1. A computer-implemented method of simulating a multi-reservoir production system to maximize fluid production, the method comprising: obtaining, by a computer system via a communication network, wellsite data for fluids produced from each of a plurality of reservoirs in a multi-reservoir system having a common surface network; generating an initial fluid model for each of the plurality of reservoirs, based on the wellsite data obtained for the fluids produced from that reservoir; matching an equation of state (EOS) characterization of the initial fluid model generated for each of the plurality of reservoirs with a common EOS model of the multi-reservoir system, the common EOS model representing common fluid components for the plurality of reservoirs and at least one marker component that is unique to each reservoir; simulating fluid production in the multi-reservoir system for different points in the common surface network, based in part on the common EOS model; determining whether or not the simulated fluid production for each of the different points include mixed fluids from different reservoirs, based on the at least one marker component represented by the common EOS model for each of the different reservoirs; calculating properties of fluids to be produced at each of the different points in the common surface network, based on the determination, wherein: the calculation for each point at which the simulated fluid production is determined not to include mixed fluids is based on the initial fluid model for the corresponding reservoir from which the fluids are to be produced; and the calculation for each point at which the simulated fluid production is determined to include mixed fluids is based on a simplified compositional model that is generated as a function of the at least one marker component represented by the common EOS model for each of the different reservoirs from which the fluids are to be produced, wherein the simplified compositional model includes one or more interpolation tables of compositional values for different phase properties of the mixed fluids that are tabulated as a function of one or more interpolation parameters, and the one or more interpolation parameters include the at least one marker component that is unique to each of the different reservoirs from which the mixed fluids are produced; determining operating settings for a selected group of the plurality of wells corresponding to the different points in the common surface network, based on the calculated properties of the fluids to be produced at each point; and controlling, using control signals transmitted from the computer system to a wellsite control unit at each of the selected group of wells via the communication network, production operations of the selected group of wells according to the determined operating settings.