Energy & Buildings 211 (2020) 109803 Contents lists available at ScienceDirect Energy & Buildings journal homepage: www.elsevier.com/locate/enbuild Waste heat and renewable energy integration in buildings Christopher Reddick a,∗, Mikhail Sorin a, Jean-Christophe Bonhivers a, Dominic Laperle b a b Department of Mechanical Engineering, Université de Sherbrooke, 2500 boul. de l’Université, Sherbrooke, Québec J1K 2R1, Canada Intégration Construction Inc., 147, rue Cynthia, Saint-Alphonse-de-Granby, Québec J0E 2A0, Canada a r t i c l e i n f o Article history: Received 18 June 2019 Revised 20 November 2019 Accepted 18 January 2020 Available online 20 January 2020 Keywords: Buildings Solar Heat pump Greywater Waste heat Pinch analysis Integration a b s t r a c t Buildings consume roughly a quarter of the annual global energy supply. Pinch analysis has been successfully applied to industrial processes, and more recently to locally integrated energy sectors. Pinch analysis minimizes the amount of energy that must be supplied to a process to achieve the desired outcome: products in the case of industries; occupant comfort and domestic hot water use in the case of buildings. For the first time pinch analysis is applied in an all-inclusive way to an individual building, integrating waste heat (e.g. greywater) and renewable energy (e.g. solar). A methodological novelty is added to the pinch analysis method to include both continuous and time dependent thermal sources and sinks. The usual hot stream to cold stream heat transfer is replaced as follows: hot stream reserve; hot stream to cold stream heat transfer; cold stream reserve. For a test building, the pinch temperature changes with time: 27.5 °C from October to May, 47.5 °C from June to September. The pinch temperature and its relationship to solar heating and heat pumping are discussed. Innovative design solutions and economic analyses are presented. Depending on the chosen design solution, primary energy (i.e. electricity) consumption can be reduced by 50%. © 2020 Elsevier B.V. All rights reserved. 1. Introduction Energy resources are finite, and the current high level of carbon dioxide emissions due to fossil fuel combustion are unsustainable. Thus, research interest grows in improving energy efficiency, while simultaneously increasing the portion of renewable energy in the energy supply. Many forms of renewable energy (e.g. solar, wind) are by nature time dependent, thus requiring the development of compact and affordable forms of energy storage. Thermal energy storage is advantageous because a significant share of global energy consumption is associated with heating and cooling, largely in buildings. Thermal energy such as waste heat, either readily available or stored, is often not at the appropriate temperature level. Thermal sources that are too hot can be adapted to process requirements through heat exchangers or mixing; sources that are too cold can be upgraded through heat pumping. Since the 1970s, energy intensive process industries have developed various methods of heat integration, improving energy efficiency and reducing the need to reject excess heat to the environment. In particular, Linnhoff and Flower introduced pinch analysis to design energy efficient heat exchanger networks [1,2]. Klemeš and Kravanja [3] wrote an excellent historical perspective ∗ Corresponding author. E-mail address: j.christopher.reddick@usherbrooke.ca (C. Reddick). https://doi.org/10.1016/j.enbuild.2020.109803 0378-7788/© 2020 Elsevier B.V. All rights reserved. on pinch analysis in the context of heat integration, and Smith [4] and Kemp [5] provide reliable reference textbooks. Importantly, Linnhoff and Hindmarsh clarified the concept of pinch temperature and its importance in minimizing the external heat that must be supplied to the process at the hot utility [6]. The pinch temperature, generally simplified to the “pinch” or “pinch point”, divides a given process into two temperature regions: a heat-poor region above the pinch (where external heat must be added at the hot utility), and a heat-rich region below the pinch (where excess heat is removed at the cold utility). Recent examples of pinch analysis to industrial applications that include renewables are a brewery (solar, thermal storage) [7] and a dairy processing plant (waste heat, solar, thermal storage, heat pumping) [8]. District heating can be traced back to the 14th century [9]. District heating began as an urban infrastructure strategy to provide multiple buildings with heat from a separate heating facility. From 1880 to the 1930s, steam was the principal thermal transport fluid [10]. Two of the early justifications for district heating in populated urban areas were the desire to avoid boiler explosions [9] and to remove fuel combustion from residential buildings [10]. District heating is common in some countries, such as Iceland, Russia, Sweden, and Denmark [10], and recently includes cooling. Recent and future versions of district heating and cooling aim to integrate a greater portion of renewables into the energy supply, and to better match the time of energy production with the time of use by incorporating thermal energy storage [10]. 2 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Nomenclature Cp CP m˙ Q˙ T Tcity W specific heat capacity (MJ/°C / Mg) heat capacity rate (MJ/ °C /time) mass flow rate (Mg/day) heat flow rate (GJ/yr.) or (GJ/time) temperature city water inlet temperature Work or power (GJ/yr.) Greek TMIN Minimum allowable temperature difference (°C) Subscripts EV Evaporator HP Heat pump Sol Referring the base case with solar input Acronyms ACS Air Conditioning, Summer AUX Electric auxiliary heating CGW Cold Greywater DHW Domestic Hot Water GDW Ground Water HFH Hydronic Floor Heating HPS Heat Pump System MGW Mixed Greywater minHD minimum Heating Duty, or hot utility minCD minimum Cooling Duty, or cold utility TSC Thermal Solar Collectors WGW Warm Greywater A significant portion of energy consumption occurs in the low to medium temperature range (i.e. up to 250 °C), and there is much recent research that applies thermal solar energy to fill this need [11]. Thermal solar collectors typically fall into the category of flat plate, evacuated tube, or concentrating [11]. Architects try to better incorporate photovoltaic and thermal solar collectors into their designs, and both kinds of solar collectors can be combined into a single component as part of the building envelope [12]. Heat pumping is not only becoming widespread in residential HVAC systems, but is increasingly applied in industrial thermal systems. Linnhoff and Townsend presented a theoretical foundation, within the framework of pinch analysis, for the ideal placement of a heat pump in a thermal process [13,14]. The most significant energy improvements occur when the heat pump is placed across the pinch point, upgrading heat from the heat-rich temperature region of a process (below the pinch) to the heat-poor part (above the pinch). Wallerand et al. presented a novel heat pump synthesis method using a superstructure-based approach, with the goal of providing an optimal design for industrial heat pump and refrigeration systems [15]. Stampfli et al. studied industrial heat pump integration in non-continuous processes, where thermal energy storage is part of the solution [16,17]. The combination of solar thermal energy and heat pumping offers many energy efficiency possibilities. Vega and Cuevas simulated a combined solar and heat pump system for a residential building in Chile [18]. Two air source heat pumps are placed in parallel with thermal solar collectors, with the heat pumps providing the second step of the thermal process. One solarcollector/heat-pump pair is the heat source to a hydronic floor heating circuit, while the other supplies the domestic hot water heating circuit. Razavi et al. simulated a solar assisted ground source heat pump residence, supplying both the building heating load and the domestic hot water requirements [19]. Neither of these references referred to pinch analysis. Waste heat upgrading is an underutilised energy resource. Waste water, in particular, can be utilised in combination with heat pumping to extract useful heat from waste water treatment plants, or from building effluent streams [20]. Mazhar et al. presented a recent review of non-industrial greywater heat harvesting, discussing the role of both heat exchangers and heat pumping for this purpose [21]. Manouchehri and Collins studied fallings film drain water heat recovery systems, which some homeowners install to preheat domestic hot water with exiting warm greywater [22]. Bertrand et al. evaluated the city-wide, or urban-scale in-building potential of waste water heat recovery. For passive single-family residences, electricity savings were 28%, while they reached 41% for multi-family buildings. I.C.Kemp applied the pinch method to a non process industry example, presenting a heat integration study for a hospital site [23]. The hospital site case was also noteworthy because of the time dependent analysis, although heat pumping was not considered [5]. Perry et al. discussed, in the context of district heating, locally integrated energy sectors [24]. Liew et al. provided a review of the application of the pinch method to total site heat integration, for the purpose of planning and design of industrial, urban and renewable systems [25]. Misevičiūė et al. reported on the application of the pinch method to a shopping centre, focusing on the air heating required for the ventilation system [26]. In this study, pinch analysis is applied to a multi-family residential building equipped with thermal solar collectors. To the best of our knowledge, this is the first all-inclusive application of pinch analysis to a building, where all potential sinks and sources are considered. The linking of the thermal demands of the building (occupant thermal comfort and domestic hot water use) to potential sources is original. For the test building, the potential thermal sources are ground water, cold greywater, energy removed from the building air in the summer by air conditioning, warm greywater and thermal solar collector fluid. The thermal sinks are hydronic floor heating and domestic hot water. A novel modification is made to the pinch analysis method to facilitate the inclusion of both continuous and time dependent thermal sources and sinks. By analogy with industrial processes, the thermal content of streams that cross the building envelop (e.g. water) are considered as possible waste heat sources. Using pinch analysis hot and cold composite curves, a graphical interpretation will explain the limitations and potential of heat pumping for a building. A strategy is then discussed for selecting design solutions for the building’s thermal system that approach the pinch analysis minimal energy target. Finally, economic analyses are completed and the energy efficiency solutions are compared. 2. Methods The problem statement in Section 2.1 provides the overall focus for the article, followed by descriptions of the test building (Section 2.2), the TRYNSYS thermal modelling (Section 2.3), and the domestic water model (Section 2.4). Section 2.5 will explain how the thermal demands of the building are linked to potential heat sources, thus allowing the pinch analysis method to be applied to a building in a robust and all-inclusive manner. 2.1. Problem statement Given a building that includes thermal solar collectors, domestic hot water production, hydronic floor heating, and summer air conditioning, how can the amount of primary energy (i.e. electricity) consumption be minimized while simultaneously maintaining occupant thermal comfort and supplying sufficient domestic hot C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 3 Table 1 Selected characteristics of the test building and the thermal solar collectors. Parameter description Value Units Value Units Foundation area Outside wall area Fenestration portion of wall area Inclined roof area, one of two sides Habitable floor area Habitable volume Window thermal resistance: R-SI and R-value Wall thermal resistance: R-SI and R-value Air infiltration: Q4PaSurf Air changes per hour (ACH) Total thermal solar collector area Reference solar collector efficiency 172 356 0.15 145 308 882 0.7 4.9 1.7 0.6 17.3 75 m2 m2 1850 3830 ft2 ft2 m2 m2 m3 °C∗ m2 /W °C∗ m2 /W m3 /h/m2 1/h m2 % 1560 3315 31493 4.2 28.0 9.5 ft2 ft2 ft3 ˚F∗ m2 ∗ h/BTU ˚F∗ m2 ∗ h/BTU ft3 /h/ft2 186 ft2 water, all at a reasonable cost? Auxiliary electric heating is available as a backup heat supply for both the domestic hot water and the building heating systems. The study of potential energy improvements should consider possible thermal contributions from available groundwater, greywater, etc., and evaluate the use of heat pumping and heat storage. Any proposed solutions must be respectful of their environmental impact. 2.2. The test building The test building is a multi-family residential concrete structure, housing 17 people, located in a rural environment, near Granby, Quebec, Canada. The building measures 11.3 m x 15.2 m (37 x 50 ), with the foundation and central roof ridge on the longer dimension, aligned along an East/West axis. There are six thermal solar collectors incorporated into the south-facing roof section, where the angle between each collector’s normal and the normal to the ground is 40˚. There are three habitable stories in the building, with the lowest being partially below grade. The building is heated by means of hydronic circuits running through concrete floor slabs, with each story having multiple temperature control zones. The hot water in the hydronic circuit can be heated with electric resistance heating. An independent system is available for the thermal solar collectors, where a mixture of propylene glycol and water circulates through the collectors and is separated from the hydronic system by a plate heat exchanger. The domestic hot water is heated by electric resistance heating. The domestic hot water can also be preheated, through a heat exchanger, by solar energy. The circulating glycol-water mixture leaves the thermal solar collectors at 50 °C. In the summer, the windows are generally left open, but an independent air conditioning system is available for hot and humid periods. It is important to note that the province of Quebec, Canada, benefits from a cost of electricity that is among the lowest in the world, around 0.075 CAD/kWh. This fact explains the widespread use of electricity for space heating and domestic hot water production in Quebec. This fact will also strongly influence the financial viability of various solutions, to be discussed in Sections 3.7 and 3.8. 2.3. Thermal modelling of the test building The test building is modelled with TRNSYS, which is a transient simulation program commonly used in building energy management projects. Given the building’s geographical location and orientation, a databank of local meteorological historical data, as well as the thermal characteristics of the building, TRNSYS calculates the required heating and cooling loads. Table 1 presents a selected portion of the input parameters for the simulations. 2.4. Domestic water model Every day the 17 occupants of the test building are assumed to use 380 litres per person, including 110 litres per person for domestic hot water (DHW). Although these values may be high compared to international standards, they represent the current situation in Quebec where electricity and city water are both inexpensive. The domestic water balance is shown in Fig. 1. To Fig. 1. Mass and energy balance of the domestic hot water system: DHW, WGW, CGW. 4 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Table 2 Monthly city water temperature and greywater flow rates. Parameter (units) Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec. Tcity (°C) WGW (m3 /day) CGW (m3 /day) 5 2.76 2.34 5 2.76 2.34 5 2.76 2.34 8 3.29 1.81 9 3.46 1.64 10 3.63 1.47 10 3.63 1.47 8 3.29 1.81 8 3.29 1.81 8 3.29 1.81 7 3.11 1.99 6 2.94 2.16 Fig. 2. Potential energy sources for the test building thermal demands. represent heat losses within this model, it is assumed that 15% of the energy required to heat the city water to the hot water tank temperature of 55 °C is lost to the environment. The temperature of the incoming city water follows the monthly profile indicated in Table 2. It is assumed that if appropriate plumbing modifications are made, according to the scenario, then the warm greywater (WGW) leaves at 30 °C and cold greywater (CGW) at 10 °C, with the flow rates shown in Table 2. In any scenario where the greywater is not separated, the mixed greywater (MGW) stream is simply the combined flow rates of the non separated greywater streams. 3. Results This section presents the results of applying pinch analysis, with appropriate assumptions, to the actual test building and related streams, starting with data extraction in Section 3.1. Quantifying the minimum heat duty through the construction of composite curves is evaluated for two situations: without heat pumping in Section 3.2, and with heat pumping in Section 3.3. Section 3.4 presents a modified grid diagram for possible design solutions, with Section 3.5 focusing on a reduced subset of chosen design scenarios. Sections 3.6–3.8 will provide economic analyses of the solutions chosen from Section 3.5. 2.5. Pinch analysis within a building 3.1. Data extraction results Fig. 2 illustrates a conceptual image of how the problem statement will be addressed. In the upper portion of the diagram are the thermal demands that must be satisfied for the test building: occupant thermal comfort and domestic hot water use. The lower portion of the diagram indicates the possible thermal sources that are considered in this study: ground water, greywater, summer air conditioning (AC) and thermal solar collectors. Notice that Fig. 2 is time independent, as we wish to consider both continuous and intermittent sources and sinks. Other applications might consider additional potential thermal sources, for example, sewage water, or wind energy converted to heat, or other possible thermal sources in proximity to the building. Depending on the temperature levels of the source and the demand, heat transfer could be through a heat exchanger combined or not with energy storage, or possibly by means of a heat pump, after upgrading the source to the appropriate temperature level. As will be detailed in Section 3.1, each of the considered sources will be associated with a stream flow, requiring an appropriate assumption for the stream’s fluid properties: mass flow, specific heat capacity, inlet temperature and outlet temperature. Notice that the auxiliary utility, electricity, is not explicitly shown in Fig. 2, as the overall objective is to maximize the use of the potential thermal sources before resorting to the backup energy supply. The pinch method data extraction step involves identifying the streams that lose heat as they pass through a process, called the “hot streams”, and those that gain heat, called the “cold streams”. Equivalently, the hot streams are heat sources, while the cold streams are heat sinks. In the application of the pinch method to a building, it may be helpful to think in terms of linking potential sources and sinks (the demands). In this preliminary step, it is important that streams be identified before any mixing occurs. This will highlight energy improvement possibilities. Each source and sink must have an associated known or assumed inlet temperature and outlet temperature. Fig. 3 illustrates how the general concept of Fig. 2 was applied to the test building, showing for each stream the inlet and outlet temperatures, and the annual results from the data extraction. It is assumed in this article, based on temperature observations of the test house installation, that the minimum allowable temperature difference (TMIN ) between any two streams transferring heat is 5 °C. In general, a larger TMIN value, such as 10 °C, would be expected to decrease the potential for energy savings, yet also decrease the size and associated cost of heat exchangers. In order to simplify the presentation of the article, the economic optimization of TMIN will not be considered here. C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 5 Fig. 3. Annual sources and sinks, without heat pumping. The hydronic floor heating, shown in the upper left rectangle of Fig. 3, assumes that the water in the circuit enters the concrete slab at a temperature of 35 °C and exits at 30 °C. This temperature range is based on characteristics of the test house hydronic system. The water that exits the concrete floor slab must be reheated to 35 °C before returning to the slab, explaining the annotation of “30 → 35 °C”. The calculation of the value 103 GJ will be explained shortly. For the domestic hot water, indicated in the upper right of Fig. 3, the temperature annotation is “~5 → 55 °C”. This indicates that the city water entering the building, close to 5 °C, must be heated to the chosen set point temperature of 55 °C. Both the hydronic floor heating and the domestic hot water are heat sinks in relation to the potential sources shown in the lower half of Fig. 3. The arrows in the diagram show possible heat transfer paths. For example, the hydronic floor heating can in part be heated by the thermal solar collectors, but not by any of the other listed sources, while respecting TMIN = 5 °C. In this study a simplifying assumption is made: water streams return to the environment at the same temperature as that of the entering city water (Table 2). It is also assumed that 1 m3 /day of ground water is available and in close proximity to the building. The assumptions related to the water temperatures are thus shown in Fig. 3, with the direction of the arrows (→) emphasizing that these streams are potential thermal sources: Ground Water (10 → ~5 °C), Cold Greywater (10 → ~5 °C), and Warm Greywater (30 →~5 °C). The thermal energy associated with the summer air conditioning is shown with the annotation 30 → ~20 °C. This simplified approach is conservative. If the electricity for this transfer is required, it will be less than the calculated value, for a cooling COP greater than one. If we are interested in using this energy as a source, it will be at least this amount, as the heat rejected at the condenser outside the building is greater than this amount. The rectangle in the lower right hand corner of Fig. 3 refers to the stream of the glycol-water mixture arriving from and returning to the thermal solar collectors (50 → 40 °C). Eq. (1) shows the basic energy balance for each stream, where the product m˙ C p is typically called the heat capacity rate, or heat capacity flow rate, symbolized by CP. A sample calculation follows for the warm greywater for the month of January. The result of 9.0 GJ can be found in Table 4 on the row identified as WGW, under the January column. A very similar calculation was completed for the other water streams (Table 4) for each month of the year: DHW, CGW and GDW. The sum of each row, for the annual value, is shown in Table 3. Table 3 Annual data extraction and pinch analysis results. Description Acronym Annual (GJ/yr.) Hydronic floor heating Domestic hot water Thermal solar collectors Warm greywater Air conditioning, summer Cold greywater Ground water minimum Heating Duty minimum Cold Duty HFH DHW TSC WGW ACS CGW GDW minHD minCD 103.4 138.2 80.3 109.1 5.2 8.3 3.9 120.3 85.6 Q˙ = m˙ C p T Q˙ WGW =  2.76 (1) Mg day  4.19 MJ Mg ·◦ C   1 ( (30 − 5 ) ◦C )(31 days ) GJ 10 0 0 MJ  Q˙ WGW = 9.0 GJ (January ) The heating (HFH) and cooling loads (ACS) required to assure occupant thermal comfort, as well as the thermal solar input (TSC), were completed for each month; the results are shown in Table 4. The annual thermal values for each of the sources and sinks are shown in both Table 3, and in the associated rectangles of Fig. 3. The bottom two rows in Tables 3 and 4 indicate the minimum heating duty (minHD) that must be supplied to the test building by the auxiliary heating system, and the minimum amount of heat (minCD) that must be rejected to the environment. The values minHD and minCD are habitually part to the “targeting” results, but are tabulated here for convenience. Further details on how the pinch method is applied in industry, including the construction of the “Problem Table”, are available in textbooks on this subject [4,5]. Sections 3.2 to 3.5 will concentrate on how the pinch method can be applied to a building. 3.2. Targeting results without heat pumping Fig. 4 presents a graphical representation of the pinch analysis in the form of composite curves, here for January, showing the relationship between the indicated sources and sinks of the test building. The dashed upper curve in the figure shows the combined or “composite” effect of the hot streams, as heat cascades 6 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Table 4 Monthly data extraction and pinch analysis results. Acronym (units) Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec. HFH (GJ) DHW (GJ) TSC (GJ) WGW (GJ) ACS (GJ) CGW (GJ) GDW (GJ) minHD (GJ) minCD (GJ) 18.9 12.3 4.2 9.0 0.0 1.5 0.6 22.1 6.2 16.4 11.1 4.5 8.1 0.0 1.4 0.6 18.6 5.6 14.3 12.3 6.6 9.0 0.0 1.5 0.6 15.1 6.2 9.9 11.2 7.8 9.1 0.0 0.5 0.3 9.3 5.7 4.9 11.4 8.9 9.4 0.0 0.2 0.1 3.4 5.8 2.4 10.7 9.0 9.1 0.0 0.0 0.0 2.4 7.4 0.0 11.1 9.5 9.4 3.0 0.0 0.0 2.5 13.3 0.0 11.6 8.4 9.4 2.2 0.5 0.3 2.5 11.6 2.0 11.2 7.0 9.1 0.0 0.5 0.3 2.4 6.0 7.4 11.6 6.1 9.4 0.0 0.5 0.3 8.7 5.9 11.0 11.5 4.4 9.0 0.0 0.8 0.4 13.8 5.8 16.2 12.1 3.9 9.2 0.0 1.1 0.5 19.7 6.1 Fig. 4. Hot and cold composite curves for January. from higher temperatures down to the environmental reference temperature of the January city water temperature of 5 °C. This hot composite curve is conceptually tied to the environment, with the heat load (enthalpy) of zero associated with the lower left extremity of the curve. The cold composite curve could be translated (shifted) to the right, but the actual position is determined by our chosen TMIN of 5 °C. The region between the two composite curves that has the shortest vertical distance, or temperature difference TMIN , characterizes the pinch point. In Fig. 4 the pinch is noted as 27.5 °C. The corresponding point on the hot composite curve is at 30 °C, the “hot pinch”, while the cold composite curve pinch temperature is 25 °C, the “cold pinch”. Any horizontal portion of the cold composite curve can be potentially supplied by the available hot sources that are directly above on the hot composite curve. The minimum heating duty that must be supplied by the auxiliary electric heating system, generally called the hot utility, is 22.1 GJ. This is the same value that is found in Table 4, in the row “minHD”. For a building, the target value, or minimum heating duty, indicates that an optimally designed energy system could achieve this low energy consumption, but it remains to be determined how the target can be economically implemented. Fig. 5 shows the monthly composite curves for one full year. An important observation is that for the test building, the pinch temperature changes with time: 27.5 °C from October to May, 47.5 °C from June to September. In the context of energy systems for buildings, the change in the pinch point as a function of the season and the weather has a significant effect on finding the most efficient energy design solution. Recall that the pinch point has importance for both the optimal matching of sources and sinks, as well as the optimal use of heat pumping, to be discussed in Section 3.3. For the efficient use of the thermal solar collectors, the solar collector system should be designed so as to always provide heat at a temperature above the pinch temperature. This feature could be retrofit in the current test building, or incorporated into possible future designs. One possible implementation of this principle would be to adjust the flow rate of the glycol-water mixture on a seasonal or monthly basis. For the purpose of producing an annual targeting analysis, we define the time averaged city water temperature (Table 2), which is 7.4 °C. Fig. 6, showing a minimum heating duty of 110 GJ/.yr, is the construction based on the annual results, taken from Table 3. The reference scenario consists of the sum of the energy requirements for the hydronic floor heating, domestic hot water, and the air conditioning during the summer months. This reference amount assumes that full use is made of the available thermal solar collectors. For example, the annual energy needs are 166.5 GJ/yr. (HFH + DHW + ACS – TSC = 103.4 + 138.2 + 5.2 – 80.3). Thus, the annual energy requirements for the building heating and domestic hot water have fallen from 166.5 GJ/yr. to potentially 110 GJ/yr., which is a reduction of 33%. If a comparison is made with the house without the solar input, where the thermal requirements are 246.8 GJ/yr., then a drop to 110 GJ/yr. represents a decrease of 55%. This significant reduction is due to the combination of the separation of greywater into warm and cold greywaters, as well as the input of energy from the solar thermal collectors. The sum of the monthly minimum heating duties in Table 3 is 120.3 GJ/yr., whereas the annual minimum heating duty, shown in the annual composite curve construction of Fig. 6 is 110 GJ/yr. In the context of the pinch method for batch processes, the monthly approach in Table 3 is an application of the time slice model (TSM), whereas the annual construction in Fig. 6 is an application of the time-average model (TAM) [23]. The value from Fig. 6 is slightly smaller because it implies that sources and sinks are available at the same time throughout the year. In other words, implicit in the C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 7 Fig. 5. Monthly hot and cold composite curves showing the changing pinch point with time. Fig. 6 construction is the idea that perfect seasonal storage was used to maintain constant sources and sinks. For the purpose of understanding the role of heat pumping in pinch analysis for buildings, the annual perspective will be maintained for Section 3.3. 3.3. Targeting results with heat pumping In order to limit the range of possibilities for heat pump selection for the test building, certain parameters will be fixed. It is assumed that the heating mode COP is 3.0, and that the hottest water temperature that the condenser can provide is 40 °C. This temperature accounts for the minimum allowable temperature difference (TMIN ) of 5°C. Fig. 7 connects the possible sources and sinks when heat pumping is included. In contrast with Fig. 3, the heat pump system potentially allows any of the considered thermal sources to be used. Given the heat pump characteristics considered for the test building, the hydronic circuit can be heated to 35 °C, and the domestic hot water can be preheated to 40 °C. The solar thermal collectors can further preheat the domestic hot water up to 45 °C. Fig. 8 shows the hypothetical situation where all available heat sources are used as thermal input to the heat pump evaporator, 8 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Fig. 6. Annual hot and cold composite curves, without heat pumping. Fig. 7. Annual sources and sinks, with heat pumping. shown as QEV . The heat pump compressor work is indicated by WHP . As a result of this hypothesis, the composite curves are shown to cross, indicating a theoretical impossibility. In other words, on an annual basis there is more source energy available for the heat pump than is required. Fig. 9 corrects the situation, reconstructing the hot composite curve in such a way that the minimum allowable temperature difference (TMIN ) of 5°C is respected. The unused portion of the potential thermal sources is rejected to the environment in the form of drain water that exits the test building above the temperature of the incoming city water. The minimum annual heating duty of 29.1 GJ/yr. is exactly the heat load required to bring the DHW to the set point of 55 °C. The following calculation, making use of Eq. (1), illustrates this result. QMIN =  1.9  Mg day 365  days yr 4.19  1  MJ ((55 − 45 ) C ) Mg ∗◦ C GJ 10 0 0 MJ  QMIN = 29.1 GJ/yr. In the updated feasible results shown in Fig. 9, the value of QEV is 54.1 GJ/yr., while the heat pump compressor work WHP is 27.1 GJ/yr., for a combined total of 81.2 GJ/yr. The quantity QEV is exactly the reduction in the electricity consumption that would otherwise need to be provided by the electric auxiliary heaters. With the incorporation of heat pumping into the pinch analysis, the recalculated annual minimum heating duty drops to 29.1 GJ/yr. This is an 83% drop compared to the solar reference case of 166.5 GJ/yr. (HFH + DHW + ACS – TSC =103.4 + 138.2 + 5.2 – 80.3). The explication of this very significant reduction in the minimum heating duty is due to the impact of fully benefitting from the thermal transfer of the warm greywater to the colder incoming city water, combined with the upgrading of energy in the colder sources to a temperature level that is sufficient to supply the thermal requirements of the building above the pinch point. If we compare 29.1 GJ/yr. to the test house without solar input, with annual thermal needs of 246.8 GJ/yr., this is a drop of 88%. For the purpose of simplifying the scope of this study for the test building, the characteristics of both the thermal solar collectors and a possible heat pump are considered fixed in this article. Ideally, the heat pump(s) specification and operation would be designed to always upgrade heat to a temperature above the pinch point [13,14]. For the test building, this means above 27.5 °C from October to May, and above 47.5 °C from June to September. A widened scope of study for the test building in the future might include the following: 1) a heat pump capable of producing hot water above 48 °C from input water as cold as 5 °C, 2) thermal solar collectors that can supply the building thermal demands from June to September. C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 9 Fig. 8. Annual hot and cold composite curves, with heat pumping and an infeasible heat cascade. Fig. 9. Annual hot and cold composite curves, with heat pumping and a feasible heat cascade. Full application of pinch principles to building design requires the following: 1) Thermal sources (e.g. solar) at temperatures above the pinch point should only supply thermal demands above the pinch; 2) Only thermal sources (e.g. warm greywater) below the pinch should supply demands below the pinch; 3) Heat pumping should only satisfy demands by upgrading sources (e.g. cold greywater or mixed cold greywaters) below the pinch to a temperature above the pinch. 3.4. Possible design solutions: grid diagram superstructure Having completed the pinch analysis data extraction and targeting steps, it is now time to address the question of finding possible design solutions that come close to providing the minimum heating duties discussed in Sections 3.1–3.3. Fig. 10 is a grid diagram [1,5] for the test building, including novelty that will be discussed shortly. Sources are generally shown in the lower portion, while sinks are in the upper portion. For each solid horizontal line, corresponding to a fluid stream, the lower temperature is placed to the left. Heat transfers are drawn with dashed lines. A circle represents a heat exchanger side, where a solid filled circle indicates the hot fluid side. The thermal design superstructure shown in Fig. 10 is intended to suggest a conceptual framework that can be applied to any thermal improvement project for a building. The values R1 to R9 represent possible thermal storage for each of the liquid streams. Recall that thermal storage becomes useful when there is a time mismatch between the source and the sink. For example, R1 represents a possible reservoir for groundwater, which may flow intermittently or may not have a sufficient flow at the required time to act as a good thermal source for the heat pump. R6 is a possible reservoir of water for the hydronic floor heating circuit. R8 is a possible reservoir for the preheated domestic hot water. Note that in the actual physical installation, adjacent units can be combined into a single device if this offers some advantage. R9 anticipates the possible seasonal storage of thermal solar energy during the summer, for use during the following winter. From a design perspective, the superstructure of Fig. 10 assures that the building thermal requirements can always be satisfied; this is indicated by the two auxiliary electric heating units for the HFH and DHW circuits. To the best of the authors’ knowledge, Fig. 10 is the first grid diagram to include the representation of thermal storage. The novel methodology presented here allows the construction of the grid diagram and the composite curves for both continuous and time variable (intermittent) thermal sources. The key feature is the replacement of the usual hot stream to cold stream heat transfer with the following combination: hot stream reserve; hot stream to cold stream heat transfer; cold stream reserve. Fig. 11 illustrates 10 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Fig. 10. Grid diagram superstructure for the test building. Fig. 11. Heat transfer representation. a Traditional. b, c. Proposed (two possibilities). the traditional heat transfer representation on the left (a), with two possible graphical representations of the proposed concept shown on the right (b and c). This approach allows the conceptual incorporation of both continuous and time dependent sources and sinks early in the design process, with the arrangement and specification of possible physical reservoirs left to a later stage. Adding a reserve or store “of hot stream” and “of cold stream” allows temporarily neglecting any possible time mismatch between the sources and sinks. 3.5. Design possibilities: chosen selected cases Keeping in mind the relative magnitude of the various sources presented in the data extraction of Section 3.1 (Table 3), and applying some engineering judgement, it is appropriate to trim down the number of design choices. The general idea is to favour process simplicity, and aim for the most significant design features that will approach the minimum energy targets. Fig. 12 presents a selected subset of the design superstructure that we wish to consider in more detail. Reservoirs R1, R2, R4, R5, R7 and R9 have been removed. The ground water, GDW, is only associated with 3.9 GJ/yr. and thus R1 was eliminated. The cold greywaters from R2 and R3 can be mixed in a single reservoir, which will retain the name R3. Warm greywater is produced when incoming city water must be heated, so reservoirs R4 and R7 were removed. The storage of a glycol-water mixture adds cost, bulk and possible environmental risk, and thus R5 was removed. R9 is required for seasonal thermal storage and was thus deleted, as this kind of storage is difficult to implement on a small scale in an inexpensive compact form. Fig. 13 is a simplified design schema superstructure that follows from the modified grid diagram of Fig. 12, where the thermal energy reservoirs R3, R6 and R8 play the same roles. The upper portion of Fig. 13 is the circuit that satisfies the domestic hot water use, while the lower portion is the circuit that assures the occupant thermal comfort. In Fig. 13 we have chosen to show at least one heat exchanger in each reservoir, as a means of visualizing the associated design functionality. Imagine, for this purpose, that each circuit could have 4 possible design options for reservoirs R6 and R8: (1) no equipment; (2) a reservoir with a heat exchanger supplied by TSC; (3) a reservoir with a heat exchanger supplied by HPS; (4) a reservoir with two heat exchangers, one supplied by TSC and the other by HPS. The domestic hot water circuit might include the separation of the greywater into cold and C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 11 Fig. 12. Chosen grid diagram for further design evaluation. Fig. 13. Design schema superstructure; also design schema WGW & HPS &TSC. warm greywaters, or not. The schema in Fig. 12 thus encompasses 32 different scenarios (4∗ 4∗ 2). Engineering judgement will again be applied to restrict the number of alternatives for economic evaluation, to be discussed shortly. Fig. 13 also illustrates the particular design solution that includes WGW, HPS and TSC. Figs. 14–16 are three additional particular scenarios, all of which include thermal solar collectors, and for which an economic analysis will be given in Section 3.6. Fig. 14 is the solar reference case, where solar input is included in the test building. Fig. 15 includes heat pumping for both circuits. Fig. 16 is the scenario of TSC in combination with the separation of the greywater into cold and warm greywaters. Greywater can be used to preheat incoming city water in some combination of two possible means: 1) Through the separation of the greywater into warm and cold greywaters, with subsequent use of a heat exchanger for the warm greywater; 2) As a thermal source to a heat pump, either for the unseparated greywater, or for the mixed cold greywaters. To the best knowledge of the authors, a specific integrated solution, shown in Fig. 13, comprises a technical novelty: separation of the used domestic hot water into warm and cold greywaters, heat recovery of the warm stream below the pinch point, mixing of the cold greywaters after heat recovery, and finally heat pumping of the mixed greywaters to above the pinch temperature. 12 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Fig. 14. Design schema TSC. Fig. 15. Design schema HPS & TSC. 3.6. Economic analysis of specific cases: overview The economic discussion presented here will consider two different perspectives. The first economic analysis in Section 3.7 will continue the perspective that has so far been considered in the article, where the reference scenario is the solar equipped home. Afterwards, in Section 3.8, a perspective that may be of more general interest will be considered. In this second economic analysis, the reference scenario is the test building without the thermal solar collectors. In these economic analyses the city water temperature follows a monthly temperature profile, and the savings are calculated for each month and then totaled for the year. In scenarios with a solar energy input, for the electricity savings calculation, solar energy was first applied toward the HFH, and then the remaining portion was used to preheat the DHW to 45 °C. This approach closely follows the implementation in the test building. 3.7. Economic analysis no. 1: reference scenario with thermal solar collectors Table 5 shows the economic comparison of HPSSol , WGWSol , and WGWSol & HPSSol, where the reference scenario energy requirement is 166.5 GJ/yr. (HFH + DHW + ACS TSC = 103.4 + 138.2 + 5.2 – 80.3). Table 5 presents the sce- C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 13 Fig. 16. Design schema WGW & TSC. Table 5 Economic analysis no. 1, where the reference scenario includes thermal solar collectors. Inputs and parameters Electricity savings (GJ/yr.) Electricity savings (kWh/yr.) Initial investment cost (CAD) Initial electricity price (CAD/ kWh) Electricity Price Increase (% /yr.) Project lifetime (yr.) Discount rate (% / yr.) Results Simple Payback Period (yrs.) Net Present Value (CAD) Internal Rate of Return (%/yr.) Energy savings (%) HPSSol WGWSol WGWSol & HPSSol 70 19 373 14 000 0.07 3 20 7 51 14 184 4 000 0.07 3 20 7 88 24 479 15 000 0.07 3 20 7 10.3 4 621 10.6 42 4.0 9 634 28.3 31 8.8 8 529 23.6 53 energy input has already been accounted for in the annual energy requirement of 166.5 GJ/yr., which explains why the payback periods are quite long, as the test house already benefits from a very significant advantage of solar energy. In other words, this analysis shows the incremental benefit of adding further thermal sources to an already environmentally friendly solar building. 3.8. Economic analysis no. 2: reference scenario does not include solar input narios without greywater separation to the left, here HPSSol . The subscript “Sol” underscores the idea that the “electricity savings” in the table do not include any savings from the solar collectors, as solar energy is part of the reference scenario. Notice that the solar In this second economic analysis, summarized in Table 6, the perspective is more general, where we are now interested in the relative, and possibly combined, economic performance of solar energy, heat pumping, and greywater separation. Here the reference scenario is the test building without solar thermal collectors. In this case the reference energy consumption is 246.8 GJ/yr. (HFH + DHW + ACS = 103.4 + 138.2 + 5.2). For example, the right most column in Table 6 indicates that the energy savings for the combined effect of greywater separation, heat pumping and thermal solar collectors (WGW & HPS & TSC) represents a reduction in the electricity requirements of 158 GJ/yr., or a 64% energy savings compared to the 246.8 GJ/yr. reference. The shortest payback Table 6 Economic analysis no. 2, where the reference scenario does not include thermal solar collectors. Inputs and parameters Electricity savings (GJ/yr.) Electricity savings (kWh/yr.) Init. investment cost (CAD) Init. elect. price (CAD/kWh) Elect. Price Increase (%/yr.) Project lifetime (yr.) Discount rate (% / yr.) Results Simple Payback Period (yr.) Net Present Value (CAD) Internal Rate of Return (%/yr.) Energy savings (%) TSC HPS HPS & TSC WGW WGW & TSC WGW & HPS WGW & HPS & TSC 80 22 306 3 000 0.07 3 20 7 105 29 039 11 000 0.07 3 20 7 149 41 439 14 000 0.07 3 20 7 51 14 047 1 000 0.07 3 20 7 121 33 554 4 000 0.07 3 20 7 111 30 844 12 000 0.07 3 20 7 158 43 986 15 000 0.07 3 20 7 1.9 18 440 56.6 33 5.4 16 913 21.3 42 4.8 25 831 23.8 60 1.0 12 502 105.3 20 1.7 28 252 63.7 49 5.6 17 647 21.8 45 4.9 27 279 23.6 64 14 C. Reddick, M. Sorin and J.-C. Bonhivers et al. / Energy & Buildings 211 (2020) 109803 Table 7 Summary of economic analysis no. 2, in order of increasing energy savings. Scenario Description Energy savings (GJ/yr.) Energy savings (%) Reference Test building without solar heating 246.8 GJ/yr. (=HFH & DHW & ACS) Warm greywater preheats the domestic hot water (DHW). Thermal solar collectors preheat the domestic hot water and provide hydronic floor heating (HFH). Heat pumping preheats DHW and provides HFH. The HPS sources are MGW, ACS and GDW. Warm greywater (WGW) preheats the DHW. HPS further preheats DHW and provides HFH. Warm greywater preheats the DHW. TSC further preheats DHW and provides HFH. TSC provides HFH and preheats DHW. Heat pumping completes HFH. HPS sources: MGW, ACS, and GDW. WGW preheats the DHW. TSC provides HFH and preheats DHW. HPS finishes HFH. HP sources: MGW, ACS and GDW. 0 0 51 20 80 33 105 42 111 45 121 49 149 60 64 158 WGW TSC HPS WGW & HPS WGW & TSC HPS & TSC WGW & HPS & TSC period for any individual technology is offered by WGW, followed by TSC, and then HPS: 1.0 yr., 1.9 yr. and 5.4 yr. respectively. The combination of greywater stream separation and thermal solar collectors, WGW+TSC, is noteworthy given the combined short payback period of 1.7 years and energy savings of 49%. It should be recalled that the air conditioning, ground water and seasonal thermal storage are not significant in this study, but might be significant in other situations. Table 7 organizes the results of economic analysis no. 2 in order of increasing energy savings. All of the scenarios offer a simple payback of under 6 years. The results are strongly influenced by the low cost of electricity in Quebec and the relatively expensive capital cost of a water/water heat pump. Government financial incentive programs have not been considered in this analysis. In any case, the “best” solution depends on the priorities of the building owner, and to what extent lowering the carbon footprint of their building is important. In analysis no. 2, where the reference case refers to the test home without solar heating, the electricity savings range from 20 to 64% for the evaluated scenarios. 4. Conclusion Pinch analysis is not currently applied to the design of energy efficient buildings. Why not? Important barriers have been the recognition of potential thermal sources, and conceptual difficulties in accounting for their time variability, especially for waste heat and renewable energies. In this article, pinch analysis was applied for the first time in an all-inclusive manner to a building, linking the building’s thermal demands (occupant thermal comfort and domestic hot water use) to potential thermal sources. The appropriate selection of flow rates, as well as inlet and outlet temperatures of the thermal streams, is part of the originality of the application. A novel modification was proposed for the pinch method to facilitate the inclusion of both continuous and time dependent (or intermittent) thermal sources and sinks. The usual hot stream to cold stream heat transfer was replaced as follows: hot stream reserve; hot stream to cold stream heat transfer; cold stream reserve. Adding a reserve “of hot stream” and a reserve “of cold stream” conceptually eliminates the time mismatch between potential thermal sources and sinks. The test building for the analysis was a multi-family residential structure in Quebec, Canada. The building includes thermal solar collectors, hydronic floor heating and summer air conditioning. The studied potential thermal sources were ground water, cold greywater, energy removed from the building air in the summer by air conditioning, warm greywater, and thermal solar collector fluid. It was observed that for the test building, the pinch tem- perature changes with time: 27.5 °C from October to May, 47.5 °C from June to September. Greywater contains a significant amount of thermal energy. Compared to the solar equipped test building, the electricity consumption could be reduced by 31% by only implementing greywater separation and thermal harvesting with a heat exchanger (WGWSol ), without heat pumping. Compared to the solar equipped test building, electricity consumption could be decreased by 42% by incorporating heat pumping into the design solution (HPSSol ), without using greywater separation. The combination of greywater separation and heat pumping (WGWSol & HPSSol ) would reduce electricity consumption by 53%. If the test house without solar heating is chosen as the reference case, then the combined benefit of implementing greywater separation, heat pumping and solar thermal collectors (WGW & HPS & TSC) reduces electricity consumption by 64%. Two economic analyses were completed for the test building: one taking the test building without solar heating as the reference, the other using the solar equipped building as the reference case. In the context of Quebec, Canada, where electricity prices are among the lowest in the world, simple payback periods ranged from 1 to 10 years. 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