Conventional studies on enzyme kinetics assume that the substrate concentration remains constant. However, for catalytic reactions taking place in intracellular compartments, the substrate molecules are fed in and out of the compartment and are catalyzed into product molecules within the compartment. In this work, we use a chemical master equation approach to study the stochastic kinetics of a single enzyme for different reaction pathways with one or more intermediate states. We obtain velocity expressions that deviate from the Michaelis-Menten expression. We study the coefficient of variation, which is a measure of the noise strength as a function of the mean substrate concentration for systems where there is influx or/and outflux of substrate molecules. Our results show that the noise strength decreases with the increase in the substrate concentration and finally remains the same when the substrate is present in abundance.