Rate Parameters fundamental constraints

Most problems associated with approximate kinetics are avoided when Michaelis Menten-type rate equations are utilized. Though this choice sacrifices the possibility of analytical treatment, reversible Michaelis Menten-type equations are straightforwardly consistent with fundamental thermodynamic constraints, have intuitively interpretable parameters, are computationally no more demanding than logarithmic functions, and are well known to give an excellent account of biochemical kinetics. Consequently, Michaelis Menten-type kinetics are an obvious choice to translate large-scale metabolic networks into (approximate) dynamic models. It should also be emphasized that simplified Michaelis Menten kinetics are common in biochemical practice almost all rate equations discussed in Section III.C are simplified instances of more complicated rate functions. 

The symbols are P for profit, / for equality constraints, g for inequality constraints, x for optimization variables, y for dependent variables, and / (constant) for updated parameters. The objective function is a scalar measure of plant profit it is usually the instantaneous profit ( /hr), because the optimization variables do not involve the time value of money. Typical equality constraints include material and energy balances, heat and mass transfer relationships, and thermodynamic and kinetic models, and typical inequality constraints include equipment limitations limit compressor horsepower, and distillation tray hydraulics. The optimization variables are flow rates, pressures, temperatures, and other variables that can be manipulated directly. The dependent variables involve intermediate values required for the detailed models for example, all distillation tray compositions, flow rates, and temperatures. Because of the fundamental models often used in RTO, the number of dependent variables can be quite large, on the order of hundreds of thousands. 

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