Method intended to optimize the operation of a system for separating the constituents of a mixture

A method for separating constituents of a fluid mixture in a simulated moving bed system including a loop having a series of interconnected beds containing an adsorbent solid phase, the loop including zones with an injection point for injecting a feedstock with an injection flow rate and points for drawing-off an extract and a raffinate with a drawing-off flow rate, the method including directly imposing an initial working point upon an optimum working point of the simulated moving bed system by selecting initial values which are imposed upon fluid flow rate, from the flow rate of the feedstock and concentrations of different constituents in the feedstock from corresponding flow rates of an equivalent true moving bed system comprising the steps:

• (A) determining a material balance and from the material balance producing equations representing a propagation velocity of the concentrations of different constituents in a countercurrent moving bed system;
• (B) determining the flow rates of the equivalent true moving bed system by:
• a) modeling an equivalent true moving bed system with a thermodynamic adsorption model,
• b) locating, along the equivalent true moving bed system, compressive and dispersive fronts in concentrations of the different constituents,
• c) determining a propagation velocity of the compressive and dispersive fronts respectively by reference to a material balance for the simulated moving bed system by solving the equations, and
• d) zeroing a propagation velocity of selected compositions at chosen points of the loop;
• C) determining flow rates of the simulated moving bed system at an initial working point;
• and
• passing the feedstock through the absorbent solid phase while imposing the determined flow rates.