Energy Costs of Energy Savings in Buildings: A Review

1. Introduction

2. Energy Return on Investment: A Revised Concept

2.1. Energy Production

In the first case, all energy required to implement a particular equipment or process (from cradle to grave) is accounted for: it is called the energy invested, E_invested. Then, all energy that this device or process will generate or produce, E_produced, during its lifetime is evaluated. Accordingly, the net energy is simply:

(1)

In the desirable situation, E_net, is positive, that is the device or process will generate or produce more energy than it took to implement it. On contrary, it could happen that the required amount of energy required from cradle to grave could be more important than the production. This could be due to a short lifetime and most of the time driven by the economics.

The concept can be applied to non-existing solutions, project starting from scratch, for which there is no production at all at the beginning. In this context it is possible to compare several solutions to one another based on this criterion.

Or, it could be applied to solutions improvements in which case the solutions will be compared to the existing one. In this latter case, E_net, has to be defined in terms of the improvement only.

2.2. Energy Saved

In a second–opposite–case, energy savings are considered. For this case, E_produced is replaced by E_saved. The savings, E_saved, are estimated for the difference between the amount of energy that the device, building or process would require provided nothing is done and the amount of energy it should consume with the implementation of the proposed device, building or process. On the other hand, E_invested does not account for the energy used by the device after the measures of economy are implemented. In this case, E_invested only accounts for the energy required to implement the solution or install the equipment (from resources extraction to commissioning not from cradle to grave). The energy used by the solution is already accounted for in the definition of E_saved.

(2)

In this case, a positive value of E_net accounts for savings (which are negawatts or a negative production) that are greater than the energy invested, which of course is desirable. To obtain a desirable effect associated with a positive value of E_net, the savings must be positive. On the other hand, the worst case solution is the case when the savings are negative, that is when, after an investment, the amount of energy used E_{consumed,after} is larger than that used previously in the original situation E_{consumed,before}. And this happens more often than we might think when the analysis failed to adequately predict the energy embodied into a solution and focused solely on the eventual savings over a somewhat short lifetime.

As for the case of production, E_net can be defined with respect to novel or additional measures of energy efficiency.

In both savings and production cases a positive E_net means a desirable effect and conversely.

2.3. The Energy Ratio: Energy Return on Investment

This analysis deals with the calculation of the ratio of the energy savings by a particular solution (over a given period of time) or the energy produced by some equipment or process to the energy required to implement the solution or install the equipment (from resources extraction to commissioning). This net energy analysis is sometimes called the assessment of energy surplus, the energy balance method, or the energy return on investment (EROI) [19,20,21,22,23]. In the case of energy production, the EROI is calculated from Equation (3):

(3)

The key challenge to obtain a meaningful value for this ratio is to correctly define the boundaries of the problem which is investigated and to include—or try to include—all the inputs and outputs in the process [22,23]. For instance, the production of gasoline should account for all the steps required to produce it and deliver it to the stations as in a life cycle analysis.

Of course, the higher this ratio, the lower the environmental impact per unit of energy is expected since less input is used for the same output and consequently less impact is felt by the environment [24].While several authors may argue that the energy consumption and its environment burden adequacy is not straightforward, it has still some merit as an indirect environmental impact indicator [25,26] it is likely to be linked with a better economic investment since the energy content is closely—but not necessarily linearily—related to the price of a product, a process or a service. As a result, energy sources involving a better EROI should be selected in preference to others [27,28]. This is especially true for renewable energy sources for which the environmental burden comes mostly from the extraction and transportation of the resources and manufacturing of the energy systems prior to their use. This concept is related to that of net energy, E_net, that is when E_net = 0, EROI = 1 and a negative E_net means EROI < 1.

Calculating the average EROI for an energy basket is complex. Nevertheless, there are some indications that the average EROI of the U.S. energy basket is close to 10 and that a lower EROI should induce negative economic impacts [29]. Hence, for the purpose of this discussion acceptable energy solutions should respect EROI > 10 or E_net > 9 × E_invested hence, energy solutions with a lower EROI should be discounted.

When a modification to a power plant or a device is carried out, the EROI can be evaluated. That is to determine whether or not the modifications lead to an increase level of energy production, ΔE_produced, is positive. This is always the case when a production project starts from scratch. There could nevertheless be projects for which the energy production after a modification is lower than what was previously obtained. Defined this way, the EROI is then:

(4)

with the obvious requirement that EROI > 1 to obtain a valid or sustainable modification.

2.4. Differences and Similarities in EROI

A practical problem arises when using the EROI metric in an energy savings application such as a building. There is a key difference between EROI calculated for energy sources and EROI calculated from energy saved. Hence, negajoules (J) and negawatt (W) are compared to joules (J) and watt (W) (to our knowledge no symbols exist for negawatt and negajoules. Hence, we propose to use these one).

(5)

While at first glance this change of definition might look only semantic, it involves much deeper consequences. The reason is that E_saved is an energy difference by itself whereas E_produced is not. Moreover, savings are positive that is the desirable situation is that after implementation of the measures one looks for less consumption while the desirable situation for production after implementation calls for more production.

EROI was originally solely conceived for energy production or energy production technologies and equipment. Hence, in this scenario energy produced and energy invested are both expected to be positive. In consequence, EROI will be always positive. Even when, the net energy production, E_net, is negative, the EROI is still positive but smaller than 1. As mentioned in the above paragraph EROI could either be positive or negative.

For energy efficiency (or savings), the concept holds with minor differences. It was said that the energy saved is a positive quantity. In rare circumstances, a poorly designed intervention might increase the lifetime energy consumption, which corresponds to a negative EROI since energy saved is then negative.

This situation might also be caused by a strong rebound effect, the Jevons paradox [30], where the users adapt their energy consumption behavior in a way that they increases the consumption of a good or a service made more affordable due to the improved efficiency to a point that the new energy consumption could exceed the original one.

In this case, there cannot be a definition of EROI of gain as the energy saved is by definition a difference. However, Equation 4 corresponds to Equation 5 when the savings are negative.

There are also situation for which the definition does not hold. For instance, energy efficiency measures may cost nothing. Energy efficiency measures like changing thermostat settings, closing an interrupter or cooling by natural convection have zero or near zero costs which means that EROI→∞.

But, there is an even more favorable situation where an improvement of one aspect of a building has for consequence the optimization of the performance of others systems leading to an overall net negative energy cost. For instance, the improvements to the insulation of the building envelope produce a given EROI for the insulation addition alone, but it may also allow for the reduction of the size of the heating system and hence produce savings on its embodied energy. This could lead to an overall lower total energy cost for the whole building, compared with the version with less insulation. Nevertheless, since in practice energy must be always used to implement a project, this situation is restricted to two cases: when comparing two hypothetical situations and when embodied energy of the replaced components can be recovered to the point that the net energy invested is negative. In the following discussion, only the first situation occurs.

From the strict mathematical point of view, this would produce a negative EROI (positive energy saved over a total negative energy cost). Hence, there are two types of negative EROI, one which is negative in term of energy savings and undesirable, and one which is positive in term of energy saved and highly desirable. Actually, this situation is better than EROI = ∞ since the embodied energy is lower than that involved in the original situation! To distinguish these two cases, the symbol † is to be used instead of—for the case where the embodied energy is lower. The reader must be warned however that the value of this type EROI must be interpreted in a different way than the usual one. Indeed, a small EROI means that little operational energy is saved compared to the embodied energy, while a large EROI means that little embodied energy is saved compare to the operational. In consequence, EROI value does not provide information about the relative desirability of the technical solutions.

2.5. A Schematic Representation of the EROI Complete Concept

To complete the picture, it should be noted that there are also the situations where the investment cost is negative and where the energy return is also negative. This situation is symmetric with the classical EROI and is treated the same way. These situations are described in the following diagram (Figure 1).

Figure 1. Energy return on investment (EROI) class (classical definition is in the upper right corner).

Figure 1. Energy return on investment (EROI) class (classical definition is in the upper right corner).

In Figure 1, there are four areas: (1) in the upper right corner, the EROI is positive that is the return and the investment are positive (which is the classical case for energy production leading to positive return with a positive investment); (2) in the lower left corner, the return and the (net) investment are negative leading to a positive EROI (symmetry of case 1); (3) in the lower right corner, the EROI is negative as the return is negative (you spend more energy) after a net positive investment; and (4) in the upper left corner is the case of a positive return with a lower embodied energy after the implementation of the measures.

2.7. The Energy Payback Time (EPT)

In several articles, the energy payback time (EPT) is given. The energy payback time is the period needed to recover the energy invested through energy saving or energy produced. By definition, it is the time after which the EROI reaches a value of one and the net energy is equal to zero. Hence, EROI over the life time is:

(6)

This brings the issue of the lifetime of components [32,33,34] and of the building itself, which are in general poorly defined. To handle this problem, it is often recommended to refer to the norm ISO 15686 Buildings and constructed assets service-life planning [35] or using a 50 years timeframe as a reference for major renovations, since it is acknowledged and used in many studies [36]. In the upcoming analysis, a 50 years period for the building life time and a 35 years period for the components lifetime are used.

3. Discussion Related to Specific Applications: Insulation and Windows

3.1. Insulation

Since a large fraction of the energy consumption in a building is used for space heating or cooling, optimization of the insulation is a critical issue. This is why optimization of insulation has been largely covered in the scientific literature and this is why the author chose to apply the above-mentioned concepts to this application.

The oldest paper known to us is the work of Muncey in 1955 [46], who worked on the optimization of insulation for Australian houses. This study has been followed by many others [47,48,49,50,51]. For all of them, the optimization was based on economic considerations. The first and only article performing optimization in term of energy uncovered by the current review has been written by Anani and Jibril in 1988 [52].

Insulation constitutes a classic case of diminishing return, since the impact of each new layer is inversely proportional to the insulation already provided by the existing layers. In consequence, it makes no sense to optimize the EROI, since the very first layer of insulation as a close to infinite EROI. This is why the objective is to minimize the total lifetime energy consumption and then calculate the EROI for this configuration.

For a simplest case, energy consumption for thermal control over the building lifetime takes the form [53,54]:

(7)

where U is the thermal conductance of the wall [W · K⁻¹], DD is the number of degree-day [K ∙ d], A is the wall area [m²], η is the efficiency of the heating or cooling system, and N the lifetime of the building [yr]. The equation is valid both for heating and cooling, but these contributions must be calculated separately. They are also valid in a constant climate. An evolving climate can skew the results compare to this static model [55,56,57,58,59,60].

The thermal conductance takes the form:

(8)

where R_w stand for the thermal resistance of the original wall(or roof) and R_i is the thermal resistance of the added insulation. Since thermal resistance increase linearly with the thickness of the insulation (t), the previous equation can be rewritten as:

(9)

where k is the “effective” thermal conductivity of the insulation material. Energy consumption for temperature control is then equal to:

(10)

The energy cost of the insulation layer is defined simply as:

(11)

where ε is the energetic cost per unit of volume of the insulation. The total energy consumed by the building over its lifetime is then equal to:

(12)

where E_h and E_c are the energy use for heating and cooling, respectively. To minimize the total energetic cost, the derivative of E_t with respect to t is set to be equal to zero. The optimal insulation thickness is then equal to:

(13)

From this expression, the energy saved for heating and cooling is simply

(14)

Substituting t_opt, yields

(15)

As the invested energy is equal to:

(16)

combining these two elements, leads to the following expression for the EROI:

(17)

In the previous equation, only insulation properties can be controlled by design. Hence, we define the insulation quality factor such that:

(18)

From this simple first order analysis, we can see that EROI is inversely proportional to the wall existing insulation, to the square root of the lifetime cumulative degree-day scaled by the efficiency, and inversely proportional to the square root of the product of the thermal conductivity. This simple relationship will be used to normalize the various reported return on investment analyses to a common DD, N, R_w and η. In addition, one shall note that the square root relationship between DD, EROI and optimum insulation thickness imply a smaller thickness and a larger energy consumption than that obtained by a simple linear relationship.

To the best knowledge of the authors, this behavior was not considered when translating the passivhaus standard [61] to other climate zones. Indeed, the standard in terms of kWh/m² is kept constant, while this standard should be relaxed if the minimum lifetime energy consumption is the overall goal, as in the original passivhaus philosophy. This approach has the unfortunate consequence of increasing the overall energy consumption over the life time of the building compared to the optimal configuration by overinsulating it in the northern countries. A similar concern has been raised by Szalay [62] in the context of the European Building directive.

In recent times, optimization studies on insulation are mostly done in countries in economic transition. Especially, there are numerous studies done in Turkey ([63,64,65,66], among many). This is fortunate since this dataset is essentially internally consistent, which helps to point the underlying factor affecting the EROI.

The data from these studies [63,64,65] have been normalized to a 50 years lifetime (Figure 2). In addition, to reduce the dispersion of the data points, the analysis has been limited to the cases were polystyrene was used as an insulator. Therefore, in Figure 2, five curves from [64] can be found along with an extra vertical one that corresponds to an analysis with different fuel for on specific climate [65]; three others points come from [63]. The residual dispersion comes from the economic assumption at the basis of the optimization and the original uninsulated wall thermal resistance. From each set of points reported, the square root relation between heating degree-days and the EROI can easily be observed.

Starting with the overall results reported in Figure 2, the EROI for optimum total energy consumption has also been calculated based on the physical data provided in reference [63,64,65] (Figure 3). Since economic assumptions are now absent, the dispersion is much lower. It is dominated by the variation of the wall thermal conductivity in the absence of insulation and the efficiency of the heating system used. Overall, the optimum EROI tend to be lower than the published values from the literature since the economics optimization is done after for shorter lifetime (10 years) than the one we used for the energy optimization (50 years).

Figure 2. Calculated EROI economically optimum insulation thickness from literature.

Figure 2. Calculated EROI economically optimum insulation thickness from literature.

Figure 3. EROI for energetically optimized of insulation layers.

Figure 3. EROI for energetically optimized of insulation layers.

It should be pointed out that air in a cavity is itself is a good insulator [66,67,68,69]. The EROI of an air insulating layer is infinite (as Q_i = ∞ since it costs nothing (ε = 0)). Moreover, adding air may reduce the amount of embodied energy in a wall insulation solution thus lowering the denominator of Equations 4 and 17. However, in practice, the situation is more complex. For example, in the previous papers [66,67,68,69], an air cavity is left within a wall. In these cases, there is no additional cost associated to the air confinement. But, since the air cavity allows the utilization of a thinner insulation, its cost is negative, while improving the overall insulation and the net energy saved compared to a wall without the air gap. Hence, from the data of Mahlia and Iqbal [69], EROI of the air gap is between †0.7 and †8.7, since the air gap allows a reduction of the embodied energy in the insulation.

We note that a similar work has been carried independently by Harvey [70], who used the energy payback time and the marginal energy payback time to optimise the insulation layer of a building. He also used a quality factor for the insulation material, that is equivalent to 1/Q_i² (Q_i is defined in the Equation 18). However, he did not notice the existence of an optimum insulation thickness excepted for greenhouse gas emission (Figure 6 of reference [70]).

It is worth noting that while studying the global energy optimization of a building, Bribián et al. [71] found that added insulation increased the cooling loads due to the increase difficulty in evacuating heat. This anti-insulation effect has been discussed extensively by Masoso and Grobler [72]. It is not captured in our simplified model, but is significant only in situation were the internal heat loads are comparable to external heat loads.

When optimizing the total energy consumption of a desert dwelling by optimizing its wall, Huberman [73] obtained an EROI of †0.97; the actual base case (reinforced concrete with 6 cm of expanded polystyrene and stone facing) having a larger embodied energy than the most efficient configuration (stabilized soil block with 6 cm expanded polystyrene and stone facing).

A comparative analysis was carried by Pulselli et al. [74] between 3 wall designs (reference, plus insulated and ventilated) in three cities (Berlin, Barcelona, Palermo). From the payback time given by the author the EROI varies from 8.2 to 13 for the plus-insulated design and from 9.7 to 15.8 for the ventilated wall.

Utama and Gheewala [75] studied the impact of using a double wall instead of a single one in a typical residential high rise building in Jakarta, Indonesia. They found that while the double wall had a larger embodied energy (79.5 GJ per apartment vs. 76.3 GJ), life cycle energy consumptions over 40 years were 283 GJ versus 480 GJ. Over this time period, this would translate in a EROI of 61.6. However, if we extend the lifetime at 50 years, maintenance for the double wall should be added (9 GJ). This was not include for the previous calculation due to its lower maintained compared to the single wall. Accordingly, this would bring the EROI over 50 years at 20.5. This analysis is a good example of the importance of the definition of the boundaries of the analysis.

4. Conclusions

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