A method of heating a fluid utilizing a process heater having one or more first combustion zones and one or more second combustion zones. The combustion of a fuel is divided between the first and second combustion zones. The oxygen is provided for combustion within the first combustion zone by one or more oxygen transport membranes that contribute between about 50 and 99 percent of the stoichiometric amount of oxygen required for complete combustion of the fuel passing through the process heater. A supplemental or secondary oxidant is introduced into second combustion zone to complete combustion of the fuel and thereby produce a flue gas stream containing between about 1 and 3 percent oxygen to ensure complete combustion of the fuel. In this manner, the surface area of the oxygen transport membranes may be reduced below the surface area that otherwise would be required if 100 percent of the oxygen were contributed by the oxygen transport membranes.