Impact of Shape Factor on Energy Demand, CO 2 Emissions and Energy Cost of Residential Buildings in Cold Oceanic Climates: Case Study of South Chile

: The increase in energy consumption that occurs in the residential sector implies a higher consumption of natural resources and, therefore, an increase in pollution and a degradation of the ecosystem. An optimal use of materials in the thermal envelope, together with efﬁcient measures in the passive architectural design process, translate into lower energy demands in residential buildings. The objective of this study is to analyse and compare, through simulating different models, the impact of the shape factor on energy demand and CO 2 emissions depending on the type of construction solution used in the envelope in a cold oceanic climate in South Chile. Five models with different geometries were considered based on their relationship between exposed surface and volume. Additionally, three construction solutions were chosen so that their thermal transmittance gradually complied with the values required by thermal regulations according to the climatic zone considered. Other parameters were equally established for all simulations so that their comparison was objective. Ninety case studies were obtained. Research has shown that an appropriate design, considering a shape factor suitable below 0.767 for the type of cold oceanic climate, implies a decrease in energy demand, which increased when considering architectural designs in the envelope with high values of thermal resistance.


Introduction
Energy consumption is reflected in the gross domestic product (GDP) of a country. There is a close relationship between GDP and the required electrical energy, which increases every year at the country level and is sustained [1]. The world has created a legal framework to respond to the need to provide energy in the context of sustainable development, given the threats [2]. As a first initiative in the regulatory framework, in 1997, 37 industrialised countries and the European Union established the Kyoto Protocol [3]. A building, especially in the operation stage, can be a great potential consumer of energy, and only using measures and strategies in the design stage which involve insignificant increases in construction costs and significant benefits in energy demand (or energy need [4]) and emission reduction can significantly affect its energy consumption [5].
The energy efficiency of a building depends not only on the thermal properties of the materials in the envelope but also on its shape; the orientation and distribution of spaces, windows and closing ratios; interior temperature; the façade colour and protection against solar radiation [6]. All these parameters influence the passive design of a building, depending on the climatic zone in which it is located. The volumetric impact on a building at the design stage produces better efficiency during the life cycle of the home, reducing energy and natural resource consumption [7,8]. To optimise architectural designs for thermal envelopes, it is essential to study the climate of the building area in detail [9,10].

Shape Factor
As the surface of the building in contact with the outside is more significant, there will be more energy exchanges, which may be beneficial or unfavourable in certain types of climates [25], depending on whether the building seeks to conserve the heat inside it or dissipate it to the environment.
SFv is a simple equation that relates the enveloping surface to the volume (Equation (1)) [26].
where the SFv is directly related to the heating energy demand in a dwelling, Se is the surface area of the exposed envelope and V is the habitable volume. The higher the SFv (for an identical habitable volume), the higher the heating energy demand of the dwelling.

Climate Data and Climatic Zones
To validate the optimal SFv in buildings in cold oceanic climates, as shown in Figure 1, capitals of the southern zone of Chile were chosen-Concepción, Temuco, Valdivia, Puerto Montt, Coyhaique and Punta Arenas. These cities generally represent the climatic characteristics that affect the buildings. According to the study carried out by Sarricolea et al. [16] on the climatic regionalisation of continental Chile, all capitals studied using the Köppen-Geiger climate classification have climate C with an oceanic or marine influence. Table 1 shows the climatic zone and climatological station of each of the different cities. In Chile, the regulation that regulates the climatic zones of the country is the OGUC [20], which divides the territory into 7 zones-where Zone 1 is the warmest and Zone 7 is the coldest. where the SFv is directly related to the heating energy demand in a dwelling, Se is the surface area of the exposed envelope and V is the habitable volume. The higher the SFv (for an identical habitable volume), the higher the heating energy demand of the dwelling.

Climate Data and Climatic Zones
To validate the optimal SFv in buildings in cold oceanic climates, as shown in Figure  1, capitals of the southern zone of Chile were chosen-Concepción, Temuco, Valdivia, Puerto Montt, Coyhaique and Punta Arenas. These cities generally represent the climatic characteristics that affect the buildings. According to the study carried out by Sarricolea et al. [16] on the climatic regionalisation of continental Chile, all capitals studied using the Köppen-Geiger climate classification have climate C with an oceanic or marine influence. Table 1 shows the climatic zone and climatological station of each of the different cities. In Chile, the regulation that regulates the climatic zones of the country is the OGUC [20], which divides the territory into 7 zones-where Zone 1 is the warmest and Zone 7 is the coldest. Climatological data for the cities were extracted in *.epw format by the software Meteonorm 7 [27]. Table 1 shows the meteorological stations from which the data were obtained, with radiation periods between 1991 and 2010 and temperature periods between 2000 and 2009.  Climatological data for the cities were extracted in *.epw format by the software Meteonorm 7 [27]. Table 1 shows the meteorological stations from which the data were obtained, with radiation periods between 1991 and 2010 and temperature periods between 2000 and 2009.

CO 2 Emissions and Energy Costs of Fuels
As shown in Table 2, the theoretical values of CO 2 emissions and the lower heating value (LHV) for different fuels were calculated according to data obtained from different official sources [28,29]. Similarly, the cost of using different types of fuels is the price collected from official reports from the Chilean government [30] and other international studies [31][32][33]. For the present study, only the cost of fuel has been taken into account. The cost of equipment installation and maintenance has not been considered. The equipment used were boilers with a thermal efficiency of 90% and an outlet water temperature of 80 • C for heating [19]. For electricity, instead, an electrical system was used.

Case Studies
To carry out the present study, five buildings with different SFv and three architectural designs in each of the six capitals of the southern regions of Chile were studied, thus obtaining a total of 90 case studies. The buildings and the energy simulations were modelled following the Building Information Modelling (BIM) and Building Performance Analysis (BPA) methodology through Autodesk© software [34] based on the calculation methodology of ISO 52016-1:2017 [4], ISO 52017-1:2017 [35] and ISO 13789:2017 [36]. All models used the same calculation parameters, with 20 m 2 /person, an 18-22 • C temperature range, 0.5 air renewals/hour, person 1680 Wh daily heat gain and 2.29 Wh/m 2 equipment thermal gain. The characteristics of the different case studies are shown below. Table 3 and Figure 2 show the five residential building models (M1, M2, M3, M4 and M5) created. Each model varies from the highest to the lowest SFv. All models have a square plan with an increase of 10 m of façade between them, a 3 m height between floors and a flat roof. However, it is necessary to clarify that the building models used do not correspond to actual buildings. These models are theoretical, and all the buildings have common characteristics, with the SFv variable to be compared between them. These theoretical models have the same SFv as more common buildings. For example, on the one hand, M3 maintains the same SFv as a two-floor building with a 9.3 × 9.3 m floor dimension. On the other hand, M5 maintains the same SFv as a six-floor building with a 21 × 21 m floor dimension.

Building Geometry
However, it is necessary to clarify that the building models used do not correspond to actual buildings. These models are theoretical, and all the buildings have common characteristics, with the SFv variable to be compared between them. These theoretical models have the same SFv as more common buildings. For example, on the one hand, M3 maintains the same SFv as a two-floor building with a 9.3 × 9.3 m floor dimension. On the other hand, M5 maintains the same SFv as a six-floor building with a 21 × 21 m floor dimension.   Tables 4 and 5 show the three thermal envelope construction solutions (S1, S2 and S3) for the models described in the previous section. The ratio of window and door area will be 26.67% on all models. According to the material used and the thickness of each layer, each solution has different thermal transmittance (U-value).   Tables 4 and 5 show the three thermal envelope construction solutions (S1, S2 and S3) for the models described in the previous section. The ratio of window and door area will be 26.67% on all models. According to the material used and the thickness of each layer, each solution has different thermal transmittance (U-value).

Results
The results obtained in the models for (i) energy demand, (ii) CO2 emissions and (iii) energy cost are shown below.

Results
The results obtained in the models for (i) energy demand, (ii) CO 2 emissions and (iii) energy cost are shown below.  The results show that the city of Concepción (climatic zone 4) was the one that had the lowest required total energy demand under any of the proposed construction solutions and established models. In contrast, Punta Arenas (climatic zone 7) had the highest total energy demand.

Energy Demand
Regarding the design characteristics of the envelope in the different construction solutions considered, S1 is the solution with the highest energy demand in all the models and areas studied, due to the high value of thermal transmittance. The results show that the city of Concepción (climatic zone 4) was the one that had the lowest required total energy demand under any of the proposed construction solutions and established models. In contrast, Punta Arenas (climatic zone 7) had the highest total energy demand. Regarding the design characteristics of the envelope in the different construction solutions considered, S1 is the solution with the highest energy demand in all the models and areas studied, due to the high value of thermal transmittance. Figure 6 shows the impact of SFv on the annual energy demand in each city, depending on the type of construction solution used. The maximum variation in demand (considering M1 and M5 for all cities) was: S1 between 135.30% and 198.70%; S2 between 162.89% and 235.12%; and S3 between 174.29% and 244.71%.

CO2 Emissions
Due to the large amount of data obtained, only the results of S2 will be shown, since it is the most representative of all, considering, in turn, a representative city of each climatic zone-Concepción (4), Valdivia (5), Puerto Montt (6) and Punta Arenas (7). Figure 7 shows the CO2 emissions generated due to energy demand. The energy used to cool the buildings was assumed as electric for all models. However, the energy source used for heating was variable, based on the values presented in Table 1. For all climatic zones, the least optimal is the exclusive use of electricity, independent of the SFv of the dwelling. However, using biomass (wood and pellets) produces low emissions, mainly due to the neutral emission factor [19].

CO 2 Emissions
Due to the large amount of data obtained, only the results of S2 will be shown, since it is the most representative of all, considering, in turn, a representative city of each climatic zone-Concepción (4), Valdivia (5), Puerto Montt (6) and Punta Arenas (7). Figure 7 shows the CO 2 emissions generated due to energy demand. The energy used to cool the buildings was assumed as electric for all models. However, the energy source used for heating was variable, based on the values presented in Table 1. For all climatic zones, the least optimal is the exclusive use of electricity, independent of the SFv of the dwelling. However, using biomass (wood and pellets) produces low emissions, mainly due to the neutral emission factor [19].
A 160.62 to 235.12% increase in CO 2 emissions between climatic zones 4 and 7 was observed when using any heating system. In turn, implementing an S1 to an S3 in the thermal envelope reduced CO 2 emissions between 22.74% and 56.67% for all energy options.

Energy Cost
The energy cost of these alternatives is represented in Figure 8. In this figure, the annual cost of heating and cooling the buildings is shown depending on the SFv and the alternative used, expressed in USD/m 2 , based on the values presented in Table 2. The use of propane gas as fuel for heating is the most expensive option of all in any area studied; on the contrary, the use of pellets is the most economical. A 160.62 to 235.12% increase in CO2 emissions between climatic zones 4 and 7 was observed when using any heating system. In turn, implementing an S1 to an S3 in the thermal envelope reduced CO2 emissions between 22.74% and 56.67% for all energy options.

Energy Cost
The energy cost of these alternatives is represented in Figure 8. In this figure, the annual cost of heating and cooling the buildings is shown depending on the SFv and the alternative used, expressed in USD/m 2 , based on the values presented in Table 2. The use of propane gas as fuel for heating is the most expensive option of all in any area studied; on the contrary, the use of pellets is the most economical.
A 160.43 to 236.25% increase in cost between climate zones 4 and 7, when using any heating system, was similar to what happened in emissions. Implementing an S1 to an S3 in the thermal envelope reduces the cost for all energy options between 22.74% and 56.72%.
Propane gas has had a wide variation in cost between 12.52% and 236.25% for all the climatic zones analysed. The rate of decrease in cost varies depending on the climatic zone. In Concepción its cost drop fluctuates from 6.00 to 26.09% between each SFv interval considered; in Punta Arenas, this range was between 4.99% and 17.49%. The cost of the heating system was reduced between 52.16% and 63.30% using M1 and M5, respectively, when implementing S1, 34.23 to 48.60% with an S2 and 27.82% and 42.65% with an S3. A 160.43 to 236.25% increase in cost between climate zones 4 and 7, when using any heating system, was similar to what happened in emissions. Implementing an S1 to an S3 in the thermal envelope reduces the cost for all energy options between 22.74% and 56.72%.
Propane gas has had a wide variation in cost between 12.52% and 236.25% for all the climatic zones analysed. The rate of decrease in cost varies depending on the climatic zone. In Concepción its cost drop fluctuates from 6.00 to 26.09% between each SFv interval considered; in Punta Arenas, this range was between 4.99% and 17.49%.
The cost of the heating system was reduced between 52.16% and 63.30% using M1 and M5, respectively, when implementing S1, 34.23 to 48.60% with an S2 and 27.82% and 42.65% with an S3.

Discussion
In the present study, implementing S2 represents a 19.68 to 48.01% decrease in required power demand compared to S1; and a 22.74 to 56.16% decrease in consumption compared to the S3, depending on the city where the building is located and the SFv. Comparing our results with the study carried out by Danielski et al. [14], similar results are obtained, where the slope between the total energy demand per square meter and the SFv increases when using a construction solution with less thermal resistance in the envelope.
The impact on energy demand from reducing SFv was studied in various investigations. In Italy, different energy models, with form factors between 0.54 and 0.78, were analysed in different cities, reaching 34.09 to 43.14% differences in energy demand [37]. In Lithuania, a 33.77% variation in the required energy was obtained by decreasing the SFv from 1.35 to 1.17 [8]. In Sweden, heating demand was decreased between 18.00% and 20.00% by reducing the SFv from 1.70 to 1.01 in different cities [14].
Additionally, when comparing the energy demand of M1 and M5, 27.82 to 62.95% reductions were reached depending on the city and the construction system considered. The impact of SFv was less in the coldest city, Punta Arenas, where consumption only decreased by 27.82 to 52.16%. In contrast, in Concepción, energy savings fluctuated between 42.57% and 62.95%.
Whenever the SFv decreases, so do the difference in emissions by improving the architectural design. When the SFv is reduced from 1.067 to 0.302: implementing an S1 caused a CO 2 decrease between 52.16% and 63.23%; while with an S3, they decrease from 27.82 to 42.64%. With these and similar data from other studies [15], it has been shown that more significant benefits are obtained by improving the thermal resistance of the envelope when there is a higher relation between the exposed surface and the m 2 of the surface of the building.
Finally, in Chile there are other studies on the form factor in buildings and its influence on energy demand. For example, Vásquez et al. [38] investigated with the SFv of office buildings in the city of Santiago, Chile. They conclude that the SFv is essential in architectural design along with other variables such as solar radiation, light, wind or the immediate context.

Conclusions
This research showed an appropriate design considering a SFv suitable for cold oceanic climates, which implied a decrease in energy demand and CO 2 emissions. The main conclusions derived from this research are the following:

•
The architectural designs with high thermal transmittance values may require from 129.44 to 227.67% of the energy demand of the same building after implementing a solution with a low U-value. Energy demand is widely affected by the weather where housing is located; maximum variations between 135.30 and 244.71% exist for the same SFv and architectural design, depending on the city where it is located. • CO 2 emissions depend directly on the climatic zone where the building is located and the fuel used. For all cities, using biomass in heating systems has the lowest emission and cost values, as opposed to what happens when using electricity for heating. Differences in CO 2 emissions from 7.43 to 235.12% can be found between the different climatic zones for the same model. Similarly, the cost of the heating system is reduced by between 31.81 and 32.95% when switching from a fossil fuel, such as propane, to a renewable fuel, such as biomass in the form of pellets. • Overall, the impact of SFv, on both energy demand and CO 2 emissions, is greater when architectural designs with a high thermal transmittance value are implemented, reducing energy demand between 22.75% and 56.16%, depending on the area located. Based on the analysis, it is highly recommended to design buildings with a SFv below 0.767 for cold oceanic climates, such as in the southern zone of Chile. Among the values shown, energy demand and CO 2 emissions tend to stabilise for all the climatic zones and construction solutions studied, with only 9.03% maximum differences in the energy requirement for heating and 10.37% in CO 2 emissions.
These results are fully extrapolated to any area with climatic conditions similar to a cold oceanic climate. This study has considered the SFv as the main variable, although for a comprehensive architectural design other variables must be taken into account, such solar exposure, wind orientation and passive design characteristics.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.