*2.2. Exergy Accounting Framework*

For the evaluation of a process system's performance regarding its environmental impacts and its sustainability, it is necessary to capture the interfaces—i.e., the inlet and outlet streams (Figure 2)—as only they have the potential for impact. The internal constraints and internal flows are resolved by the system calculation model; i.e., simulation or optimisation. EXA and EXL denote the exergy assets and the exergy liabilities of a stream, respectively.

Consider again Figure 2, in which the input and output streams are highlighted. The process inputs are the streams labelled as ethylene feed, water feed, and water (wash water). The outputs are the streams labelled as "purge", wastewater, and ethanol product.

Inputs and outputs can be distinguished from the interface streams. An output stream is either a product or waste. In the case of product output, liabilities are not assigned because a product stream only carries useful value but does not involve the exergy penalty. Exergy assets can be assigned to a product stream only if the stream content implies or has the goal of retrieving exergy capable of driving economic activities such as chemical processes or transport operations.

For waste streams, the determination of exergy assets or liabilities employs a notional (potential) workflow (Figure 5). The workflow involves attempted operations for exergy extraction/recovery first, followed by the end of pipe treatment of the residual stream and finally discharge. Any potential for

exergy extraction and utilisation is defined as an asset, and the need to add exergy to the remaining potential workflow is added to the liabilities.

**Figure 5.** Procedure for assigning exergy assets and liabilities.

The input streams to the processing system have to be considered. For this, it is necessary to realise that the input to any human-operated process system is a product output of an upstream system. This includes, besides intermediate products, the resource streams extracted from nature (since the extraction itself is already an operation). Following the principles defined for products, the direct exergy liabilities are not assigned to the input streams, while exergy assets are assigned only in the case of an energy conversion system as the main object of evaluation.

The above discussion only reflects the perspective of the local to downstream impacts of a process system. To enable accounting for complete supply chains as well as the overall LCA [75], it is important also to include the upstream environmental impacts, leading to the need to account for the embodied exergy [28]. In this case, instead of the potential downstream exergy flows, the account includes the upstream exergy inputs (liabilities/credit) and the exergy content of the evaluated streams, assigned as assets.

Having estimated the exergy assets and liabilities for each of the interface streams for a process system, they are summed up, producing the total exergy assets (Equation (2)) and the total exergy liabilities (Equation (3)) of the system.

$$\text{EX}\_{\text{assset}} = \sum\_{\text{input},i} \text{EX}\_{\text{assset},i} + \sum\_{\text{output},j} \text{EX}\_{\text{assset},j} \tag{2}$$

$$\mathbb{E}\mathbb{X}\_{\text{liabilities}} = \sum\_{\text{input},i} \mathbb{E}\mathbb{X}\_{\text{liabilities},i} + \sum\_{\text{output},j} \mathbb{E}\mathbb{X}\_{\text{liabilities},j} \tag{3}$$

Equations (2) and (3) can be applied to various contours, including specific process systems, supply chains or complete life cycles. They can be used to evaluate downstream and/or upstream impacts.
