Simulation of Recycles

Equations 13.19 to 13.26 form a set of 8 equations and 13 variables (mA and mB for each stream, X,rA,rB). Specifying the feed stream mA i and mB1, and X,rA and rB allows the set of equations to be solved. There are two basic approaches that could be adopted. 

Equation-oriented. The equation-oriented or equation-based approach solves the set of equations simultaneously. If the problem involves n design variables, with p equations (equality constraints) and q inequality constraints, the problem becomes one of  

Then the equations can be solved simultaneously to give m,1,5 = 39.8601 kmol mBt5 = 5.1527 kmol mA,4 = 2.0979 kmol m 4 = 97.9021 kmol 

If a material balance is to be solved, then the convergence variables can be taken to be the component molar flowrates. When a material and energy balance is to be solved, the additional convergence variables are usually taken to be pressure and enthalpy. 

Care needs to be taken if some components are present in trace quantities. If an estimated concentration is 0.5 ppm and the calculated value is 1 ppm, the scaled error is 100%. This is much too large an error for most variables and yet the absolute error might be acceptable for a trace component. In other situations, it might be necessary to define trace components with a high precision. A trace component threshold can be set, below which the convergence criterion is ignored. 

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Unfortunately, agglomeration is not yet an exact science that would allow calculation of equipment type and size. Rather, tests must be carried out, preferably with a representative sample of the material to be treated. In those cases where (sometimes substantial) amounts of preagglomerated material are recirculated, testing must include actual recirculation of comparable amounts or the simulation of recycle addition. 

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