Matlab Programs for Steady-State Design

For the ideal chemical cases, a dynamic model is simulated in Matlab. This model consists of ordinary differential equations for tray compositions and algebraic equations for vapor-liquid equilibrium, reaction kinetics, tray hydraulics, and tray energy balances. The dynamic model is used for steady-state design calculations by mnning the simulation out in time until a steady state is achieved. This dynamic relaxation method is quite effective in providing steady-state solutions, and convergence is seldom an issue. 

Specifying the conversion usually sets the product purities. The unreacted reactants wiU be impurities in the product streams. For the base case A + B = C + D system, the distillate will contain most of the umeacted A, and the bottoms will contain most of the unreacted B. For example, suppose 100 mol of both A and B are fed. If the conversion is 95%, there will be 5 mol of A and B that will leave the colmnn in the products. Most of the lighter reactant A will leave in the distillate with product C. Most of the heavier reactant B will leave in the bottoms. There will be some B in the distillate and some A in the bottoms. However, there will be essentially no D in the distillate and no C in the bottoms. 

If the distillate and bottoms impurity levels are equal, there will be 5 mol of impurities in each product stream in this example. Then, the total distillate will be 100 mol. The amount of C in the distillate will be 95 mol, so the composition of the distillate is 95 mol% C. Likewise, the total bottoms will be 100 mol. The amount of D in the bottoms will be 95 mol, so the composition of the bottoms is 95 mol% D. 

With all feed conditions and the column configuration specified (number of trays in each section, tray holdup in the reactive section, feed tray locations, pressure, and desired conversion), there is only one remaining degree of freedom. The reflux flowrate is selected. It is manipulated by a distillate composition controller to drive the distillate composition to 95 mol% C. The vapor boilup is manipulated to control the liquid level in the base. Note that the distillate and bottoms flowrates are known and fixed as the dynamic model is converged to the steady state that gives a distillate composition of 95 mol% C. The composition of the bottoms will be forced by the overall component balance to be 95 mol% D. 

Similar approaches are used for other chemical systems with different stoichiometry. In most cases the columns converged to steady-state conditions in about 15-20h of process time, which takes about 5-10 min on current personal computers. 

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