**3. Aggregated embodied and operational carbon**

While the connection between U-values and operational energy/carbon is generally linear (**Figure 2**), embodied carbon tends to rise at a faster rate as buildings are insulated to better efficiencies. Only thermal conductivity is positively associated with operational carbon (i.e. the line is not dependant on the insulation type).

Embodied carbon however, is directly dependent on the type of insulation and increases in the level of insulation progressively increase the embodied carbon values relative to thermal conductivity of the material and its associated embodied carbon burden.

**Figure 2.** *Linear relationship between operational carbon and U-value.*

**Figure 3.** *Total carbon curve.*

**Figure 3** illustrates the total carbon curve (for PUR insulation as an example) for a typical dwelling. The key feature is that the aggregated total of the linear and nonlinear relationship is inevitably non-linear. The graph demonstrates a progressively diminishing return for incremental improvement in U-value measures. Reducing the total carbon value therefore becomes more challenging to achieve using the building fabric insulation levels.

The graph indicates an optimum thickness for the insulation level beyond which the additional embodied carbon investment cannot be recovered through operational carbon savings (the marked point on **Figure 3**). The optimal point can change as the base assumptions are adjusted in the analysis e.g., insulation type, climate, occupancy levels, etc. The key feature however is that the three lines form a curve that repeats in all comparable scenarios. Such curves will eventually flatten for a longer service life or the use of an insulation material with lower associated embodied carbon. Such analyses demonstrate where optimum net benefit is achieved. Beyond these optima embodied carbon burdens exceed operational savings, whilst in advance of these points embodied carbon investment usefully reduced operational requirements.

This form of analysis is key when it comes to designing low/zero energy buildings where the existing standards tend to move towards even lower U-value requirements. On a material level, the analysis demonstrates that many conventional insulation materials cannot achieve very low U-values without incurring carbon disbenefits, whilst other conventional or novel materials with lower embodied carbon relative to their thermal conductivities, can justifiably achieve ambitious U-values.

The flat nature of the total carbon curve naturally creates comparative points on the graph, where lower levels of insulation show parity to the more extreme measures. The identified areas on **Figure 4** are referring to the insulation levels that are within 5% variation of the sweet spot i.e., the total carbon level associated with the 300mm insulation is identical to that of 100mm, in this specific case, but within 5% similarity to the total carbon level on the sweet spot. The operational only approach suggests 50% savings for the same range. This is crucial to be incorporated in all future building design strategies if the lower emission targets are to be met where a decarbonised grid coupled with electricity dominated operational energy demand is in the horizon.

Such findings will have significant financial implications as well for building design where higher levels of insulation would be more difficult to justify in the future zero energy building codes and standards. This similarly applies to setting the energy efficiency targets for retrofitting the existing building stock around the world. *An Aggregated Embodied and Operational Energy Approach DOI: http://dx.doi.org/10.5772/intechopen.103073*

**Figure 4.** *Areas on the total carbon curve where lower levels of insulation show parity to the higher levels.*

It is important to realise that the optimal points on the total carbon curve may move towards lower or higher insulation levels depending on the occupancy patterns, climatic conditions, building function and service life, source of energy, HVAC type and settings, and the type of insulation used, but the approach will be valid and its key feature still applicable, as identified above.

In order to demonstrate the extent of variability in results, the following section demonstrate the application of a series of insulation materials on a case study building in the UK. The assessments were conducted on a three-bedroom semi-detached house built in compliance with the most recent Building Regulations in the United Kingdom, as outlined in L1A Conservation of fuel and power. The building has a total floor area of 80 m2 .
