A rational exergy management model for curbing building [CO.sub.2] emissions.

INTRODUCTION

Today's inability to cope with the real issues of global warming stems from the fact that all energy projections, model studies, carbon emission and mitigation calculations, protocols, and energy system designs are based on energy efficiency. In contrast, the root cause of the irreversible impact of harmful emissions on nature with the end result of global warming lies within the scope of rational exergy management, which deals with the quality of energy resources and the quality of energy requirements of the built environment. The quality of energy that is defined as exergy is the amount of useful work that can be derived from a given amount of the energy source supplied. For example, the exergy of one kWh electric energy is higher than the exergy of one kWh thermal energy at 400 K (260[degrees]F) and even higher than the exergy of one kWh thermal energy at 300 K (80[degrees]F). Currently, there is a large imbalance among the required exergy and the supplied exergy. This imbalance compounds resource spending and harmful emissions in the case of fossil fuels. This is because the opportunities of utilizing most of the quality of supplied energy resources are missed. A simple exergy input and output type of exergy balance, similar to the energy balance, cannot show the large-scale imbalances at large, either. A key definition and a new methodology are necessary to bring all the energy supply, demand, and environmental issues and parameters on a common platform with a unified metric of rational allocation of energy resources in both quality and quantity so that humanity may reestablish a sustainable balance with nature. In order to satisfy this need, the Rational Exergy Management Model (REMM) was developed (Kilkis 2007).

DEVELOPMENT OF REMM

Figure 1 shows System (i) that bridges an energy source at temperature [T.sub.resource] and a useful application at temperature [T.sub.a] with an energy demand [P.sub.i]. During combustion of the energy resource at a flame temperature of [T.sub.f], the fossil fuel emits ci amount of [CO.sub.2] (kg or lb) to provide one kWh (one Btu) unit energy. Assuming that this temperature is uniform in System (i), [T.sub.f] may s[T.sub.a]nd for [T.sub.resource]. Fuel provides an exergy (useful work potential) of [[epsilon].sub.max], to the application with an energy load [P.sub.i], where it could be satisfied by a minimum exergy of [[epsilon].sub.min]. In order to satisfy [P.sub.i], however, System (i) must spend enough fuel equivalent to [P.sub.i]/[eta.sub.i] amount of energy. The emissions bear the same proportion.

[FIGURE 1 OMITTED]

Exergy is the useful work potential of a given amount of energy at a specified s[T.sub.a]te, based on the ideal Carnot cycle efficiency. Based on this, the basic exergy efficiency (second-law efficiency) compares the efficiency of a single actual process to an ideal Carnot heat engine, both of which are operating at the same conditions. Exergy efficiency is a measure of irreversibilities in actual processes and [T.sub.a]kes into account the exergy destroyed, whereas energy amount is not destroyed but only lost. Therefore, exergy is a better metric in analyzing the environmen[T.sub.a]l impacts of processes. Beyond a single process, environment is mostly impacted by sectoral imbalances among the supplied exergy and required exergy of many processes in the energy mix at large. In the built environment, such as buildings, usually the condition [[epsilon].sub.max] [much greater than] [[epsilon].sub.min] holds, which leads to missed opportunities of useful work potential and ends in avoidable additional [CO.sub.2] emissions. If, for example, a fossil fuel with high exergy [[epsilon].sub.max] is used in System (i) in a building only for space heating purposes, which have a very low [[epsilon].sub.min], most of the high exergy of the fossil fuel [[epsilon].sub.max], which could otherwise be used for electricity generation, etc., is wasted in an amount of ([[epsilon].sub.max]--[[epsilon].sub.min]). This is the amount of the useful work potential loss of the fuel spent. This loss represents the missed useful work opportunities that otherwise could be delivered for other applications by System (i). Now, another System (j) is required to make up the exergy loss at an expense of additional fossil fuel and to satisfy other applications that System (i) missed that it could otherwise satisfy with the original amount of fuel in[T.sub.a]ke. Therefore, the to[T.sub.a]l [CO.sub.2] emissions for which System (i) is responsible have two components: one is direct emissions from System (i), as shown in Figure 1, and the other component is the second-hand emissions from System (j), which has to [T.sub.a]ke over to satisfy missed application opportunities by System (i). The latter is usually unrecognized in emissions and environmen[T.sub.a]l models and left unaccounted for. In fact, the real global warming magnitude depends on the composite emissions of direct and secondhand emissions, not only due to energy inefficiencies, but, more impor[T.sub.a]ntly, rational exergy inefficiencies. In order to be able to [T.sub.a]ke into account such gross imbalances rather than a single process, rational exergy management efficiency (REME) was defined. The REME of System (i), shown by the symbol [[PSI].sub.Ri] that is associated with the arrangement shown in Figure 1, is

[[psi].sub.Ri] = [[[epsilon].sub.min]/[[epsilon].sub.max]]

Here, [[epsilon].sub.min] is the minimum exergy that can satisfy the unit energy demand [P.sub.i] of a system. A typical system may be a building with its thermal comfort system, and then [P.sub.i] becomes the heat loss from the building [T.sub.o] the outdoors when the indoor air temperature is higher than the outdoor temperature. While the heat load is primarily a function of the indoor comfort design air temperature [T.sub.a], indoor thermal comfort is primarily a function of the indoor operative temperature [T.sub.o]. If the indoor airflow is small, [T.sub.o] is the arithmetic mean of the indoor air temperature [T.sub.a] and the mean radiant temperature. Therefore, [T.sub.o] is a more comprehensive comfort metric than [T.sub.a], and it describes human comfort better. For forced-air heating systems, both temperatures are close enough that [T.sub.a] may substitute for [T.sub.o] for comfort calculations if the insulation level of the building envelope is good. However, especially for radiant panel heating systems, [T.sub.o] may be different from [T.sub.a], and this rule does not apply. According [T.sub.o] Equation 1, the avoidable loss of useful work potential (exergy destroyed, [[epsilon].sub.des]) between the resource and the application may be expressed in terms of [[PSI].sub.Ri]:

Lost useful work potential = ([[epsilon].sub.max] - [[epsilon].sub.min])

= [[epsilon].sub.max](1 - [[epsilon].sub.min]/[[epsilon].sub.max]) = [[epsilon].sub.max](1 - [[psi].sub.Ri]) (2)

On the energy source side, thermal efficiency [[eta].sub.i] must be taken into account in order to calculate the total useful work potential that is lost. Then, [[epsilon].sub.max] on the fuel input side becomes

[[epsilon].sub.max] = (1 - [T.sub.ref]/[T.sub.resource])(1/[[eta].sub.i]) {[P.sub.i]unity} (3)

Although the final sink of any process is the outdoor air temperature (IEA and ECBCS 2003), it varies much during the heating and cooling season. In order to establish a less timevariant common base for this model, the reference temperature [T.sub.ref] may be taken equal to the ground temperature [T.sub.g]. [T.sub.ref] may also be selected to be the temperature of the sea or lake that might be present in the close vicinity of the applications. In the heating season, because the ground temperature is about 283 K (50[degrees]F), such that

[[T.sub.ref]/[T.sub.resource]][much less than]1.

Equation 2 approaches

Lost useful work potential = (1/[[eta].sub.i])(1 - [[psi].sub.Ri]) {[P.sub.i] is unity} (4)

Another System (j) needs additional fossil fuel in order to make up the exergy loss. Therefore, [CO.sub.2] emissions are compounded due to rational exergy ineffi[c.sub.i]ency (exergy mismatch). This compound emission has two components:

* Direct [CO.sub.2] emissions: While System (i) satisfies demand [P.sub.i], it spends enough fossil fuel to receive energy of [P.sub.i]/[[eta].sub.i]. For the sake of simpli[c.sub.i]ty in mathematical formulations, [P.sub.i] will be taken as unity in the rest of this paper ([P.sub.i] = 1 kWh or 1 Btu). Then direct [CO.sub.2] emission from System (i) can be simply calculated from the given fuel property [c.sub.i]:

[CO.sub.2i] = ([c.sub.i]/[[eta].sub.i]) {[P.sub.i] is unity} (5)

* Avoidable [CO.sub.2] emissions: The amount of avoidable [CO.sub.2] emissions from System (j) attributable to the exergy mismatch of System (i), which is designated by the term [[delta]CO.sub.2j], is proportional to the lost useful work potential given by Equation 4, and [c.sub.j] is the property of fuel used in System (j).

[DELTA][CO.sub.2i] = ([c.sub.j]/[[eta].sub.i]) (1 - [[psi].sub.Ri]){[P.sub.i] is unity} (6)

The derivation of Equation 6 is given in Appendix A. In a sense, the avoidable emissions are analogous to second-hand smoking: nature is affected both from the primary pollution sources and from the additional fossil fuel burning to make up the exergy losses.

Compound [CO.sub.2] Emissions-Base Case (Business as Usual Scenario)

For two separate systems, namely, System (i) and System (j), which are shown in Figure 2, the value of the compound [CO.sub.2] emissions [summation over][CO.sub.2i] is a simple summation that is defined in Equation 7. In Figure 3, this concept is illustrated in more detail for a building that is heated by a natural gas-fired boiler and receives electricity from a distant natural gas-fired power plant. The power conversion and transmission efficiency [[eta]].sub.T] in thermal power plants and national grids are not better than 0.75. This efficiency includes thermo-mechanical conversion (such as steam turbine), mechanical to electrical energy conversion (electric generator), other parasitic losses, and transmission line losses. Therefore, this efficiency needs to be factored in, whenever applicable. Otherwise, [[eta]].sub.T] is one. Any end-user measure for reducing emissions, such as better insulation to reduce a building's thermal load, is factored in to Equation 7 when it is multiplied by [P.sub.i]. The lower the [P.sub.i], the lower will be the total compound emissions. As shown in Figure 3, System (i) consists of a natural gas-fired boiler that is used to heat a building to a comfort indoor temperature [T.sub.a] of 293 K (68[degrees]F). If the ground reference temperature is 283 K (50[degrees]F), and the flame temperature [T.sub.f] of the natural gas is about 2000 K (3140[degrees]F), then [[PSI].sub.Ri] is just 0.04. This means that 96% of the exergy available in the spent fuel is lost. In fact, exergy is destroyed, because exergy is not conserved as energy is. Instead, the same amount of fuel could be used first to satisfy other useful tasks, such as generating electricity to satisfy electric power demand in the same building or elsewhere. This option will be analyzed later in the section on Case Three.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[SIGMA][CO.sub.2i] = [CO.sub.2i] + [DELTA][CO.sub.2j] = ([c.sub.i]/[[eta].sub.i]) + ([c.sub.j]/[[[eta].sub.i][[eta].sub.T]])(1 - [[psi].sub.Ri]) {[P.sub.i is unity} (7)

Instead of taking this opportunity in the base case, the building heating system that is System (i) is connected via grid to a distant power plant that is System (j), in order to satisfy the electric power demand of the building. The distant power plant--if a thermal one--most likely uses exactly the same type of fossil fuel, such as natural gas, and due to the increased electric power demand due to this particular building, the power plant spends an extra but avoidable amount of fossil fuel, which in turn emits avoidable [DELTA][CO.sub.2i]. Rational exergy boundary encompasses first-law balance boundary, and beyond that, it provides a connected model by letting the rational exergy efficiency term chase the emission sources and relate all constituents. Because the power plant only generates electric power to the grid, the waste energy in the form of heat is released to the atmosphere through cooling towers, which serve as the necessary thermal sink for the thermodynamic process of the plant. If natural gas is used at both the power plant and the building, (ci = cj), and with typical values of [[PSI].sub.Ri] = 0.04, average [[eta].sub.i] = 0.75 and [[eta].sub.T] = 0.75, according to Equation 7; the compound [CO.sub.2]i emissions for unit energy demand [P.sub.i] are calculated below:

[SIGMA][CO.sub.2i] = ([c.sub.i]/0.7) + ([c.sub.i]/[0.7 X 0.75])(1 - 0.04) = 3.3[c.sub.i]

Instead of impacting nature with compound pollution, waste heat from the power plant could be used in the built environment for several purposes, such as district heating. Because the district will also become the thermodynamic sink for the power plant, the need for cooling towers will also be reduced. This option will be discussed below. As will be shown below in different cases, this model offers a way to find a matching suitable/possible source for a given exergy demand and can provide a design tool.

AVOIDING AND REDUCING [CO.sub.2] EMISSIONS (BUSINESS NOT AS USUAL)

The Rational Exergy Management Model gives important clues about sustainable ways and means of avoiding and reducing the [CO.sub.2] emissions. For example, Equation 2 clearly shows that this is possible by establishing a balance between the available exergy of the source and the required exergy on the demand side. Matching the demand side and resource exergies is a win-win situation because it eliminates exergy destruction on both sides. There are three obvious cases for sustainable solutions to avoid and reduce [CO.sub.2] emissions, which are detailed below.

Case One: Use of Plant Waste Heat in the Built Environment--District Energy System

Figure 3 gives a hint about a quite logical and sustainable solution, which is simply to deliver the waste heat from the power plant to the buildings in the district. This case, which is shown in Figure 4, eliminates boilers in every building that is served by the district energy system. Consequently, buildings do not consume fossil fuel for heating. The immediate result will be the elimination (avoiding) of the [CO.sub.2i] term in buildings. However, nothing has changed from the electric power demand point of view because buildings keep demanding electricity as before. Therefore, the [DELTA][CO.sub.2j] term remains:

[FIGURE 4 OMITTED]

[SIGMA][CO.sub.2i] = [DELTA][CO.sub.2j] = ([c.sub.j]/[[[eta].sub.i] X [[eta].sub.T]])(1 - [[psi].sub.Ri]) {[P.sub.i] is unity} (8)

Equation 8 may be interpreted as equal to the lost opportunity of generating electric power in the boiler system, which is now eliminated. With the same values about the replaced boiler--with [[eta].sub.i] = 0.7, transmission losses [[eta].sub.T] = 0.75, and [[PSI].sub.Ri] = 0.04--the compound carbon emission for Case One reduces to 1.8 [c.sub.i], which is only 55% of the base case. From Equation 8,

[SIGMA][CO.sub.2i] = ([c.sub.j]/[0.7 X 0.75])(1 - 0.04) = 1.8[c.sub.l].

It is imperative that even a simple modification may cut harmful emissions almost to half when compared to the base case (1.8 [c.sub.i] / 3.3 [c.sub.i]). Because the power plant delivers both power and heat at the same time with the same amount of fossil fuel, it becomes a combined heat and power system (CHP) (OECD 2006). A secondary advantage is the elimination of cooling towers because buildings have become heat sinks. Assuming that the district serves enough buildings such that the entire waste heat is consumed and neglecting exergy losses in the district hot water piping and pumping, the win-win situation is shown in Figure 5. Appendix B gives the details. Although the exergy loss is reduced, the overall efficiency, including transmission losses of electricity supply from large power plants to distant buildings, is not more than 35%. Therefore, Case One needs improvement.

[FIGURE 5 OMITTED]

Case Two: Use of Combined Heat and Power System in Buildings

Case One may be further improved by domestically replicating the CHP (combined heat and power) concept in a miniature scale in each building, which eliminates the large power plant. This is called a micro CHP system when the capacity is less than 50 kW. A micro CHP system may consist of a natural gas-driven internal combustion engine, which mechanically drives an electric generator. Waste heat from the engine and the exhaust gas satisfy the space-heating load of the building. The same engine delivers the electric power needed in summer for domestic use, and at the same time, its waste heat may be utilized in an absorption type chiller or a liquid desiccant system in satisfying summer comfort conditions in the building. DHW (domestic hot water) loads are also satisfied from the waste heat in both heating and cooling periods. Figure 6 shows Case Two. In this case, the [[DELTA]CO.sub.2j] term is eliminated because there is no need left for the central power plant. This also eliminates transmission losses ([[eta].sub.T] = 1). Above all, the overall efficiency [[eta].sub.i] of the system approaches 0.9, while [[PSI].sub.Ri] remains practically the same (0.75). From Equation 7,

[SIGMA][CO.sub.2i] = [CO.sub.2i] = ([c.sub.j]/[[eta].sub.i]) = ([c.sub.i]/0.9) = 1.1[c.sub.i]

[FIGURE 6 OMITTED]

Therefore, Case Two reduces carbon emissions further by 38%. This is now 67% less than the base case. The only emission is from the exhaust of the internal combustion engine.

CASE Three: Use of Alternative Fuels in Micro CHP Systems

In spite of all its advantages of reducing emissions and avoiding secondary emissions, Case Two, shown in Figure 6, is using fossil fuel. This can be avoided if the fossil fuel is replaced by alternative/renewable energy sources such as wind, solar photovoltaic, or alternative fuels such as biogas. In this case, [C.sub.i] will be negative (see Appendix B). Negative [C.sub.i] means that an alternative energy source is replacing a fossil fuel with a property [C.sub.i]. For example, if a wind turbine replaces the natural gas supply to an existing building in the stock and simultaneously satisfies the electric power and space heating demand of the building, then the emissions after the retrofit in that building stock will be negative. Mathematically speaking, the retrofitted building will become a negative-carbon building (Appendix B). Case Three is shown in Figure 7.

[FIGURE 7 OMITTED]

[SIGMA][CO.sub.2i] = [DELTA][CO.sub.2j] = ([-0.2]/0.7)(1 - 0.04) = 0.27 kg [CO.sub.2]/kWh

In Case Three, the building is retrofitted with renewable energy sources. A hydro-mechanical system such as a wind turbine or a zero-emission engine running on renewables such as solar energy operate a Stirling engine or a solar steam engine delivers mechanical power to an electric generator. The high-exergy electrical energy provided by the wind turbine is primarily consumed for domestic purposes in the building. The remaining electric power or the shaft power may be used in a ground-source heat pump (GSHP) to satisfy the comfort loads. Because the COP (coefficient of performance) is greater than one, the exergy efficiency will be proportionately high, although space conditioning is a low-exergy demand. GSHP satisfies both heating and cooling loads.

For the wind turbine case, a backup of the system can be any system running on renewables, such as a biomass CHP (combined heat and power). However, for economic feasibility and sustainability, these energy sources must be optimally balanced. If this system is retrofitting a base-case building, it is effectively replacing a 1.4 [c.sub.i] amount of [CO.sub.2] from the building stock, which is shown in Figure 8. If, however, a new building with a Case Three configuration is added to the same building stock, that new building shall have zero carbon status (see explanation in Appendix B).

[FIGURE 8 OMITTED]

RESULTS AND DISCUSSION

The base case and the other three cases explained above are compared in terms of their [CO.sub.2] emissions in Table 1 and Figure 8. The figure shows how the sustainable trend can be and should be followed for a greener, safer, and sustainable environment in the quest of using the last ten-year window of opportunity to reduce and, in effect, remove [CO.sub.2] emissions to stop global warming due to human activities. Figure 8 starts with business-as-usual scenario (base case) and then continues with several opportunities that are now quantified by the rational exergy management model. Case One is the first step in reducing emissions, but it is not sufficient. Case Two has the potential to cut emissions by almost 70% compared to the business-as-usual scenario. However, on a mathematical exergy balance sheet, negative carbon emissions are indeed possible if fossil fuel spending in micro CHP systems is replaced by renewables.

Table 1 lists data for the heating season. For an annual analysis, the cases given above need to be subjected to cooling loads and cooling systems. In the base case, cooling is generally provided by electric power-driven chiller units, with some market penetration of heat-operated units such as absorption chillers. In the first case, i.e., electric-driven chillers, electric power demand is higher than in the winter season. Except for the hot water boilers and heat-operated chillers in the summer period, there is virtually no heat demand for the base case (business-as-usual scenario). Although it seems that direct emissions from the building (no boiler) are eliminated, the secondary emissions at the central plant increase due to increased electric power load. Therefore, when the issue is the compound, total emissions for a given actual total electric power load of a building, the situation should not be expected to be much different from the heating case. In a similar manner, Case One may retain its benefits if heat-activated chillers utilize the waste heat from the power plant. The remaining cases also seem to be not too sensitive to the season of operation in terms of ranking. However, especially for an annual assessment regarding economics, savings, and reduction of annual carbon emissions, this model must be used on a case-by-case basis in order to achieve accurate results.

Carbon Wedge for Case Three

As of 2000, there were 81 million buildings (76 million residential, 5 million commercial) in the US, of which 75% were built before 1979 and need a substantial HVAC retrofit or replacement (EERE 2004; SCN 2000). Today, total electricity use in buildings worldwide accounts for 53% of the total global demand, up from 38% in 1971 (IEA 2006). Buildings are also responsible for about 40% of the total annual [CO.sub.2] emissions, more than any other sector (Torcellini et al. 2004; DOE 1998; EEET 2007). Some 38 million more buildings are expected to be built by the year 2010, which means that about 3.8 million new buildings will be built on average each year between 2000 and 2010 (EERE 2004). Therefore, at the beginning of 2007 in the US alone, there must be about 100 million buildings. Because of the large number of buildings in the US and the fact that about 75% of existing buildings require a heating or cooling retrofit, it is the right time and geographic location to implement Case Three applications for both building retrofit and new buildings in the US, without any delay. Of course, it is equally important to widely implement Case Three type of solutions in every country.

Table 1. Summary of Cases and Comparison with the Business-as-usual Base
Case

       Values for Cases                  Case Descriptions

[eta]i              0.70           Base Case: The exergy of the fuel
                                   input to the building does not
                                   have a match with the exergy
                                   demand. As a result, an
                                   additional amount of fuel input
                                   proportional to the exergy
                                   destroyed is needed from the
                                   power plant for electricity.

[psi]Ri             0.04

[[SIGMA]CO.sub.2i]  3.3[c.sub.i]

[eta]i              0.70           Case One: The fuel input is no
                                   longer supplied to the building
                                   for its heating needs; this
                                   replaces the boiler. It still
                                   acquires electricity from the
                                   power plant as before. As a
                                   change, the waste heat of the
                                   power plant is supplied to the
                                   building.

[psi]Ri             0.75

[[SIGMA]CO.sub.2i]  1.8[c.sub.i]

[eta]i              0.90           Case Two: The building is
                                   completely disconnected from the
                                   power plant. It satisfies all of
                                   its exergy demand from a
                                   decentralized combined heat and
                                   power system inside the
                                   building.

[psi]Ri             0.80

[[SIGMA]CO.sub.2i]  1.1[c.sub.i]

[eta]i              1.2

                    (0.4 . COP)    Case Three: The combined heat and
                                   power system is substituted with
                                   renewable sources. Wind power is
                                   used for electricity and a
                                   ground-source heat pump is driven
                                   by the same wind turbine to
                                   satisfy the heating demand.

[psi]Ri             0.91

[[SIGMA]CO.sub.2i]  0 or
                    -1.4[c.sub.i]

Case Three uses heat pumps, and according to a recent study (Halozan and Gilli 2001), there are 14 million heat pumps in US. However, almost all of these installations operate on electric power derived from central power plants (base case). Assuming an average COP value of 2.5 with today's HVAC technology (Halozan and Gilli 2001) and the overall electric supply efficiency of 0.37 (OECD 2006), this case with a primary energy ratio (PER) of 2.5 x 0.37 = 0.92 is not any better than a condensing type of high-efficiency boiler ([[eta].sub.j] = 0.97) belonging to the base case. Therefore, the number of buildings equipped with heat pumps is not excluded in estimating the total number of buildings in the US that qualify for Case Three. Keeping the new building rate between 2006 and 2055 constant (a conservative assumption), if the US building industry applies Case Three to 20% of new buildings built every year (3.8 million x 0.20 market penetration per year [approximately equal to] 0.8 million new buildings with Case Three per year) and retrofits 5% of the existing buildings every year, the carbon wedge in the next 50 years can be calculated. For the US power industry, an average carbon content of 0.6 kg [CO.sub.2]/(kWh) is used (OECD 2006).

Unit carbon wedges were calculated in the following manner, depending upon the application:

* For new buildings: (3.3-0)[c.sub.i], {per kWh unit demand of a building}

* Retrofits: (3.3-(-1.4)[c.sub.i] = 4.7[c.sub.i]. {per kWh unit demand of a building}

Carbon wedge per unit annual building energy demand (1 kWh) in the year Y is

[W.sub.carbon](Y) = [(Y - 2007) X 0.8 [10.sup.6] X 3.3 X 0.6 + [{(Y - 2007) X 3.0 + 100 X [(1 - 0.05).sup.(Y - 2007)]} [10.sup.6] X 0.05] X 4.7 X 0.6]/[10.sup.12] {2007[less than or equal to] Y [less than or equal to]2057} (9)

When Equation 9 is multiplied with the product of the peak power demand, annual average base load to peak load ratio (load diversity), and the annual building operating hours, the annual carbon wedge can be determined. On average, typical household peak power demand in the US is about 5 kW (EERE 2004), where it may be higher in office buildings and commercial buildings per square meter of floor area. When combined with domestic service water heating, total heat demand is 47% and electric demand is 53% on average (EERE 2004). However, smaller homes may have less energy demand and a different breakdown than commercial buildings. Based on a US average energy demand of 5 kW total, results of this research regarding carbon wedge are given in Figure 9. On the global scale, if the number of buildings is about 450 million and increase at the same rate as the US building sector (might be higher due to higher population growth), the global average of household energy demand (due to the wide scale of underdeveloped and poor housings globally) is estimated to be 1.7 kW only. US data may be extrapolated in order to estimate the global wedge. These results are also shown in Figure 9. With the CMI definition shown in Figure 10 (CMI 2006a), carbon emissions of the 2005 level (7 Gton/year) can be stabilized (stabilization triangle) until 2055 when projected emissions will be 14 Gton [CO.sub.2]/year if seven wedges are realized (see the inset in Figure 10). Then, one wedge equals one Gton [CO.sub.2] reduction per year by the year 2055 (CMI 2006b). Therefore, we understand that the rational exergy-based new wedge of Case Three will satisfy three wedges alone on global scale. Because the already identified seven stabilizing wedges defined by several authors (Pacala and Socolow 2004) do not factor in Case Three solutions presented in this paper, which are based on the rational exergy management model (Kilkis 2007), Case Three is introduced into the CMI scenario as an additional (8th) wedge and, thus, it will effectively reduce the [CO.sub.2] emissions by 2.7 Gton in 2055 from today's level of 7 Gton/year to 4.3 Gton/year, which is shown in Figure 11. This new wedge will be even bigger when the cooling season is also considered.

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

The figures above indicate the importance of balancing supply and demand exergies such that good exergy management may introduce an important wedge. However, the analysis should also address certain trade-offs. For example, biofuels may cause eutrophication besides the [CO.sub.2] emission reduction benefits. Although the life-cycle cost analysis (LCA) is very important in sustainability analyses, it is felt that unless exergy losses are quantified in terms of environmental costs and a consensus is achieved, an exergy-based LCA would be incomplete. Yet in this respect, this paper is a strong indication and motivation that exergy losses must be quantified in order to complete the sustainability picture in the near future.

NOMENCLATURE 

[c.sub.i] = carbon content of resource used in System (i), kg [CO.sub.2]/kWh (lb [CO.sub.2]/Btu)

[CO.sub.2i] = direct component of [CO.sub.2] emission from System (i), kg [CO.sub.2]/kWh (lb [CO.sub.2]/Btu)

Pi = energy demand (load) in System (i); taken as unity in the analysis, kWh (Btu)

Pj = energy demand (load) in System (j); taken as unity in the analysis, kWh (Btu)

REME = rational exergy management efficiency, dimensionless

[T.sub.a] = temperature of a useful application; for indoor thermal comfort, it is the indoor design air temperature, K ([degrees]F)

[T.sub.appj]= temperature at which the resource is rejected from System (i), K ([degrees]F)

[T.sub.appi] = temperature at which the resource is rejected from System (j), K ([degrees]F)

[T.sub.f] = flame temperature during combustion of the energy resource (fuel), K ([degrees]F)

[T.sub.g] = ground temperature, K ([degrees]F)

[T.sub.o] = operative temperature of the indoor space, K ([degrees]F)

[T.sub.ref] = reference environment temperature, K ([degrees]F)

[T.sub.resource] = energy resource temperature, K ([degrees]F)

[W.sub.carbon](Y) = carbon wedge per unit annual building energy demand in the year Y, Gton CO2/year

Greek Symbols

[eta] = energy efficiency, dimensionless

[[eta].sub.T] = electric grid transmission and parasitic losses attributable to a power plant, dimensionless

[epsilon] = useful work (exergy) that can be obtained from unit energy of the resource, kWh (Btu)

[[epsilon].sub.des] = destroyed component of the actual exergy of the resource due to exergy mismatch ([[epsilon].sub.max]--[[epsilon].sub.min]), kWh (Btu)

[[epsilon].sub.max] = resource exergy supplied to satisfy the unit load of a system, kWh (Btu)

[[epsilon].sub.min] = minimum exergy that could satisfy the same unit load of a system, kWh (Btu)

[[PSI].sub.Ri] = rational exergy management efficiency (REME) of System (i), dimensionless

[[eta].sub.i] = thermal efficiency of System (i), dimensionless

[SIGMA][CO.sub.2i] = compound CO2 emissions from System (i): [CO.sub.2i] + [DELTA][CO.sub.2i], kg CO2/kWh

[DELTA][CO.sub.2j] = avoidable component of CO2 emission from System (j) attributable to exergy mismatch in System (i), kg [CO.sub.2]/kWh

REFERENCES

Betz, A. 1926. Wind-Energie und ihre Ausnutzung durch Windmuhlen (Wind energy and its use by windmills). Gottingen: Bandenhoeck & Ruprect.

Campbell, P.R.J., and K. Adamson. 2003. Estimation of energy yield from wind turbine generators. Proceedings of Track 434, PowerCON 2003 -- Special Theme: BLACKOUT -- 2003.

CMI. 2006a. Carbon Mitigation Initiative, Princeton University, www.princeton.edu/~cmi/.

CMI. 2006b. The Stabilization Triangle, Princeton University, www.princeton.edu/~cmi/resources/CMI_Resources_new_files/CMI_Stab_Wedges_Movie.swf.

DOE. 1998. Emissions of Greenhouse Gases in the United States-2, Carbon Dioxide Emissions. Report No. EIA/ DOE-0573. Washington DC: U.S. Department of Energy.

EEET. 2007. Encyclopedia of Energy Engineering and Technology, 3 vols. B.L. Capehart, ed. New York: Taylor & Francis.

EERE. 2004. U.S. Department of Energy, Energy Efficiency and Renewable Energy, www.eere.energy.gov/buildings/ tech/.

Halozan, G., and P.V. Gilli. 2001. Heat pumps for different world regions--Now and in the future. Proceedings of the 18th WEC Congress, Bournes Aires, Argentina.

IEA. 2006. World Energy Outlook. Paris, France: Organization for Economic Cooperation and Development/International Energy Agency.

IEA and ECBCS. 2003. Guidebook to IEA ECBCS Annex 37 -- Low Exergy Systems for Heating and Cooling of Buildings. Finland: Valtion Teknillinen Tutkimuskeskus.

Kilkis, S. 2007. Development of a rational exergy management model to reduce [CO.sub.2] emissions with global exergy matches, honors thesis, Georgetown University, Washington, DC.

OECD. 2006. Energy Technology Perspectives: Scenarios & Strategies to 2050, in Support of the G8 Plan of Action/ International Energy Agency. Paris: Organization for Economic Cooperation and Development/International Energy Agency.

Pacala, S., and S. Socolow. 2004. Stabilization wedges: Solving the climate problem for the next 50 years with current technologies. Science, August, pp. 968-72.

SCN. 2000. www.smartcommunities.ncat.org/buildings/ gbintro.shtml. Smart Communities Network.

Torcellini, P.A., R. Judkoff, and D.B. Crawley. 2004. Highperformance Buildings. ASHRAE Journal 46(9):4-12.

APPENDIX A

Derivation of Secondary [CO.sub.2] Emission Equation

The exergy lost by System (i) must be made up by another system, System (j), which operates between [T.sub.resourcej] and [T.sub.ref] at an efficiency of [[eta].sub.j].

(1-[T.sub.ref]/[T.sub.resource]) ([P.sub.j]/[eta]) [greater than or equal to]Lost useful work potential = ([P.sub.i]/[eta])(1 - [[psi].sub.Ri]) (A1)

From the condition [[T.sub.ref]/[T.sub.sourcej]][much less than]1,(1/[eta])[greater than or equal to](1/[eta])(1 - [[psi].sub.Ri]) {[P.sub.i] and [P.sub.j] are unity} (A2)

If System (j) is using fossil fuel with property [c.sub.j], then at the limiting condition in Equation A2, the avoidable emission from this system is the responsibility of the rational exergy inefficiency of System (i). Then, [DELTA][CO.sub.2j]; can be expressed in the format given in Equation A3. This equation shows that the secondary emissions from System (j), namely, [DELTA][CO.sub.2i], depends on the performance of System (i) and the fuel property of System (j).

[DELTA][CO.sub.2j] = ([c.sub.j]/[[eta].sub.j]) = ([c.sub.j]/[[eta].sub.i])(1 - [[psi].sub.Ri]) (A3)

APPENDIX B

Rational Exergy Model for Central and Distributed Energy Systems Including Renewables

Consider the base case and Case One in Figure 5. Here, System (j) is the power plant. Natural gas is used to generate and then supply electric power to the grid. The waste heat exits the electric generation system in the plant at [T.sub.appj]. This heat is rejected to the air from cooling towers without being used in another useful application that can be realized at and below [T.sub.appi]. Independent from this available waste heat, the built environment spends additional fossil fuel to heat the buildings, which is shown in the second bar from the left in Figure 5. In this case, typically a natural gas boiler is used for space heating, which requires low exergy at about 350 K, where the flame temperature of the natural gas is around 2000 K. Therefore, this time, a large exergy is lost at the beginning of the process. When the waste heat is connected to the build environment with a district energy system, lost opportunities of useful work potential in the thermal power plant become captured opportunities. The rational exergy efficiency of any system for a given application is calculated from the following two equations for two different conditions regarding the sequence of exergy loss and application.

* If the exergy loss precedes the application (as in a System (i) building): In this case, a high-exergy (high-temperature, [T.sub.f]) resource such as natural gas is used in a low-exergy application such as building heating. In this case, the exergy between [T.sub.f] and [T.sub.appi] is lost and the loss precedes the application. Then,

[[psi].sub.Ri] = [[[epsilon].sub.min]/[[epsilon].sub.max]] = [(1 - [T.sub.ref]/[T.sub.appi])/(1 - [T.sub.ref]/[T.sub.resource])] (B1)

* If the exergy loss follows the application (as in System (j): power plant or (i+j): district energy): This is the case when the high-exergy resource is first utilized in a high-exergy application such as electric generation, but then the remaining useful work potentia [[epsilon].sub.des] is destroyed. This destruction could be avoided if some other useful applications were served by the remaining work potential. Because exergy destruction follows the application and all calculations for exergy are always referenced to [T.sub.ref], the rational exergy efficiency in this case is the complementary part of the above equation:

[[psi].sub.Rj] = 1 - [[[epsilon].sub.des]/[[epsilon].sub.max]] = 1 - [(1 - [T.sub.ref]/[T.sub.appj])/(1 - [T.sub.ref]/[T.sub.resource])] (B2)

For example, if [T.sub.resource] = [T.sub.f] = 2000 K, [T.sub.appj] = 650 K, [T.sub.appi] = [T.sub.a] = 293 K, [T.sub.ref] = [T.sub.g] = 283 K, [T.sub.appi+j] = 360 K:

[[psi].sub.Ri] = [(1 - 283/293)/(1 - 283/2000)] = 0.04 {Base case, building}

It should be noted that if the above reference temperature would be selected as 278 K instead of 283 K, [[PSI].sub.Ri] would change to 0.06, which is 2% points of increase. This gives an idea of the magnitude of the sensitivity of the rational exergy efficiency on the reference temperature. When the resource temperature is much lower than 2000 K, the dependence slightly increases. The following are sample calculations.

[[psi].sub.Ri] = 1 - [(1 - 283/650)/(1 - 283/2000)] = 0.34 {Base case, plant}

[[psi].sub.Ri+j] = 1 - [(1 - 283/360)/(1 - 283/2000)] = 0.75{Case one}

For the latter case (district energy), if more applications with lower temperature requirements, such as greenhouse heating, fish farm applications, etc., could be cascaded to building heating in the district such that [T.sub.appi+j] [right arrow] [T.sub.ref], i.e., 360 K [right arrow] 283 K, then from the latter equation above the rational exergy efficiency would reach 1 (maximum exergy efficiency).

Applications that Include Nonthermal Energy Resources

In Case Three for example, where a wind turbine locally generates mechanical power first and then drives both a GSHP, to satisfy the heating load of the building, and a generator, to satisfy the electric power demand, the above model is completely valid provided that the mechanical power derived from the wind turbine is mapped (transformed) to an exergy equivalent thermal process based on the Carnot cycle. For example, if the wind turbine delivers an exergy [[epsilon].sub.wind] of one kWh, which ideally requites at least 27/16 kWh of wind energy [P.sub.wind] (Campbell and Adamson 2003), the Carnot process maximum equivalent [T.sub.resource] temperature of the wind turbine exergy supply is

[[epsilon].sub.wind] = 1 = (1 - [T.sub.ref]/[T.sub.resource])(27/16) (B3)

Then,

[T.sub.resource][less than or equal to] [[T.sub.ref]/(1 - 16/27)] {[T.sub.resource]>[T.sub.ref]} (B4)

From the Betz condition about the maximum wind energy that can be harnessed from a wind turbine (Betz 2003), [T.sub.resource] is 695 K for [T.sub.ref]: 283 K. According to actual wind turbine efficiency, which is about 2/5 (Campbell and Adamson, 2003), a more practical value will be 470 K. Therefore, once the equivalent resource temperature of the wind turbine is calculated like the above, the rational exergy management model can be seamlessly applied to Case Three. If the wind turbine power is used directly and only in electric power production, the resource and application temperatures are the same. In this case, the rational exergy efficiency approaches one because all available wind power is utilized directly in electricity production without exergy loss:

[[psi].sub.wind] = 1 - [(1 - 283/470)/(1 - 283/470)] = 1.0 {Only electricity production}

If, however, the wind power is used through a heat pump or electric resistance heater in the building, part of the available exergy is destroyed because the heating process requires lower exergy than electric power generation and the difference of the supply and demand exergy is lost. Here, application temperature is the indoor air temperature (293 K):

[[psi].sub.wind] = 1 - [(1 - 283/293)/(1 - 283/470)] = 1.91

The above value is the exergy efficiency for a heat pump with its COP (coefficient of performance) equal to one, which corresponds to a simple electric resistance heating system. In fact, the GSHP COP in space heating is in the range of four. Depending upon how much of the mechanical power is split between electric generation and space heating, the actual rational exergy efficiency with a GSHP will be between 1.0 and 0.91. In such a wind energy system, because the [c.sub.wind] is negative, the impact of Case Three will be to remove [CO.sub.2] because it displaces an equivalent amount of emissions on the general exergy balance sheet. This condition is explained in Figure B-1. If, for example, one of the three buildings (Building 3) in a given building stock of the base case is retrofitted with a wind turbine, which replaces the natural gas boiler and the central power plant connection for building 3 altogether, the exergy balance on the original building stock [c.sub.wind] for that building will be -- 0.2 kg [CO.sub.2]/(kWh). Physically speaking, the total [CO.sub.2] of the three buildings will be reduced to the emissions of Buildings 1 and 2. Building 3 by itself is a zero carbon building but extracts emissions from the original building stock. Then the "secondary emission" [DELTA][CO.sub.2j] corresponding to the original boiler and power plant connection that are now replaced the wind turbine retrofitted Building 3 is negative. Because the building now has been completely disconnected from any System (j) and generates it own electric power, [DELTA][CO.sub.2j] is replaced by [DELTA][CO.sub.2i]:

[FIGURE B-1 OMITTED]

[SIGMA][CO.sub.2wind] = [DELTA][CO.sub.2i] = (-0.2/0.7)(1 - 0.04) = -0.27kg[CO.sub.2]/kWh {at building stock level for retrofit}.

Therefore, Building 3, based on the original balance sheet shown in Figure B-1, may be mathematically regarded as a negative carbon building. However, if a new building with a wind turbine system like Building 4 in Figure B-1 is added to the building stock, its [DELTA][CO.sub.2i] is zero (carbon neutral building).

[SIGMA][CO.sub.2wind] = [DELTA][CO.sub.2i] = 0 kg [CO.sub.2]/kWh {at building stock level for a new wind energy building}.

Exergy transformation may apply to any system or process. For example, the rational exergy efficiency of a dam that holds the potential energy of stored water behind the dam can be calculated by first transforming it to equivalent temperature [T.sub.resource]. For an automobile internal combustion engine, however, [T.sub.resource] is already known, which is the flame temperature of fuel; therefore, no transformation is required. For cases where chemical exergy besides the physical exergy becomes an issue in determining [CO.sub.2] emissions, [T.sub.resource] ([T.sub.f]) may be accordingly adjusted.

Siir Kilkis

Student Member ASHRAE

Siir Kilkis is a graduate researcher at Georgetown University, Washington, DC.