## 1 Introduction  
Greenhouse gas (GHG) emission is a global problem that affects environmental and human health, and the industrial and transport sectors are responsible for 75% of the CO2 emissions [1]. In this scenario, strict regulations have been imposed by governments in order to control and reduce these GHG emissions. The European Union has defined key targets for GHG emission reduction of at least 40% [2], promoting the use of renewable energy up to 32% of the total energy share by 2030. In addition to CO2, combustion systems used in industrial and transport applications are responsible for other hazardous emissions such as CO and NOx, resulting in the interaction of carbon-based fuels and the nitrogen present in air [3]. To attend to the regulations, one possible solution is to find new technologies that improve the performance of current compression-ignition (CI) engines, combining them with sustainable fuels (like bio-fuels or e-fuels) and new combustion strategies. In this situation, oxy-fuel combustion appears as a good alternative [4]. In the oxy-fuel combustion concept, the air supplied to the system is replaced by a mixture of high-purity oxygen. In a real engine this mixture should be diluted with high exhaust gas re-circulation (EGR) rates for reducing the combustion temperature [5]. The clear advantage is the absence of N\({}_{2}\)-rich atmosphere, then the NO\({}_{x}\) formation is theoretically eluded, but the practical implementation is difficult because the production of pure O\({}_{2}\) is expensive. In a vehicle, the storage and transport cost of O\({}_{2}\) can negatively affect the application of this concept. A solution for the O\({}_{2}\) production can be cryogenic air separation (CAS), which can deliver oxygen with the acceptable purity level in a large-scale context [6]. However, the use of this CAS system has a high energy penalty combined with high costs [7]. Another possibility is to separate the O\({}_{2}\) from the air by using mixed ionic-electronic conducting membranes (MIEC). They appear as a potential alternative because they are around 10.5-17% cheaper and offer a reduction in energy consumption over 0.5-9% in comparison with the CAS technology [7]. [PERSON] et al. [8] developed a MIEC with high O\({}_{2}\) permeation and a production capacity around 62 mL/min/cm\({}^{2}\) of O\({}_{2}\) at 1000 \({}^{\circ}\)C made of Ba\({}_{0.5}\)Sr\({}_{0.5}\)Co\({}_{0.8}\)Fe\({}_{0.2}\)O\({}_{3-\delta}\) (BSFC). [PERSON] et al. [9] experimentally and numerically studied the performance of the oxygen transport through a MIEC BSFC under several fluid dynamic conditions. Combining experimental results with one-dimensional models and CFD simulations it was possible to obtain a high-accuracy, specific permeation model that characterizes the O\({}_{2}\) transport phenomena in a MIEC. Their results show that is possible to improve the O\({}_{2}\) transport through a MIEC and its production rate with a temperature increment from 700 \({}^{\circ}\)C to 1000 \({}^{\circ}\)C.  
The oxy-fuel combustion process has already been studied in different industry fields like power generation of the thermal industry [10; 11], oil refineries [12], and cement production [13]. In the field of internal combustion engines (ICE), some studies using the oxy-fuel combustion strategy have been reported. [PERSON] et al. [14] performed experiments in a spark-ignition engine under oxy-fuel combustion conditions by using methane with wet and dry EGR. Their objective was to determine the peak performance conditions for both EGR configurations and to make comparisons with methane-in-air engine conditions. Results showed that when the engine operates under oxy-fuel combustion, the engine efficiency was reduced due to the lower ratio of specific heats of the EGR if compared with regular air. [PERSON] and [PERSON] [15] studied the emissions from a CI engine with several volume proportions of N\({}_{2}\), O\({}_{2}\), and CO\({}_{2}\) in the working fluid.