Fraction reconciliation

In more practical terms there will be SOPs to describe sample preparation, equipment set-up including programming, and an SOP for operation of the equipment. The documentation does not stop here since there will be defined instructions for fraction analysis, fraction reconciliation and recovery of product from the fractions. 

Record any additional notes on fraction reconciliation below. 

Remark 2 It is worthwhile to mention that the breaking point of the M-estimator, the fraction of outliers that can be tolerated without the estimator potentially breaking down, is about 1 /(g + 1), where g is the dimension of the data (Maronna, 1976). In data reconciliation, outliers refer to the abnormal observations and are a small fraction of the whole data set. In our view, the breaking point property is reasonably good for practical implementations. 

Record the fate of all fractions on the process record for Reconciliation of Fractions. 

Unfortunately, no such simple solution is available for the ESA effect at the high frequencies at which it is ciu-rently used. Goetz and El-Aasser (24) attempted to compare the electroacoustic and electrophoretic behavior of concentrated miniemulsion systems of toluene in water, stabilized by cetyl alcohol and sodium laiuyl sulfate. They concluded that the simple correction which works well for CVP does not produce a similar reconciliation in the case of the ESA effect. Their conclusions are, however, suspect because of uncertainties arising from the dilution of the emulsion system this can so easily lead to changes in siuface properties, no matter how carefully it is done. Texter s results (34) referred to above are perhaps more definitive in this case. He showed that in the range from 2 to 5% by volume where his particles showed a nonlinear dependence of the ESA signal on volume fraction, the Levine and Neale model (3 8) was unable to account for the nonlinearity. His particles were, however, nonspherical and that may at least partially explain the discrepancy. 

In what follows, for the sake of simplicity let us suppose that the measured values are given directly as mass fractions, with known variances. The component balances (10.6.1) are of the general form examined in Chapter 8 and can be used as such for the reconciliation. So as to further simplify our example, let us transform the equations into another, equivalent form. By summation and using (10.6.1b) we obtain, with y/ = y... 

Until now two online applications of the blending tanks model have been implemented at the smelter a simulation model estimating the slag concentrate mass fraction in the feed mixture and a Kalman filter estimation of the feed mixture composition. Both models include a shared data reconciliation part, which estimates the masses and mass flows in the process and a shared calculation of state space model parameters according... 

The one-sided polarisation of ISO 13849-1 towards theoretical probabilities is a disadvantage, because the relative frequencies would enable the theory to be objectively verified. For the practical design engineer, a reconciliation with statistically acquired data or experimental results is necessary, as well as with subjective empirical values, e.g. by enumerating the relevant events (in the numerator) with regard to the total quantity of all events (in the denominator). This fraction is the original definition of a probability (see e.g.. 

We describe the generalized step-by-step instruction of the reactor model development in Section 6.4.1. However, the procedures are not applicable to the process with an unusual process flow diagram, such as the HP HCR process, which includes two parallel reactor series. The two parallel reactor series that shares one fractionation unit makes it unachievable to distinguish the production data from one series to the other. For example, there is no way to split the heavy naphtha product into two streams to represent the performance of each reactor series. In addition, it is difficult to start with building the model of two parallel reactor series because model reconciliation of two reactor series is a time-consuming and difficult task. Therefore, we develop the following procedures to build and reconcile HP HCR reactor model ... 

---