Within this work, a detailed measurement with a temporal resolution of 3 s of flow rate and temperature of a house-central graywater system was carried out. Individual discharge events could be identified and assigned to specific types of use via user surveys and current measurements. Due to the consistent recording of measurement errors, the accuracy of the determined data could be improved. Error rates of approximately 0–30% were determined, depending on the tab. Thus, accurate statements on the existing temperature distribution for the graywater of specific tabs could be determined. Tab-specific temperature distributions were calculated with ranges of 16–50 °C and an overall mean value of approximately 28 °C. Furthermore, a novel database could be provided by evaluating the time-related rate of change of temperatures. This enables more precise simulations to be carried out. For some tabs, significant differences to previous assumptions became apparent. The high temporal resolution of the data also enables simulative considerations that go beyond previous longer-scale energy balances.

  • This work contains detailed measurements of gray water temperatures and flow rates.

  • The measurements were carried out with a very high temporal resolution.

  • Measurement data could be linked to individual usage events.

  • This provided deep insights into the dynamics and potential of heat recovery from gray water.

Due to increasing demands on the efficiency of domestic energy systems, there is a growing interest in the thermal utilization of wastewater and its sub-streams (Frijns et al. 2013; Elías-Maxil et al. 2014; Hao et al. 2019). There are already practically proven systems on the level of individual tabs, houses, or neighborhoods (Hepbasli et al. 2014; Sun et al. 2014). While only heat pump systems are used at the neighborhood level due to the low temperatures of mixed wastewater, there is the possibility of thermal heat recovery within the building using existing temperature gradients, which can reduce system complexity and energy consumption (Ni et al. 2012; McNabola & Shields 2013; Nolde 2013; Deng et al. 2016). In this case, a separate collection of gray and black water is essential to avoid the cooling of warm wastewater by mixing. A further benefit is the reduced load of organics and particulate matter and thus the easier utilization of separated graywater in terms of process engineering. In this field, system concepts have already been developed to market maturity at the tap and house level. Further targeted separation of hot and cold graywater streams could further increase the effective temperature gradients (Meggers & Leibundgut 2011; Nolde 2016). One fundamental problem of passive domestic central heat recovery systems is the temperature mixing in collection tanks, which prevents a more efficient countercurrent design and reduces achievable preheating temperatures. Nolde (2016), therefore, recommends the use of plate heat exchangers with low thermal inertia and combination to thermally stratified storage tanks, the dimensioning of which would require a database on the temperature dynamics of domestic graywater systems.

In parallel, the use of active system combinations (use of heat pump) is continuously studied and developed in an increasing number of publications (Hervás-Blasco et al. 2020; Hadengue et al. 2022). By Hadengue et al. (2022), an average electrical energy saving of 1.8 kWh/week was calculated for the combination of an air-source heat pump and active graywater heat recovery. For a closed-loop configuration for the sole supply of hot water, the coefficient of performance could even be improved by about 20% over the course of the year. There is also the possibility of integrating upstream passive heat recovery, which could further increase recovery efficiencies. However, no literature could be found on this topic. The probability of individual water uses over the course of the day was investigated by Sitzenfrei et al. (2017) and Wärff et al. (2020). Based on these findings, a statistical model was developed by these authors to calculate wastewater volume flows and temperatures in larger collecting systems.

Input for these calculations includes estimations on the mean temperature of different types of graywater and their statistical distribution. In Bertrand et al. (2017b), a compilation of tab-specific generation types of graywater, including their usual end-of-use temperatures, frequencies, and durations, is provided. The work states a lack of valid temperature measurement data. The data used originates from Yao & Steemers (2005) and Recknagel & Schramek (2007), which, however, only contain planning figures for hot water systems and therefore do not represent a valid measurement. As a source of values in Yao & Steemers (2005), a PhD thesis is cited, which could not be accessed (Marsch 1996). By Wong et al. (2010), heat losses within shower (SH) cabins were investigated and a correlation for heat losses based on their temperature was introduced. Here, an average drain temperature of 40.9 °C was measured but the drainage in the house system was not included. In Wärff et al. (2020), temperature values are derived from Sitzenfrei et al. (2017). However, in Sitzenfrei et al. (2017), a Bachelor thesis, which could not be accessed, is cited as the source of these values (Hillebrand 2014). Similarly, in Frijns et al. (2013), a research report, which also could not be accessed, is cited for the mentioned wastewater temperatures (SenterNovem 2006).

Some studies have already been carried out measuring the volumes and temperatures of graywater at a building level (Nolde 2013, 2016; Sievers et al. 2018). The median inhabitants (inhab)-specific daily volume flow of graywater is 67 L/(inhab*d) with a range of 19–108 L/(inhab*d) (Sievers et al. 2018). The temperatures measured showed a range of 10–50 °C with median values of 20–30 °C (Masi et al. 2007; Hernández Leal et al. 2010; Sievers et al. 2018). However, the data mentioned in the existing system are often conducted as supplementary measurements, so a detailed description of the measuring method is lacking, and measurement intervals are in the range of hours or days. No work could be found containing temperature monitoring data of graywater systems with high temporal resolution.

In view of the development of passive or active heat recovery within medium to larger buildings or smaller quarters, it is still unclear which temperature profiles of graywater can be expected depending on the number of occupants, the taps connected, and the piping system. Especially for thermal uses that are limited in their heat consumption (e.g. hot water preheating), the question arises of which taps should be optimally connected for specific use in order to create maximum graywater temperatures. However, for a realistic analysis, it is essential to represent the heat losses as well as the flow behavior in domestic drainage systems as accurately as practically possible. Despite the multitude of literature, there is no detailed analysis of heat losses of wastewater and graywater within domestic drainage systems.

Following this, there is also no research on the design implications of domestic graywater drain systems in the context of heat recovery. Especially for systems on the building level, this results in a large planning uncertainty. Within this work, the thermal behavior of graywater within domestic drainage systems is described in detail on the basis of a measurement campaign within a single-family house with separate graywater collection and discharge. The aim of this work is to provide a database for dynamics of temperatures and volume flows of individual discharge events within a single-family house with separate graywater collection and discharge in gravity flow. This includes especially a differentiated recording of the temperatures present in the graywater after discharge in the building and their temporal behavior. This work thus provides a novel database, which on the one hand can make existing simulation work more precise and on the other allows new simulative considerations. In particular, the time scale of control loops within systems for graywater heat recovery can be considered in a differentiated way for the first time, and more efficient system solutions can be developed.

The measurements were carried out in the period from 01 October 2021 to 02 November 2021 within a single-family house with two residents in Weimar, Germany. Within the two-story building, there are two bathrooms, each with a handwash basin (HW) and SH, a bathtub (BT) in the upper floor bathroom, and a washing machine (WM) in the lower floor bathroom. Furthermore, within the kitchen, there is a kitchen sink (KS) as well as a dishwasher (DW). The graywater is collected via two DN 60 PET pipes systems, which are both vented through the roof. In the design of the piping system, a separate collection of bathroom and kitchen graywater was provided. In the basement of the building, these are joined together, whereby a separate collection is possible via valves.

A measuring set-up for graywater volume flow and temperature was mounted in direct proximity to this graywater extraction point (Figure 1). It consists of a DN28 stainless steel pipe inclined by 10° in the direction of flow, which is connected to the graywater system via DN 30 PET pipes. The temperature measurement was also located within a DN 30 PET pipe. A permanently immersed PT100 temperature probe was installed in the inlet of the measuring pipe. It was connected to a Raspberry Pi as a data logger using the MAX31865 amplifier. The volume flow measurement was done via ultrasonic sensors made by Flexim, which are mounted on the pipe. The sensors (C(DL)Q1EZ7) were connected to the corresponding converter (FLUXUS F601). It transmitted the measured values and the associated diagnostic values to the Raspberry Pi for storage via RS232 protocol. With this configuration, measurement and storage of volume flow and temperature data were carried out every 3 s. The measurement data were stored on a cloud application at hourly intervals. The measurement campaign was followed by a consistency check of the volume flow measurement data. Measurement errors caused by interfering substances were identified and discarded on the basis of the associated diagnostic values (sound velocity and signal amplitude).
Figure 1

Schematic overview of temperature and flow rate measurement of the in-house graywater system.

Figure 1

Schematic overview of temperature and flow rate measurement of the in-house graywater system.

Close modal

All measurements are shown in the Supplementary material. Parallel to the measurement, user behavior was recorded using questionnaires, on which the users noted on which time and date an individual tab was used. The results of the questionnaires are also shown in the Supplementary material. For DWs (Bosch) and WMs (AEG), electricity consumption (Voltcraft Energy Logger 4000) was also measured on a long-term monitoring basis in order to ensure that the time of individual operating and emptying cycles was reliably recorded. The results are included in the Supplementary material. Discharge events could be identified by the comparably small current demand of the pump of each device.

Due to the large number of measured values, the data sets were evaluated using Rstudio IDE. The code used is also included in the Supplementary material. Figure 2 shows the algorithms schematically. The data were imported as a data frame and its data types (numeric and POSIXct) were defined. Existing measurement errors were identified using the instrument output and diagnostic values (signal amplitude). If the output of the FLUXUS F601 was an empty value or the signal amplitude was below 40, the individual data point was marked as a potential error. Then, an interpolated curve of the volumetric flow rate was calculated. This operation was chosen because of the high error rate of volumetric flow measurement in graywater so that individual valve discharges could not be detected completely without measurement errors. However, only interpolations between two flow rate values >0 were used in the evaluation of the individual peaks.
Figure 2

Schematic overview of the evaluation methodology.

Figure 2

Schematic overview of the evaluation methodology.

Close modal

By means of a function, a vector was generated, which contains a check for a discharge event based on a limiting volume flow of 0.5 L/min. Using this vector, subsets of individual contiguous discharge events were stored within a list. For a complete mapping of the events, a period of 15 s for and after a change of state of the above vector was included. For each subset, a statistical evaluation of the event was performed and stored within a data frame.

A manual assignment of the recorded usage according to the handout and electricity measurement was added to this data frame. If no match in questionnaires or current measurements could be found peaks were marked as unidentified peaks. For the BT, in addition to the actual use (drain bath water after use), smaller rinses with cold water were also recorded. This was excluded from the assignment of this event. The data frame shown with the assignment of each peak is included in the Supplementary material. Thus, each discharge event is available as a separate data frame with an assignment to the respective tab and can be evaluated individually and summarily. To determine the temporal behavior of these peaks, their temperature curve was modeled using functional data analysis functions and its derivative was calculated. To improve clarity, the rates of change were normalized to the maximum absolute temperature difference within a peak using the following formula:
(1)
where is the respective derivative of the temperature curve, is the maximum measured temperature of the respective peak, and is its minimum temperature.
An overview of the measured values is shown in Figure 3. Figure 3(a) shows the entirety of flow rate and temperature measurements. Temperatures from 20 to almost 50 °C and volume flows up to 40 L/min were measured here. With the exception of the 23.10, a significant number of daily discharge events were recorded. A typical diurnal flow can also be recognized here. Figure 3(b) shows the daily volume-weighted average graywater temperature and the daily resident-specific volume. Significant variability is evident for both parameters, which appear to be correlating. The temperature values fluctuate with 20–35 °C around a mean value of 25 °C. For the resident-specific volume flow, a mean value of 27 L/(inhab*d) was measured with extreme values of 1.2–116 L/(inhab*d). The measured values are thus consistent with previous studies, although significant fluctuations are evident (Zeeman et al. 2008; Sievers et al. 2014; DWA 2017; Sievers et al. 2018).
Figure 3

Overview of all flow rate and temperature measurements in time course (a) and overview of the daily mean values of temperature and resident-specific daily graywater flow rate in time course (b).

Figure 3

Overview of all flow rate and temperature measurements in time course (a) and overview of the daily mean values of temperature and resident-specific daily graywater flow rate in time course (b).

Close modal
Within these measurements, a large number of measurement errors, especially for larger discharge events, could be identified by evaluating the diagnostical parameters of the ultrasonic volumetric flow measurement. Their temporal distribution is shown in Figure 4. It becomes clear that measurement errors occurred in conjunction with larger discharge events. Probably the discharge of particles is the main source of error. In total, 8,728 discharges (Q > 0) and 3,252 measurement errors were recorded in 950,399 measurements during the study period. After approximation, this resulted in a number of 11,798 discharges (Q > 0) of which 11,728 were identified as discharge peaks (flow rate >0.5 L/min). From this, 731 separate discharge events were identified, of which only 696 fulfilled the criteria for usability (only interpolations between two flow rate values >0). This results in 1,481 measurement errors included in the 11,449 data points used in the following evaluation.
Figure 4

Overview of all flow rate measurements in time course divided by correct measurements (blue) and interpolated measurement errors (red).

Figure 4

Overview of all flow rate measurements in time course divided by correct measurements (blue) and interpolated measurement errors (red).

Close modal
An overview of the measurement errors included in the evaluation is provided in Figure 5. A significant number of errors were measured for the BT, WM, and UP. Regarding the error rate, the maximum is reached for BT discharge with a value of 58%. SH and WM showed error rates between 10 and 20%, whereas HW, KS, and DW error rates were below 5%.
Figure 5

Overview of interpolated measurement errors for each tab utilized in the following evaluations of temperature characteristics: (a) total number of error values and (b) error rate.

Figure 5

Overview of interpolated measurement errors for each tab utilized in the following evaluations of temperature characteristics: (a) total number of error values and (b) error rate.

Close modal

A consistent error analysis of the determined measured values could only be found in Sievers et al. (2018). However, due to the data acquisition via impulse output, no distinction can be made between zero values and measurement errors. In Alnahhal & Spremberg (2016), for example, temperatures were measured outside the drainage pipe and volume flows were only recorded on the drinking water side. Due to the small number of measurements published in peer-reviewed journals, some gray literature was used as a comparison. However, this literature lacks methodological descriptions of the measurement techniques used (Nolde 2016, 2013). In conclusion, it must be emphasized that volumetric flow measurement in untreated wastewater is susceptible to measurement errors and there is a need for differentiated measurement value processing and discussion with the aid of metadata.

Based on these measured values, individual discharge events were identified as described in the methods section and assigned to the respective taps/uses via the questionnaires and current measurement. A total of 696 discharge peaks were identified with the following distribution: BT: 4, DW: 146, HW: 287, KS: 108, SH: 14, UP: 61, and WM: 76. Their distribution over the studied period is shown in Figure 6. Here, a pronounced variance is evident especially for WM and BT, while HW, KS, and DW occur consistently with some exceptions. In total, 3–50 events per day were recorded with a mean value of 20.5.
Figure 6

Number of detected discharge events per day with assignment to tabs (BT, DW, HW, KS, SH, UP, and WM).

Figure 6

Number of detected discharge events per day with assignment to tabs (BT, DW, HW, KS, SH, UP, and WM).

Close modal

In this evaluation, an under-sampling of larger discharge events (especially SH and BT) is to be assumed, caused by the increasing proportions of measurement errors along with the discharge volumes. These figures refer to the quantifiable discharge events and thus allow a valid statement to be made on the flow rate and temperature curves of various tabs, but not on their frequencies. Furthermore, DW and WM, depending on the type of device and program, show coherent peak series for each use, which are included here as individual events. For this reason and the relatively low number of users, a comparison with existing literature data on usage frequencies (Bertrand et al. 2017a, b; Sitzenfrei et al. 2017; Wärff et al. 2020) is not suitable. However, there appears to be an overall lower frequency of use of these devices.

A summary analysis of the tab-specific measurement series is given in Figure 7. Expected differences regarding volume and discharge duration of the respective valves are recognizable. For smaller discharge events (DW, HW, KS, and WM), individual outliers of duration and volume are apparent, which can be attributed to measurement errors. It can be assumed that several discharge events were combined due to errors in the volume flow measurement and the subsequent interpolation. For smaller discharge events a largely error-free measurement was achieved. For DW, HW, and KS, almost no measurement errors were present. For discharge events from SH and WM, measurement errors occur in some cases, although a large proportion of the events do not show any measurement errors here either. A significant source of error was found for the BT discharge. Here, a median of 117 measurement errors was found for the delimited number of events (n = 4).
Figure 7

Boxplot of volume (a), duration (b), and number of measurement errors (c) of the identified peaks with assignment to tabs (BT, DW, HW, KS, SH, UP, and WM) (n, number of peaks; Mn, median).

Figure 7

Boxplot of volume (a), duration (b), and number of measurement errors (c) of the identified peaks with assignment to tabs (BT, DW, HW, KS, SH, UP, and WM) (n, number of peaks; Mn, median).

Close modal

Compared with the statistics on wastewater generation used by Wärff et al. (2020), the total duration of some discharge events and thus also the volumes were determined to be lower. For SHs, for example, mean durations of 576 s with 12 L/min and thus a volume of 115 L were applied in this source. Thus, a more economical usage behavior (lower SH duration) as well as a more economical SH head (6–8 L/min) was found in this study. The determined duration is in greater agreement with other authors (Bertrand et al. 2017b). However, the determined BT data are nearly identical to those in Wärff et al. (2020) (duration 444 s; flow rate 10.5 L/min). A comparison of the WM and DW data is not possible due to more variable representations (individual peaks vs. total volume per cycle). Basically, the determined values seem to be within the range of variation possible for single-family buildings.

An analysis of tab-specific temperature profiles is shown in Figure 8. The volume-weighted temperature portions are shown here as cumulative curves. In addition, the overall volume-weighted temperature distribution of the measurement campaign is shown. Temperatures of 16–50 °C with a median of about 28 °C were measured. Temperatures above 38 °C, however, were only present in very small proportions. In the temperature range 20–38 °C an almost linear increase of the total sum curve can be observed. The cumulative curves of the respective tabs are characterized by individual patterns. The BT discharges show a very narrow temperature distribution in the range of approximately 38 °C, with a very small proportion of colder temperatures. For SH as a similar usage type, a deviating behavior is present with larger cold water shares (25%: 20–30 °C) and more variable higher temperatures (10%: 32–42 °C). The DW tab shows a quasi-linear distribution of temperatures from 20 to 40 °C, which can be explained by increasing rinse water temperatures within a program run. Deviating from this, the WM peaks show a large temperature share in the range of 28–30 °C and only 25% of the volume shows higher temperatures. KS and HW show similar curves, with a slightly higher temperature level for KS. In sum, the importance of graywater temperature profiles for the efficiency of downstream recovery steps becomes apparent. Furthermore, it becomes evident that a clear division into hot and cold graywater based on individual taps is only possible to a limited extent. Thus, an efficient temperature separation is only possible on a temporal level.
Figure 8

Sum curves of the measured graywater temperatures related to the respective tabs (BT, DW, HW, KS, SH, UP, and WM).

Figure 8

Sum curves of the measured graywater temperatures related to the respective tabs (BT, DW, HW, KS, SH, UP, and WM).

Close modal

Compared with the measured values in Nolde (2013), similar progressions of the cumulative curve can be seen. Here, the median is 32 °C with a temperature range of 24–43 °C. A multi-family building was investigated where only the graywater from the BT and SHs of 56 residential units was connected to the separated system. Furthermore, a fluctuation of the median of approximately 2 °C in the course of the year was determined here. In the winter months, the proportion of colder temperatures was higher, while higher temperatures were present in equal proportions. The exact reason for this fluctuation (lower cold water temperature, heat losses in the piping system or exhaust air) cannot be defined on the basis of these investigations. In Knerr et al. (2009) with a range of 15–43 °C and in Menger-Krug et al. (2010) with a mean value of 30 °C an identical fluctuation range of the graywater temperatures are also determined. More significant differences exist in simulation input data. In Hadengue et al. (2022), the following mean values were assumed: SH: 36 °C, KS: 35 °C, HW: 35 °C, WM: 37 °C. Especially the temperatures of smaller tabs are strongly overestimated. The same can be seen for the drain temperature assumptions in Hervás-Blasco et al. (2020) (SH: 33 °C, BT: 33 °C, HW: 31 °C, WM: 30 °C, KS: 38 °C, DW: 46 °C) and other authors (Bertrand et al. 2017a; Wärff et al. 2020).

Regarding the causes of the temperature profiles of graywater two basic processes can be distinguished (if a mixture of different discharge events is neglected):

  • Individual discharge events show variable discharge temperatures due to user- and device-specific influences (especially HW, KS, DW, and WM).

  • Instationary temperature losses cause an initial rise of graywater temperatures toward a quasi-stationary plateau (especially SH, and BT).

In practice, there is an overlapping of both processes within all discharge events. In addition, the observed behavior is practically influenced by the thermal inertia of the respective temperature probe and the hydraulic volume of any siphons it is placed in. Within these measurements, these effects were reduced as far as possible.

With regard to the dimensioning of technical systems for temperature-sensitive graywater heat recovery (temperature-controlled separation/layering and fast heat exchange), the question of the necessary reaction time of these systems arises. For single-family buildings or smaller numbers of connected systems, the thermal delay of temperature peaks defines the significant reaction time. Figure 9 shows the rates of change of graywater temperatures over the duration of individual discharge events. The rates of change were normalized to the maximum temperature difference within an event, whereby the maximum temperature of an event was indicated by the color of the measurement series. A similar pattern can be observed for HW, KS, DW, and WM, where a maximum rate of change occurs with a delay of about 25 s and significant temperature changes are completed after about 50 s. Here, both temperature increases and decreases are present, depending on the discharge temperature of the graywater and the initial condition of the piping system. Due to the diversity of discharge events, there is a large scatter of the rates of change with values of about −0.06–0.06 K/(K*s). There is no clear temperature dependence of the relative rate of change. For SH and BT, a more uniform pattern is seen, with temperature decreases being the exception. For BT discharges, a shorter lag of the temperature rise is present with maximum rates of change after about 15 s and a plateau formation after 30 s. For the SH tab, the most prolonged course of temperature change was measured. Here, maxima of the rate of change are in the period of 30–50 s and a plateau formation is reached only after approximately 100 s. It is assumed that this additional inertia is caused by the initial heating of the SH body in addition to the graywater pipe system. Initial temperature decreases, presumably caused by rinsing the SH with cold water, can also be observed here.
Figure 9

Time course of the relative rate of change of graywater temperatures during discharge events as related to the respective tabs (BT, DW, HW, KS, SH, UP, and WM).

Figure 9

Time course of the relative rate of change of graywater temperatures during discharge events as related to the respective tabs (BT, DW, HW, KS, SH, UP, and WM).

Close modal

Within this work, a detailed measurement of flow rate and temperature of a building-central graywater system was carried out. Individual discharge events could be identified and assigned to specific types of use. Due to the consistent recording of measurement errors, the accuracy of the determined data could be improved. Thus, accurate statements on the existing temperature distribution for the graywater of specific tabs could be determined. Furthermore, evaluating the time-related rate of change in temperatures could provide a novel data basis. This enables more precise simulations to be carried out. For some tabs, significant differences to previous assumptions became apparent. The high temporal resolution of the data also enables simulative considerations that go beyond previous longer-scale energy balances. Especially the separation of graywater based on its temperature prior to heat recovery should be investigated in more detail using this data.

The validity of this data is limited by the small statistical coverage due to the necessary restriction to one residential object in Germany. A transfer to multi-family buildings, neighborhood solutions and cultures with significantly different water use is not applicable. Further limitations arise from experienced measurement errors of graywater flow rates, which require careful consideration of their validity.

In conclusion, a subsequent extension of the data basis is recommended. Here, a more specific investigation of the influence of the respective object and the construction of its drainage systems should be carried out. In view of possible efficiency increases, the investigation of heat losses in the piping system should be a core aspect. In addition, there is the question of the optimum linkage size, with increasing numbers of connections also leading to increasing exergy losses due to dilution and energy losses due to longer pipes. On the other hand, specific investment costs and maintenance costs are decreasing. This question requires combined investigations at the neighborhood and building level. Therefore, more detailed measurements in multi-family buildings are recommended. For this, an automated identification of individual tabs seems necessary assuming an increasing error rate of inhabitant questionnaires and simultaneous discharge events.

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

The authors declare there is no conflict.

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