With the ever-increasing awareness of the importance of utilizing the waste heat in air-conditioning and ventilation systems in green buildings, A-A HE is becoming a vital component of nZEB and nZEXB cases. According to the EU Directive 2010/31/EU [25] on the energy performance of buildings (with the First Law of Thermodynamics), starting from the 31^st December of 2020, all new buildings will be required to be nearly-zero energy buildings. EU has not yet realized the importance of the Second Law in the quest for decarbonization. Yet, Tronchin and Fabbri [26] have developed a new simplified method of evaluating the exergy of the energy consumed in buildings to find a relationship between the HVAC loads of buildings including envelope heat transfer and the energy conversion plant and its sub-systems like radiators. They argued that the exergy analysis of energy consumption in heating and cooling of buildings could be a tool to evaluate an exergy tariff to promote low-exergy HVAC plants. They further argued that such an exergy-based building performance tool based on Annex 37 may be utilized to evaluate the relationship between energy/exergy consumption: their new model evaluates the energy performance of buildings by establishing a direct relationship among exergy, temperature variations, and TOE. The originality of their model, which they name ‘Exergy Performance of Buildings’, emanates from the fact that their exergy-based model is structured on the energy-based EU Energy Performance in Buildings Directive. They compared the two approaches and concluded that the exergy-based model provides a more comprehensive analysis technique such that it reveals exergy destructions, which are not acknowledged by an energy analysis. HRV is a sub-system in their model and therefore it may be instrumental also for the HRV performance.

Among many different types and means of recovering heat from the exhaust air, fixed-plate heat recovery is a simple yet widely used technology. The structure of fixed-plate HE is based on several thin plates arranged together to separate internal airflows. The airflow between these plates create an additional pressure drop, namely P and thus lead to additional fan power demand in electrical form, namely E, that must be satisfied by either by fan oversizing or adding more fans. It must be remembered that E only relates to the HE of HRV over the ventilation system without heat recovery.

Regarding the airflow arrangement, there are three types of fixed-plate exchangers: counter-flow, cross-flow, and parallel flow [27]. The typical efficiency of fixed-plate heat recovery is in the range of 50-80% [27]. In the existing building stock, however, there is less than 1% of HRV in Europe [28]. According to the same publication, in new buildings, MEU still dominates the market, while the share of HRV units is increasing rapidly.

Figure 1, which is a reproduction from the ASHRAE Handbook-HVAC Systems and Equipment, shows the basic model for a fixed-plate, A-A type HRV unit. In this figure, the stand-alone HRV model considered as isolated from its surroundings and the additional/oversized fans and the power grid [29]. Even if such factors are included, they are limited to the quantity of energy recovered and spent by neglecting their different qualities. The unit exergy of thermal power gained or extracted (in cooling), ε_H is substantially lower than the unit exergy of electric power, ε_E which is virtually 1 W/W.

Figure 1.

Air flows and DB temperatures in a stand-alone HRV [29]

There is an exergy imbalance between them. Furthermore, Figure 1 does not question the origin of power generation and the fuel used. The fan power must be limited somehow for positive exergy gain from the exhaust air. The only ASHRAE source available, which deals with the limiting of fan power in air handling is the ASHRAE Standard 90.1 [30]. In Tables 6.5.6.1-1 and 6.5.3.1 of Standard 90.1 regarding the fan power limitations, the fan power is limited by a ratio of 1.2 BHP per 1,000 cfm (1.896 kW/m³s^-1) for flow rates less than 20,000 cfm (9.44 m³s^-1) and for the given US climate zone of 7, B. To give an example, consider Table 1, which reproduces an edited version of a typical data set from the commercial literature [31]. This stand-alone HRV unit reclaims 18.24 kW of heat, Q at an airflow rate, V of 0.83 m³/s.

The First Law efficiency (η_I) is 0.65. Outdoor air at 273 K is preheated to a temperature (T₁) of 290.8 K. It requires 2 × 0.65 kW dedicated fans for heat recovering purpose in the HRV unit itself, apart from the basic ventilation system. According to the traditional COP definition, this HRV unit has a COP value of 14.03 [18.24 kW/(2 × 0.65 kW)]. This is a favorable value in terms of the First Law. If ASHRAE Standard 90.1, which permits a total fan power ratio of 1.896 kW/m³s^-1 is applied to the first column of Table 1, 1.58 kW of fan power is permissible (1.896 kW/m³s^-1 × 0.83 m³/s), which is above the 2 × 0.65 kW fan power, installed by the manufacturer. If the ASHRAE rule applies then COP and COPEX values would reduce to 11.5 and 0.50, respectively. From the Second Law perspective, the total permitted fan power needs to be conservatively less than 0.83 kW instead of 1.58 kW. This is only about half of what ASHRAE Standard 90.1 permits. ASHRAE Standard 90.1 does not refer to the Second Law at all and causes avoidable exergy destructions and thus more CO₂ emissions, because CO₂ emissions are proportional to exergy destructions [see eq. (25) in the following sections]. In this example, the supply air to the indoors needs to be temperature peaked by 6.2 K to raise it to a temperature of 299 K at the air terminal units in the indoor spaces, because the preheated air temperature T₁ in Figure 1 is not high enough to satisfy the comfort heating loads and to maintain the DB comfort indoor air temperature (T_i). This means that additional unit exergy (E_XTP) of (1 - 290.8/299) W/W must be provided by an auxiliary air-heating system. On the return cycle of the air stream, part of this unit exergy, which is about 44% of the unit exergy (1 - 273/290.8) W/W of heat recovered by the HRV unit from the exhaust air may be treated in the form of exergy input (E_XA) in the quasi-closed loop of ventilation with an efficiency of η_I from the exhaust air. Then the net exergy-based COP (COPEX) of the HRV unit with electrical and thermal inputs is (1 - 0.44 η_I) × (E_XH/E) is 0.613, a value which is quite less than one.

The most common five commercially available products with different capacities were further compiled in Table 2. None of the manufacturers did supply COP or COPEX data. The nearest value provided by a manufacturer was the specific fan power. The calculated values corresponding to these products with the above approach regarding COPEX values are always far from one, although COP values seem to be impressively high. It is obvious that without any reference to the COPEX term, design, rating, and operation will not be rational and HRV units will keep being responsible for avoidable CO₂ emissions due to rather large exergy destructions. Therefore, an exergy-based holistic model is necessary, which also provides the answer to the question of where the electric power comes from and how it is generated.

All previous studies covering either energy analysis or exergy analysis or both, do not include the embodied exergy in their LCA. Furthermore, they do not address additional but avoidable CO₂ emissions, which are the result of exergy destructions. These unaddressed emissions may be equal or even higher than the direct CO₂ emissions. Besides, previous studies did not address the ozone depletion and global warming potentials that are associated with the HRV systems in conjunction with their power generation supply fuel and association with HPs, if coupled to them.

Examples, which are given in Table and Table 2 show that a new exergy-based model is needed to fully understand the environmental performance and benefits of HRV units if there are any. The following implications are expected:

• A method, capable of analyzing “Sustainable” equipment by the Second Law;

• A method, capable of estimating the actual CO₂, ODP, and GWP footprint of heat recovering systems in buildings, including the origin of the energy input;

• New design and rating metrics based on the Second Law;

• Lifetime analysis method, which is a collection of the following payback periods:

• Embodied exergy payback;

• Embodied CO₂ payback;

• Embodied energy payback;

• Investment payback.

A new exergy-based evaluation model is expected to fill the gap in theory and practice by addressing the missing points in the literature like the analysis of the return of embodied CO₂, energy, and exergy. These returns are far important than simple investment returns because they are all related to CO₂ emissions and global warming potential. Furthermore, the electric power source (thermal power plants) and thermal recovery and conversion systems on-site like HPs with refrigerant leakages or even wind and solar systems and geothermal systems due to their associated exergy destructions and embodied exergy, are responsible for ozone layer depletion and global warming. The model shall address and quantify these points, which are novel in HRV and similar applications in the built environment. In this respect, the model shall permit to quantitatively analyze emissions and embodiment returns of combined systems like HRV and HP units, or HRV and small fuel cell units in residential green buildings. This will provide a complete account of the environmental footprint.

This model recognizes the presence of fans and their motors simply dedicated or attributed to the HRV boundary. It also recognizes the unit exergy of heat and power. According to this model, exergy gain from the exhaust heat transfer (Q) is given in eq. (2). This exergy gain raises the outdoor air temperature from T_o to T₁:

$E_{\text{XH}1}=\left(1-\frac{T_{\text{o}}}{T_1}\right)\times Q$ (2)

The exergy gain in the HRV unit must be greater or at least equal to the exergy demand of fan motors on the outdoor and the exhaust side of the HRV unit:

$E_{\text{XH}1}\ge E_{\text{XEO}}+E_{\text{XEHRV}}$ (3)

The subscript 1 denotes HRV. If there is a coupled system like an HP, it is denoted by the subscript 2. Thermal exergy gain in the HRV unit, namely E_XH1 is a linear function of the airflow rate (V) where fan power, thus the corresponding fan exergy demand is a power function of V [see eq. (8)]. Therefore, there is a limit on the maximum airflow rate and the corresponding thermal exergy gain. The maximum flow rate allowed in many cases is less than the hourly fresh air requirement for maintaining the indoor air quality. Therefore, the remaining fresh air needs to be heated by another HVAC system, like an HP and the mix must be brought to the final supply air temperature (T_f). This requires the optimization of the outdoor airflow rate split between the HRV unit and another air heating system, like an A-A HP, operated by grid power.

To optimize the split of the total flow rate of the outdoor air intake between the HRV and the HP units for maximum exergy-based performance, a new model was developed, which is shown in Figure 3.

Figure 3.

Isolated model for the operational diagram of the method with a parallel HP (note: Main HVAC fans that are served by the HPs are excluded)

This method identifies two parallel air flow ducts. One of them delivers outdoor air to the HRV unit. The second duct delivers the remaining outdoor airflow to the HP. Hereby, the outdoor air split ratio is represented by ratio x. If x is zero, it means that HRV is not functioning (or absent). If x is 1, then it means that the HP is not functioning (or absent). Airflow rates in the HRV unit are limited such that thermal exergy gain obtained (E_XH1) by heating the incoming outdoor air to a temperature of T₁ must be higher than the electrical exergy demand of the two fans motors and the fan drive. This system designed and operating under optimum conditions is expected to also improve the ratio of energy consumption of the building to the energy consumption of the ventilation system, which may be similarly defined in terms of the PUE factor for data centers [5].

Across the HRV unit, there are two counter-air flows, namely the exhaust air at a flow rate of yV and the fresh outdoor airflow rate of xV. Assuming that fans at both sides of the HRV unit are identical, then:

$\underset{E_{XH1}}{\underbrace{Q\left(1-\frac{T_{\text{o}}}{T_{\text{o}}+\Delta T}\right)}}=\underset{Q}{\underbrace{xV\rho C_p\Delta T}}\underset{{\epsilon }_H}{\underbrace{\left(1-\frac{T_{\text{o}}}{T_{\text{o}}+\Delta T}\right)}}\ge \left(E_{\text{XEHRV}}+E_{\text{XEO}}\right)=\frac{f\Delta P\left(x+y\right)V}{{\eta }_{\text{F}}{\eta }_{\text{bm}}}\left(1 \text{W}/\text{W}\right)$ (7)

Here, f in the last term represents the fan characteristic, η_F and η_bm are the fan and motor-belt efficiencies, respectively. They are assumed to be approximately constant concerning their flow rates during operation. E_XEHRV and E_XO represent the exergy demand of both fans, which operate on electricity. For standard air conditions at sea level and 15 °C, it may be taken that ρ is 1.225 kg/m³ and C_p is (1.026 kJ/kg·K). Then, along with the following relationship between ΔP and V for rectangular ducts:

$\Delta P=d V^m$ (8)

$\Delta T\left(1-\frac{T_{\text{o}}}{T_{\text{o}}+\Delta T}\right)\ge \frac{e V^m}{{\eta }_{\text{F}}{\eta }_{\text{bm}}}\left(\frac{x+y}{x}\right)$ (9)

The power (m) is 1.82 for the galvanized ducts. For other inner linings, sizes, and geometry, m changes between 1.8 to 1.9 [30]. According to eq. (7), the maximum flow rate between T_o and T₁ (ΔT) in the HRV unit is limited:

$V\le \sqrt[m]{\frac{\Delta T\left(1-\frac{T_{\text{o}}}{T_{\text{o}}+\Delta T}\right){\eta }_{\text{F}} {\eta }_{\text{bm}}}{\left(\frac{x+y}{x}\right)e}}$ (10)

$\Delta T=T_1-T_{\text{o}}$ (11)

$T_{\text{f}}=x T_1+\left(1-x\right)T_2$ (12)

then solving for T₁{T₁ > T_o}:

$\begin{array}{l}{T}_1=\frac{T_{\text{f}}-\left(1-x\right)T_2}{x}\\ \left\{x>0.40\right\}\end{array}$ (13)

The term x is subjected to the optimization algorithm [see eq. (17) and eq. (19a)]. The ratio y is separately controlled by optimized operating conditions of the HP for a given x ratio. T₁ is a function of x for a required supply air temperature T_f. To solve T₁, T₂ is solved first for optimum exergy output in terms of the exergy-based COP_HP, namely COPEX_HP written only for the HP itself according to the ideal Carnot cycle as represented in Figure 4:

$COPE{X}_{\text{HP}}=CO{P}_{\text{HP}}\left(1-\frac{T_{\text{o}}}{T_2}\right)$ (14)

The COP_HP term may be linearly expressed in a given, narrow operating range:

$CO{P}_{\text{HP}}=q-r\left(T_2-T_{\text{o}}\right)$ (15)

When the partial derivative of the simultaneous solution of eq. (14) and eq. (15) with respect to T₂ is equated to zero the optimum value of T₂ for maximum COPEX_HP is obtained. In eq. (15), q and r factors are the linearization coefficients for the COP_HP. If q is equal to 6 and r is 0.05 K^-1 for a given HP operating in a temperature range between 273 K and 300 K at an outdoor temperature, T_o of 283 K then the optimum T₂ is 337.7 K:

$T_2=\sqrt{\left[\left(\frac{q}{r}\right)+T_{\text{o}}\right]T_{\text{o}}}$ (16)

Figure 4.

Exergy input and output in an A-A HP

If the required supply air temperature T_f is 310 K and x is 0.75, then, from eq. (13) T₁ is 300.8 K. Therefore, the optimum temperature T₂ for the HP is out of range. To avoid this condition, a different type or model of the HP with different q and r values may be selected. This solution, however, is subject to the maximum allowable airflow rate (V) that is limited by eq. (10). Now, knowing the optimum T₂ and knowing T₁ in terms of T₂, for a known total fresh air flow rate requirement V, an optimization function (OF) may be written in terms of x for maximum exergy gain from the exhaust air. If the electric motor of the additional/oversized fan is inside the HRV duct, the last term in eq. (17) represents the heat gain from the electric motor and its drive casing. This term adds exergy in winter (heating) but reduces exergy from the OF term in summer (cooling). If the electric motor and the casing are placed outside the ducts, this term drops:

$\begin{array}{l}OF=\underset{\text{HRV }\left(E_{XH1}\right)}{\underbrace{\rho C_{p}xV\left(T_1-T_{\text{o}}\right)\left(1-\frac{T_{\text{o}}}{T_1}\right)}}+\underset{\text{HP }\left(E_{XH2}\right)}{\underbrace{\rho C_{p}yV\left(T_2-T_{\text{o}}\right)\left(1-\frac{T_{\text{o}}}{T_2}\right)-E_{\text{XEHP}}}}-\underset{\text{HRV fans}}{\underbrace{\frac{cd\left[x+\left(1-a\right)x\right]V^{\text{m}+1}}{{\eta }_{\text{F}} {\eta }_{\text{bm}}}}}\pm \underset{\text{HRV fan}}{\underbrace{Q_{\text{FO}}\left|1-\frac{T_{\text{o}}}{T_{\text{av}}}\right|}}\\ \left\{a=\left(1-y\right)/x\right\}\end{array}$ (17)

The approximation in eq. (18), which was derived from the information available in [31], [33], calculates Q_FO. In this equation, H is a number less than one, which represents the net conversion ratio of the electrical power input, which is not converted to the shaft power to the heat transferred to the airflow in HRV:

$Q_{\text{FO}}=\left(H-{\eta }_{\text{F}} {\eta }_{\text{bm}}\right)\left(cd x V^{\text{m}+1}\right)/\left({\eta }_{\text{F }}{\eta }_{\text{bm}}\right)$ (18)

To bring the supply temperature to the required design temperature T_f at the exit of terminal units for proper satisfaction of the sensible indoor space heating load, the temperature may require to be peaked by an auxiliary heating system, which is arranged in tandem to the HRV unit with or without the HP (see Figure 3). This auxiliary system might use fossil fuel or power, and therefore additional ODP and GDP take place. E_XTP denotes the additional exergy spending for temperature peaking. In the quasi-closed outdoor/indoor system of the HRV unit, the exhaust air bears part of this thermal exergy and transfers it back to the outdoor fresh air drawn in with a thermal efficiency η_I across the HE of HRV or HP. Because this thermal exergy is finite, as opposed to ambient (practically infinite) sources like air or water, and fossil fuel or power input takes place during temperature peaking upstream in the indoor ducts, it may not be treated as ambient energy like the ground heat, ambient air, seawater, etc. Therefore, it must appear in the definition of COPEX, while traditional COP calculations often ignore this term (ambient sources). Referring to eq. (17), the overall COPEX of the system modeled in Figure 3, namely the HRV+ parallel HP Case 1, is given in eq. (19a). The objective is to maximize COPEX_HRV+HP:

$COPE{X}_{\text{HRV}+\text{HP}}=\frac{\rho C_{p}xV\left(T_1-T_{\text{o}}\right)\left(1-\frac{T_{\text{o}}}{T_1}\right)+\rho C_{p}yV\left(T_2-T_{\text{o}}\right)\left(1-\frac{T_{\text{o}}}{T_2}\right)\pm Q_{\text{FO}}\left|1-\frac{T_{\text{o}}}{T_{\text{av}}}\right|}{E_{\text{XEHP}}+\frac{cd\left(x+\left[1-a\right]x\right)V^{\text{m}+1}}{{\eta }_{\text{F}} {\eta }_{\text{bm}}}+\underset{E_{XA}}{\underbrace{E_{\text{XTP}} {\eta }_{\text{I}}}}}$ (19a)

In eq. (19a), E_XTP is the sum of the partial contributions of E_XH1 and E_XH2:

$E_{\text{XTP}}=\left[E_{\text{XH}1}\frac{\left(1-\frac{T_1}{T_{\text{f}}}\right)}{\left(1-\frac{T_{\text{ref}}}{T_1}\right)}+E_{\text{XH}2}\frac{\left(1-\frac{T_2}{T_{\text{f}}}\right)}{\left(1-\frac{T_{\text{ref}}}{T_2}\right)}\right]$ (19b)

and:

$E_{\text{XEHP}}=\frac{\rho C_p\left(1-x\right)V\left(T_2-T_{\text{o}}\right)}{CO{P}_{\text{HP}}},\left(1\text{W}/\text{W}\right)$ (20)

All terms in the objective function OF and the COPEX_HRV+HP function given in eq. (17) and eq. (19a), respectively, contain the split factor x, in such a manner that the objective function is a single function of this variable x with all other given and independently solved variables like T_o and T₂, respectively. Therefore, this model also provides an exergy-based control algorithm to maintain the maximum exergy rationality during operating under dynamic outdoor and indoor conditions. For the x < 1 condition, y is (1 - x). For x = 1 condition, y is either equal to 0 (Case 1) or equal to x, which is also equal to 1 when the HP is in series with the HRV unit (Case 2).

In this case, HP is placed downstream of the HRV unit in series such that the total airflow passes through both the HRV and the HP units. Therefore, x and y are equal to each other, and mathematically speaking, both are equal to one. The downstream position is a better position for the HP, compared to an upstream position where colder air supply will reduce the COP of the HP. The same eq. (19a) applies with x = y = 1 to determine the maximum COPEX value for a given design or operating conditions. Furthermore, in eq. (17) and eq. (19a), T_f replaces T₂. T₁, which is determined from the HRV specifications, replaces T_o in eq. (16). Consequently, eq. (12) and eq. (13) are not used.

The same eq. (17) applies with x = 0, y = 1, which means that there is not any HRV unit and the HP is exposed directly to the outdoor air at temperature T_o and has to deliver heat at the final supply temperature T_f because another auxiliary temperature-peaking system is not desirable from the cost and exergy points of view. This means that the HP has to operate at a lower COP_HP, while a larger T, which is equal to (T_f - T_o) exists. In Case 3, T₂ directly replaces T_f at the absence of an auxiliary temperature-peaking heating system. See also eq. (14) and eq. (15) for temperature replacements.

In the same model, the additional (avoidable) CO₂ emissions responsibility, namely ΔCO₂ due to exergy destructions is explained by the REMM [34]. Figure 5 shows a sample exergy flow bar according to REMM for a single HRV unit that is driven by grid power.

Figure 5.

Exergy flow bar for HRV unit in space heating mode (not to scale)

This is a simple exergy flow bar, which covers only one application, one system, and one energy source. This bar is drawn starting from top showing the primary energy source temperature T_f to the final application temperature in the HRV unit (indoor supply temperature at 300 K) and then to the environment reference temperature (T_ref) (283 K) at the bottom. It is assumed that electric power is supplied through the grid where the electric power is generated in a natural-gas power plant. 2,235 K is the adiabatic flame temperature of the natural gas. In this sample case, the exergy utilized (for the space heating demand), _dem starting from an outdoor temperature T_o of 283 K, and ending at the outdoors is given by eq. (21), according to the ideal Carnot cycle:

${\epsilon }_{\text{dem}}=\left(1-\frac{T_{\text{ref}}}{T_{\text{f}}}\right)=\left(1-\frac{283 \text{K}}{300 \text{K}}\right)=0.056\frac{\text{kW}}{\text{kW}}$ (21)

while the original exergy supplied (_sup) at the power plant is given by eq. (22):

${\epsilon }_{\text{sup}}=\left(1-\frac{T_{\text{ref}}}{T_{\text{sup}}}\right)=\left(1-\frac{283 \text{K}}{2,235 \text{K}}\right)=0.87\frac{\text{kW}}{\text{kW}}$ (22)

According to REMM, if the major exergy destruction takes place at the upstream of the useful application (heat recovery), like in Figure 5, then ψ_R, which is the Rational Exergy Management Efficiency is the ratio of _dem and _sup [34]. According to this definition, ψ_R is 0.064 for the above numerical example:

${\psi }_{\text{R}}=\frac{{\epsilon }_{\text{dem}}}{{\epsilon }_{\text{sup}}}$ (23)

For 1 kW of exergy power supply:

$\begin{array}{l}{\epsilon }_{\text{des}}={\epsilon }_{\text{sup}}-{\epsilon }_{\text{dem}}\Rightarrow {\epsilon }_{\text{des}}=1-\left(\frac{{\epsilon }_{\text{dem}}}{{\epsilon }_{\text{sup}}}\right)\equiv 1-COPEX\\ \left\{\text{for ambient exergy input}\right\}\end{array}$ (24)

Here, _des is equated to 1 - COPEX. Referring to eq. (23) and the identity in eq. (24), ψ_R seems to be equal to COPEX. However, because ψ_R is a measure of exergy rationality in terms of ideal Carnot cycle while COPEX is a measure of exergy efficiency in terms of various exergy destructions taking place in the system, this identity may not hold for other more complex systems, while COPEX definition approaches to the Second Law efficiency. If part of the exergy input to preheating is from the reclaimed heat that is a result of temperature peaking E_XTP, appears in the denominator of the COPEX term given in eq. (19a). Therefore, for non-ambient exergy inputs, COPEX in eq. (24) must be corrected by a factor w. This factor is about 0.85 in building applications of HRV and HPs. If there is no temperature peaking, then w is 1. This rule also applies to eq. (25) given below.

For a given unit exergy destruction ε_des taking place in any energy conversion system or equipment like an HRV, its natural-gas equivalence that is necessary to spend to replace the said destroyed exergy will be (ε_des/0.87). Assuming that this exergy destruction is replaced in an equal amount of exergy generation in a non-condensing natural-gas boiler with an average reference thermal efficiency of 0.85, one may find the associated avoidable CO₂ emissions responsibility. In eq. (25), 0.2 is the unit CO₂ emission of natural gas per 1 kWh of its lower heating value c_i. Then, eq. (25) simply relates the avoidable CO₂ emissions to the destroyed unit exergy per kWh of heat. For the heat pump-alone case (Case 3), Figure 5 applies where ε_dem is replaced by ε_dem × COP. If COP is 5 then ψ_R is 5 × 0.064, which is 0.32:

$\begin{array}{l}\Delta {\text{CO}}_2=\left(\frac{{\epsilon }_{\text{des}}}{0.87}\right)\left(\frac{0.2}{0.85}\right)=0.27{\epsilon }_{\text{des}}=0.27\left(1-w COPEX\right)=0.27\left(1-{\psi }_{\text{R}}\right)\\ \left\{w=1\right\}\end{array}$ (25)

In this case, CO₂ from eq. (25) is 0.18 kg CO₂/kWh of unit heat, Q = 1 kWh, supplied assuming that no temperature peaking takes place (w = 1). Depending on the x value for an HRV and HP combination, the average ψ_R may be calculated by an algebraic weighted sum. If a fuel cell or micro-cogeneration unit replaces HRV and the HP, the exergy flow bar looks similar to the one given in Figure 6, because both systems generate electricity on the site from the natural gas fuel input. Fuel cell, however, has a lower heat output temperature T_E. In this case, ψ_R has a different definition [34]. If for example, T_E is 500 K for the micro-cogeneration unit and 350 K for a fuel cell, then Ψ_R values are 0.56 and 0.87, respectively:

${\psi }_{\text{R}}=1-\frac{{\epsilon }_{\text{des}}}{{\epsilon }_{\text{sup}}}=1-\frac{\left(1-\frac{310}{T_{\text{E}}}\right)}{\left(1-\frac{283}{2,235}\right)}$ (26)

Figure 6.

Exergy flow diagram for fuel cell and micro-cogeneration units

Until now, ODP and GWP have been separately treated regarding the impact of systems in the built environment, by ignoring the important relationship between the two. Therefore, a so-called zero-ODP refrigerant used in the compressor of an HP (for example, R227ea), which has a very high GWP value ‒ about 2,300 is recommended for reducing the ozone depletion effect in the atmosphere. Any increase in GWP increases ODP. While the air temperature in the lower atmosphere increases with an increase in greenhouse gases, air temperature in the stratosphere cools due to the blanketing effect of the greenhouse gases. This cooling triggers more ozone depletion. Therefore, GWP has a definite relationship with ODP. Conversely, any expansion in the ozone hole increases global warming. Although verified by observations this relationship was not mathematically expressed practically. To simply show the combined effect of a system like an HP with refrigerant leakages, a new expression, namely ODI was developed:

$ODI=\frac{sGW{P}^t}{1-ODI}\times {\left(\frac{ALT}{1}\right)}^u$ (27)

This equation combines ODP and GWP of a given refrigerant by also referring to the atmospheric residence time ALT. The power (t) regarding the GWP term in eq. (27) includes the combined effect of water vapor released to the atmosphere due to fossil fuel combustion, from attached cooling towers or increased evaporation from warming seas, lakes, or rivers, which accept the reject heat from thermal power plants that provide electricity to air conditioners and HPs. Collection of condensates from condensing boilers do not help, because additional exergy destructions taking place during condensing the flue gas overweighs them in terms of avoidable CO₂ emissions responsibility of condensing boilers. Accordingly, there is neither any refrigerant nor heating and cooling equipment with compression or absorption cycle with actually non-zero ODI even if their reported ODP values are 0. For example, compare R744 and R227ea:

${\text{CO}}_{\text{2}}\left(\text{R744}\right)\text{ values}:ODP=0,GWP=1,ALT=120\text{ years}$ (a)

$\text{R227ea }\left(\text{F gas}\right)\text{ values}:ODP=0,GWP=3,500,ALT=33\text{ years}$ (b)

For s = 0. 1, t = 0.03 (including water vapor effect), and u = 0.01 values in hand, their ODI values are:

${\text{for CO}}_2\left(\text{R}744\right)ODI\text{ is }0.115$ (a)

$\text{for R}227\text{ea }\left(\text{F gas}\right)ODI\text{ is }0.132$ (b)

These calculations ignore the additional effect of cooling towers, while they release moisture to the atmosphere with additional ODI. Therefore, cooling towers need to be eliminated or minimized by utilizing the reject heat. Dry cooling towers on the other hand use more electrical energy and they are again responsible for additional ODI, depending upon where the electricity comes from and how it is generated.

In this study, the base case (HRV-only case), HRV with HP (parallel and series), HP-only, boiler, micro-cogeneration, fuel cell, and electric resistance heating with grid power were compared according to their direct CO₂ emissions and the avoidable CO₂ emissions, namely CO₂, and ODI responsibilities. The results are given in Table 5.

The $\frac{\Delta {\text{CO}}_2}{{\text{CO}}_2}$ values listed in Table 5 for various systems and equipment remarkably show that avoidable CO₂ emissions, which are directly related to exergy destructions are as large as direct CO₂ emissions of equipment and systems. This might be a clue for the latest findings that sea levels will rise twice as much as previously anticipated.

Because exergy is not measured but calculated, the rather hidden to many CO₂ emissions are avoidable by improving COPEX values and this puts exergy analysis into an important game maker role for avoiding global warming challenge, which is becoming a state of emergency lately. It may be argued that the major reason for low COPEX values in the reclamation of waste heat originates from the use of electric fans, pumps, and other ancillaries and they may be avoided by the use of heat pipes.

This argument may seem to be valid at a first glance but certain heat pipes, especially containing refrigerants, like R-134a [35] are claimed to have zero ODP, but in fact, they have non-zero ODI [see eq. (27)]. Therefore, while CO₂ emissions from power plants are avoided by reducing the use of grid power in heat recovery systems and equipment, ODI increases, which interrelates GWP to ODP. Therefore, the result is almost the same in terms of global warming. The use of water-ethanol, acetone, methanol mixtures with very low ODI may be other options but they have high smog-formation potential. Then the remaining solution for a sustained avoidance of large amounts of exergy destructions is new exchanger designs, extending even to morphing HRV units with 4D printing technology, with embedded flexibility along with higher fan (including morphing fan blades) and higher motor efficiencies, supplied with renewable electricity on site.

The above discussion may hold from the tiniest HRV unit in a small home to waste heat recovery from thermal power plants like heat recovery from stacks of coal-fired power plants. In such cases, again, the exergy recovered from the waste heat in the stack may be less than the exergy spent for the heat recovery mechanisms like pumps and additional stack fans if a careful design and exergy-based optimum control is not implemented. The boiler-only option has the lowest COPEX value. The highest COPEX value, which is 0.95, belongs to HRV + Series HP case, provided that COP_HP is 11. Otherwise, i.e., for the condition of COP_HP < 11, there is no optimum solution and the singular solution goes to the x = 1 point (HRV only). The next better case is the parallel HP case and then the base case with COPEX = 0.613. The lowest COPEX is for electric resistance heating case that is running on grid electricity. This case has also the highest total CO₂ emissions rate.

The new composite index, namely ψ_R/ODI, which rates a system according to its exergy rationality per environmental footprint in terms of ODI is highest for HRV + Series HP case (Case 2). Therefore, it seems that the series coupling of the HP is a better alternative compared to parallel coupling with HRV. In turn, the HRV option has the lowest ODI value indexed to F gas. ODI originates from the GWP of the fossil fuels used in generating the electric power necessary for driving the oversized/added portion of the ventilating fans of the HRV unit.

A COP_HP value greater or equal to 11 is only possible for industrial HPs, using ammonia refrigerant. Figure 8 shows different cases of evaporator and condenser temperature cases. Obviously, in industrial scale, COP_HP > 11 may be achieved at a small condenser and evaporator temperature differences (see Figure 9). According to Figure 9, the difference must be less than 20 K. This provides the condition that first the outdoor climate must be moderate and the building must be nZEXB type, which demands lower heating temperature, second, due to the industrial size of such HPs, district energy systems must replace individual heating and cooling systems. It is hard to achieve such high COP values in smaller application sizes, like residential and small office buildings, unless the condenser/evaporator temperature differences are very small.

Figure 8.

Change of COP_HP with condenser and evaporator temperatures in industrial scale [37]

Figure 9.

Change of COP_HP with the condenser and the evaporator temperature difference [37]

This requirement for satisfying the condition COP_HP > 11 may be derived by referring to eq. (15) by writing the temperature difference between the outdoor and supply temperatures. This derivation imposes a lower limit on the outdoor air temperature:

$\begin{array}{l}{T}_{\text{o}}\ge T_{\text{f}}-\left(\frac{q-11}{r}\right)\\ \left\{q>11\right\}\end{array}$ (28)

A simultaneous solution of eq. (27) and eq. (28) may further relate E_XP to T_o. Thus, a variable-speed fan motor, which follows the outdoor temperature is essential. Eq. (28) further indicates that a residential HP with high q value and the low r-value is desirable. At the same time, to operate the HP at lower outdoor temperatures in colder climates, lower T_f must be applied. This is only possible by decoupling the sensible heating (or cooling) loads and ventilation loads and dedicating sensible loads to radiant panel systems [36]. For example, if T_f for ventilation only case is 295 K (22 °C) in an nZEXB, q is 12, and r is 0.05 K^-1, then from eq. (28), the outdoor temperature must be higher than 275 K (2 °C). This is a serious restriction for the operation of the HP in HRV coupled applications, particularly during cold climates.

On the other hand, the electrical power exergy demand E_XF for an HRV unit for a given sensible load Q is limited and must be related to the T_o limit given in eq. (28):

$E_{\text{XF}}\le Q\left(1-\frac{T_{\text{o}}}{T_{\text{f}}}\right)$ (29)

Table 5 shows that for all known electro-mechanical systems used for heat recovery in buildings, which seem to be very profitable and environment-friendly, COPEX values, which reveal and evaluate their global sustainability aspects better than COP are less than 1, which indicate that all electromechanical systems naturally destroy exergy and the best alternative is to minimize exergy destructions by an exergy-based method, like the one presented in this paper.

However, Table 5 deals only with HRV-dedicated systems and equipment covered by the isolated model shown in Figure 3. The origin of the electrical power supply is not included. If a holistic insight about the performance and responsibilities of HRV units and their ancillaries in the built environment is required, an expanded model is possible if the domain is stretched upstream back to the origin of the electrical power generation, transmission, and transformation simply by introducing their total efficiency η_T to eq. (17), which is shown in eq. (30). This expansion affects the isolated model in Figure 3 at the HRV and HP power inputs. This simple introduction makes it possible to trace the responsibilities of HRV units back to the primary fuel input concerning the electrical power supply through the grid (Figure 10). Terminal units in this model are represented by the last term regarding Q_FO in eq. (17) and eq. (30):

$OF=\rho C_{p}xV\left(T_1-T_{\text{o}}\right)\left(1-\frac{T_{\text{o}}}{T_1}\right)+\rho C_{p}yV\left(T_2-T_{\text{o}}\right)\left(1-\frac{T_{\text{o}}}{T_2}\right)-E_{\text{XEHP}}-\frac{cd\left[x+\left(1-a\right)x\right]V^{\text{m}+1}}{{\eta }_{\text{F}} {\eta }_{\text{bm}} {\eta }_{\text{T}}}\pm Q_{\text{FO}}\left|1-\frac{T_{\text{o}}}{T_{\text{av}}}\right|$ (30)

The current average η_T value in EU28^- countries is 0.4 [37]. Therefore, the HRV fan term (the third term) in eq. (17) increases by a factor of 2.5 (1/0.4). The OF values plotted in Figure 7 will decrease but the overall conclusions will remain unchanged. While eq. (1) already includes the term η_T, the holistic model may be applied to modify the CO₂ emission responsibility term, because there are additional exergy destructions taking place at the thermal power plants.

Two types of plants were identified namely a coal-fired (anthracite) plant with economizers and a combined-cycle, natural gas plant. Respective adiabatic flame (exergy source) temperatures are 2,453 K and 2,343 K. Reference temperature is 273 K. Exit temperature from the power generation stage is 550 K for a coal-fired plant and 450 K for the combined cycle, natural gas plant.

Figure 10.

Expanded (holistic) model of heat recovery in a building with grid power

Figure 11 shows the destroyed unit exergy of these two types of power plants. Let c_ic and c_iNG are the capacity-weighted factors of unit CO₂ emissions of installed thermal power plants, namely coal-fired and natural-gas-fired, respectively. Then for the energy mix of a given country, represented by c_imix that may be approximated from eq. (32), the second term of eq. (1) is modified in the following form:

$\Delta {\text{CO}}_2=0.27\left[{\epsilon }_{\text{des}}+\left(C_1{\epsilon }_{\text{desc}}+C_2{\epsilon }_{\text{desNG}}\right)\right]$ (31)

$c_{\text{imix}}=C_1\left(0.6c_{\text{ic}}\right)+C_2\left(0.2 c_{\text{iNG}}\right)$ (32)

Here, 0.6 and 0.2 are the unit CO₂ emission rates of anthracite coal and natural gas, respectively, at adiabatic conditions in the air. The unit is kg CO₂/kWh of fuel LHV.

Figure 11.

Exergy destructions in two types of thermal power plants

A better approach to eliminate the power supply-related disadvantages that have been revealed by the holistic model for the built environment is to move on towards passive houses. A renewable energy system example is the passive preheating of the outdoor air with a solar air heater system, typically installed on the roof of the sustainable building, which operates with the natural convection of colder outdoor air passing through the sandwiched duct beneath the PV panel. While colder air enters the PVT from the bottom, it rises and the indoor ventilation air is preheated. According to Figure 12, solar radiation intensity normal to the PVT surface I_n is 750 W/m². The Carnot cycle-equivalent solar source temperature T_sol, corresponding to I_n is calculated from eq. (33) [34]. 1,366 W/m² is the average value of the solar constant. Even when the A-A PVT operates without a fan (natural convection) it is responsible for avoidable CO₂ emissions:

$\frac{I_{\text{n}}}{1,366}=\left(1-\frac{T_{\text{ref}}}{T_{\text{sol}}}\right)$ (33)

Figure 12.

A-A (PVT) panel with natural circulation: winter mode

In the summer period, additional equipment and exergy sinks are involved, which are shown in Figure 13. The PVT panel is cooled by air, which in turn, is cooled by the utility water. Utility water after being warmed by exchanging heat with the exit air from the PVT panel is further heated through a ground-source HP on demand and at the absence of the cooling load, to avoid the Legionella disease risk and then stored in a DHW tank. Part of the electric power generated by the PV cells drives the GSHP, which satisfies the space cooling loads during the day time. The reject heat goes to the ground well. The air loop normally depends again on natural convection while a water pump is introduced for the ground loop. However, water pumps require less power than fans in transferring the same amount of heat [31]. In this arrangement, there is direct emissions responsibility at the power plant feeding the pumps through the grid.

Regarding a PVT system, the total output is not a simple addition of electricity and heat, because of their different unit exergy. Heat and cold also have different unit exergy. Depending on the ratio of power and heat generation, the rational exergy management efficiency ψ_R varies, which directly affects the added value of a PVT. Therefore, the cost of a PVT must be levelized according to exergy in terms of ψ_R. In this study, ELC has been developed, which combines exergy rationality in terms of ψ_R, the selling price PC, embodied costs EM, panel area A, and panel weight W [38]. ELC serves for establishing a new comparative metric, which may also be used for rating the exergo-economic performance of a PVT system:

$ELC=\frac{PC+EM}{{\psi }_{\text{R}}\left(A/W\right)}$ (34)

Furthermore, a second new metric, TI evaluates any system in terms of its energy efficiency (First Law), energy rationality (Second Law), and ODI. This gives a total evaluation index:

$TI={\eta }_{\text{I}} {\psi }_{\text{R}}\left(1-ODI\right)$ (35)

Figure 13.

A-A (PVT) panel with natural circulation: summer mode