## 2 Materials and Methods
### Studied Gas Turbine  
The simulations contained in this article were performed using GSP, release 11, by the Netherlands Aerospace Centre (NLR). GSP is NLR's in-house simulation software dedicated to studying the performances of gas turbines and Brayton-derived power and propulsion systems. To perform this task, GSP performs the required calculations in a nondimensionalized way, averaging the fluid magnitudes of the cases over their cross areas and using 2 to 5 different variables. Efficiency maps can also be used in the case of compressors, turbines, and combustion chambers. The obtained solution at the outlet of one model's component is used to calculate the inlet conditions of the following one. The design point of the model is initially calculated in GSP, solving the nonlinear differential equations of energy, mass, and momentum balances [24; 25]. The program then calculates the different machine's operating points, calculating the deviations to the previously obtained design point. The employed general equations are shown in Equations (1) to (4) before being nondimensionalized and particularized. The mass conservation equation is shown in Equation (1), where \(\rho\) is the density and \(\overset{\rightarrow}{V}\) is the velocity. \[\frac{\partial\rho}{\partial t}+div\bigg{(}\rho\overset{\rightarrow}{V} \bigg{)}=0 \tag{1}\]  
The momentum conservation equations [26] are shown in Equation (2), where \(\tau\) represents the stress tensor, \(P\) is the pressure, and \(\overset{\rightarrow}{g}\) is the gravitational acceleration. \[\frac{\partial\bigg{(}\rho\overset{\rightarrow}{V}\bigg{)}}{\partial t}+div \bigg{(}\rho\overset{\rightarrow}{V}\overset{\rightarrow}{V}\bigg{)}=- grad(P)+div\big{(}\overline{\tau}\big{)}+\rho\overset{\rightarrow}{g} \tag{2}\]  
The energy conservation equation is shown in terms of the enthalpy in Equation (3), where \(\overset{\rightarrow}{\cdot\cdot}\) represents the contraction of two tensors, \(p\) represents the momentum change due to viscous dissipation and pressure, \(q_{r}\) represents the heat generation due to radiation, and \(\overset{\rightarrow}{J_{q}}\) represents the heat flux density. \[\frac{\partial(\rho h)}{\partial t}-\frac{\partial p}{\partial t}+div\bigg{(} \rho\overset{\rightarrow}{V}h+\overset{\rightarrow}{J}_{q}\bigg{)}+p:grad \overset{\rightarrow}{V}-div\bigg{(}p\overset{\rightarrow}{V}\bigg{)}=q_{r} \tag{3}\]  
\(\overset{\rightarrow}{J}_{q}\) is modeled according to [PERSON]'s law. This law can be written as shown in Equation (4) if only the conduction heat is considered, which is appropriate for the studied case. \[\overset{\rightarrow}{J}_{q}=\overset{\rightarrow}{J}_{q}^{\rightarrow}=- \lambda gradT \tag{4}\]  
\(\overset{\rightarrow}{J}_{q}^{c}\) represents the heat flux density caused by conduction. The different fuels studied in this article were tested in a gas turbine model representative of the medium-sized gas turbine range. This range is appropriate to study biofuels because it takes into account the current power demand needs (electrical) in society and the difficulties that may be found when producing biofuels. Accordingly, the chosen gas turbine model to study the effect of biofuels was the General Electric LM2500 PE. This gas turbine is an aero-derivative model derived from the GE CF6 turbofan engine family. This model has a single shaft, with its low-pressure turbine (component which is connected to an electricity generator) being a free power turbine. Its compressor has a 19.1:1 pressure ratio. This gas turbine provides, in nominal conditions, 23,292 kW when generating 60 Hz electricity [27]. This gas turbine uses natural gas as design fuel with a lower heating value (LHV) of 47,680 kJ/kg [28]. This natural gas has a lower LHV when compared to methane, which can be explained by the presence of inert components or larger hydrocarbons in it [28].