Fuel system having a coke filtration system

A fuel system for a gas turbine engine, the fuel system comprising:

• a fuel metering unit configured to meter a flow of a hydrocarbon fuel;
• a first heat exchanger fluidly connected to the fuel metering unit downstream of the fuel metering unit to receive the flow of the hydrocarbon fuel, the first heat exchanger being configured to heat the hydrocarbon fuel to a temperature from four hundred degrees Fahrenheit to nine hundred degrees Fahrenheit;
• a first plurality of fuel nozzles fluidly connected to the first heat exchanger downstream of the first heat exchanger to receive the hydrocarbon fuel heated by the first heat exchanger;
• a first coke filtration system including a plurality of filters in series, each filter of the plurality of filters including a filter element formed of a metal, a filter of the plurality of filters has a nominal micron rating from a half micron to forty microns, the first coke filtration system being located upstream of the first plurality of fuel nozzles and directly downstream of the first heat exchanger;
• a second heat exchanger fluidly connected to the fuel metering unit downstream of the fuel metering unit to receive the flow of the hydrocarbon fuel, the second heat exchanger being configured to heat the hydrocarbon fuel;
• a second set of fuel nozzles fluidly connected to the second heat exchanger downstream of the second heat exchanger to receive the hydrocarbon fuel heated by the second heat exchanger;
• and
• a second coke filtration system including at least one filter, the second coke filtration system being located upstream of the second set of fuel nozzles and directly downstream of the second heat exchanger.