Wastewater heat recovery (HR) is one of the renewable energy sources. The associated harmful environmental, health, and social effects of traditional biomass, fossil fuel, and other polluted sources have enhanced the growing interest in the search for an alternate cleaner energy source globally. The major objective of this study is to develop a model to assess the impacts of wastewater flow (WF), the temperature of wastewater (TW), and internal temperature in sewer pipes (TA) on the performance of HR. Sanitary sewer networks in Karbala city of Iraq were chosen as a case study in the present research. Statistical and physically based models such as the storm water management model (SWMM), multiple-linear regression (MLR), and structural equation model (SEM) were used for this purpose. The model outputs were analyzed to assess the performance of HR in the context of changing WF, TW, and TA. The results showed that the total amount of HR from wastewater in Karbala city center during the 70 days was 136,000 Mw. The study clearly showed that WF in Karbala played a major role in HR. Basically, the heat from wastewater is CO2-free and represents a significant opportunity for the energy transition in the heating market.

  • HR ranks among renewable energy sources.

  • It is used to develop a model to assess the impacts of wastewater flow (WF), the temperature of wastewater (TW), and internal temperature in sewer pipe (TA) on HR.

  • Statistical and physically based models such as SWMM, MLR, and SEM were used for this purpose.

  • HR is CO2-free and represents a significant opportunity for the energy transition in the heating market.

Heat recovery (HR) from wastewater is a process that involves extracting heat from wastewater before it is discharged into the environment. The recovered heat can then be used for a variety of purposes, such as space heating, domestic hot water, or industrial processes. This process is often referred to as HR. There are several technologies used for HR, including heat exchangers (HEs), heat pumps (HPs), and heat wheels. HEs are the most common technology used for HR. They work by transferring heat from the wastewater to a heat transfer fluid, such as water or air. The heat transfer fluid is then circulated to a heat sink, where the heat is released (Sun et al. 2022; Wehbi et al. 2022). Moreover, HPs are another technology used for HR. They work by using electricity to move heat from the wastewater to a higher temperature level, which can then be used for heating. HPs are more efficient than HEs because they can produce more heat than the amount of electricity used to run them (Chae & Ren 2016; Serrat et al. 2023).

In addition, heat wheels are a less common technology used for HR. They work by rotating a wheel containing a heat-absorbing material through the wastewater, which then transfers heat to a heat transfer fluid. The heat transfer fluid is then circulated to a heat sink, where the heat is released. The benefits of HR from wastewater include reducing energy consumption and greenhouse gas emissions, as well as lowering operating costs for businesses and households (Jouhara et al. 2018; Ononogbo et al. 2023). Additionally, HR can help to reduce the demand for freshwater by using wastewater as a source of heat. However, it is important to note that the effectiveness of HR depends on several factors, such as the temperature of the wastewater, the amount of heat that needs to be recovered, and the available technology (Saagi et al. 2022).

Numerous countries aim to increase secondary energy sources, including HR. A reason behind that is strengthening energetic self-sufficiency and rescuing the environment affected by the exploitation of fossil sources. One effective solution is using warm wastewater's thermal energy as a secondary energy source (Stransky et al. 2016). Sewage HR applications are becoming widespread in energy-saving applications. A sustainable and low-emission operations in air conditioning and heating processes is achieved by harvesting the otherwise wasted energy in wastewater through specially developed HEs lying at the core of HPs (Culha et al. 2015). For instance, in central cities, 10% of the total energy spent in the whole urban water cycle is lost in the sewer systems and the primary energy consumption for collecting and transporting wastewater (Elías et al. 2014; Stransky et al. 2016). Therefore, HR from sewage is considered an efficient and energy-generating source. It is classified as a renewable energy source and can be optimally used in low-energy buildings for low-temperature heating, high-temperature cooling, and to preheat household hot water (Perackova & Podobekova 2013).

Cipolla & Maglionico (2014) reported that the amount of energy that can be obtained from wastewater and the optimal design of HR systems depend on the knowledge of the flow rate and the temperature in the sewer system in Bologna (Italy). The data analysis they used allowed them to identify the daily trend for the wastewater flow, whose coefficients in relation to the average flow (where average flow = 1) vary between 0.25 and 1.50, and for the wastewater temperature in which the coefficients is ranging from 0.90 to 1.05. Moreover, raw wastewater contains considerable amounts of energy that can be recovered by means of a heat pump and an HE installed in the sewer (Dürrenmatt & Wanner 2014). Hot wastewater is considered a valuable source of energy that could be recovered (Wehbi et al. 2022). Wastewater from domestic, industrial, and commercial developments maintains considerable amounts of thermal energy after discharging into the sewer system. It is possible to recover this heat by using technologies like HEs and HPs, and to reuse it to satisfy heating demands (Nagpal et al. 2021). In December 2018, wastewater was officially recognized by the European Union as a renewable source of energy, thus wastewater HR can be included in efforts to reduce greenhouse gas emissions. As the world's population continues to increase and the economy continues to develop, all scientists and research centers are looking for green energy sources and managing the current sources. The European Union Directive 2018/2001 recognized wastewater as a renewable heat source in compliance with the European environmental goals (Nagpal et al. 2021). Besides, global warming, greenhouse gas, and carbon footprint are deemed the most important, particularly in the water and wastewater sectors. Moreover, rising energy prices and concerns about global warming highlight the need to improve energy independence in wastewater treatment plants (WWTPs) (Chae & Kang 2013; Perackova & Podobekova 2013). Nevertheless, HR from wastewater can help decrease natural gas energy consumption, the associated energy costs, and greenhouse gas emissions, but the investment rate for the selected community size will be low (Garmsiri et al. 2014).

Many studies reported the mechanism of HR from wastewater using three components: household, sewer networks, and municipal WWTPs. Culha et al. (2015) reported that there are three different locations to recover heat from sewage. The first, HE, could be installed inside the facility to recover waste heat from household hot water, called domestic utilization. The second HE is located inside or outside the sewage networks, delivering considerable extra heat from wastewater to supply heating/cooling for multiple buildings. The principal requirement is that the sewer dimension should be more than 800 mm. Sewage flows are usually insufficient to get high heat efficiency in smaller sewer diameters, and the plant installation becomes complicated because of the diameter size of the sewer pipes (UHRIG 2022). The third HE can be installed downstream of WWTP to efficiently utilize the energy in the treated wastewater on a larger scale (UHRIG 2022). For instance, under some circumstances, 50% of energy could be stored or recovered using the HR system. In addition, all systems are considered economical as well as environmentally effective methods (Wehbi et al. 2022).

The objective of the study is to create a physical model to predict HR from wastewater, then what are the input parameters that should be provided for this model, and study the challenges. The model in this study has covered all aspects of HR from wastewater. The novelty of this study is to create a model to predict HR from wastewater. The model could be applied at any location in the world having similar issues.

Methods

The descriptions of the methods used in the study are given in the following:

Storm water management model

The storm water management model (SWMM) keeps track of the flow rate, flow depth, runoff volume generated within each sub-catchment and the quality of water in each pipe and/or channel at different times of the simulation. SWMM Version 5.2.1, running under Windows was used in the present study, as it provides simulations, an environment for editing study area input data, running hydrologic, hydraulic and water quality simulations, and viewing the results in a variety of formats. These include the color-coded drainage area and conveyance system maps, time series graphs and tables, profile plots, and statistical frequency analyses. ArcGIS Pro 3.0 version was used as a tool for preparation of input data for SWMM5.

Multiple-linear regression

The multiple-linear regression (MLR) based on the statistical analysis approach is also used to quantify the performance HR variation in sanitary sewer system in Karbala city. It is an approach used for modeling the relationship between a scalar dependent variable, y and one or more explanatory variables denoted, x. In the case of more than one explanatory variable, the process is called MLR (Wang et al. 2010). In this paper, the linear regression model was used to estimate impacts of WF, TW, and TA on HR. The unknown model parameters were estimated from the collected data, based on the following linear regression function (Equation (1)):
formula
(1)

Least squares approach (SmartPLS)

Least squares approach is widely used to fit the linear regression models. However, other methods can also be used for model fitting. In the present study, the regression model is fitted by minimizing a penalized version of the least squares loss function similar to ridge regression (Yang et al. 2022.) The path coefficients and the coefficient of determination (R2) are used in SmartPLS to evaluate the structural model. Figure 1 illustrates the type of hierarchical component model which is Reflective–Reflective Type I (Jarvis et al. 2003; Wetzels et al. 2009) which is used in this study (Ringle et al. 2012).
Figure 1

Hypothetical model of HR from wastewater by using the SEM.

Figure 1

Hypothetical model of HR from wastewater by using the SEM.

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The variance shared by observed variables and the latent unobserved variables which are supposed to explain the observed variables, can be modeled with a standard equation for measurement as below (Equation (2)):
formula
(2)
Yi is the manifest variable (e.g., item of TA, TW, and WF); Ʌy refers to loading the first order of loading value (LV); ηj refers to the first-order LV (e.g., HR); εi refers to the measurement error.
The evaluation process of the inner model incorporates several steps as recommended by researchers (Götz et al. 2010). A model with lower-order factors and significant correlations among the factors indicates that the model has at least one second-order factor. The standard exogenous model can be substituted using an endogenous model as in the following (Equation (3)):
formula
(3)
ηj is the first-order factor; Г refers to the loading of second-order LV; ξk is the second-order LV (e.g., system reliability); ζj is the error of first-order factors.

Materials

Study area

Karbala, with an area of 5,034 km2, is a city in Iraq, located about 100 km (62 mile) (Latitude: 32°36′51″ N, Longitude: 044°01′29″E) southwest of Baghdad. It has an estimated population of 395,411 at the city center, and 675,000 in the whole Karbala Governorate (Macrotrends 2022). Figure 7(a) is the map of Iraq showing Karbala and other cities. The top sheets of the study area were collected from the Directorate of Urban planning in Karbala City. The base map is created by delineating the boundary from top sheets by means of creating a shape file. Several features such as settlements, roads, water bodies, vegetation, and industrial areas have been digitized, and corresponding maps generated. A total of 64 sub-catchments were found in the top sheets. The boundary of these sub-catchments was delineated using GIS, which was also used for preparing the base map. The base map showing the sub-catchments of the city is shown in Figure 2.
Figure 2

Map of Iraq showing Karbala city generated by GIS based on DEM data (Directorate of Urban planning of Karbala 2019).

Figure 2

Map of Iraq showing Karbala city generated by GIS based on DEM data (Directorate of Urban planning of Karbala 2019).

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Hydraulical data

Hydraulical data are very rare in the study area. This is particularly true for sewer data. Sewer data are rarely collected in Karbala city. Hourly data were collected only for a few days (total 70 days) from 1 November 2019 to 10 January 2020. The WF and TW were collected by Directorate of Sewerage of Karbala from six manholes using sensors. These include manholes, inlets, inverted siphons, pumping stations, etc. Figure 3(a) shows the map of the sewer networks and WWTPs in the city center of Karbala.
Figure 3

(a) The sewer networks map in the city center of Karbala generated by GIS. (b) The six main sewer lines in the city center of Karbala generated by the SWMM.

Figure 3

(a) The sewer networks map in the city center of Karbala generated by GIS. (b) The six main sewer lines in the city center of Karbala generated by the SWMM.

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There are seven types of reinforced concrete manholes in the sanitary sewer of the Karbala city center, namely, AS, BS, CS, BD, CD, CD1, CD2. Table 1 lists the specifications and dimensions of these manholes (Directorate of Karbala sewerage 2022).

Table 1

The details of the sewerage manholes at the city center of Karbala

Types of MHInvert depth(m)Dia. of outgoing pipe (mm)Number of incoming pipesDia. of chamber ring (cm)
AS 1.25–1.69 200–400 Any number  
BS 1.70–2.99 200–400 <2 110 
BD >3.25 200–400 <2 110 
CS 1.70–3.24 200–400
450–700 
>3
Any number 
150 
CD >3.25 200–400
450–700 
3 or more
Any number 
150 
CD1 (Special MH) >2.00 800–1,000 Any number According to the design 
CD2 (Special MH) >2.00 >1,000 Any number According to the design 
Types of MHInvert depth(m)Dia. of outgoing pipe (mm)Number of incoming pipesDia. of chamber ring (cm)
AS 1.25–1.69 200–400 Any number  
BS 1.70–2.99 200–400 <2 110 
BD >3.25 200–400 <2 110 
CS 1.70–3.24 200–400
450–700 
>3
Any number 
150 
CD >3.25 200–400
450–700 
3 or more
Any number 
150 
CD1 (Special MH) >2.00 800–1,000 Any number According to the design 
CD2 (Special MH) >2.00 >1,000 Any number According to the design 

The topography of Karbala city has made it necessary to include pump stations in certain locations of the sewer network system, in order to facilitate wastewater flow through the sewers reaching the discharge point. Two types of pump stations were used in the design of the sewage project for Karbala city. These are submersible pump stations and screw pump stations (Directorate of Karbala sewerage 2022).

There are two WWTPs in Karbala city center, the old WWTP located east of the city with a maximum capacity of 70,000 m3/day. There is another new WWTP with a capacity of 700,000 m3/day. The plant has been designed to receive wastewater from Karbala neighborhoods. The location of the plant is about 13 km southwest of Karbala city center along the road of Karbala – Najaf as shown in Figure 3(b) (Directorate of Karbala sewerage, 2022).

Hydrology data

In hydrology, the catchment area is defined as the surface area that contributes runoff to stream. However, in urban geography, a catchment area is defined as the area of a city that attracts population to use their services. Generally, local governments establish or modify a catchment area based on their need. Services provided in different catchments may vary largely depending on their geographical or commercial importance. Unlike hydrological catchment, urban catchments may overlap (Jenkins & Campbell 1996; Schuurman et al. 2006). The area of Karbala city center is about 2,134.145 ha, and it consists of 64 sub-catchments as shown in Figure 4(a). This map is generated by GIS based on provided data. The width of each sub-catchment in the city center of Karbala varies up to 7,892 m as shown in Figure 4(b). The ground elevation for each sub-catchment ranges from 24 m to more than 36 m as shown in Figure 4(c).
Figure 4

(a) The sub-catchment area of Karbala city center (ha) generated by GIS based on the observed data (Directorate of Urban planning of Karbala 2019), (b) the width (m) for each sub-catchment of Karbala city center generated by SWMM5, and (c) the ground elevation (m) for each sub-catchment of Karbala city center generated by SWMM5.

Figure 4

(a) The sub-catchment area of Karbala city center (ha) generated by GIS based on the observed data (Directorate of Urban planning of Karbala 2019), (b) the width (m) for each sub-catchment of Karbala city center generated by SWMM5, and (c) the ground elevation (m) for each sub-catchment of Karbala city center generated by SWMM5.

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Furthermore, hydrological data such as time series of rainfall, temperature, evaporation, and the time of concentration (duration) of rainfall were prepared as inputs for SWMM5. Karbala is situated in the semi-arid region of Iraq. The climate of the city is characterized by cold winters and prolonged dry season. It experiences a hot desert climate with extremely hot and dry summer and cool winter. Most of the rainfall is received between November and April; however, rainfall is not high in any month (World Weather Information Service- Karbala 2021). The monthly distribution of rainfall in Karbala city is shown in Figure 5. In this study, it has been assumed the internal temperature in sewer pipe equals to weather temperature.
Figure 5

The climatological data of Karbala city (1980–2020) (World Weather Information Service- Karbala 2021).

Figure 5

The climatological data of Karbala city (1980–2020) (World Weather Information Service- Karbala 2021).

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Temperature of weather in Karbala city center was collected and managed as shown in Figure 6 for the period from 1 November 2019 to 10 January 2020 (Weatherspark 2022).
Figure 6

Temperature of weather in Karbala city center for November and December 2019, and January 2020.

Figure 6

Temperature of weather in Karbala city center for November and December 2019, and January 2020.

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Figure 7

Distribution of permanent population of Karbala city generated by GIS.

Figure 7

Distribution of permanent population of Karbala city generated by GIS.

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The main components of the external wastewater HR system are HE and HP. HR systems inside buildings consist of HEs built into the sewage pipe and connected to the mixer tap or the storage tank (Perackova & Podobekova 2013). For instance, Therm-Liner HE has been used to generate HR from wastewater in Germany (UHRIG 2022). The channel HE calculation method can be simplified to two formulas by using constant figures for certain fluid combinations, however, to determine HR by using Equation (4) (Hisaka 2022).
formula
(4)
Q is the heat load, kW; ṁ is the flow rate, kg/h; Cp is the specific heat, kJ/kg °C; T is the inlet/outlet temperature, °C; ṁ = W (m3/h) × ρ (kg/m3); W is the volumetric flow rate; ρ is the density.

This study presents the results obtained using physically based and statistical models. These results are selected and analyzed to fulfil objectives of this study. They are divided into two sections: results of sewer quantity modeling and results of HR modelling. Finally, the obtained results are analyzed and discussed to fulfil the objectives of the study.

The sewer network in the city center of Karbala is already fully implemented. Some outlying areas of the center, as well as nearby agricultural areas are still out of the sewer network. Both networks are more than half a century old. The sewer discharge is first modeled using the SWMM using input data to simulate WF for the period 1 November 2019 to 10 January 2022. The daily distribution of the total population in the city, including permanent residents, is shown in Figure 7. The figure shows that the population in the area varies between less than 305 and close to 40,000 persons during normal days.

The water consumption at each sub-catchment of Karbala city center for the normal days is shown in Figure 8(a). Following the directives of the directory of water supply of Karbala city, the per capita per day water consumption for permanent resident is considered between 200 and 400 L. The figure shows that water consumption in the study area varies from sub-catchment to sub-catchment, between less than 76 m3/day to about 17,672 m3/day. High water consumption was estimated in highly dense residential areas of the city during normal periods. The sewer discharge from each sub-catchment of the Karbala city center (m3/d/sub-area) was estimated considering that per capita per day sewer delivery is from 160 to 320 L. The sewer delivery of 160 to 320 L is based on the estimation proposed by the Directorate of sewerage of Karbala. The sub-catchment wise distribution of sewerage discharge is shown Figure 8(b). The spatial distribution of sewer discharge follows the same pattern of water consumption.
Figure 8

(a) Water consumption at each sub-catchment of Karbala city center (m3/day/sub-area) and (b) the sewer discharge from each sub-catchment of Karbala city center (m3/d/sub-area) during normal days.

Figure 8

(a) Water consumption at each sub-catchment of Karbala city center (m3/day/sub-area) and (b) the sewer discharge from each sub-catchment of Karbala city center (m3/d/sub-area) during normal days.

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To fulfill the objectives of the study, the sewer discharge of Karbala city is first modeled using the SWMM. A number of parameters are required in order to model the sewer discharge. The values of parameters are defined in a few ways. Few parameters are defined based on the availability of data on sub-catchments, drainage structure and slope. Few parameters are obtained by calibrating the observed discharge using the width of sub-catchment and the Manning's roughness coefficients for pervious and impervious surfaces and channels. The default values suggested in the SWMM are adopted for other parameters. Furthermore, the modeling results of the SWMM were exported in different forms for the convenience of analysis, such as graphs, tables, reports, etc. SWMM5 also provides different statistics of input and output data such as average, maximum, total time, etc. at daily, monthly, and yearly time scales in different graphical forms. The period for modeling using SWMM5 is from 1 November 2019 to 10 January 2020. Spatial and temporal susceptibility of sewer overflow points during normal as shown in Figure 9 and sewer discharge of a few selected sewer lines are thus discussed in the following.
Figure 9

Spatial and temporal susceptibility of sewer flow in Karbala city center.

Figure 9

Spatial and temporal susceptibility of sewer flow in Karbala city center.

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The peak flow was calculated by multiplying the average flow with peak factor. The peak factors in the sewerage network generally decreased from upstream to downstream. Therefore, the value of the peak factor is decided based on sewer type or position in the sewer network. This research established that the peak sewerage flow factor (1.256 < Pf = 1.68 < 1.77) and significant difference (p < 0.001) during the period of this study. Gaines (1989) conducted a study for monitoring sewer wastewater in the city of Denver in Colorado. He plotted the rates of flow that are higher than the average rate of peak flow, approximated the normal probability distribution, and showed accurate prediction of flow rates. Following similar procedure in the present study, the peak factor value was estimated as 1.68 < 2.4 in critical condition. The value was similar to that reported by EPA (2004), i.e., maximum peak factor closes to 2.4.

Results obtained using statistical models namely, MLR analysis and structural equation modeling (SEM) are described in this section. For the modeling of HR from wastewater, the available data were divided into two parts: 70% of available data were used for model calibration and the rest 30% data were used for model validation, in addition the verification model with others previous studies. It was mentioned earlier that wastewater data in the study area is available only for a few days (from 1 November 2019 to 10 January 2020). Therefore, model results for both calibration and validation periods are presented together in this study. Variance inflation factors (VIF) for WF, TW, and TA were achieved with the requirement for a reflective measurement model. Since the model was reflective and flexible between the first and second order, the direction of causality from construct to measure was used. As such, it is required to check multi-collinearity, as shown in Table 3.

An MLR-based statistical analysis approach was used to quantify the impacts of WF, TW, and TA variations for HR in Karbala city to fulfil the objectives of the study. Average distribution of TA, TW, WF, and HR for the period 1 November 2019 to 10 January 2020 as shown in Figure 10. However, the sewer networks of Karbala city consist of 8,500 manholes with a depth ranging from 1.3 to 7 m, and 8,100 conduits with a diameter, which ranges between 200 and 1,800 mm. The distance between two manholes is in the range of 30–150 m. Therefore, the total volume of the networks is approximately 764,275 m3, which is sufficient to increase HR amounts. The sewer flow in the network depends on the number of populations.
Figure 10

Average distribution of TA, TW, WF, and HR for the period 1 November 2019 to 10 January 2020.

Figure 10

Average distribution of TA, TW, WF, and HR for the period 1 November 2019 to 10 January 2020.

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The most important assumption of MLR is that both dependent and independent variables should be normally distributed. Therefore, the distribution of HR is tested for normality using the Kolmogorov–Smirnov test. The result reveals that the HR data are fully normally distributed at a significant level of 0.05. This study found the relationship between TW and TA, HR and WF, and HR and TW as shown in Figures 11(a)–11(c), respectively.
Figure 11

(a) The relationship between TA and TW, (b) the relationship between HR and WF, and (c) the relationship between HR and TW.

Figure 11

(a) The relationship between TA and TW, (b) the relationship between HR and WF, and (c) the relationship between HR and TW.

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Correlations of TW, TA, WF, and HR are listed in Table 2. The table shows a strong correlation between WF and HR in the study area. This indicates that HR in the area is highly sensitive to WF. On the other hand, partial correlation between WT and HR was found to be low, which indicates low influence of WT in HR in Karbala. Since the sewer networks are basically installed underground, a low influence of TA on HR is expected (p-value = 0.53). Hence, in this study, it has been assumed the internal temperature of sewer networks equals to weather temperature which may it considered as a cap of this study.

Table 2

Correlation and covariance of TW, TA, WF, and HR

HR (kw)TW (°C)TA (°C)WF (m3/h)
HR (kw) 1.000 0.689 0.463 0.773 
TW (°C) 0.689 1.000 0.666 0.097 
TA (°C) 0.463 0.666 1.000 0.075 
WF (m3/h) 0.773 0.097 0.075 1.000 
HR (kw)TW (°C)TA (°C)WF (m3/h)
HR (kw) 1.000 0.689 0.463 0.773 
TW (°C) 0.689 1.000 0.666 0.097 
TA (°C) 0.463 0.666 1.000 0.075 
WF (m3/h) 0.773 0.097 0.075 1.000 

MLR analysis yields equation relating TW, WF, and TA in the study area. To quantify the influence of these factors on HR, the data were merged and jointly analyzed. The regression equation showing the relation of TW, WF, and TA with HR from wastewater in Karbala city. The obtained equation of the study model is given below (Equation (5));
formula
(5)
The residuals and P–P plot, and histogram of regression standardized residual for HR is shown in Figures 12. The plots show that the residuals are fully normally distributed. This indicates that the regression equations are free from any systematic bias and can be used for prediction.
Figure 12

Residuals and normal P–P plot and histogram of the residuals for HR from wastewater.

Figure 12

Residuals and normal P–P plot and histogram of the residuals for HR from wastewater.

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The observed and predicted HR by the regression equation (Equation 5) are shown in Figure 13. The figure shows that regression models can predict HR, this also indicates that the regression equation can be used to quantify the sensitivity of HR to TW, WF, and TW. The parameters determined during calibration process are used for validation of the model, the resulting R2 was 0.9545 and NSE values are found to be 0.99 (very good). The percentage difference between modeled and observed data is also found to be 5.2 less than 10 (very good). In addition, goodness-of-fit ratings for model calibration (An & Gianvito 2012) ISE was 0.27 less than 3 (Excellent).
Figure 13

Observed vs. predicted HR from 01.11.2013 to 10.01.2014 (ISE = 0.99 < 3 is an excellent rating).

Figure 13

Observed vs. predicted HR from 01.11.2013 to 10.01.2014 (ISE = 0.99 < 3 is an excellent rating).

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Structural equation-based models were developed to simulate HR parameters in the present study, the wastewater parameters were analyzed. TW, TA, and WF were considered as the defining factors of HR. Transmission of temperature between sewer pipe and soil was considered ignored during the period of study because there is no data available. The results of the structural model illustrated that R-squared is 0.949 for TW and 0.700 for WF, but it was 0.214 for TA which is less than 0.26 as suggested by Cohen (1988) as shown in Figure 14.
Figure 14

The structural model of HR generated by the SEM.

Figure 14

The structural model of HR generated by the SEM.

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Since the model was reflective and flexible between the first and second orders, the direction of causality from construct to measure was used, and as such it is required to check multi-collinearity (Table 3). Variance inflation factors (VIFs) for WF, TW, and TA was achieved with the requirement for reflective measurement model.

Table 3

The collinearity statistics of structural model of the HR

VIF
WFTWTA
HR 1.010 1.804 1.797 
VIF
WFTWTA
HR 1.010 1.804 1.797 

Table 4 shows the item's loading and t-statistic on their corresponding constructs for HR. The results showed that all the items considered in the present study have satisfactory indicator reliability, and t-value of HR → TW, HR → TA, HR → WF, TA → TW, TA → WF, and WF → TW are more than 1.28 (Hair et al. 2010). Also, the path coefficients of HR → TA, TA → TW, TA → WF, and WF → TW are less than 0.5. However, HR has most influenced by wastewater temperature and flow.

Table 4

Summary of the structural model of HR

HypothesesPathPath coefficientMean sampleStandard deviationT-valuesP-valueDecision
H1 HR → TW 1.456 1.457 0.113 12.896 0.000 Supported 
H2 HR → TA 0.463 0.463 0.075 6.209 0.000 Non-supported 
H3 HR → WF 0.940 0.938 0.050 18.738 0.000 Supported 
H4 TA → TW 0.070 0.069 0.029 2.367 0.018 Non-supported 
H5 TA → WF − 0.360 −0.363 0.065 5.570 0.000 Non-supported 
H6 WF → TW − 1.034 −1.036 0.103 10.024 0.000 Non-supported 
HypothesesPathPath coefficientMean sampleStandard deviationT-valuesP-valueDecision
H1 HR → TW 1.456 1.457 0.113 12.896 0.000 Supported 
H2 HR → TA 0.463 0.463 0.075 6.209 0.000 Non-supported 
H3 HR → WF 0.940 0.938 0.050 18.738 0.000 Supported 
H4 TA → TW 0.070 0.069 0.029 2.367 0.018 Non-supported 
H5 TA → WF − 0.360 −0.363 0.065 5.570 0.000 Non-supported 
H6 WF → TW − 1.034 −1.036 0.103 10.024 0.000 Non-supported 

These relationships are shown more clearly in the histograms in Figure 15 to represent the distribution of numerical data of these parameters. Statistically, normality can be evaluated by obtaining the result of skewness (the symmetry of distribution) and kurtosis values (peakness or flatness of distribution) (Pallant 2007).
Figure 15

Histograms of the following parameters: WT, WF, WA, and HR.

Figure 15

Histograms of the following parameters: WT, WF, WA, and HR.

Close modal
Figure 16 illustrates the connection between HE and HP. This model has some assumptions regarding temperature, for example, Tout hot, Tout cold, and Tin cold have been assumed 14, 12, and 8 °C, respectively. Thus, WT (Tin hot) is hourly data and has been collected from Directorate of sewerage of Karbala for 7 days.
Figure 16

Schemes of HR and HP.

Figure 16

Schemes of HR and HP.

Close modal
The results of this model showed the HR quantity extracted from sanitary sewer networks during the 70 days in Karbala city in Table 5. This model is applied to six HRs that are situated in sewer pipe main lines as shown in Figure 17.
Table 5

HR (Mw) quantity extracted from the sewer lines for 70 days in Karbala city center

Sewer lineHR (Mw) for 70 daysArea of HE plates (m2)No. of HE platesNTUaLength of HE in sewer pipe (m)
Line 1 10,066 0.49 249 1.26 < 1.5 124 
Line 2 23,756 0.49 585 1.26 < 1.5 292 
Line 3 34,716 0.49 854 1.26 < 1.5 427 
Line 4 36,796 0.49 904 1.26 < 1.5 452 
Line 5 29,073 0.49 715 1.26 < 1.5 358 
Line 6 1,613 0.49 42 1.26 < 1.5 21 
Sewer lineHR (Mw) for 70 daysArea of HE plates (m2)No. of HE platesNTUaLength of HE in sewer pipe (m)
Line 1 10,066 0.49 249 1.26 < 1.5 124 
Line 2 23,756 0.49 585 1.26 < 1.5 292 
Line 3 34,716 0.49 854 1.26 < 1.5 427 
Line 4 36,796 0.49 904 1.26 < 1.5 452 
Line 5 29,073 0.49 715 1.26 < 1.5 358 
Line 6 1,613 0.49 42 1.26 < 1.5 21 

aNTU = Number of Heat Transfer Unit.

Figure 17

Locations of HEs in the main sanitary sewer networks in Karbala city center.

Figure 17

Locations of HEs in the main sanitary sewer networks in Karbala city center.

Close modal

The physically based and statistical models were used to simulate HR form wastewater by some factors such as TA, TW, and WF. The obtained results revealed that the models were capable of estimating the influence of TA, TW, and WF on HR quantity. The study clearly showed that WF in Karbala, played a major role for HR. Conclusions can be made based on the results presented. A model has been developed in this research to estimate the performance of HR, which can be used for solving this major problem of heat consumptions in the cities across the world.

The results indicate that the models developed in the present study are capable of providing results which are in good agreement with the observed data. Therefore, the models can be used to simulate the HR from wastewater. A key requirement for integrated HR models is data to TW, TA, and WF, ideally including uncertainty estimates. In this model for the 70 days, the largest HR quantities form wastewater were from LINE4, it was 36,796 Mw, then LINE3 with amount 34,716 Mw, the third quantity of HR was 29,073 Mw from LINE5, then 23,756 and 10,066 Mw from LINE2 and LINE1 respectively, the lowest value of HR was 1,613 Mw from LINE6. However, the total amount of HR from wastewater in Karbala city center during the 70 days was 136,000 Mw.

HR from sewage is considered the most important source of renewable energy. Having proven to be a practicable and promising technology, it has been very successful and a very reliable and clean source of energy when proper management programs are followed. The associated harmful environmental, health, and social effects of traditional biomass, fossil fuel, and polluted other sources have enhanced the growing interest in the search for an alternate cleaner energy source globally. The major objective of this study is to develop a model to assess the impacts of WF, TW, and TA on the performance of HR. Sanitary sewer networks in the Karbala city of Iraq were chosen as a case study. SWMM, MLR, and SEM were used for this purpose. The model outputs were analyzed to assess the performance of HR in the context of changing WF, TW, and TA. The results showed that the total amount of HR from wastewater in Karbala city center during the 70 days was 136,000 Mw. The study clearly showed that WF in Karbala played a major role for HR. Basically, the heat from wastewater is CO2-free and represents a significant opportunity for the energy transition in the heating market.

The authors thank Institut für Energietechnik – Technische Universität Berlin for their support in preparing this study. They would like to thank Directorate of Sewerage of Karbala for providing data and University of Karbala/Engineering College for supports.

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

The authors declare there is no conflict.

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