Developing a numerical approach for monitoring the degradation of water quality parameters in an urban water supply system of the rapidly growing African city of Kinshasa Open Access

Water is essential for life, yet millions of people in Africa lack access to clean and safe water. According to UNICEF (2022), approximately 319 million people in sub-Saharan Africa do not have access to reliable and improved drinking water sources. This lack of access poses significant health risks and perpetuates a cycle of poverty and inequality (Kwakwa 2024). Waterborne diseases like cholera, typhoid fever, and diarrheal illnesses, which disproportionately affect children and the most vulnerable members of society, expose communities with no access to safe drinking water. Thus, public health is directly threatened (WHO 2023). Moreover, access to clean water is crucial for socio-economic development. The lack of access to water particularly affects women and girls, who are often responsible for collecting water for their families. This task can consume considerable time and energy, limiting their opportunities for education and economic empowerment. Ensuring universal access to clean water and sanitation, particularly for women and girls, is a guarantee for improved livelihoods but also for sustainable economic growth. Therefore, it is imperative to act to ensure equitable access to this vital resource (Kwakwa 2024).

This means that studies are required to establish applicable quality standards to protect consumers' health.

In general, water leaving a treatment plant has acceptable quality according to international standards. However, the quality of the water can deteriorate in a water supply system (WSS) for several reasons (Ardila et al. 2024; Dereje Kitila 2024). The WSS effectively acts as a reactor, influencing water quality based on several factors. Among these factors are the condition of the pipes (Riyadh et al. 2024), and the composition of materials from which they are constructed. Ageing or corroded pipes can release contaminants into the water. Additionally, hydraulic parameters such as residence time, flow velocity, and temperature play critical roles. Prolonged residence time can promote the proliferation of microorganisms, while excessively low flow velocity may lead to sediment build-up in the pipes. These various elements interact in complex ways and can compromise the quality of the distributed water. Therefore, rigorous monitoring of water quality within the WSS is essential to ensure that the water-reaching consumers meet safety and potability standards.

Efficient monitoring of water quality in the WSS is therefore an essential step in preventing any risks of contamination. This monitoring aims to quickly identify any deviation from regulatory thresholds in order to implement the necessary corrective actions, and thus guarantee a healthy and quality distribution of water suitable for human consumption (Larsen et al. 2017). Nevertheless, different factors, notably the extent of the networks, the high costs of analysis, as well as the strategic plan of sampling sites, make the monitoring of water quality complex. Faced with these challenges, innovative approaches are urgently needed to identify the most relevant points to monitor, thereby improving the efficiency and reliability of monitoring the quality of the WSS.

The African WSS suffers from routine quality monitoring. In this context, the city of Kinshasa in the Democratic Republic of Congo (DRC), with a population of 17 million (World Population Review 2024), faces a significant challenge in ensuring the supply of high-quality water in the WSS. Although quality water is produced at the exit of the plant, the quality deteriorates considerably in the WSS, which may affect consumer health. The network's efficiency is estimated at 55.7%, and the age of the network varies between 30 and 70 years (REGIDESO 2022). These factors directly influence the water quality in the WSS, making the monitoring of this quality essential to ensure that the water-reaching consumers' taps is safe and of good quality. Given the lack of studies conducted in real conditions on distribution networks in Africa, and facing the challenges that managers encounter in a real water distribution system, many old water supply infrastructures lack information on pipe materials, their age, and their condition, making water quality monitoring difficult. To overcome these gaps, the objective of this research is to develop and apply an innovative numerical model to monitor the degradation of free residual chlorine (FRC) under large-scale conditions in the WSS of the city of Kinshasa using coupling between EPANET and Python via WNTR. To achieve this objective, our work follows these steps: (i) develop a model that tracks the hydraulic characteristics that indirectly influence water quality degradation, notably flow, and pressure; (ii) calibrate the hydraulic model with in situ observations data of flow and pressure; (iii) experimentally determine the coefficient K_b in the laboratory and estimate the coefficient K_w; (iv) automatically calibrate and validate the FRC model with in situ observations data using an algorithm that couples EPANET with Python via WNTR to select the optimal model parameters that provide the best qualitative and quantitative metrics. The developed model can help managers make appropriate decisions and reduce potential costs associated with secondary disinfection management with chlorine and the rehabilitation/renewal of the distribution network.

The loss of chlorine in the WSS can occur due to two primary mechanisms (Vieira et al. 2004). The first is external contamination, which often happens during pipeline breaks and maintenance operations (Fish et al. 2020). The second is natural decay, which can be attributed to three main processes (Ozdemir & Ucak 2002):

• – Bulk reactions with chemical substances present in the treated water (Frederick et al. 2024);

• – Wall reactions with the material of the network elements (Alsaeed et al. 2024);

• – Natural evaporation in storage tanks (Mostafa et al. 2013).

Degradation of chlorine can also occur within the tank, just as in the WSS. When water is stored in the tank, chlorine reactions with the water mass may take place (Rossman 2000). Using the same Equation (1) for chlorine degradation in the water mass that is applied to the WSS, we can determine the rate of chlorine degradation in the tank.

We have to note, that the specificity of the Kinshasa water networks is a direct water injection system, without water tanks for storage and for pressure equilibrium, which makes the study more challenging.

A water demand measurement investigation was conducted to track how water consumption varies throughout the day, identifying both periods of low demand and periods of high demand. The results of the aforementioned investigation helped us to understand better the water consumption patterns in our community and will later be used for the hydraulic calibration of our model.

An in situ pressure measurements campaign was conducted to collect observed pressure data over the water distribution network to calibrate the results of our model regarding pressure. These measurements allowed us to adjust the model parameters more accurately and reduce errors.

Chlorine concentrations were measured in situ in several sites, starting from the treatment plant to determine the initial concentration, as well as in the distribution network to calibrate and validate our water quality model. We conducted the measurements during the dry season in June 2024. The locations of FRC sampling sites for calibration and validation are illustrated in Figure 2.

To develop a WSS model, two essential steps were implemented. First, a network database was created. Second, water demand was calculated for each consumption point. Integrating these two components resulted in a WSS model ready for monitoring.

The methodology for creating our GIS database for the WSS is based on the integration of collected data. This includes a 30-m resolution digital elevation model from the USGS (available at https://earthexplorer.usgs.gov), and network infrastructure components such as the water production plant, water demand points, and pumping/booster stations. Pipeline data, including length, material, diameter, and roughness, is also integrated.

All of these data were integrated into a GIS tool, allowing for the development of a geometric network composed of pipes and junctions. The pipes, defined by their physical properties, are connected to junctions representing critical points in the network, such as water demand points, the production plant, and the pumping and booster stations. In order to ensure accurate modeling, we established connectivity rules to maintain consistency in the interconnections within the WSS.

For the water demand, the nodal flow rate at each point in the WSS was calculated based on the specific discharge, assuming that water consumption is uniform throughout the WSS. This method is considered suitable for calculating flow rates in large-scale networks with a very high population.

EPANET is a widely used tool for hydraulic and water quality modeling. It is software written in the C language and developed by the United States Environmental Protection Agency (USEPA) available from (https://www.epa.gov). It is freely available for download over the World Wide Web and has been proven worldwide for its wide use and reliability (Rossman 2000).

This model can be used to determine FRC at any point in the distribution system. Three parameters are used to model the chlorine reaction in the distribution system with the EPANET model. These are the initial chlorine dose, the bulk decay rate, and the wall decay rate (Tiruneh et al. 2019). The bulk decay rate allows modeling using first and second-order rates or even for concentration-limited rates following Equation (1). The EPANET program allows modeling of the wall decay of chlorine at both the zero-order and first-order decay rates following Equation (3). We can see the reaction of FRC in the WSS (Gómez-Coronel et al. 2023) in Figure S1 (see the Supplementary Documents).

After the creation of the WSS, a warm-up hydraulic simulation was conducted using the EPANET model.

Water demand and pressure in the WSS are the two parameters considered for the calibration of the hydraulic model.

To calibrate the water demand, a flow-rate recorder (flowmeter) was installed at the exit of the N'Djili treatment plant to measure changes in water demand over time. The results show that the water demand of the residents in the study area varies throughout the day. The total production capacity of the plant is 330,000 m³/day, spread unevenly over 24 h. After collecting hourly flow data from the plant, the water consumption pattern was exported to EPANET to calibrate the water demand over a 24-h period based on the observed data.

A pressure measurement campaign was conducted to evaluate how the hydraulic model behaves compared to reality. Generally, we cannot rely on a model's behavior unless it is adjusted to real data. Pressure measurements were taken at three points in the WSS over one day. We will use this data to calibrate different parameters responsible for the variation of pressure in the WSS. First, the estimation of the actual roughness of the pipes is crucial, as it significantly affects pressure losses. Additionally, the condition of the shut-off valves, whether they are open or closed, and their tightness directly affect the pressure in the WSS. The ageing of the WSS, with an average age ranging from 30 to 70 years, also contributes to this issue. Moreover, the network's efficiency, estimated at 55.7%, indicates that 44.3% of the distributed water is lost due to leaks, which directly affects the measured pressure (REGIDESO 2022). To address this issue, we will consider the roughness of the pipe materials and the individual pressure losses related to the network's equipment during the calibration of our system.

It is important to note that the diameter of the pipes influences the hydraulic outcomes of the model. There is an inverse relationship between diameter and water velocity: when the diameter decreases, the velocity increases. Additionally, the diameter also affects both flow rate and pressure within the system (Süme et al. 2024). In our study, we used the actual diameters from the distribution network in the city of Kinshasa. This is why diameter was not a factor in hydraulic calibration, as we worked with established values that reflect the real conditions of the network.

The EPANET model is also used in this study for water quality modeling, to assess the FRC. In this regard, three major steps are considered.

To determine the initial dose of chlorine, it is necessary to measure this concentration directly at the water production source of the agglomeration. We conducted in situ measurements of the initial chlorine dose at the water treatment plant using a spectrophotometer and DPD reagents. These measurements allowed us to obtain the initial chlorine concentrations at the production plant over a 24-h period.

The bulk decay constant K_b was measured in the laboratory using a series of bottle experiments over time (Rossman et al. 1994; Rossman & Boulos 1996; Karadirek et al. 2024). With a first-order degradation significance according to Equation (2). To measure the chlorine decay constant K_b following the method of Powell et al. (2000), a water sample was collected from the N'Djili water treatment station. The experiment was conducted at room temperature (30 ± 1 °C). A 2.5 l bottle and four brown glass bottles of 125 ml were used. Before the experiment, all bottles were thoroughly cleaned, rinsed with distilled water, and dried up in order to minimize photodegradation of chlorine. A spectrophotometer and the reagent N,N-diethyl-phenylenediamine (DPD) were employed for laboratory analysis.

To start the sampling, the 2.5 l bottle was filled with the water sample and allowed to stand for 15 min to ensure a homogeneous chlorine concentration. The sample was then distributed among the four sealed 125 ml brown glass bottles, which were tightly capped. FRC concentrations were measured at predetermined time intervals (t1, t2, t3, and t4 hours) using the spectrophotometer and the DPD reagent. After that, we can determine the chlorine decay constant K_b. Table 1 shows the results of K_b by different study.

We have estimated the coefficient K_w based on existing literature, as it effectively represents the degradation of FRC due to interactions with pipe walls. Given the extensive nature of our WSS and the variety of pipe materials, obtaining experimental measurements of this coefficient presents significant challenges. Therefore, we initially assumed a value of K_w = −0.49 m/day, as reported by Minaee et al. (2019). Moreover, we have calibrated this coefficient with the observed data.

Regarding the mechanism of natural evaporation in storage tanks, in our specific case study, direct pumping was carried out in the WSS, and there were no tanks in the network. Therefore, the mechanism of natural evaporation in storage tanks is not a relevant factor in this particular scenario. Table 2 shows the values of K_w by different studies.

After establishing the WSS, calibrating the hydraulic model, and gathering the essential input data for water quality, an initial simulation of FRC was performed using the EPANET software. The input water quality parameters included the initial chlorine concentration measured in situ at the treatment plant. Additionally, the degradation coefficient of FRC K_b was experimentally determined through laboratory tests, while the degradation coefficient of chlorine in contact with the pipe walls Kw was sourced from the literature, with an initial value of −0.49 m/day. These data were integrated into the EPANET model to conduct the simulation, enabling the acquisition of initial outputs necessary for evaluating the dynamics of FRC within the WSS.

In the calibration section of the water quality model, the adjustment parameter is the chlorine degradation coefficient with the pipe walls K_w, as in our research the initial chlorine dose was measured in situ. The FRC degradation coefficient with the mass of water K_b was measured experimentally in the laboratory. In contrast, K_w was estimated based on values from the literature.

In this section, we will adjust the K_w coefficient based on the different pipes, according to their materials and age. The age of the pipes is indicative of their conditions; in our case study, we classify the pipes into two main categories:

• – Steel pipes: These are the oldest in the network and are likely to have higher degradation rates due to wear and corrosion;

• – Plastic pipes: This category includes HDPE and PVC pipes, which have been installed more recently and generally exhibit low degradation rates.

To optimize K_w, we developed an algorithm in Python available from (https://www.python.org) using the WNTR simulator available from (https://usepa.github.io/WNTR). This algorithm aims to refine K_w by comparing simulated values with observed data.

Initially, the EPANET simulation model was exported to Python, using the WNTR simulator (Chu-Ketterer et al. 2022), with the observed data. The second step involved performing an initial comparison between the simulation results and field observations, producing useful decision-making metrics such as root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R²). The algorithm improves these metrics by adjusting K_w. The value of K_w will be modified based on the materials of the pipes and their age. The algorithm will loop through each category of pipes, adjusting K_w, simulating water quality, comparing it with the in situ observed values, and calculating the metrics (RMSE, MAE, and R²). Finally, the algorithm will select the optimal K_w for each category based on the improvement of the metrics between the simulation and the observations.

To achieve the model validation for this study, the model outputs were compared with FRC concentrations measured at different points in the network over various days. We collected chlorine observations at different times and days, considering multiple measurement points throughout the network. This approach ensured that the model outputs accurately reflect the reality on the ground.

DRC is facing a critical challenge for urban water supply, especially in the city of Kinshasa with a rapid population increase, currently estimated at 17 million, with no increase in appropriate hydraulic infrastructure constitutes a major bottleneck. An innovative approach is urgently needed to monitor the water quality of the urban WSS, reduce loss, increase efficiency, and prevent risks of contamination. The results of this study include the calibration/validation of the hydraulic model, encompassing water consumption patterns, water demand, and pressure, as well as the calibration/validation of FRC as a key water quality parameter.

The value of the coefficient k_b was determined in the laboratory from water samples taken at the outlet of the treatment plant. The most important characteristics that affect k_b are the water temperature and the initial concentration of residual chlorine (C₀). Therefore, the results for k_b are based on these two parameters.

After the measurements, we obtained a coefficient k_b of 23.2 × 10⁻³ h⁻¹ at a temperature of 30 °C, with a C₀ value of 0.85 mg/l. These results fall within the same range as those found in the studies mentioned in Table 1 for k_b, notably by Hallam et al. (2002), Saidan et al. (2017), McGrath et al. (2021), and Maleki et al. (2023). Such low values of k_b reflect a high efficiency of water treatment in removing organic matter.

The range of k_w for different categories was compared based on the materials of the pipes and their age. In our distribution network, there are two categories of pipelines: the first consists of steel pipes, which are the oldest, and the second includes plastic pipes, specifically PVC and PEHD, which were installed more recently.

As expected, the steel pipes exhibit the highest values of k_w, with a value of 50 × 10⁻³ h⁻¹, followed by the plastic pipes, which have a k_w value of 37.5 × 10⁻³ h⁻¹. It is not surprising that chlorine wall degradation in metallic pipes is greater than in plastic pipes. In our case study, chlorine degradation in steel pipes is more significant than in PVC and PEHD pipes.

Regarding the PVC and PEHD pipes, the k_w value obtained in this case study (37.5 × 10⁻³ h⁻¹) is broader and includes values reported by McGrath et al. (2021) (8.5–27.5 × 10⁻³ h⁻¹) and is lower than the values obtained by Hallam et al. (2002) (90 × 10⁻³ h⁻¹). For the steel pipes, we obtained a value of 50 × 10⁻³ h⁻¹, which is lower than the values reported by Mompremier et al. (2022) (43 × 10⁻³ h⁻¹).

The differences between the values obtained in this study and those in the literature (see Table 2) may be due to regional variations, as the water temperatures in McGrath et al. (2021) study were in the range of 11–14 °C, while in our study, they were at 30 °C, which can affect the range of k_w. Overall, the high k_w value was obtained in the category of the oldest steel pipes, which necessitate renovation.

This study models water quality in Kinshasa's urban WSS to understand its variability and identify areas of degradation, ultimately informing improved water quality management strategies. This research represents the first water quality modeling study conducted on Kinshasa's urban WSS, a previously unexplored area of scientific research in the DRC.

Studies in other countries, such as the one done by Al-Mamori & Al-Musawi (2017), examined the simulation of FRC in the urban WSS. A key limitation of their study is the lack of hydraulic modeling before addressing water quality modeling, which is required for a successful water quality modeling of a WSS.

Recently, a study by Musz-Pomorska et al. (2019) examined water quality simulation; their study was limited to simulation without calibration or validation, affecting the applicability of their model for the numerical monitoring of water quality in their study area. In their discussion, the authors discussed the importance of calibrating FRC models to ensure that the outputs are close to the observed concentration of FRC in the network, and they recommend that future research do the calibration of FRC using measurements in situ at various points in the WSS.

Our study started by calibrating and validating the hydraulic model of flow rate and pressure using in situ data. Since hydraulic parameters influence water quality, calibrating the hydraulic model with field observations enhances the reliability of the water quality model. The acceptable statistical parameters obtained by comparing the simulated and observed results reveal the true potential and importance of such tools. Our study successfully calibrated and validated the FRC model using in situ data. The validation approach employed in the methodology yielded a reliable model for numerically monitoring water quality within the network. The acceptable statistical parameters obtained comparing the simulated and observed results reveal the real potential and importance of such tools, by improving the structure of the water network and designing an efficient monitoring system, we can improve the robustness of the developed models (hydraulic and quality ones).

This study highlights the importance of continuous monitoring of water quality throughout the network to ensure the safety of the WSS, protect consumer health, and prevent any risks of contamination. It is worth noting that this study was conducted during the dry season, with temperatures around 30 ± 2 (°C). Future studies should examine the impact of temperature variations across different seasons on water quality in the urban WSS, using the same methodology as this study. This will allow us to update our model to different seasons of the year.

In this study, a model for monitoring the degradation of FRC in the actual distribution network of Kinshasa city, the capital of the DRC in Africa, was developed.

As part of the development of this model, a hydraulic model was created to represent the hydraulic parameters that influence the degradation of FRC. This model was calibrated with field observations regarding flow and pressure. For flow, a measurement sampling was taken at the outlet of the treatment plant during the dry season in June 2024 over a 24-h period, and for pressure, three measurement samples were taken in the distribution network over the same 24-h period in the dry season of June 2024. Subsequently, an experiment was conducted in the laboratory to determine the coefficient K_b using bottle samples, followed by the estimation of K_w. After determining the direct and indirect parameters that influence FRC in the distribution network, a calibration and validation step was conducted with in situ observation data of FRC, with seven points for calibration in the summer season in June 2024 over a 24-h period, and nine validation points under the same temporal conditions.

The results showed that (i) the FRC model provides good results compared to field observations with the following metrics: R² = 0.9, RMSE = 0.18 mg/l, MAE = 0.14 mg/l, R = 0.932, KGE = 0.542, RE = 9.25%, validating the use and application of this model for managing FRC in the distribution network of Kinshasa. (ii) This model is a valuable tool to address the challenges of manual monitoring currently employed by operators, helping to reduce costs associated with manual monitoring, such as purchasing measuring devices, buying reagents, using laboratory tools, paying personnel involved in manual measurements, and the transport costs across the network. So, this model represents a solution that the company that manages the WSS in the city of Kinshasa can use for a rapid monitoring of water quality. (iii) The developed methodology can be used in large-scale distribution networks to monitor the degradation of FRC. (iv) The values of coefficients K_b and K_w based on the following characteristics (temperature and initial chlorine concentration for K_b, and the materials and age of the pipes for K_w) were obtained. (v) The degradation of chlorine in the older metallic pipes (50 × 10⁻³/h) is higher compared to the degradation of chlorine in plastic pipes (37 × 10⁻³/h).

Generating a monitoring model for secondary disinfectant based on a hydraulic model calibrated with in situ observations is essential for good decision-making, such as identifying pipes for rehabilitation, renewal, and re-chlorination, especially in areas of the WSS with low chlorine concentrations (vulnerable zones). Future studies could focus on calibrating and validating the model under hydraulic conditions and secondary disinfection during the rainy season.

The authors give thanks to God for His grace and mercy throughout this work. The authors thank the (AWaRMN) program for funding the research mobility. The authors also thank the Congo Basin Water Resources Research Center (CRREBaC) and the Regional School of Water (ERE) of the University of Kinshasa.

The African Water Resources Mobility Network (AWaRMN) which has received funding from the Intra-Africa Academic Mobility Scheme of the European Union funds this project. Grant Agreement No. 2019-1973/004-001.

S.B. wrote the original draft, developed the methodology, and analyzed the results; A.A. and R.M.T. supervised the study, wrote and reviewed and edited the article; J.P.B.D. supervised the work.

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

The authors declare there is no conflict.