Introduction

There are many water-related challenges facing Egypt. The limited amounts of rainfall make the country dependent mainly on its share of water from the Nile River. The current available water resources in Egypt are limited, and there is a big gap between water supply and water demands due to urbanization and population growth. The expected total water shortage in 2025 would be 26.0 BCM/Y (Omar and Moussa 2016). To satisfy the Egyptian water demands, the water shortage should be accomplished through the dependence on non-conventional water resources, such as agriculture drainage water.

The main constraint for reusing the drainage water is the degradation of the quality of the drainage. Huge amounts of urban municipal, industrial wastes and rural domestic wastes are dumped in agricultural drains without treatment. Based on the strategic plan for 2037 (MWRI 2005) and considering the water balance for 2015, around 12.37 BCM/year from sewage and industrial wastes return back to the drainage system. Part of this amount is primary treated, and the rest is untreated. As a result, agricultural drains are collecting huge amounts of mixed pollutants, such as high salt concentration, toxic chemicals, nutrients, and dissolved oxygen depletion (El-Sadek et al. 2003). Drainage water reuse has different approaches in Egypt. The official reuse approach is planned and managed by Ministry of Water Resources and Irrigation (MWRI) as collecting these wastes in the main drains and mixing them with freshwater into canals through lifting stations (Abd El-Aziz and El Gammal 2014). With such approach and considering the degradation of the quality of the drainage water, the quality of the water bodies is vulnerable to a wide range of pollutants (Korfali and Jurdi 2011).

The current strategy of Ministry of Water Resources and Irrigation (MWRI) in Egypt to sustain water quality standards in the main canals is through rigid determination for the quality of the water to be lifted from the drains. This can result in overly stringent effluent permit, which limits the reuse of the drainage water. Likely, this is not the most appropriate strategy, and it might be better to violate water quality standards for small areas near outfalls as long as water quality meet the standard values before the points of water use. Using such rigid strategy led to stopping many pumping stations that were lifted the drainage water from the drains to the main canals. During the past years, twelve pumping stations that were lifting an average of 2.3 BCM/year to the irrigation network were stopped. As result, the direct dependence on polluted drainage at tail end reaches increased, which is threatening the sustainability of these reaches. With the gradual increase in the dependence on the drainage water, more precise and flexible approach should be used to define the exact amount of the drainage water to be lifted to the main canals in order to maintain water quality standards while make use of the existed lifting stations. Water quality model and simulation models provide such flexible and precise approach, and it could reduce overall treatment complexity, capital costs, and operations & maintenance costs.

Many researchers used water quality and simulation models to investigate the problem of water quality in the drains in Egypt. Allam et al. (2015) assessed the suitability for reuse drainage water by “QUAL2Kw” model to meet the irrigation requirements alongside Gharbia drain, Nile Delta, Egypt. The authors mentioned that the most common problem for the decision for official agricultural drainage water reuse is defining the mixing ratio between drainage water and fresh irrigation water to satisfy water quality standards. Helal et al. (2021) used the statistical quality control models for managing the reuse of the agricultural drainage water from El-Delengat drain with the El-Hager irrigation canal in the Nile Delta, Egypt. The authors concluded that agricultural drainage water reuse gives safe mixing between drainage water with freshwater.

Other models, such as Cornell Mixing Zone Expert System (CORMIX), which was used in this study, provide more details about the dilution, trajectory, and width of the effluent stream from a pollution source into a water body of an irrigation canal. This can give exact information about the locations where the water of the main canals could be used safely. No previous studies applied CORMIX model in water quality and water management fields in Egypt, and the current study is a pioneer work to apply CORMIX in these fields.

CORMIX model was originally developed by the United States Environmental Protection Agency (USEPA) and Cornell University to use for prediction of water quality in the ambient after wastewater effluent discharged. CORMIX model can evaluate the ambient receiving water that can be protected without requiring an effluent to meet water quality criteria at the point of discharge. The CORMIX model has different sub-models depending on characteristics of the outfall. The current study used CORMIX3 sub-model.

However, there were many internationals’ studies about using CORMIX in irrigation field and other fields. Heiden (2017) used CORMIX model to investigate a point source oil contamination scenario for surface flow resulted from a pipeline failure. The author concluded “CORMIX” proved it was capable of modeling a positive buoyant, point source contaminant for multiple different river types. These river types included a wide, slower moving, regulated river such as the Missouri River and a narrow, fast moving, slightly meandering river such as the St. Croix River. CORMIX was proficient in modeling the near-field mixing zone for all trials and displayed those results in a pleasing manner. The model was used to model concentration of the near-field, starting from the source of the contaminant and throughout the region of interest. CORMIX takes the fundamental behaviors of an oil spill to provide an accurate and easy-to-use fate and transport model. The severity of the oil spill is categorized into three groups based on the interaction with two water quality standards. These water quality standards are the Criteria Continuous Concentration (CCC) and the Criteria Maximum Concentration (CMC). These concentration levels are based on values that are potentially harmful to aquatic fish and plant life in the rivers. The hypothesis is that there will be at least one trial for each river type that both the Criteria Continuous Concentration (CCC) and the Criteria Maximum Concentration (CMC) will not be met in the region of interest (16,000 m or 10 miles). This hypothesis has been supported. When reviewing the results, seventeen of thirty-six hypothetical oil spills were determined to be harmful to the environment. Twelve of the seventeen were classified as severe, with concentrations ending the region of interest above the CMC. Generation PGM (2021) used CORMIX model (sub-model CORMIX2) to study the excess water from the water management pond to Hare Lake in order to maximize the mixing potential and reduce the spatial extent of the mixing zone. The model was used to predict the rate of mixing of the discharge with distance downstream from the diffuser. The author concluded that rapid mixing of discharged waters is predicted, and it will limit incremental changes in water quality to a very small zone in the immediate vicinity of the discharge location. Stantec Consulting Ltd. (2023) used CORMIX (version 12.0) three-dimensional model to determine the mixing zone for parameters of concern in the reject process water effluent discharge from the facility’s reverse osmosis and deionization process. Near-field modeling using CORMIX indicated that the mixing zone extends 6 m for temperature and 5 m for salinity from the outfall before meeting respective CCME guideline values. No exceedances of marine water quality objectives were observed at the end of the 6 m mixing zone.

The current study used CORMIX model (sub-model CORMIX3) to analyze the buoyant surface discharges of effluent from Mehalet Rough pumping station through a channel into Mit Yazid canal. Mit Yazid canal is a main canal in the middle Delta that serves around 82,000 ha, and it has many municipal stations. Mehalet Rough pumping station lifted the water of Waslet Mehalet Rough, which collects the drainage water of five secondary drains. The drainage water in these drains is highly polluted. The model assessed the dilution and mixing zone for two selected water quality parameters; BOD and TDS. BOD is an indicator for organic pollutants. The high concentrations of BOD, the high depletion of dissolved oxygen in the water body. TDS is considered as an inorganic pollutant, and their high concentration is affecting different water uses.

The objective

The aim of this mixing zone analysis was to assess the effects of the diffuser configuration on plume dispersion and determine the effects of discharge effluent on the size of the mixing zone. The objective of the current study is to develop a flexible and reliable strategy for mixing the polluted drainage water with surface water in Egypt. This approach uses CORMIX model to assess the dilution of pollutants and to predict water quality characteristics of the mixing zone, and in consequence, it could define the suitable amount of the drainage water to be lifted in order to maintain water quality standards at the required points. The current strategy in Egypt depends only on the quality of the drainage water without considering the relation between the volume and the quality of lifted drainage water and the flow and the quality of the water in the main canal. Simulation models, such a CORMIX, consider such relationship, and it could evaluate near-field mixing characteristics of the proposed discharge location.

The study was applied for the mixing zone between Mehalet Rough drain and Mit Yazid canal that receive the effluent of the drain through a pumping station. To predict the water quality characteristics of the mixing zone, the study had specific steps including determining the CORMIX sub-model that was used, collecting different information, such as the geometry of the ambient and the outfall, discharge configuration for pumping station, and water quality for the drainage effluent and the irrigation canal. The results were analyzed to determine water quality inside the mixing zone.

Materials and methods

The core of this study is to use CORMIX model to predict the water quality in Mit Yazid canal after lifting polluted drainage water from Waslet Mehalet Rooh pumping station. The activities include collecting different required information to apply the model. These required information include surveying the cross-section of Mit Yazid close to outfall effluent point, measuring the flow in the canal, and assessing water quality data for Mit Yazid canal and Waslet Mehalet Rooh drain. These activities were conducted during a short-term field study conducted by Water Management Research Institute (WMRI) in September 2020. After collecting the required information, the simulation in this article was performed in Environment and Climate changes Research Institute (ECRI) by using the CORMIX3 (Version 11. 0 GTD) modeling program. Average wind speed was collected from the nearest available metrological station in 23-9-2020 which is available in website; https://en.tutiempo.net/climate/09-2020/ws-623660.html.

Theoretical background and model description

One type of the mathematical models that were developed for submerged round buoyant jets are length-scale models. In these models, surface discharge flows can be divided up into different regimes each dominated by particular flow properties such as the initial momentum, the buoyancy flux, or the ambient cross flow [Jones et al 1996].

CORMIX is one of the length-scale models, which is a rule-based mixing model for surface water that predicts mixing and dilution of several types of effluent into various water bodies (Doneker and Jirka 2017). CORMIX contains about 80 generic flow classifications for submerged single-port, multiport, and surface discharge sources (Jirka et al 1996).

CORMIX simulates the hydrodynamics of both near-field and far-field mixing zones. The mixing in the near-field is highly dependent on the discharge conditions, whereas it is dependent solely on the ambient conditions in the far-field (Jones et al 1996).

CORMIX model deduces which hydrodynamic method is best fit for each simulation by referring to what is known as a rule-based expert system. CORMIX has four core hydrodynamic mixing zone simulation models to simulate diverse discharge situations. These hydrodynamic models are CORMIX1, CORMIX2, CORMIX3, and DHYDRO for single port, multiport, surface, and dense/sediment discharges, respectively. The model allows working with five different types of pollutants including conservative pollutants, where the parameter does not undergo any decay/growth process and non-conservative pollutants, where the parameter suffers decay of the first order decay or growth process, for heated discharge, brine discharge, and sediment discharge. In CORMIX, the interaction between the ambient conditions of the receiving body and the discharge characteristics governs the mixing behavior of any wastewater discharge. Regarding the calculation process, CORMIX assumes the receiving water body as rectangular cross-section (Jones et al 1996) and (Doneker and Jirka 2017). In addition, the discharge configurations in CORMIX3 have three types; flush, protruding, and coflowing.

Regarding the assistant tools, the CORMIX package has some post processing tools, including CorVue, which is an interactive 3D visualization tool that displays mixing zone processes and the behavior of wastewater plumes. In addition, CORMIX has preprocessor tools for computation of data input including CorSpy, which is a tool for interactive 3D visualize, display, and specification of outfall properties, including ambient (Doneker and Jirka 2017).

Study area

The investigated system (Fig. 1) consists of Mit Yazid canal that represent the ambient water body and the outlet of a drain (Mehalet Rough pumping station) that dump the drainage water of Waslet Mehalet Rough drain into Mit Yazid canal (km 3.0 on the canal).

Fig. 1
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Study area

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Mit Yazid canal is one of the main canals in the middle Delta. The canal that off-takes from Bahr Shibin canal (96.50 km) is 63.0 km long, and it is located within the administrative boundaries of Gharbiya and Kafr El Sheikh Governorates (71% of the total area is within Kafr El Sheikh). Mit Yazid main canal is feeding 60 branch canals, and it generally flows in a northern to north-western direction and ends immediately south of El Burullus Lake (IWMI 2013). One main characteristic of Mit Yazid canal is the spreading on municipal water stations along the canal, which requires maintaining the water quality in the canal within the standard values according to the Egyptian law for the Ministry of Water Resources and Irrigation, to protect the Nile River and Waterways from Pollution (law 48/1982-article No. 49) (EMWRI 2013). The closest municipal station to Mehalet Rough pumping station is at km 6.2 on Mit Yazid canal.

Mehalet Rough pumping station is the outlet of Waslet Mehalet Rough drain that collected the drainage water from five drains; namely, Tukh drain, El-Santah drain, Bilay drain, Samatai El-Ala drain, and Mehalet Rough drain. Average effluent from the pumping station to Mit Yazid canal is 300,000 m3/day (IWMI 2013). The station has four electric pumping units with an average capacity of 2.50 m3/sec (Total capacity of the station is 10.0 m3/sec). Only two units are operated together with a total discharge of 5.0 m3/sec. The flow regime for the pump station outfall into Mit Yazid canal is surface discharge. According to CORMIX classification, it is considered CORMIX3 configuration.

Collected data

Collected data included the geometry, the configuration, and the flow characteristics of the ambient and the pumping station.

The ambient data

Figure 2 presents the cross-section of Mit Yazid canal at km 3.0 (close to the outlet of Mehalet Rough pumping station). From the figure, the bed level is around 2.80 m, and the bed width is around 40.0 m. Average water level in September 2020 (simulation time) was 5.18 m, and therefore, the water depth for the ambient was 2.38 m. The flow rate in the canal during the studied period was 70.8 m3/s. Based on recent study that investigated this reach of Mit Yazid canal (Helal et al. 2021), Manning coefficient for this reach of the canal is 0.03.

Fig. 2
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Cross-section of Mit Yazid canal at km 3.00

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Pumping station data

Mehalet Rough pumping station is located at the left bank of Mit Yazid canal. The configuration structure for pumping station is flush with the bank. The horizontal angle of discharge (sigma angle-σ) with the canal is 53 degree (Fig. 3).

Fig. 3
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Schematic diagram for the connection between the station and the canal

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Water quality data

The Egyptian water quality standard provides conditions for freshwater and for the agriculture drainage water before discharging into freshwater.

For the freshwater (Mit Yazid canal), BOD should not exceed 6.0 ppm, and TDS should not exceed 500 ppm (law 48/1982-article No. 49) (EMWRI 2013). Based on field measurements, BOD and TDS values in Mit Yazid canal upstream the study were 2 ppm and 265 ppm, respectively (Table 1).

Table 1 Discharge and water quality values for the ambient and the outfall
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For the agriculture drainage water (Mehalet Rough), BOD should not exceed 10.0 ppm, and TDS should not exceed 500 ppm (law 48/1982-article No. 64) (EMWRI 2013). Based on field measurements, BOD and TDS values in Mehalet Rough drain were 19 ppm and 598 ppm, respectively (Table 1).

The discharge channel geometry for CORMIX3

Figure 4 presents the general specifications required for CORMIX3. These specifications include location of the nearest bank, ambient depth near the surface discharge channel entry (HD), discharge channel width (B0) of the rectangular channel, discharge channel depth (H0), actual receiving water depth at the channel entry (HD0), bottom slope (SLOPE) in the receiving water body in the vicinity of the discharge channel, and horizontal angle of discharge (SIGMA) is the angle of the surface shoreline discharge channel with respect to the downstream bank.

Fig. 4
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CORMIX3 discharge channel geometry (Doneker and Jirka 2017)

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In the immediate area of the discharge, the actual depth of the receiving water, “HD,” may be somewhat different from the average ambient depth, “HA.” The bottom of the channel may be sloping away from the discharge bank at an angle θ, beginning with the depth immediately in front of the discharge channel, HDO.

Input data

There are three types of input data that are required for using the CORMIX model; environmental ambient data, effluent data, and disposal type information as subaquatic emissary data. The collected data in this article for discharge type (CORMIX3 model) are presented in Table 2.

Table 2 Environmental, effluent, and subaquatic emissary data
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Results and discussion

Simulations were carried out through the mathematical model; CORMIX3, to estimate the dispersion of the effluent from Mehalet Rough pumping station into Mit Yazid canal, and to check the water quality standards in the studying canal after mixing with the effluent from the pumping station. The flow class description for this simulation is “Shoreline-attached discharges in cross flow (SA1),” which was applied to the full water depth at the discharge site. This flow is dynamically attached to the downstream bank, and the penetration into the cross flow is reduced due to this dynamic attachment.

Two parameters, which are biochemical oxygen demand (BOD) and total dissolved solids (TDS), were investigated. For the two parameters, the prediction was observed, and the size of plume was calculated. The outputs of the model included the effluent dilution for both parameters and a near-field mixing characteristic of the proposed discharge location.

Applying CORMIX simulation model

The simulation was implemented for BOD and TDS parameters. The surface outfall configuration for pumping station on the canal is shown in Fig. 5, and the simulation output is displayed in Table 3.

Fig. 5
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Surface outfall configuration

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Table 3 Simulation outputs
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Estimating BOD excess and dilution values

The neutrally buoyant BOD plume dispersion as output from “CorVue” is presented in Fig. 6. Figure 7 presents the plume dilution of BOD. Figure 8 presents excess concentration above the ambient background value as mentioned in Table 1. It can be observed that, the BOD plume above the ambient water reaches 8.66 ppm just after discharge out from the outlet structure by about 12.55 m, and its dilution is 2.0 at the edge of near-field region. At the distance 61.93 m from the pumping station, the BOD concentration above the ambient water is 4.56 ppm with a dilution of 3.7. The BOD concentration above the ambient water reached water quality standard at a distance of 448.36 m with dilution of 4.3. Figure 8 also shows the dispersion of pollutants with just about only 12 m along the width of the canal.

Fig. 6
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BOD simulation for the dispersion plume in three dimensions

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Fig. 7
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BOD dilution for the outfall pump station

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Fig. 8
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BOD excess (ppm) for the outfall pump station

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Estimating TDS excess and dilution values

The neutrally buoyant TDS plume dispersion as “CorVue” output is observed in Fig. 9. Figure 10 presents the plume dilution of TDS, and Fig. 11 presents the excess in TDS concentration above the background value (265 ppm) in the Met Yazid canal. TDS concentration at the near-field edge is 169.7 ppm above the ambient water at a distance of about 12.55 m, with a dilution value equal 2. Water quality standard for TDS is observed at a distance of 4.46 m with a dilution value is 1.4. Figure 11 illustrates the pollutants dispersion with just about only 12 m along the canal width.

Fig. 9
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TDS simulation for the dispersion plume in three dimensions

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Fig. 10
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TDS dilution for the outfall pump station

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Fig. 11
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TDS excess (ppm) for the outfall pump station

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As presented in Table 3, the area of mixing zone was 6913.7 m2 for BOD and about 16.6 m2 for TDS. The highest length along the canal to reach to WQ standard is about 5.0 m for TDS and 449 m for BOD. The nearest intake for water treatment plant is found at km 6.2 on the canal (3.2 km downstream the discharge from the pumping station). Therefore, there is no impact observed from the drains on the WQ of the canal with respect to the studied pollutants.

Finally, the plume dispersions for BOD and TDS are illustrated in Google Earth as in Figs. 12 and 13, respectively.

Fig. 12
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The plume dispersion for BOD in Google Earth

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Fig. 13
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The plume dispersion for TDS in Google Earth

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Conclusion and recommendation

With the increase in the dependence on the drainage water in Egypt, due to the gradual increase in water gap between water supply and water demand, better approach should be followed to provide flexible and sustainable procedure for using this resource. The current stringent effluent permit, which depends merely on the quality of the drainage water limits mixing the drainage water with the freshwater in the main canals, and in consequence increase the direct dependence on polluted drainage water at tail end reaches. Mathematical models, such as CORMIX model, provide such flexible and sustainable approach. The idea is to maintain water quality standards at point of use and based on the requirements for such use like maintaining water quality for drinking water at the locations of the municipal stations. However, a mixing zone where ambient concentrations may exceed the required criteria in small areas near outfalls could be accepted as long as water quality meet the standard values before the points of water use.

The current study provides an example for applying such approach by using CORMIX3 model. CORMIX model was used in the previous researches internationally, but this is the pioneer study to apply CORMIX in the irrigation field in Egypt. The aim of the study is to use CORMIX3 model to define the dilution, trajectory, and width of the effluent stream from a pollution source (effluent discharges from Mehalet Rough pumping station) into a water body of an irrigation canal (Mit Yazid canal). The model investigated two pollutants (BOD and TDS), and the results were evaluated based on the Egyptian water quality standard (law 48/1982-article No. 49) that provides conditions for freshwater not exceed than 6.0 ppm for BOD and 500.0 ppm for TDS. Although the water quality of effluent discharges from Mehalet Rough pumping station violated water quality standard, the results illustrated that water quality standards for BOD and TDS were met at 448.36 m and 4.46 m, respectively, downstream of the pumping station outfalls from Mehalet Rough drain. The closest municipal station on Mit Yazid canal is 3.2 km downstream Mehalet Rough pumping station. Using the current stringent effluent permit will stop using such drainage water. On the other hand, using the approach introduced by the current study with all intersected drains of Mit Yazid canal could improve the situation of the tail end of the canal, as 25% of the served area of Mit Yazid canal depends mainly on the drainage water (IWMI 2013). The same scenario could be applied for other water quality parameters especially toxic heavy metals, and if water quality standards are met for all parameters in the main canal before the point of use, the drainage water could be accepted regardless its situations in the drain.

Such approach of using the simulation models instead of the current stringent effluent permit is highly important in Egypt considering the necessity to reuse the drainage water to fill the water gap between water supply and water demand. This approach is also important to improve the integrated water management through distributing the dependence on the drainage water between head and tail reaches. Using such approach could also help reducing overall treatment complexity, capital costs, and operations & maintenance costs while still meeting in stream WQ standards.