The natural gas (NG) constitutes a great energy source, economic and accessible, having an impact in the world energy balance, considered as an alternative source of fuel and other petrochemical products. The activation and the direct conversion of methane are a promising approach for the utilization of natural gas resource and also a great challenge in the science of catalysis. In previous works, the aromatization of C1 using various light paraffin as co-reactant was reported using Zn-ZSM11 catalyst [1-3]. C1 would be activated under non-oxidizing condition by interaction with C2 and with LPG. Very high levels of C1 conversion to Aromatic Hydrocarbons were obtained by interaction with C2 (molar fraction in the feed: C1/C1+C2 = 0.4-0.8) over Zn-ZSM-11 (molar fraction Zn/Zn+H=0.86) at 550 ° C and total pressure of 1 atm; with the aromatic hydrocarbon yield between 10-40 mol % C1 [3]. Anunziata et al. [1] reported that, in the activation of C1 with LPG, Aromatic Hydrocarbons were the main products in the whole range of C1 molar fractions (0.4-0.85), reaching to higher levels of C1 conversion (10-45%). Anunziata et al. reported the optimizations of methane activation with ethane over Zn-H-ZSM-11 zeolite, on one response: C1 Conversion [4].

The statistical experiments design is the process of planning an experiment to obtain appropriate data that can be analyzed by statistical methods, to produce concrete and valid conclusions. The objective of all experiment includes the descriptions of the responses to the treatment factors. The origin of the experiments design was in the twenties by the mathematician Fisher [5]; also Box [6-8], Cox [9], Kempthorne [10] and Cochran [11], have contributed on the design of experiments. Box and Wilson’s work [6] and statistical methods, developed for modeling phenomena and to find combinations of a number of experimental factors led to most favorable response. One of the main advantages in the response curve is to visualize the response for all levels of the experimental factors [6]. Specifically, the response surface design is classified as a simultaneous method, being used in the stage of optimization [12]. Their application allows selecting the optimum combination of levels, to obtain the best response for a specific condition [13]. In the RSM, factorial designs are carried out and the results are adjusted using mathematical models. They are known as displacement and design stages, respectively; they are repeated several times, screening the response surface obtained in the direction of the region of the optimum point.

The response surface allows inspecting, in a visual way, the response for certain area of the levels of the factors, allowing us to:

• Determine the combination of the factors levels that provides a good operative condition.
• Find the combination of levels that provides economic improvements.
• Investigate the mutual influence of the factors on the response variables, in analytic studies of fundamental processes.

Specifically, the response surface design is classified as a simultaneous method, being used in the stage of optimization. Their application allows selecting the optimum combination of levels, to obtain the best response for a specific condition [13]. The response y is described by a polynomial function of various independent variables xi [13]:

The response surface design and the strategic analysis implied that the response variable (μy) is in function of the levels of quantitative factors represented by the variables x1, x2, . . ., xk.

The polynomial models are used as practical approach to the real response function. The polynomial models commonly used for the analysis response surface are [6]:

- the lineal models of first order, applied to two factors:

- the quadratic model, or of second order, for two factors:

One approach to optimal performance is to vary one factor while keeping the other factors constant in order to get improved response with respect to the varied factor. This often does not bring about the effect of interaction of various parameters as compared to factorial design [11]. Response surface methodology is a useful model for studying the effect of several factors influencing the response by varying them simultaneously. The experimental design recently has been applied in the optimization of several processes [14-18].

Process modeling and optimization are very important matters in engineering to meet the stringent quality requirements in a globally competitive market [19]. The success of a process depends on the use of artificial intelligent techniques which are able to code operational knowledge and use this information for deciding optimal strategies for operations. In most of processes, more than one response has to be considered for optimization of process parameters. Therefore it is necessary to simultaneously optimize the responses that the researcher desires. In essence, the problem of optimization of various responses involves the selection of set conditions or independent variables that give an ideal result [20]. The hope is to select the levels of independent variables that optimize all the responses at the same time. Experiment design—response surface methodology (RSM) is used in this work to model and to optimize two responses in the process of activation of methane (C1) using ethane (C2) as co-reactant into higher hydrocarbons, over Zn-containing zeolite catalyst. The application of this methodology allows a better understanding of the influence of the different factors: time on stream (TOS), space velocity of C2 (GHSV-C2), molar fraction of C1/(C1 + C2) (XC1) and reaction temperature, on two responses simultaneously: C1 conversion and its conversion to Aromatic Hydrocarbons, achieving efficiency and effectiveness of this process. Box–Behnken design was development with different levels of the factors, determining its influence on the C1 conversion to Aromatic Hydrocarbons in order to obtain responses surfaces.

A design of experiment was carried out in order to optimize the C1 conversion to aromatic hydrocarbons. The statistic model applied in this work allowed us to optimized two responses simultaneously. Applying the statistic methodology, the best operation conditions can be found. The highest C1 conversion (mol% C) and the higher Aromatic yields were achieved working at these conditions. In the same way, the statistic methodology indicates that the following factors: XC1, the reaction temperature and the TOS–temperature interaction, have the higher effects to C1 conversion; and the factors: GHVS_C2, XC1 and reaction temperature have the higher effects to Aromatic Hydrocarbons yields.

According to our previous results of C1 activation with C2 [2, 21], the reaction mechanism seems to be a Rideal type. Ethane is adsorbed onto the catalyst surface generating active ad-species, which are impacted for C1 from gas phase. As the extend of the reaction modeled by a Rideal type take place with one ad-species and other in gas phase, the reaction ride increases with the partial pressure of the gas phase species and the number of the chemisorbed ad-species. We suggest that, this is the reason because the XC1 between 0.2 – 0.4 produces sufficient quantities of C2 ad-species and optimum partial pressure of C1 for the reaction. Remember that we work at a total pressure equal at 1 atm, as the XC1 increases to 0.8 it influences negatively tuned with lower C2 ad-species. If the reaction temperature increases to 580 ° C, C1 conversion increases but at higher reaction temperature such as 700 ° C, C2 is transformed alone in gas phase. When the time on stream increases over the levels of the factors selected by us (i.e. 100 min), the catalyst begins to deactivate slowly, producing the diminution of C1 and C2 conversion. The Zn-species incorporated into catalyst are active because its lower energy of its LUMO (lower unoccupied molecular orbital, acting as new and strong Lewis acid sites), allowing the chemisorption of active C2 ad-species, by the direct abstraction of a hydride producing a carbenium-like surface species through electron-donor-acceptor adducts (EDA) formation. Then, these species react in order to produce intermediates as C₃ and C₄ and more reactive olefins (C₂₌, C₄₌) and latter isoparaffin (i-C₄). The carbenium ad-species formed from them interact with C₁ producing its transformation to naphthenic and aromatics. It is interesting to observe, that the presence of strong Lewis sites (SLS) on the catalyst prevents the hydrogenation of intermediate alkenes, which would be efficiently introduced into polymerization, cyclization, dehydrogenation and aromatization complex mechanism. The statistic model applied in this work is a powerful tool to interpret the overall process from the multivariate parameters.