Twenty five percent of the world’s coal supply is located in the US. Thirty percent of all generated electricity in the US originates from the burning of coal. Existing thermoelectric plants burn a mixture of coal and air that results in an exhaust product of NOx, considered to be harmful for the environment. In many coal plants, other fossils fuels are also used in conjunction with coal, such as methane. Methane can be used as tool for the burning of coal in a combustion unit. Thus, this research investigates the use of a High-Pressure Combustor fitted with a shear coaxial injector operating on a mixture of methane and oxygen. Burning with oxygen instead of air results in emissions of carbon dioxide and water, which can be processed and stored. The goals of the current project are twofold: 1) To design a feed system that will supply the combustor with methane, oxygen and carbon dioxide at predetermined flow rates and pressures and 2) To calculate the pressure drops across this system which include multiple components and fuel injector. Results presented include the final design of the piping layout, selection and list of components, and corresponding pressure drops. Detailed drawings of the feed system are also developed as part of this work. ANSYS Fluent is used to model the flow and pressure drop through the injector for carbon dioxide, oxygen, and methane lines. Pressure drops are presented as a function of flowrate for the system analysis.