Parameter Estimation and Reconciliation

While some reconciliation models only have material balance relationships, more meaningful reconciliation results are obtained with models that include material balances, heat balances, equilibrium constraints (both in the separation and reaction domains), rate relationships (heat transfer, mass transfer, momentum transfer, and kinetics), as well as equipment-specific relationships. In other words, one should include more than just material balance constraints when reconciling a model. Heat balance, kinetics, transport relationships—if needed for the 

DOFs in an optimization case are independent variables that have final control elements, such as valves. These DOFs include FICs, PICs, TICs, and AICs. Objective functions typically are ones that maximize operating profit (EProduct values — TFccd costs EUtility costs). The aforementioned objective function can serve well in both sold out and market limited economic environments. The different economic environment can be imposed by simply bringing a product flow limit into play (for the market limited situation) or out of play (for the sold out 

SUMMARY OF SIMULATE/OPTIMIZE/PARAMETER/ RECONCILE CASES 

Both the Parameter and Reconcile cases determine (calculate) the same set of parameters. However, these cases do not get the same values for each parameter. A Parameter case has an equal number of unknowns and equations, therefore is considered square in mathematical jargon. In the Parameter case, there is no objective function that drives or affects the solution. There are typically the same measurements, and typically many redundant measurements in both the Parameter and Reconcile case. In the Parameter case we determine, by engineering analysis beforehand (before commissioning an online system for instance) by looking at numerous data sets, which measurements are most reliable (consistent and accurate). We believe these, that is, we force the model and measurements to be exactly the same at the solution. Some of these measurements may have final control elements (valves) associated with them and others do not. The former are of FIC, TIC, PIC, AIC type whereas the latter are of FI, TI, PI, AI type. How is any model value forced to be exactly equal to the measured value The offset between plant and model value is forced to be zero. For normally independent variables such as plant feed rate, tower 

Parameter to Reconcile to Simulate to Optimize cases without changing specifications. The great majority of variables are of Calculated specification. Far fewer are Constant, and even fewer are DOFs (i.e., of Reconcile and Optimize specification). The specifications assigned to variables, their values, their upper and lower limits, along with the Case type (Parameter, Reconcile, Simulate, or Optimize) and an objective function determine the problem that is being posed. 

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