The adiabatic, turbulent, and partially premixed combustions of several shale gases and air in a co-axial type combustor are computationally examined under the effects of different equivalence ratios, inlet temperatures, flow rates, humidity ratios, pressure, oxid inlet temperatures and flow rates, and swirl velocities in this study. Shale gases are extracted from Barnette, New Albany, Fayetteville, and Haynesville areas of USA. ANSYS software is used for numerical calculations of combustion. Results show that the maximum NO emissions for Barnette, New Albany, Fayetteville, and Haynesville shale gas occur at the equivalence ratio of 1.42, 1.41, 1.4, and 1.39. The rising fuel inlet temperature increase NO and reduces CO emissions after 300 K. The increasing humidity ratio causes NO and CO mass fractions to decrease. The ascending pressure raises NO up to 4 bar and lowers CO emissions. The increasing oxid flow rate abates the mass fractions of both NO and CO. The rising swirl velocity escalates NO up to 15 m/s and decreases CO emissions for all the shale gas combustions.