## 2 Methodology
### Goal and Scope
#### 2.1.1 Function and Functional Unit  
The overall function of the system is the recovery and purification of hydrogen from two waste streams, and the use of this product for electricity production. The functional unit (FU) should reflect this function allowing the comparison in the life-cycle inventory [34]. The FU is the measurement of the function of the systems analyzed that enables these to be totally comparable among them. Due to the fact that a separation process was included here, so hydrogen is an intermediate product for the final electricity generation, it is reasonable to perform a fair comparison to other previous published references, which entails the definition of three different output-based and process-based functional units to reach all the intended functions:  
* Function 1: Generation of one unit of mass of the hydrogen at the requested purity of 99.97%, imposed on feeding a PEM fuel cell for stationary applications (Type I, Grade D) [35]. Based on this function, 1 kg of hydrogen with a molar purity of 99.97% was selected as a functional unit. This FU enabled direct comparison versus conventional hydrogen production processes to evaluate the possible environmental benefits associated with the recovery of the compound from waste gases.
* Function 2: Generation of one unit of electrical energy in the PEM fuel cell. To evaluate this function, the FU was 1 kWh of energy obtained from the fuel cell, which provided further information about the environmental burdens associated with the complete process and its viability as an energy source.
* Function 3: Treatment of one mass unit of the residual gas stream. As a result, the FU chosen was 1 kg of COG or APG introduced to the system, which allowed the analysis of the influence of the type of residual gas stream selected on the entire process. This function and FU were considered to benchmark against no treatment for the leaving gas stream. Therefore, it can be guaranteed that the recovery and further electricity generation is better from a life-cycle perspective than the direct release to the atmosphere.  
The most common functional units are grouped into fuel production in units of energy [36]; mobile application in units of covered distance [37], system production based on the power of the fuel cell [38], the type of vehicles [39], the type of fuel cell [40] or units of the area of the electrode [41]. However, it is possible to use two functional units at the same time and discuss the differences [42]. The selection of multiple functional units could be more accurate, providing better performance of the sustainability of the system, making the study more comparable with other LCAs. The use of several functional units was previously considered, in agricultural production systems [42], in food systems or waste management systems to provide a complete overview of the study. For instance, this procedure was considered when evaluating the management of several by-products [43], in fishmeal plants [44], or in the consumption of pilchard [45]. Moreover, other studies proposed the use of a dual FU for dairy products, combining both productivity and land use [46].