Electrical resistivity tomography applied for monitoring backwash efficiency in drinking water filters Open Access

Denmark's drinking water is derived from its groundwater sources (EPA 2022). The anaerobic groundwater is pumped from deep-lying aquifers and is typically purified by numerous simple but effective purification methods, including oxygenation of the water and filtration through sand filters (EPA 2022). This filtration process, also called rapid sand filtration (RSF), has a filter design and operation that allows in-depth filtration within the granular filter bed (Ives 1970). Depending on the chemical components of the groundwater, the sand filters must be periodically cleaned to ensure optimum functionality in terms of performance and drinking water quality (Cleasby et al. 1977). A regular maintenance includes a backwash (BW) of the filters by using a reversed and increased water flow, while additionally using airflow alone or in combination with reversed water flow to ensure filter porosity also are used (Amirtharajah 1993). Since the relationship between the filter materials, raw water quality and filter design is complex, the site-specific procedure for BW will be adjusted as part of the start-up of a new or renovated sand filter at the waterworks (Cleasby et al. 1977; Haarhoff & Van Staden 2013; Breda et al. 2019). Today, different strategies are used to determine how often and which BW procedure is needed. If the backwashing is too short or too infrequent, the result may be a gradual clogging of the filter material. This, in turn, can gradually deteriorate the water quality and cause an earlier-than-necessary replacement of the filter materials, reducing their lifespan. Alternatively, backwashing for too long or too often can cause water and energy wastage and even reduce the water quality (Cleasby et al. 1977; Fitzpatrick 1993; Haarhoff & Van Staden 2013).

Several studies have discussed how an applied BW procedure can be determined as adequate. The most common approach is the sampling of water and filter media materials (which is time-consuming, expensive and may require specially designed equipment) along with the logging of the operational parameters (Lopato et al. 2012). These methods provide highly valuable knowledge in a snapshot, i.e., as trouble-shooting tools for a specific operational challenge. However, for a continuous monitoring of the BW efficiency, these are insufficient. Even in-situ observations via video endoscopy turned out to be limited by the video resolution (Ives 2002). However, recent developments in geophysical imaging have opened new possibilities for a continuous monitoring of the RSF process. For instance, an acoustic imaging technique has been developed and tested in a drinking water treatment plant in The Netherlands (Allouche et al. 2014). It allowed the researchers to qualitatively follow the clogging state of the uppermost layers (5 cm) of the granular filter. Micro-seismic beta equipment was developed and tested in full-scale open sand filtration (Nørmark et al. 2016), indicating a possible application of the method within the uppermost layers of the granular filter as well. However, this method must be developed further to qualitatively and quantitatively use it for a continuous monitoring of RSF operations. Time domain reflectometry and ground penetrating radar methods have been suggested as potential methods as well, not only within the uppermost layers but for the entire filter's depth (Lopato et al. 2012). However, no literature has been found where these methods have been demonstrated for monitoring the state and function of a granular RSF.

The objective of this study is to develop a geophysical method to evaluate the BW efficiency in a drinking water filter, based on electrical resistivity tomography (ERT). This method could provide data with a different depth sensitivity and translate it into vertical resistivity profiles by geophysical inversion. As the electrical resistivity of the water and filter material differ by more than an order of magnitude, it is expected that the vertical and temporal variations in the filter media's capability can be observed in the resistivity image, as a function of the filter clogging during a filter-run. The spatial performance of an RSF in general is not known, therefore this study includes an evaluation of the actual state of the case study RSF. These case-specific observations on the spatial performance of the filter will be used to challenge and discuss the developed ERT monitoring strategy, resistivity data and resulting inversion models. In this study we present the results from a full-scale RSF study in Denmark, with six months of ERT data collected during normal operation.

The case study was conducted at the Engbjerg waterworks in Lemvig, Denmark. The Engbjerg waterworks comprises six open sand filters that are operated by gravity filtration and have a yearly drinking water production of 850.000 m³. The local groundwater source contains iron, manganese and ammonium. These are the main components that must be filtered via RSF to meet the drinking water quality requirements of Denmark (EPA 2022), and this study primarily focuses on iron. The size and costumer profile of the case study waterworks are typical for Danish waterworks. Its filter operation is regulated by water demand and is, thereby, discontinuous. During active operation periods, the operational flow is constant; either 50 m³/h (3.4 m³/m² h) or 70 m³/h (4.8 m³/m² h), while the water level above the filter media is held constant by regulating the butterfly valve at the filter outlet. The sand filter BW occurs after a fixed amount of treated water is produced (7,000 m³). At the start of the project period, the filter had produced around 2,000,000 m³ drinking water and had been backwashed 337 times since its commissioning in the year 2000. The BW procedure consists of 5 mins of air rinsing at 56 m³/(m² h) followed by 7 mins of water BW at 29 m³/(m² h). The water production is fully automated and facilitates monitoring, regulation and control through the water supply's central system.

The operational data for the case-study filter is extracted from the operational central system. This data includes raw water control, operational flow, water level above the filter in cm, opening percentage of the butterfly valve and turbidity at the filter outlet. These data show the overall performance of the RSF. To analyse the spatial performance, water samples were collected via a multi-depth sampling device that pumped water from specific filter depths with 10 cm spacing (−110 to 0 cm). Samples were also collected above the filter bed (groundwater after aeration) and at the outlet of the filter. A total of 13 water samples were collected and analysed by spectrophotometry (DR3900 Hach Spectrophotometer) for iron (LCK 521, 0.01–1.0 mg/L) and ammonium (LCK 304, 0.015–2.0 mg/L). The water quality criteria, WQC, for drinking water in Denmark are 0.05 mg/L for ammonium and 0.2 mg/L for iron (EPA 2022).

Analyses of the BW effluent samples and the filter media samples are used to evaluate the BW efficiency. The BW effluent samples were collected manually during a full BW cycle with time intervals of 15 s (at the beginning) to 1 min (by the end). A total of 22 samples were collected. Total suspended solids (TSS) was determined by vacuum filtration with glassfiber Grade A filters, nominal pore size 1.6 μm (dm 47 mm), dried at 105 °C for 24 h and 550 °C for 2 h, the TSS found by mass difference to initial glassfiber Grade A filters. Iron content was determined by spectrophotometry (DR3900 Hach Spectrophotometer) and used for calculation of the mass balance.

The filter materials were sampled in a drained filter bed with depth intervals of 5 cm for the upper 40 cm of the filter bed. They were, in fact, sampled twice, once a few hours before BW (end of run-time) and once a few hours after BW (beginning of run-time). The grain size distributions of dried samples were determined by a photometric particle analyser using dynamic imaging (Camsizer^® 2006, Retsch Technology GmbH, Germany). The grain size used in the present analyses is the shortest chord of the measured set of maximum chords of a particle projection (⁠⁠).

The surface coatings were removed on a few selected samples to estimate the former's influence on grain size and grain size distribution. They were removed by acid digestion, recording mass loss.

The conductivity of the water column was also measured with a TetraCon^® 925 at around 410–420 μS/cm (∼24 Ωm). These measurements were meant to be continuous for the project duration, but iron oxides quickly started to form on the instrument, making the measurements useless after a short period. Thus, the data obtained from the first two weeks of the project were used as a reference for the whole project period. Since the raw water originates from a single borehole in an aquifer at ∼80 m below ground, the conductivity and temperature of the water are not expected to vary. For time periods without an operational flow, the RSF is left with a constant water level above the filter bed–water interface, at the constant temperature of the waterworks (9 °C). Experiences from other Danish RSFs show temperature variation with depth to be within 0.1 °C.

Errors in the ERT data will affect the results. Inaccurate geometry, e.g., slightly bent electrodes, and 3D effects, such as the walls of the filter, will result in affected resistivity models if not accounted for. However, as the geometry is constant over time, any effects arising from incorrect geometry or filter walls should not result in any apparent temporal variations.

The full-waveform data was processed for harmonic de-noising, spike removal and background potential drift correction after following the procedure by Olsson et al. (2016). Harmonic denoising was necessary, especially, as the 50 Hz noise from the surrounding electrical installations was challenging. Furthermore, the unreasonably high and low apparent resistivity values were removed prior to inversion.

The inversion of the ERT data was performed using the AarhusInv code (Auken et al. 2015), an integrated modelling and inversion code for electrical and electromagnetic data. Each dataset model was inverted in 1D with lateral constraints on the neighbouring datasets in time. Each model comprised 90 layers of varying vertical constraints and thicknesses. To account for the varying water level, the layers representing the air/water boundary (layers 1–7) did not have a fixed thickness in the inversion, or any constraints. All the layers below were fixed at 1 cm thickness. The layers representing the water column (layers 8–23) had tight vertical and horizontal constraints (0.02 and 0.01), as the water conductivity was expected to be uniform in the water column and had limited variance in time.

The remaining layers constituted the filter bed and the boundary between filter bed and water column (layers 24–90). In this section, the layers had to accommodate the large changes expected to occur in relation to BW events; hence, no horizontal constraints were applied. The vertical constraint was heuristically chosen as 0.2. As a result, the higher values resulted in a lower data misfit but produced sharp and unrealistic models, while the lower values could not accommodate the water column–filter bed transition.

A 10% uncertainty was assumed on the data. This is higher than usual but accommodates the modelling and measurement inaccuracies. The size of the electrodes (5 mm), compared with the electrode distance (6 cm), conflict with the electrodes being modelled as point sources in the inversion. On the other hand, any operational changes in the filter that occur in the 4 min. acquisition time of an ERT dataset may result in the resistivity values changing mid-measurement. In general, ERT data was fitted within 25%.

The resistivity of the filter bed depends on many factors. Before iron accumulation, the situation can be simplified to that of conductive water in a non-conductive quartz matrix (>10³ Ωm), with resistivity being a function of the porosity. However, in operation, the filter bed also contains iron oxides, flocs, potentially trapped gas bubbles and biological activity. Thus, no simple model exists for the expected resistivity. During a filter-run, fine material/flocs of iron oxides get deposited in the filter bed along with the degassing of air or gas bubbles and alteration of the pore spaces (Scardina & Edwards 2001; Gülay et al. 2014). The organic matter or gases from bacterial growth and the air bubbles from degassing are likely to increase the resistivity (Ta et al. 2018). All these effects make quantitative interpretations challenging, due to which the our interpretations are solely qualitative.

As the data-to-model mapping is non-unique, this, and any, inversion scheme may result in erroneous resistivity models. The present inversion scheme, however, results in smooth transition of resistivity values, so the actual resistivity contrasts and boundaries are likely sharper than the inversion images.

Based on the depth-specific water samples, the volumetric removal rate of the active upper 20 cm filter bed is 7.26 g/(h m³) (Lee et al. 2014) and the iron removal capacity of the active part of the RSF is 0.7 kg/m³. The latter corresponds to the previously reported iron removal capacity values of mature RSF in Denmark (Søgaard et al. 2000; Ramsay et al. 2018). The removal of the surface coating shows a higher mass removal at filter depths of 0–10 cm (<10%–15% mass reduction) indicating a larger amount of surface coating, compared with a filter depth >15 cm (mass changes 5%–8%), supporting the observed indication of high iron removal at a low filter depth.

The removal of ammonium can be seen within the upper 70 cm of the filter where the WQC is met (Figure 2(a)). Within the active depth of the filter, the volumetric removal rates were found to be 2.09 g/(h m³) for a depth of 70 cm (Lee et al. 2014). These ammonium load rates and removal capacities are comparable to what has been reported for a well-functioning mature RSF in Denmark (Lee et al. 2014; Tatari et al. 2016; Ramsay et al. 2018). The nitrification is a two-step biological process that involves an active biofilm (Lee et al. 2014; Tatari et al. 2016; Breda et al. 2019). The present data demonstrates that these processes are active within the upper 70 cm of the filter.

The BW effluent analyses demonstrate TSS to be zero at the end of BW (Figure 2(b)). Due to the raw water composition of iron, the shown correlation between TSS and iron content is as expected. Turbidity at the filter outlet shows turbidity is reduced to a stable and minimum level after one bed volume of water produced (15 min). The mass balance for iron demonstrates BW iron removal of 89.4% of total iron load

The grain size distribution of the filter media samples can be seen in Figure 2(c) for three selected depths. The volume fraction of the fine materials is higher in samples before BW than after BW, illustrating that BW removes fine materials.

The grain size distribution illustrates a segregation of the grain sizes, where the finer grains are located in the upper part of the filter bed and the coarser grains dominate at +30 cm filter depth compared with the original filter bed (quartz 0.8–1.4 mm). At 5 cm depth the <1.1 mm fraction has changed from 50 vol% in the original filter to 70–77 vol% at present in the mature RSF.

The diagnostic evaluation of the case study RSF is that the filter is well-performing, including high removal rates of both iron and ammonium demonstrating a healthy and effective sand filter in which depth filtration is active. Depth samples of filter media demonstrate media segregation compared with virgin commissioned RSF. The applied BW strategy cleans the filter for fine particles with a strong correlation to iron. During the applied BW procedure, a high iron removal rate is demonstrated. The time for the RSF to mature after BW equals one bed volume of water. These results indicate the applied BW strategy results in good BW efficiency.

The data acquired from 48 ERT configurations during six months of the normal operational period (a total of 1,486 datasets) were analysed and compared with the standard observation parameters (flowrates and open bottom valve in %) of the normal operations at Engbjerg waterworks. Processing and inverting all the ERT configurations for each dataset facilitates data analysis as a function of both time and filter depth.

Upon comparing Figures 3 and 4, it is evident that for the normal operational conditions, the ERT data and the resulting inversion model repeatedly return to a similar level of resistivity at a specific filter depth after a BW event.

The observed ERT response during a continuous flow repeatedly shows a standard level of resistivity which is similar to the previous periods of continuous flow (comparing Figure 5 [17/2–19/2] and Figure 3 [26/11/18–30/11/18]). The ERT configurations with the deepest sensitivity (Figure 5 [top]: green and magenta curves) show increasing ρ_a values simultaneously with the outlet butterfly valve opening, while the ERT configurations with the shallowest sensitivity (blue curve) are not affected until a few hours before the alarm.

During the entire operational period following the alarm and the BW (22/02/19), the observed ERT response showed higher resistivity values. This is different from the previous examples where resistivity was lowered by BW events. After a period of an otherwise normal operation, another ordinary BW was performed (03/03/19). Following this BW, a resistivity drop was observed which is comparable to the previous ERT levels and observed tendencies of other time intervals (as seen in Figures 3 and 4).

When evaluating the geophysical method with respect to the normal operational filter status, one can see that the ERT data were clearly affected by the dynamic operation of the filter (Figure 3, bottom), with some general tendencies being observed as well. An operation with constant flowrates results in almost constant or slightly decreasing ρ_a values (Figure 3, 27–28/11). The flowrate is inversely related to ρ_a, as high flowrate (70 m³/h) results in lower ρ_a values, while the lower flowrate (50 m³/h) results in higher ρ_a values (Figure 3, 25/11–1/12). The analyses of the filter state demonstrate that the applied normal operational procedure leads to deep filtration (Figure 2(a)). In deep filtration, the physical–chemical retention mechanisms highly rely on inertia, Brownian diffusion and adhesion (and thereby, surface forces), all of which will be influenced by the velocity (the dragging forces) of the water while passing through the filter grain skeleton. During periods of inactive operations, an increase in ρ_a values is observed which then drops again as the operational flow resumes (Figure 3, 1–2/12; 5/12). At the end of the filter-run, the ρ_a values remain high and do not drop after periods without operational flow (Figure 3, 12/12). The origin of the observed increase in resistivity needs to be found within the activities present in this steady state of the filter bed. In this state, the activities that benefit from longer residence time of the water can be expected to influence the filter bed. Upon shifting from the steady-state condition to operational flow, a sudden decrease in resistivity is observed. Hence, the flowing water and the active dragging forces within the filter grain skeleton highly influence the resulting filter resistivity. Homogeneous iron removal would benefit from longer residence time, resulting in the formation of iron oxide flocs (Beek et al. 2016) which will clog the filter bed. However, the hydrous and amorphous nature of these granular surface coatings has the potential to increase the resistivity. The weak adhesion of these iron oxide flocs to the grain skeleton will result in their detachment upon operation (Amirtharajah 1993). This can explain the observed resistivity drop upon resuming operational flow.

During the filter-run, the ρ_a values increase (Figure 3), and the resistivity models show structure with distinct, high resistivity layers. The layer structure also appears to recur after filter-run periods with similar usage (Figure 4) where nearly identical resistivity patterns appear at the end of two adjacent filter-runs. The first developed layer structure of high resistivity is related to a filter depth of −25 to −30 cm (Figure 3, 1/12). From analyses of the filter state, we know that iron is present in the water in low concentrations at this depth, whereas ammonium is present at concentration ∼0.25 mg/L and the removal of ammonium is active (Figure 2(a)). Furthermore, the grain size distributions, in <30 cm depths, have an approximately normal distribution around a grain size of 1.2 mm. Meanwhile, at a depth ranging from 20 to 30 cm, the distribution is skewed towards smaller grains of 0.8 mm, especially before BW (Figure 2(c)). By the end of the filter-runs, two additional high-resistivity layer structures are present at 5 and 15 cm depth (Figures 3 and 4). At these filter depths, iron removal is active and the iron concentration of the water at 5 and 15 cm is just above and below WQL, respectively. Ammonium removal is also active at these depths (Figure 2(a)). The grain size distribution at −5 cm is dominated by fine grains of 0.8 mm and well sorted with U ∼ 1.5 (uniformity coefficient, U = d60/d10). Below −5 cm, the distribution is less well sorted with U ∼ 1.7–1.8 due to an equal volume fraction of fine and coarser grains (Figure 2(c)). The observed development of the resistivity layer structure could be assumed to be related to these changes in the filter grain skeleton (packing of filter materials) and, thereby, the flow-path and the flow velocities of the water across these depth intervals.

In the six-month data acquisition period, the ERT method is evaluated with respect to the normal dynamic operation and including normal BW. In the ERT data, BW results in a very sharp drop in ρ_a values, reaching the same level as after the previous BW (Figure 3, 24/11 & 14/12). The analyses of the effluent water of the BW revealed that the applied BW has a high efficiency for removing iron. Figure 2(c) demonstrates that the applied BW removes small particles from the filter, even at a filter depth of 40 cm. After a BW, the resistivity model demonstrates a fairly homogeneous structure with low resistivity throughout the monitored filter depth. These observations indicate that the homogeneous resistivity model is associated with the well-operated filter state as a result of a highly efficient BW procedure. To challenge this, the ERT method was evaluated in relation to a forced continuous flow operation resulting in an alarm-triggered BW event. The observed increase in water level towards the end of this period indicates a large head-loss increase for the filter, implying that the filter bed is clogged. The filter bed's clogging may increase the pore flow and force the filtration even deeper. The removal mechanisms could also be expected to take up larger and deeper parts of the entire filter bed. If the water level increase was caused by clogging at the filter-top, it would be expected that the ERT signal from this volume of the filter would change. However, little to no change is seen even in the ERT configuration with the shallowest sensitivity (Figure 5, blue curve).

There is a potential formation of gas bubbles that will act as isolators and increase the resistivity of the filter bed. Hence, a prolonged residence time of the water could indicate de-gassing of potential supersaturated gases in the raw water, as well as the mobilisation of (potential) excess air from BW. In the present case-study, there is no knowledge of the potential amount and origin of gas present within the filter bed. The filter analyses show the presence of microbiological activity. This activity can also benefit from longer residence time as long as nutrition is present. A laboratory study of saturated sand, including bacterial dextran growth, showed the resistivity increasing as the produced dextran occupied the pore spaces (Ta et al. 2018). The same study also observed sudden resistivity drops in the saturated sand mixture, especially when the flow increased in relation to the permeability measurements. Hence, our observation of the increased filter resistivity could be related to the microbiological activity present within the filter bed as the produced dextran can be seen in parallel to the increased amount of biofilm (the microbiological activity of ammonium removal in RSF) (Tatari et al. 2016; Breda et al. 2019). However, based on the present data, the quantification of the individual causes of the observed changes is not possible.

The resistivity values in the upper 40 cm of the filter bed after the alarm-forced BW are higher than the previous ‘standard values’ (Figure 3 vs Figure 5). The ERT values here are closer to the range of resistivity values seen at the end of a filter-run period. The standard operational observation parameters (water level above filter bed, opening of bottom valve) do not indicate an inefficient cleaning of the filter bed (Figure 5, bottom). For the next BW (Figure 5, 3/3) the ERT again shows a sharp drop in the ρ_a values, reaching values comparable to Figures 3 and 4. With reference to the high BW efficiency documented during normal operational conditions, the repeated ERT values reaching ‘standard values’ after BW (Figures 3 and 4) likely correspond to the ERT signal of a well-cleaned filter bed. However, the normal operational BW procedure was not adequate for cleaning the filter bed, resulting from the operational changes of the forced continuous flow.

The developed ERT-based method may be used to diagnose the state of a given RSF by using its temporal and spatial resolution capabilities to investigate the depth of the active sand filter. A better understanding of the processes in the filter bed is required to fully utilise the potential of an ERT-based monitoring method. However, the present initial full-scale testing of the developed method demonstrates that the combination of known snapshot diagnostic tools, standard operational parameters and the ERT monitoring method can be used to increase the spatial understanding of the active processes within the filter depths. While we in this study were limited to a one-dimensional image, 2D and 3D images can be achieved with other electrode configurations, which may be inserted in existing RSFs or be integrated into new RSF designs. With the measurement instrument integrated into the RSO, measurement may be carried out automatically before and after planned BW for evaluation of BW, or the RSO may start initiating BW based on the ERT instead of standard parameters. The ERT method is a unique method that allows for an (after installation) non-intrusive snapshot of the filter, at any given time.

The project has developed and demonstrated an ERT-based method for the real-time monitoring of active drinking water production. It provides data with different depth sensitivities that get translated into vertical resistivity profiles by geophysical inversion. This, in turn, demonstrates the temporal and spatial resolution capabilities within the monitored filter depth within a six-month period. The presented ERT data created resistivity images of the active RSF resolving the filter bed in each depth interval, detecting the overall microstructure and its ability to guide the water through the filter. The presented ERT results indicate that the method may be sensitive to the development of biofilms within the filter bed and may also be used to resolve areas that have air-binding issues. What the method detects is a result of the overall microstructure of the filter bed and the sum of these different elements given as its resistivity. Thus, the ERT response can be related to the phenomenological level of filtration. The above discussion clearly illustrates the need for a detailed understanding of the active processes and their interrelated signatures within the filter bed of RSF to develop appropriate tools for optimising the operational conditions. Further development and data analyses are needed to fully reveal the potential of the application of this method for operational usage within drinking water production.

The objective behind developing this equipment and monitoring method was to monitor the applied BW's efficiency and, in turn, facilitate a tool for continuously optimising the BW parameters during an RSF's lifetime. The present project has shown a proof of concept for the application of the ERT-based method. The ERT results and resistivity images of the filter bed show significant differences before and after a BW where the supporting manual analyses demonstrate that the BW was effective. Upon changing the operational parameters of the filter-run (forced continuous flow) without changing the following BW procedure, the ERT results and resistivity images do not return significant differences before and after BW. This indicates that the method can be used to monitor BW efficiency within the observed filter depth.

This project was financed in part by the Water Sector Development and Demonstration Program of the Danish Water and Wastewater Association (VUDP) in connection with the project ‘Geophysics in filters – 3D mapping of filter cake’. The authors acknowledge the triple helix project collaborators: Lemvig Vand, NIRAS, Aarhus University and VIA University College, and bachelor student Olga Alieksieienko.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.