Newton gmres method application to the methane partial oxidation reaction

Methane partial oxidation is one of the manufacturing processes of synthesis gas which can then be used as an environmentally friendly energy sources. to produce an optimal synthesis gas required an appropriate comparison of the reactants by modeling the problem in a mathematical model. the aim of this paper is to determine the ratio of the feed gas (oxygen and methane) which produces synthesis gas in a partial oxidation of methane by using newton's gmres method. other than that,to analyze the possibility of the formation of solid carbon compounds in the reaction. as if it is done directly through a chemical process is costly and time that is large enough. establishment of mathematical models is done by utilizing the laws and the general assumptions that apply in the chemical equilibrium reaction. modeling results in the form system of non-linear equations (snle) which will facilitate the analysis of the partial oxidation of methane. settlement is done using a numerical approach to the newton gmres method implemented using matlab program. the optimal ratio of the number of moles of o2 and ch4 obtained with newton gmres method with the same result using newton's method,which is 0.576715395935549. however,number iterations ie 6<8. so that the process with the use of newton's gmres method is faster than newton's method.