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This paper shows the potential benefits of implementing four configurations of reed valves at the inlet of the two-stroke compressor used in the double compression expansion engine (DCEE) concept or 8-stroke engines over the conventional poppet valves used in 4-stroke internal combustion engines. To model the reed and poppet valve configurations, the discharge coefficient was estimated from RANS computational fluid dynamics simulations using ANSYS Fluent 2020 R1, with a pressure difference up to 0.099 bar. The calculated discharge coefficients for each case were then fed in a zero-one dimension model using GT-Power to understand the valve performance i.e. the volumetric efficiency of the compressor cylinder and the mean indicated pressure during the compression process at 1200 rpm.