## 1 Introduction  
Dimethyl ether (DME) is receiving increasing attention as alternative fuel and raw material. Its properties (low toxicity and ease of storage, transport, and distribution, high cetane index) are suitable for its use as fuel in different sectors (domestic, automotive, and electric power generation) [1; 2; 3]. Besides, DME is a potential raw material for the production of diesel fuels (such as dimethoxymethane and polyoxymethylene dimethyl ethers, via oligomerization) [4], and chemicals (methyl acetate, formaldehyde, ethanol, among others) [5], replacing methanol. Moreover, it can replace methanol for light olefin production [6; 7] and it is a H\({}_{2}\) vector through steam reforming [8; 9; 10]. In 2015 a DME production market of US$5.2 billion was reported, with an annual growth projection of 9.9% until 2024 [11], produced by methanol dehydration. The demand corresponds in a 65% to the consumption in Asia (mainly in China) as domestic fuel, replacing liquefied petroleum gases (LPG), being its price dependent on the market of methanol and of LPG, which can be estimated as the 75 to 90% of the price per unit mass of LPG [12]. The synthesis of dimethyl ether (DME) in a single-stage (STD process) is more effective than the conventional route in two-stages, and is of great interest for the utilization on a large-scale of the CO\({}_{2}\) co-fed with syngas, which can be obtained from sources alternative to oil and with greater availability (natural gas, coal, biomass, and wastes) [13; 14; 15]. The STD process co-feeding CO\({}_{2}\) together with syngas involves the following reactions:  
Methanol synthesis:  
\[\text{CO}+2\text{H}_{2}\leftrightarrow\text{CH}_{3}\text{OH}\ (\Delta\text{H}^{0}=-90.56\ \text{ kJ mol}^{-1}) \tag{1}\]  
\[\text{CO}_{2}+3\text{H}_{2}\leftrightarrow\text{CH}_{3}\text{OH}+\text{H}_{2} \text{O}\ (\Delta\text{H}^{0}=-49.43\ \text{ kJ mol}^{-1}) \tag{2}\]  
Water gas shift (WGS):  
\[\text{CO}+\text{H}_{2}\text{O}\leftrightarrow\text{CO}_{2}+\text{H}_{2}\ ( \Delta\text{H}^{0}=-41.12\ \text{ kJ mol}^{-1}) \tag{3}\]  
Methanol dehydration to DME:  
\[\text{2 CH}_{3}\text{OH}\leftrightarrow\text{CH}_{3}\text{OCH}_{3}+\text{H}_{2} \text{O}\ (\Delta\text{H}^{0}=-23.56\ \text{ kJ mol}^{-1}) \tag{4}\]  
Secondary reactions of paraffin formation (mainly methane):  
\[\text{CO}+3\text{H}_{2}\leftrightarrow\text{CH}_{4}+\text{H}_{2}\text{O}\ ( \Delta\text{H}^{0}=-206.30\ \text{ kJ mol}^{-1}) \tag{5}\]  
It is well established that the direct synthesis of DME is thermodynamically more favored than the synthesis of methanol and than the synthesis of DME in two-stages, because the in situ conversion of methanol into DME (Equation (4)) displaces the thermodynamic equilibrium of the reactions of methanol synthesis (Equations (1) and (2)), favoring the conversion of CO and CO\({}_{2}\)[16; 17; 18; 19]. Therefore, the STD process is an attractive route to accomplish two objectives, that is, the production of DME, and the utilization of CO\({}_{2}\). Combining both targets, the economy of DME would partially fund the CO\({}_{2}\) capture costs, which condition the implementation of the different technologies for its utilization [20]. This economic compensation would be achieved by replacing fossil fuels by DME in different industries (iron and steel, cement, oil refining, pulp, and paper) in which CO\({}_{2}\) capture is a priority [21]. The effort of the refineries to reduce CO\({}_{2}\) emissions is also to be highlighted [22], and the investment costs could be offset by the commercialization of DME as green fuel (without emissions of particulate matter and post-combustion shoot).