 Belgrade, Serbia; E-mail:
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### Abstract

This paper presents a novel method for selection of Ranney wells for regeneration based on hydraulic modeling. In order to quantify the effects of clogging on lateral screens, it is necessary to determine hydraulic losses and a range of other parameters. The paper presents modelling concept which is based on measurements results, and which is tested and calibrated on selected group of Ranney wells of the Belgrade drinking water source. Model is aiming to maximize water yield from Ranney wells over a certain period of time by installation of new lateral screens. Model results are provided in the paper and discussed and recommendations for well and aquifer monitoring are provided.

**Keywords:** groundwater, Ranney well, lateral screen, hydraulic losses, regeneration.

Introduction

The Belgrade groundwater source drinking water supply consists of 99 radial and 45 tubular wells, located along the banks of Sava River, at a length of about 50 km (Dimkić & Pušić 2014). The aquifer has a saturated thickness of about 20 m and consists of the following layers from the confining bed to the ground surface: gravel sand, sandy gravel, sand and silt. Two zones can be distinguished in the vertical profile: the lower zone containing coarser particles, and the upper, fine-grained zone. The wells are located in the alluvial sediments of the Sava River and Pleistocene rivers, with well screens placed mainly in the lowest part of the aquifer (Dimkić & Pušić 2014). The main source of aquifer recharge is the river, although the hydraulic connection is weakened by riverbed clogging and the existence of thin layers with low hydraulic conductivity unevenly distributed in the horizontal plain. The existence and number of these layers is the result of several sedimentation cycles (up to four), which is associated with the quaternary (Pleistocene) glacial and interglacial periods (Institute "Jaroslav Cherni" 2010).

The groundwater aquifer of the Belgrade drinking water source can be characterized as predominantly mildly anoxic with little (rarely more than 0.5 mg / l) or no dissolved oxygen, with an average dissolved oxygen concentration of 0.17 mgO_{2}/l (Dimkić & Pušić 2014). Dissolved iron is present in groundwater with an average of 1.51 mg / l (Dimkić & Pušić 2014).

A wide range of bacteria exists in the groundwater surrounding the wells: iron-oxidizing, heterotrophic aerobic, slime forming, sulphate reducing and denitrifying bacteria (Dimkić et al., 2011b) have been identified. Biofouling on well screens exists and is caused by microbiological activity, while a high rate of well screen corrosion has also been observed. Therefore, the wells are periodically cleaned and, eventually, new laterals are installed. Local hydraulic resistance on the filter and the filter zone of the well is a parameter indicating the degree of clogging, according to which it is possible to evaluate the effectiveness of the well screen cleaning. The effects of well screen cleaning are temporary and it is necessary to repeat the procedure periodically. The effects of installing new well screens are longer lasting, largely because new well screens are made of non-corrosive materials that eliminate the problem of corrosion damage to the screen. Therefore biofouling has become a key cause of the deterioration of new laterals and well screens and the groundwater abstraction regime significantly affects the rate of well screen clogging.

Methods

*Local well screen losses: definition, determination and relation with the flow, redox potential, concentration of dissolved bivalent iron and the microbilogical parameters.*

In order to quantify the effects of clogging (encrustation and biofouling) on lateral screens, it is necessary to define and determine minor hydraulic losses. Figure 1 shows a typical vertical cross section of a Ranney well lateral screen in operation with groundwater flow pattern (isopiestic and stream lines).

Figure 1: Vertical cross-section of a typical flow pattern surrounding the Ranney collector lateral.

Figure 1 shows there is a large hydraulic gradient in the vertical direction in the well screen zone, therefore, in order to make a precise determination of the hydraulic potential near the lateral screens, the filter column of the piezometer should be near the well screens and up to 1 to 2 m long. In order to determine the changes in local hydraulic resistance (LHR) on the lateral screen, it is also possible to use piezometers outside of the well screen zone, but the significant differences between piezometer and well water levels occurs due to groundwater flow through the aquifer material leading to overestimation of LHR values. In this case the LHR values can only be determined by subtracting a calculated or estimated difference between the water levels in the piezometer and the well generated by groundwater flow through the aquifer material.

For a realistic assessment of the effects of well screen regeneration, it is necessary to quantify changes in the LHR of the filter zone and the near well zone before and after regeneration (Dimkić et al., 2011b). LHR is defined as the ratio of the difference in piezometric levels between the well and the piezometer (*ΔS*) and the flow through the lateral screen (*q*):

(1)

The flow through the lateral screen is determined by the difference in hydraulic potential inside and outside the lateral screen, lateral screen dimensions and thickness (*d*), and the filtration coefficient of the clogged layer (*K _{L}*):

(2)

where *q* represents lateral screen flow, *L* is the length of the lateral screen, *v* is the inlet filtration velocity of the groundwater at the filter perimeter, and *r* is the lateral screen radius - Figure 2 (Dimkić et al., 2011b). For the purpose of simplification, it was assumed that the values of the filtration coefficient of the clogged layer and the difference in hydraulic potential inside and outside the lateral screens do not change along the length of the lateral screen. ΔS(t) is the difference between the levels in the near-piezometer and the well, and consists of a depression due to filtration in aquifer - *S'*, and the depression resulting (variable at constant flow) from hydraulic losses at the lateral screen - *S"*, Figure 2 (Dimkić et al., 2011b). If filtration characteristics of the material remain unchanged outside the near-lateral screen zone, the following shall apply:

(3)

The rate of change in local hydraulic resistance, i.e. kinetics of local hydraulic resistance - KLHR, remains the same and can be defnied as:

(4)

Figure 2: Loss of the piezometric level along the groundwater path from the near well location, through the clogged zone, to the inside of the lateral screen, under constant flow conditions.

The change of *LHR* over time is most pronounced following regeneration, and then it is most often negative. In cases where the well flow is maintained at an approximate constant and without regeneration, *KLHR* usually remains relatively unchanged over time, i.e. *LHR* exhibits an approximate linear growth over time. The value of *KLHR* is mostly influenced by the concentration of dissolved bivalent iron in water* c(Fe ^{2+})*, the redox potential

*E*, the flow

_{h}*q*, the number of microbial populations

*B*which, by their metabolic activity, lead to clogging - biofouling of wells, and the granulometric composition of the filter zone

*Γ*:

(5)

The influence of bivalent iron concentrations and redox potential on linear hydraulic loss kinetics is largely reflected in well flow rates because the linear losses exhibit a slower increase as the concentration of divalent iron decreases and the redox potential increases, resulting in higher average flows during well operation - Figure 3. The diagram shows data for wells with new lateral screens and wells with older lateral screens with assumed biofouling processes, for which more than three LHR data sets exist for the period between 2006 and 2013. The criterion based on wells with severe biofouling buildup was the number of active lateral screens - 6 or more active lateral screens in 2013. In this way, 26 wells with older well screens were identified.

Determining the relationship between the rate of biofouling and the aforementioned parameters that influence decisions pertaining to the projected number of lateral screens and well maintenance is very important from a financial perspective. The possibility of predicting LHR changes over time also allows for complex calculations and simulations of the effects of well operation at different flows, where the effects of well interaction on piezometric levels can be calculated along with changes in LHR over time depending on the concentration of dissolved bivalent iron, redox potential and flow through the lateral screen, which allows for the complete determination of level change in each well in a group of wells during the observed time period. This level, i.e. the difference between it and well screen elevation determines the feasible flow and whether well regeneration is needed.

Figure 3: The relationship between mean well flow (above) and *KLHR* (below), and the mean concentration of dissolved bivalent iron in water, in wells with pronounced biofouling processes.

Regeneration of Well Screens and Quantification of the Effects

Since 2000 (and even earlier), regeneration of the lateral screens of Belgrade water source is performed using only mechanical techniques. The regeneration procedure is performed after stopping the operation of the well and installing the necessary equipment which is followed by a visual inspection of the lateral screens by using a special camera. In accordance with the results of the image analysis, the lateral screens are rinsed with high pressure water jetting with pressures above 100 bar. Lateral screen rinsing is done in segments for several hours, which depends on the on-site assessment. Many old lateral screens are damaged by corrosion, so it is often necessary to shorten or completely close off certain lateral screens.

For a realistic assessment of the effects of regeneration, it is necessary to quantify the LHR value before and after regeneration. The coefficient of reduction of local hydraulic losses due to regeneration yreg is defined as:

(6)

where LHR1 i LHR2 are LHR values before and after regeneration, respectively.

By multiplying yreg with LHR prior to regeneration and the lateral screen flow q after regeneration, leads to a piezometric drop at the lateral screen after regeneration:

(7)

Field measurements of the required parameters are performed after achieving a (quasi) steady state flow of groundwater to the well.

For a comparative analysis of the change in local hydraulic resistance and measured well flow rates, data related to 27 performed regenerations on 24 wells were selected (Table 1), for which sufficient LHR values data were available before and after regeneration. Regression analyses was used to determine LHR function over time in the period before and after regeneration and their values were defined by extrapolation before and after regeneration.

From Table 1 it can be seen that the ratio between well flow before and after regeneration is in the range between 0.39 and 13.8, on average 2.39, the coefficient of reduction of linear hydraulic losses due to *y _{reg}*, regeneration is between 0.019 (decrease of 98.1%) and 1.13 (increase of 13%) . The average value of the LHR reduction coefficient due to regeneration is 0.41 (i.e. average reduction of 59%).

Not even monitoring of the effects of regeneration through LHR change can provide a completely accurate picture, since some of the lateral screens will often partially or completely be closed, while openings on screens at previously clogged zones will partially or completely be opened, changing both the local groundwater flow patterns and the flow distribution in relation to the period prior to regeneration. Since lateral screen flow measurements data are practically never available, and piezometers are not available at each lateral screen, it is only possible to take into account the change in the number of active lateral screens. The ratio between lateral screen flow before and after regeneration ranges from 0.37 to 2.67, with an average of 1.18.

Insertion of Lateral Screens and Quantification of Effects

Since 2005, a complete replacement of existing lateral screens of individual wells using the Preussag method has been implemented on the wells at the Belgrade drinking water source. This method includes insertion of new stainless steel lateral screens (bridge openings, height of bridges from 2.5 mm to 3.5 mm) into the pre-pressed pipe and subsequent installation of the filter layers. The original Ranney method included direct pressure insertion of steel lateral screen pipes (dimensions 6 mm x 80 mm) into the aquifer porous media.

By analyzing the results of long-term monitoring of the operation of five wells with new well screens at the Belgrade water source, along with their nearest piezometers (Rb-15, Rb-16, Rb-20, Rb-8 and Rb-5m), a functional dependence between redox potential, bivalent iron concentrations in water, the number of microbial populations, well screen flow, the granulometric composition of the zone around the screen filter and the filter, and the rate of biofouling of new lateral screens was established (Institute "Jaroslav Černi" 2010):

(8)

whereby the concentration of bivalent iron *c(Fe ^{2+})* in water is expressed in mg/l, redox potential

*E*in mV, flow rate per lateral screen

_{h}*q*in l/s, while

*B*is the geometric mean of the number of potentially active mucus-producing and the number of potentially active iron bacteria in the sampled well water analyzed using BART tests.

*φ*is the factor of

_{(Γ)}*KLHR*dependence on the granulometric composition of the aquifer material around the filter material in the filter zone. In the case where a lateral screen is installed by the Ranney method, finer granulometric fractions are removed from the prefiltration zone during well operation, or if a coarser filter material is successfully installed during insertion of the well screens using the the Preussag method, the factor

*φ*is less than one. The predicted increase in

_{(Γ)}*LHR*is obtained by multiplying the calculated value of

*KLHR*and time period. The level drop due to local hydraulic resistance is calculated by dividing the well flow with the number of lateral screens and multiplying that with the calculated

*LHR*.

Distribution of Flow Between Old and New Lateral Screens

Insertion of new lateral screens, if the old ones have not been closed, will lead to a redistribution of flow between the lateral screens. The equilibrium is established when the head losses on the old and new lateral screens are equalized - equation (9):

(9)

where *LHR _{1}* and

*LHR*are local hydraulic losses on old and new lateral screens, respectively,

_{2}*n*and

_{1}*n*are the number of old and new lateral screens,

_{2}*x*is the proportion of the flow rate through new laterals in the total flow, while

*Q*represents well flow. The local drop in level at the time

*t*is calculated based on the corresponding values of KLHR, the duration from the injection of the lateral and the initial values of LHR - equation (10):

(10)

whereby *t* is the time period and* t _{ut}* is time elapsed since injection of the lateral. Equation (10) yields equation (11) which calculates the fraction of the flow rate through new lateral screens in the total well flow rate:

(11)

Minor losses that occurred before lateral injection - *LHR _{1tut}*, is calculated as the sum of minor losses at the beginning of the simulation period (

*LHR*) multiplied by the time elapsed from the beginning of the simulation period to the moment of injection, and by the

_{10}*KLHR*of the old lateral screens (which is considered to be the same before and after regeneration), whereby

*LHR*and

_{10}*KLHR*are obtained by processing the data obtained by observing the well and a nearby piezometer. The calculated losses are multiplied by

_{1}*y*, in the event of regeneration of old well screens prior to injection of the lateral. Minor hydraulic losses on new lateral screens immediately following injection (

_{reg}*LHR*), i.e. the losses per unit of flow through the new lateral screen are fixed to 0.02 m/(l/s) based on water level data in the well and nearby piezometer following injection of the new lateral screens. In this way equation (12) is obtained from equation (11):

_{20}(12)

Lateral screen loss, based on equations (9) and (12), can be calculated as:

(13)

*KLHR _{2}* depends on the new lateral screen flow rate (equation (8)), and the flow rate in the new well screen depends on fraction

*x*of the flow rate through new lateral screen in the total flow rate, which, among other things, depends on

*KLHR*(equation (12)). Therefore, function Q = f (x) is calculated for each well, so that for the three selected well flows (20, 50 and 80 l/s),

_{2}*KLHR*is calculated in equation (12) by using equation (8), where the value of fraction

_{2}*x*is assumed until the fraction calculated by equation (11) is equalized with the assumed value. After the values of

*x*were obtained for all three flows, it was established that the ratio

*Q*and

*x*can be successfully described by the linear function for each well. Excel Solver was used to obtain coefficients of linear functions for all wells, by minimizing squared differences between assumed and calculated fractions

*x*.

This calculation is based on the assumption that the fraction of the flow through new lateral screens in the total flow has not changed from the moment of injection to the end of the simulation period. This assumption is incorrect because linear losses on new lateral screens are very low immediately following injection, even though the rates of screen clogging are faster than those of the old lateral screens, therefore a greater flow will pass through new lateral screens in the period immediately following injection than that which is estimated by this calculation. Therefore, a calculation was done for the moment immediately following injection, and then for each subsequent year. Equation 12 was used, where losses from previous years were entered into the initial linear losses per flow unit (*LHR _{10} *and

*LHR*) while the

_{20}*KLHR*was multiplied with the unit, for both the old and new lateral screens, because the time elapsed since the end of the previous step is one year. Figure 4 shows the results for the well Rb-19, for which the share of the flow through new lateral screens was the smallest and therefore the described problem related to flow estimation is potentially the most evident.

Figure 4: The share of the flow through the new lateral screens (dashed line) and linear losses (full lines) in the case of the basic calculations (red lines) and the calculations perfored for each year (blue lines), when 40 l/s (up) and 100 l/s (bottom) is being abstracted from well Rb-19.

Figure 4 shows that calculations performed year for year provide significantly higher fractions of flows through new well screens and larger linear losses in the period immediately following injection of the laterals than that of the basic calculation, but that the difference in both variables is small towards the end of the ten-year simulation period.

Hydrogeological Schematization and Selection of an Analytical Flow Equation

Based on the data from the lithological columns of numerous structural boreholes, groundwater level observations in piezometers whose filter columns are located both in lower and higher aquifer layers and the results of numerical simulations of the well discharge tests hydrogeological schematization was adopted where interlaced impermeable layers are represented as one interlayer. Figure 5 shows the distribution in the plan and thickness of this interlayer.

The riverbed does not cut into a low-permeability interlayer and only the upper aquifer layer is directly recharged from the river. Therefore, along with a significant approximation, the groundwater flow can be modeled and the aquifer flow, which is recharged through a low-permeability upper layer of a certain thickness and filtration coefficient value, in which the piezometric level is constant - Figure 8. Due to the direct hydraulic contact between the river and the upper aquifer layer, the level in it is much less variable than in the lower aquifer, and therefore there is an assumption that the constant piezometric level in the aquitard that separates them is sufficiently close to the real state.

Figure 5: Distribution and interlayer thickness of the Belgrade water source area (Institute "Jaroslav Černi" 2010).

A part of the source which is modeled is framed by the red line in Figure 5 and shown in Figure 6, with objects included in the model and analysis. The mean value of the groundwater levels measured in the piezometers, the filter column of which is located in the upper aquifer (Figure 6), for the period from the beginning of 2006 to the end of 2013, is 68.5 masl, which is about three meters lower than the mean level of the Sava River, which measured 71.3 masl for the same period. Figure 7 shows the results of observed levels in piezometers Rb-16 / p-3-Rb-16 / p-2 and Ps-55-3-1-Rb-15 / p-2 adjacent to the Ranney wells, from which it can be concluded that the level in the upper aquifer does not change significantly even in the immediate vicinity of the well, while the piezometric level in the lower aquifer layer is several meters lower.

Figure 6: A group of 12 selected wells on the right bank of the Sava River on Ada Ciganlija (red circles) and piezometers with filter columns in the upper aquifer layer (blue circles).

Figure 7: Mean piezometric levels (2006-2013) in the piezometers near Ranney wells Rb-15 and Rb-16.

The Hantush and Jacob's analytical solution is used (Delleur 1999) to calculate groundwater flow in this scheme.

Figure 8: Schematic of the flow towards an isolated well in the aquifer with a constant piezometric level in the aquitard (taken from Delleur 1999).

In order to apply Hantush and Jacob's solution, boundary conditions must be determined from the following assumptions:

- The aquifer and aquitard have infinite distribution in the horizontal plain with constant thickness and filtration characteristics,
- The aquifer filtration coefficient is at least 100 times greater than the aquitard filtration coefficient,
- The flow through the aquitard is exclusively vertical, while the flow in the aquifer is exclusively horizontal.

The solution is represented by equation:

(14)

where *s (r, t)* is depression which depends on the time elapsed t and the distance from well* r, Q* is the flow abstracted from the well, *T* is the transmissibility of the aquifer and *W* is the dimensionless Hantush function (Delleur 1999). The flow factor* L* is determined by equation:

(15)

where the hydraulic resistance of the aquitard* c* is determined by equation:

(16)

where* D'* is the thickness of the aquitard and *K'* is its filtration coefficient in the vertical direction. The value of parameter *u* is determined as:

(17)

where *S* is the storativity. In order for equation (14) to be applied to the problem of groundwater flow towards a Ranney well, it must be reduced to an equivalent vertical well. For the calculation of the equivalent well radius, the Citrini equation can be used:

(18)

where* l* is the length of the well screen and *n* is the number of lateral screens (Babac & Babac, 2009).

A part of the depression in the observed well created by flow through the aquifer occurs as a result of superposition of depressions from flows towards the surrounding wells and the depression resulting from flow to the observed well, at a distance from the center of the well which is equal to the equivalent diameter of the observed well, calculated using equation (14). In order to calculate the level in the well itself the loss in the hydraulic potential due to the restricted flow resulting from clogging of the lateral screen and nearby filter zone is added to the calculated depression value due to flow through the aquifer. Local losses on the well screens of a particular well are monitored by measuring and recording levels and flows in the well, as well as levels in one or more of the nearby piezometers. A *KLHR* is obtained from the results of these observations, which is usually approximately constant or increases over time if the well flow does not significantly change and the well has not been regenerated. Based on this data, the water level in the Ranney well can be calculated as the sum of the depression in the observed well due to flow through the aquifer, and the flow from the well multiplied by the sum of local losses at the starting point and the new losses calculated by multiplying *KLHR* and the time that has elapsed from the starting point. Depression due to flow through the aquifer quickly reaches a quasi steady-state value, while local losses increase over time.

The Model and its Application to a Selected Group of Wells

For the development and testing of the optimization algorithm, a group of 12 wells located on the right bank of the Sava River on Ada Ciganlija was chosen: Rb-11, Rb-12, Rb-13, Rb-14, Rb-15, Rb-16, Rb-17, 18, Rb-19, Rb-19-1, Rb-20, Rb-20-1 (Fig. 9). Precise coordinates of the wells are obtained which allows superposition of the depressions and calibration of the hydrogeological model. There are several reasons why these wells were selected:

- The interlayer, is continuous and approximately of equal thickness distribution in the selected area. This allows the same analytical solution for radial flow for all wells to be applied and for the solutions to be superposed without greatly distorting the conditions of the infinite distribution of low-permeability layer between the upper and lower aquifers, whereby the low-permeability layer and the lower aquifer are of constant thicknesses and filtration characteristics.
- Well flows are large enough that the effects of the adjacent wells on depressions are significant.
- New corrosion-resistant stainless steel well screens were installed on 3 wells (Rb-15, Rb-16 and Rb-20) in 2007 and 2008, which enabled the determination of the kinetics of the clogging process as a function of flow, the concentration of divalent iron in groundwater, and redox potential, while screen corrosion can be neglected.
- There are required data available for calculations for most wells
- The wells at Ada Ciganlija near the the Savsko Lake were producing only about 130 l/s at the initially chosen time, and therefore their impact on the selected wells could have been neglected.

The duration of the simulation time period in the optimization algorithm was determined for 10 years, among other things, because this is the period during which each of the 12 selected wells should be regenerated. By 2013, the average interval between well regeneration for Belgrade waterworks was about 7 years. This interval varies from well to well, and ranges between 2 and 20 years. This is a long enough time period in which to observe the differences between different pumping regimes and the selected wells for installing new lateral screens.

The flows on the basis of which the algorithm calculates levels outside and within the well correspond to the average actual well flows, and do not change over the 10-year simulation period.

There are two basic well options in the model: regeneration only, or injection of new laterals in the 4th year (after which it can also be regenerated):

1) When new lateral screens are not injected into the well, the linear losses per unit of flow resulting from the clogging created during current well operation are multiplied by the present flow and summed up with new losses (which arise from newly created clogging during the observed period), by a certain multiplication of *KLHR* with the length of the time period being observed and the flow. In a few cases when a square regression function is used - Figures 10 and 12, the *LHR* at the end of the time period is obtained from a quadratic function.

From this calculated depreciation value due to local losses on the well screen, the assumed reduction of local losses due to regeneration is subtracted when the level in the well is lowered to the level which is a pre-defined distance from the lateral screens (taken if the level drop is 14.3 m at the time) - Figure 11. The water level in the well is obtained by subtracting the depression due to flow through the aquifer and local resistance (factoring in reduction due to regeneration) from the angle of the level in the upper aquifer. Excel Solver was used to calculate the value of the well flow where the angle/level in the well for the predetermined value is higher than the level of the lateral screens at the end of the simulation period. Therefore it is assumed that the maximum possible flow rate during the simulation period was chosen for the given predicted regeneration effects. In this case, *y _{reg}* = 0.26, the flow

*q*is 30% greater than the flow

_{2}*q*(flow at the same facility without regeneration), and in this case, according to equation (8),

_{1}*KLHR*is 30% greater than

_{2}*KLHR*. This example demonstrates that if the well is regenerated during the 10-year simulation period, it allows for a 30% increase in flow.

_{1}

Figure 9: Change of depression over time due to flow through the clogged layer with regeneration (red line) and without regeneration (blue line).

During regeneration, the *LHR (ΔS / q≈ΔS "/ q)* - Figures 14, 16, 23 and 25, is sharply reduced, and if the flow remains approximately the same, the decrease in the piezometric level due to flow through the clogged layer is *S"*. For example, in the regeneration of Rb-13, the decrease in *ΔS* and *S"* was small because the flow after regeneration was significantly increased - Figure 15. In Figs. 18 and 19, on the example of Rb-16, it is seen that *ΔS* increases linearly as does *LHR* when flow remains approximately the same. *KLHR (ΔS / q / Δt ≈ S / q / Δt)* usually remains the same or its value increases over time - Figures 12, 14, 16, 18, 20 and 22. For some wells - Rb-13, Rb- 15, Rb-19-1, Rb-20, a change in LHR due to regeneration could be determined on the basis of previous observations - Figures 16, 18, 26 and 28. The decrease in *LHR* during regeneration of new lateral screens was 57% what is the mean value obtained for the four wells with the injected lateral screens in 2007 that were regenerated, of which those with sufficient available data were selected so that the effects can be quantified.

2) When the new lateral screens are installed, it is arbitrarily taken that it is carried out in the fourth year because introducing the possibility of selecting the injection time would increase the number of combinations to be examined by 10-fold. It has been determined that 5 Ranney wells will be installed within the next 10 years because only 4 Ranney wells within the entire Belgrade water source have been currently selected for well screen installed this year, while at the same time the wells belonging to the analyzed group make up slightly less than a ninth of the total number of wells. There are three scenarios within the lateral screen installation option that differ in the way old well screens are treated, and according to the number of lateral screens that are installed:

a) In one scenario, old lateral screens are regenerated during installation of the 4 new lateral screens. For old and new lateral screen flows, it is assumed that in such a mutual relationship the level drops occurring in the old and new well screens at the end of the simulation period are the same. It is not foreseen that regeneration will be carried out on wells with newly-injected lateral screens in the period following installation. The equivalent diameter is calculated by dividing the lengths of old and new lateral screens and dividing the sum with the total number of laterals, and this value is applied in the equation (18). The value of the decrease in the piezometric level at the end of the simulated period is calculated using equation (19), where *Π _{0}* is the level in the upper aquifer,

*ΔH*is the minimum difference between the water level in the well and the level of lateral screen openings (denoted by

_{wdmin}*H*), depression due to flow through the aquifer

_{d}*S + S'*, and the variable

*U*has a value of 1 if the installation of new lateral screens is performed, and 0 if not.

*KLHR*and

_{2}, LHR_{20}, KLHR_{1}*LHR*, i.e.

_{10}*KLHR*and

*LHR*initially for new and old well screens respectively, are calculated as described in Section 2.4.

(19)

b) In the second scenario, a total of 4 lateral well screens are installed, and the old lateral screens are closed (equation (20)), except in the case of Rb-15, Rb-16 and Rb-20 with stainless steel well screens (equation (19)). Then the equivalent diameter either slightly changes or decreases with respect to that prior to injection in the event that 4 lateral screens are installed (except for the three wells when it increases significantly), which reduces the effects in terms of prolonged increase in well flow, as the losses in aquifer material are not reduced. More importantly, *KLHR* (according to equation (8)) and *LHR* are higher than they would have been if the flow was divided into multiple lateral screens. It is foreseen that a regeneration in the period following installation on wells with new lateral screens should be made due to their significant load, except for Rb-15, Rb-16 and Rb-20 which, when selected for installation, have 7 or 8 lateral screens.

(20)

c) In the third scenario, due to the above-mentioned impact of the number of new lateral screens on *KLHR* and *LHR*, 8 well screens are installed, except in the case of Rb-15, Rb-16 and Rb-20, in which 4 lateral screens are also injected in this case, whereby the old ones are not closed - equation (19). In this version, no regeneration is foreseen on wells with new lateral screens in the period following installation - equation (21). The value of *n _{2}* is 8.

(21)

The correlation that enables the prediction of the KLHR2 value (equation (8)) is defined on the basis of the observation of five wells with new lateral screens at the Belgrade source and their nearby piezometers (Rb-15, Rb-16, Rb-20, Rb-8 and Rb- 5m).

The Optimization Algorithm and the Model Calibration

The optimization algorithm, which includes the described model, allows for the testing of different scenarios and finding a combination of wells for injection of new lateral screens that will enable maximum total flow, using automatic maximum searching or by solving the model for each combination. The optimization algorithm has two versions: the first is executed using only Excel Solver, to automatically determine the optimal combination of wells in which new lateral screens are to be injected, and the second is executed using Excel Solver and a macro written in Visual Basic for Applications programming language to determine the flows for all possible combinations of wells in which new lateral screens are to be injected. The Excel Solver varies the value of predefined cells in the table automatically (with the ability to limit the range of variations and the number to be a real number, an integer or 0 or 1) in order for the target value in one cell to be close to a predetermined value, or to reach a maximum or minimum possible value. In addition, the limit in the range of values can also be assigned to any other cell in the table, so that the final values of the cells that are varied must be such that the conditions for the target cell value are met, with the restrictions of the other cells being respected.

Automatic Determination of the Optimum Combination of Wells in Which the Lateral Screens are to be Injected

In the version of the algorithm that automatically determines the optimal combination of wells, the function given in the target cell, in this case, contains the sum of the flows of all wells at the end of the ten-year simulation period. By automatically varying the value of the cells in which the flow is assigned, as well as by automatically determining the values of the cells whose value determines whether the lateral screens will be injected (one) or not (zero) into the corresponding well during the simulation period, the algorithm searches for a combination that will give the maximum value in the target cell whereby the condition of the minimum difference between the levels in the well and lateral screen levels at the end of simulation period must be met. Prior to starting the calculation, it is determined how many wells will be injected with new lateral screens during the simulation period, at what difference between the levels in the well and the levels of the lateral screens will be regenerated and what is the minimum difference between the levels in the well and the lateral screen at the end of the simulation period. The function in the target cell has the form given by equation (22),

(22)

where *Q _{i}* is the flow of the Ranney wells, and

*n*is the number of units in the column in which cells with ones and zeros and

_{nd}*n*is the number of wells in which new lateral screens will be injected during the simulation period. This results in a rapid decrease of the value in the target cell if the number of units in the column in which the cells with ones and zeros are greater or smaller than the specified number of wells in which new lateral screens will be injected, and after a couple of iterations, Excel Solver very quickly begins to search only combinations in which

_{nd0}*n*equals

_{nd}*n*.

_{nd0}

Calculating the Flow For All Combinations of Wells in Which Lateral Screens are Being Injected

In the version of the algorithm that determines flows of wells for all possible combinations of wells in which new lateral screens are going to be installed, the target cell only contains the sum of the flows of all wells at the end of the ten-year simulation period. Using the macros written in Visual Basic for Applications programming language, the values of the cells are determined based on the value which determines whether injection of lateral screens will be performed during the simulation period, so there will be as many units as there will be injections, with the values in other cells in the column equal to zero. Then, through the macro, Excel Solver is activated which automatically changes the values of the cells in which the flow is assigned and searches for the flows for which the maximum value in the target cell will be obtained, which means that the overall depression in each well corresponds to the given minimum difference between the levels in the well and the level of the lateral screens. By macro command which invokes Excel Solver, the difference between the levels is given for the wells and the lateral screen level in which the regeneration will take place, and the minimum difference between the levels in the well and the level of the lateral screen at the end of the simulation period. The macro is executed as many times as there are possible combinations of wells in which well screens are to be injected during the ten-year period. The obtained results provide flows for all possible combinations, such as the combination with the highest flow rate, the distribution of the probability of the total flow of the analyzed group of wells, the average total flow for all combinations of injection of lateral screens, and others.

Model Validation and Calibration, Obtaining Input Data for Simulation

*Preliminary Calibration of Filtration Coefficients*

Prior to the start of the simulation and the optimization process, the first calibration of the model was performed using data on flows and levels in selected wells and their nearby piezometers for 20/11/2013 - Fig. 24. Parameters that are automatically changed to obtain a minimum mean square deviation calculated from the recorded levels in the wells are the filtration coefficients of the low-permeability interlayer and the lower aquifer layer, while the thicknesses of these layers are fixed at 1 m and 5 m, respectively. The values obtained as a result of the calibration are 1.75 ∙ 10^{-7} m / s and 1.17 ∙ 10^{-3} m/s for the low-permeability interlayer and the lower aqueous layer, respectively. The calibration data set existed for 31/10/2012, and performed calibration resulted in filtration coefficients values of 2.00 ∙ 10^{-7} m/s and 1.35 ∙ 10^{-3} m/s, for the low-permeability interlayer and the lower aquifer layer, respectively. The level of matching the calculated results and the measured values of the levels in the selected wells is graphically depicted in Figure 24, and can be considered satisfactory with regard to the size of the approximation with only two varying parameters.

*Fine Calibration of Filtration Coefficients*

The following step was a fine calibration to get more accurate flow and level matching for each well. The coefficient of filtration (horizontal) of the aquifer layer, determined in the first step, provides a good approximation of the characteristics in the area, and was used to calculate the mutual influence of wells. Depression in the well caused by the work of the well itself is calculated using the coefficient of filtration determined in the first calibration multiplied by the correction factor for the given well. The correction factors are determined automatically using the Excel Solver so that the mean square deviation calculated using the recorded levels in the wells is minimized (equal to zero). The calibration results are shown in Figure 24.

*Simulation of the Observed Period and Obtaining Input Data for the Simulation*

In the third step, model testing for all wells was performed by simulation in the period from 1/10/2008 to 20/11/2013, starting from the drop in the level due to clogging S"(≈ΔS) and the flow at the beginning of that period, where the value of *KLHR*, and yreg (and values obtained from measurements, and assumed values for wells which did not have the required measurements). The *LHR* value is eventually multiplied by the lateral screen flow to get a calculation *S* and a level in the well.

In the fourth step, input data for the simulation of the 10-year period was determined: *LHR* and *KLHR* values for a particular well at the end of the period from 1/10/2008 to 20/11/2013, the mean value of *y _{reg}* for that well for the specified period if there was a regeneration, and if there were none - the mean value for all regenerations is given in Table 1. The

*LHR*value is eventually multiplied by the flow rate in order to obtain the calculated value of

*S*and water level in the well.

Depression due to flow through the aquifer was calculated on the basis of the flow at the end of the simulation periods, according to Hantush and Jacob's analytic solution - equation (14). Calculation of minor losses in the simulation period from 1/10/2008 until 20/11/2013 was performed using equation (23),

(23)

whereby the elapsed time *t _{regi}* since 1/10/2008 until the moment when regeneration was carried out and the elapsed time since 1/10/2008 until 20/11/2013, while the

*y*coefficient of reduction of

_{regi}*LHR*due to regeneration

*i*. The period from 1/10/2008 until 20/11/2013 for each well is divided into smaller periods separated by regenerations, if any. The greatest number of regenerations performed on a well during this period was two.

Figure 10: Change of *LHR* (square function regression) and *KLHR* over time in Rb-11 (Piezometer Ps-18-4). In the *KLHR* equation for Ps-18-4 t, the time elapsed in years since the first measurement in the diagram.

Figure 11: Change of local losses due to flow through the clogged layer in Rb-11 over time.

Figure 12: Change of *LHR* (linear and square regression functions) and *KLHR* over time in Rb-13 followed by Ps-30-6 piezometer, yellow field represents regeneration performed. In the *KLHR* equation t is the time elapsed since the first measurement in the diagram.

Figure 13: Change of local losses due to flow through the clogged layer in Rb-11 over time.

Figure 14: Change of *LHR* and *KLHR* over time in Rb-15 followed by the Rb-15 / p-1 piezometer, the yellow field represents the regeneration performed.

Figure 15: Change of depression due to flow through the clogged layer in Rb-15 over time.

Figure 16: Change of *LHR* over time and *KLHR* in Rb-16 measured by piezometer Rb-16 / p-1.

Figure 17: Change of depression due to flow through the clogged layer in Rb-16 over time.

Figure 18: Change of *LHR* over time and *KLHR* for Rb-19-1, for piezometers Ps-125-7, Ps-125-8, Ps-125-15. Yellow field represents regeneration performed.

Figure 19: Change of depression due to flow through the clogged layer for Rb-19-1, for piezometers Ps-125-7, Ps-125-8, Ps-125-15. Yellow field represents regeneration performed.

Figure 20: Change of *LHR* over time and *KLHR* for Rb-20, for the piezometer P-Ut-20-4. Yellow field represents regeneration performed.

Figure 21: Change of depression due to flow through the clogged layer for Rb-20, for the piezometer P-Ut-20-4. Yellow field represents regeneration performed.

Figure 22: Change of *LHR* over time and *KLHR* for Rb-20-1, for piezometer Ps-20-7. Yellow field represents regeneration performed.

Figure 23: Change of depression due to flow through the clogged layer for Rb-20-1, for piezometer Ps-20-7. Yellow field represents regeneration performed.

Figure 24: Calculated water levels in the well after preliminary calibration (red spots and curves) and levels recorded on 20/11/2013 (blue spots and curves) - up; Calculated water levels in the well after fine calibration (redspots and curves), levels recorded on 20/11/2013 (blue points and broken curves) and values of the correction factor (green points and curves).

Results of simulation for the period from 1/10/2008 until 20/11/2013 show a perfect match for wells that were based on assumptions (Rb-12, Rb-14, Rb-17, Rb-18 and Rb-19), while for other wells it is somewhat weaker because the values of linear losses, KLHR and the reduction coefficient of LHR due to regeneration calculated on the basis of measurements performed in that period - Figure 25.

Figure 25: Results of simulation in the period from 1/10/2008 until 20/11/2013 - calculated water levels in wells for 20/11/2013 (red point and line) and levels recorded on 20/11/2013 (blue points and lines).

An additional check of the model, as well as the values of the filtration coefficient of the bottom aquifer layer, interlayer and the correction factors for wells, determined during the calibration process, was also performed by calculating the levels in wells with newly injected lateral screens on certain days when measurements were made during the first year following injection, using the recorded values of well flow, levels and linear losses. The results of simulations and recorded flows, well levels and linear losses are shown in Table 3.

Results

Simulations have been made for the following three scenarios for the installion of lateral screens:

- Installion of 4 new lateral screens with the regeneration of the old ones
- Installion of 4 new lateral screens with the closing of the old ones (except in Rb-15, Rb-16 and Rb-20 in which 4 lateral screens are installed with the regeneration of the old ones)
- Installion of 8 new lateral screens with the closing of the old ones (except in Rb-15, Rb-16 and Rb-20 in which 4 lateral screens are installed with the regeneration of the old ones)

For all three scenarios, two sets of simulations were performed (one simulation for each of the total of 792 possible combinations of installion of lateral screens in 5 of the 12 Ranney wells), in cases where the value is φ(Γ), the dependence factor KLHR on the granulometric composition of the aquifer zone or filter layer in equation (8)), 1 and 1/3. This was done in order to illustrate the importance of the quality of execution of new lateral screen installation.

For the first scenario, when *φ _{(Γ)}* = 1, the best combination gives 657 l/s for 10 years (Rb-17, Rb-16, Rb-15, Rb-11, Rb-20), the mean flow is 595 l/s, while the minimum flow rate of 535 l/s is obtained for installing new lateral screens into Rb-18, Rb-13, Rb-19, Rb-19-1 and Rb-20-1. Given that the average flow for the period from 2006 to 2013 according to the available data was 633 l/s, only 3.29% of the combinations give a higher mean flow over the next 10 years. When

*φ*= 0.33, the best combination gives 754 l/s for 10 years (Rb-17, Rb-16, Rb-15, Rb-11, Rb-20), the mean flow is 656 l/s, while the minimum flow rate of 557 l/s is obtained for installing new lateral screens into Rb-18, Rb-13, Rb-19, Rb-19-1 and Rb-20-1. 73.0% of the combinations give a total flow that is higher than the mean flow for the period from 2006 to 2013 (633 l/s). The distribution of the probability of total flow is given in Figure 26.

_{(Γ)}For the second scenario, when *φ _{(Γ)}* = 1, the best combination yields 650 l/s for 10 years (Rb-17, Rb-16, Rb-15, Rb-11, Rb-20), the mean flow is 506 l/s, while the minimum flow rate of 337 l/s is obtained for installing new lateral screens into Rb-18, Rb-13, Rb-19, Rb-19-1 and Rb-20-1. Only 4.29% of the combinations give a higher average flow in the next 10 years than was the case for the period from 2006 to 2013. In relation to the scenario in which 4 lateral screens are installed without closing the old laterals, the maximum total flow is slightly lower - 3 wells with stainless steel well screens, representing the best combination, give the same flow as in the first scenario, and since in the first scenario the proportion of flow through the old lateral screens into Rb-11 and Rb-17 is less than 10%, their flows are slightly lower in the second scenario. When

*φ*= 0.33, the best combination gives 757 l/s for 10 years (Rb-17, Rb-16, Rb-15, Rb-11, Rb-20), mean flow is 593 l/s , while the minimum flow rate of 409 l/s is obtained for installing new lateral screens into Rb-18, Rb-13, Rb-19, Rb-19-1 and Rb-20-1. Of the total, 26.4% of the combinations give a total flow that is higher than the mean flow for the period from 2006 to 2013 (633 l/s).

_{(Γ)}For the third scenario, when *φ _{(Γ)}* = 1, the best combination yields 700 l/s for 10 years (Rb-17, Rb-16, Rb-15, Rb-11, Rb-12), the mean flow is 568 l/s, while the minimum flow rate of 413 l/s is obtained for installing new lateral screens into Rb-18, Rb-13, Rb-19, Rb-19-1 and Rb-20-1. In this case, 11.9% of the combinations give higher mean flow over the next 10 years than was the case for the period from 2006 to 2013. When

*φ*= 0.33, the best combination gives 817 l/s for 10 years (Rb-17, Rb-16, Rb-15, Rb-11, Rb-14), the mean flow is 668 l/s, while the smallest flow rate of 496 l/s is obtained for installing new lateral screens into Rb-18, 13, Rb-19, Rb-19-1 and Rb-20-1. Out of the total, 69.6% of the combinations give a total flow that is higher than the mean flow for the period from 2006 to 2013 (633 l/s).

_{(Γ)}

Figure 26: Distribution of the probability of the total flow of the analyzed group of wells for the 1st scenario, for two values of the factor of dependence of KLHR from the granulometric composition.

Conclusions

The results of the simulations for *φ _{(Γ)}* = 1 indicate the importance of a good selection of wells for injection of new laterals because only a small percentage of the combination of wells for injection gives an increase in the total flow of the well group. Large differences in flow between the same scenarios for the same combinations, for

*φ*= 0.33 and

_{(Γ)}*φ*= 1, indicate the extraordinary importance of washing the fine fractions when developing wells and installing a large granulate when injecting laterals using the Preussag method. In order to examine the relationship between certain parameters and the effect of installing lateral screens into a particular well, an average total flow for all the combinations in which the laterals were installed into that well was compared to the concentration of bivalent iron, the redox potential, the correction factor for the coefficient of filtration (indicates the permeability), the

_{(Γ)}*LHR*at the beginning of the simulation (indicates the initial accumulated local losses), the initial flow of the well and the depth of the lateral screens. Strong correlation is observed between the concentration of bivalent iron and the average total well flow - Figure 27. These values are compared to the concentration of bivalent iron, the redox potential, the correction factor for the coefficient of filtration (indicates the permeability of the environment), the LHR at the beginning of the simulation (indicates the initial accumulation), the initial flow of the well and the depth of the lateral screens. Strong correlation is observed between the concentration of bivalent iron and the average total well flow.

The results of the performed analyses shown in this study indicate the great importance of the selection of wells in which new lateral screens will be installed based on the following data:

- Current flow
- The current level difference in the well and the level of the lateral screens
- KLHR and LHR
- Concentration of bivalent iron in water
- Redox potential
- The number of active bacterial cells (BART analysis)
- Number of active well screens
- The effects of the previous regenerations
- The existence of a low-permeability layer
- Granulometric properties of the material in the layer in which the lateral screens are placed

Figure 27: The relationship between the concentration of dissolved bivalent iron in the well and the average total flow for all combinations of installation of lateral screens, which include this well (φ_{(Γ)} = 0.33).

It is very important to correctly determine the flow to be maintained in each well, as well as the point in time when regeneration should be made. When hydraulic losses on the lateral screens are small and/or slowly growing (*KLHR* is low), regeneration should not be performed because it is not only unnecessary but can also be counterproductive - Figure 22.

In order to be able to make decisions as to the regime of operation of the well and to apply measures for increasing the well flow (by applying injection of new lateral screens and regeneration), it is necessary to regularly and sufficiently monitor the following:

- water levels in wells
- flow rate of wells
- water levels in at least one near piezometer
- water levels in a "shallow" piezometer between two wells and close to the nearby piezometer
- physico-chemical composition of water in the well

These measurements should be carried out at least once a year on all wells, and immediately before and after (as soon as the operating conditions are established) each regeneration and injection of new lateral screens. A necessary prerequisite is that every Ranney well has at least one nearby piezometer, preferably two or three with different active well screens. It is particularly important to examine how a particular well reacts to regeneration in terms of the initial reduction in linear losses per flow unit (*LHR*), the rate of their growth (measuring of *KLHR*), and changes of well operational parameters in relation to previous regenerations.

Acknowledgement

The authors are grateful to the Ministry of Education, Science and Technological Development of the Republic of Serbia for financial support provided by the the project TR37014: "Methodology for estimating the design and maintenance of groundwater sources in alluvial environments, depending on the degree of aerobicity"

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