Example of Input–Output LCA: Aluminum

4.4.3.1 Functional Unit, Reference Flow, and Final Demand

Let us revisit the example from Section 4.2.3 of an aluminum front-end panel of a car to illustrate a simplified I/O application, considering the same FU of a front-end panel with a given rigidity, transported over a distance of 200,000 km. Table 4.9 presents the major reference flows for the aluminum scenario, which by definition represent what is bought to achieve the FU (Section 3.3). It is thus straightforward to associate a price to each flow and to determine the final monetary demand (y) by FU.

This demand by sector will be the basis for calculating the inventory of emissions and resource extractions.

Our goal is to calculate the inventory of emissions and extractions using I/O fac-tors rather than process-based facfac-tors. Equation 4.9 is used to calculate this inven-tory, using the relevant economic and environmental matrices that characterize the interactions among economic sectors and the associated emissions and extractions.

Inventory Analysis of Emissions and Extractions 79

4.4.3.2 Economic Data and Determination of the I/O Economic Matrix As described in the previous section, each element of the I/O economic matrix à is calculated by dividing each entry in the relevant national transaction matrix Z by the total industrial output x of each column’s industry (Table 4.10). Z represents the expenses of each sector in every other sector, so $13,240 million is the amount spent by the electricity sector in the coal and petroleum sector. The total economic output of each sector is represented by x, so $132,400 million is the total amount spent by the electricity sector in every other sector, plus the value added by the sector itself.

The complete matrix Z reveals the principal supplying and consuming sectors for every other sector. In this simplified example, the dominant supplier to the alumi-num sector is the electricity sector, providing $1518 million of electricity. The largest consumer of the aluminum sector, out of the three industries considered here, is the aluminum sector itself.

The matrix à expresses intersector spending as a fraction of the total monetary output of a given sector, thus each ãij = zij/xj (the expenses of sector j in sector i divided by the total output of sector j).

TABLE 4.9

Quantity and Price Data for Aluminum Front-End Panel of a Car

Purchased Good

Aluminum 3.8 kg/panel $2.5/kg $9.50 Aluminum $9.50

Electricity for manufacturing

15.2 kWh/panel $0.07/

kWh

$1.06 Electricity $1.06 Oil for manufacturing 1.8 L/panel $0.32/L $0.58 Coal and

petroleum

Simplified Transaction Matrix Z and Total Industrial Output x˜ for Three Economic Sectors

Transaction Matrix Z Aluminum Coal and Petroleum Electricity Total Output x˜

Aluminum 976 0 0 5,688

Coal and petroleum 0.50 5,877 13,240 109,680

Electricity 1,518 1,243 27 132,400

Source: U.S. Bureau of Economic Analysis (see website listed in Appendix I).

Note: Values are in millions of dollars.

80 Environmental Life Cycle Assessment

The term 0.27, for example, means that for $1 of aluminum produced, the alumi-num sector has spent $0.27 in the electricity sector.

4.4.3.3 Environmental Data and Determination of the Environmental Matrix

Each element of the environmental matrix B is calculated by dividing the direct environmental emissions or extractions of a sector (Table 4.11) by the total output x of that sector (Table 4.10).

The first row of B lists the direct extraction of nonrenewable energy per amount spent in each sector (MJ/$M, where $M is millions of dollars), and the second row contains the direct CO₂ emissions per amount spent in each sector (kg_CO2/$M). It may seem surprising that the aluminum and electricity sectors have zero primary energy consumption per dollar. This is because rather than directly extract nonre-newable energy sources from the environment, these two sectors buy energy from another sector. In practice, most of the nonrenewable energy extraction is done by the “coal and petroleum” sector, with the extraction of uranium often not considered.

CO₂ emissions, on the other hand, occur in all sectors considered above, since almost any sector that uses energy directly emits CO₂.

TABLE 4.11

Direct Extraction of Nonrenewable Primary Energy from the Environment and Direct CO₂ Emissions, by Sector and by Year

Sector

Direct Extraction of Nonrenewable Primary Energy (MJ/year)

Direct CO₂ Emissions (kg/year)

Aluminum 0 1.1 × 10⁹

Coal and petroleum 6.26 × 10¹³ 7.6 × 10¹⁰

Electricity 0 1.5 × 10¹²

Inventory Analysis of Emissions and Extractions 81

4.4.3.4 Calculation of Total Monetary Output per Functional Unit

As described in Subsection 4.4.3.1, the total monetary output x per FU is the amount of money spent by each industry in all sectors to meet the demand y of one FU. It is calculated (Equation  4.8) by combiningy with (I − Ã)⁻¹, the associated indirect demand from all other sectors. In this example,

I A = demand in the aluminum sector induces $0.32 spent in the electricity sector when accounting for the entire supply chain. This also induces $0.034 spent in the coal and petroleum sector and $1.2 spent within its own sector over the whole supply chain.

The total output per FU for a front-end panel is thus calculated as follows:

The front-end panel thus induces $11.4 worth of goods or services produced by the aluminum sector, $12.7 by the coal and petroleum sector, and $4.3 by the elec-tricity sector.

4.4.3.5 Primary Energy and CO2 Emissions per Functional Unit over the Supply Chain of Front-End Panel and Gasoline

To reach an inventory of emissions and extractions over the FU, we multiply the output of each sector over the FU by the emissions and extractions per dollar in each sector. The environmental matrix B multiplies by the total output x to yield ũ, the life cycle environmental emissions and resource extractions per FU (Equation 4.9):

According to these calculations, the manufacturing and use of this front-end panel (including gasoline) requires 7520 MJ of primary energy and results in 59.5 kgCO2

emitted over the whole supply chain.

82 Environmental Life Cycle Assessment To have a general matrix that can be applied to any final demand, we calculate the E of the cumulative pollutant emissions and resource extractions over the whole supply chain per amount of demand (Equation 4.9):

As described previously, the vector ũ can also be calculated by directly multiply-ing E by the final demand per FU y.

4.4.3.6 CO₂ Emissions during Usage Stage

The I/O calculation in the previous subsection accounts for the supply chain of the aluminum front-end panel and consumed gasoline, but does not include the direct emissions during the use of the car. The combustion of 30.4  L of gasoline, with 2.32 kgCO2 emission per liter (Table 4.1), results in 70.5 kg of CO2 emitted during the use stage. Adding this to the 59.5 kg calculated in the previous subsection yields 130 kg of CO2 emitted over the manufacturing and use of a front-end panel on a car that travels 200,000 km.

4.4.3.7 Comparison with Process LCA

According to results from a process-based life cycle assessment (Section 4.2.3), an aluminum front-end panel uses 2193 MJ of nonrenewable primary energy and emits 135 kg_CO2 over its life cycle (Table 4.6). Compared with the I/O result of 130 kg_CO2, the two approaches appear to give similar results.

On the other hand, in this very simplified example, the nonrenewable primary energy consumption calculated by the I/O approach is over three times that of the process-based approach. Such differences are not uncommon, and it is therefore important to be aware of differences in the approaches and to carefully verify the compatibility of I/O and process data if they are ever combined in a single study.

4.4.3.8 Analysis of Impacts by Supply Chain Tier

An advantage of the I/O approach is the ability to separately consider the matrix for each tier of the supply chain, and thus analyze which tier results in the dominant contributions to emissions and resource use—do greater impacts result from the final production step or throughout the supply chain?

Figure 4.8 presents the cumulative contributions of energy use in each supply chain tier for the aluminum front-end panel. The three tiers closest to final production are responsible for 90% of the energy used in manufacturing. The third tier is responsible for the largest energy consumption, since the aluminum sector (first tier) spends a lot in the electricity sector (second tier), which itself spends a lot in the coal and petroleum sector (third tier), which is directly responsible for substantial energy consumption.

Inventory Analysis of Emissions and Extractions 83