Fitting Distillation Curves

Distillation curves for FCC feedstock can be limited. Because of the nature of the feedstock, complete true boiling point (TBP) analysis without D-2887/SimDist methods is frequently not possible. Many refiners still use a limited D-1160 distillation method to obtain some information about the distillation curve. Table 4.9 shows a typical D-1160 analysis for a heavy FCC feedstock. 

This curve does not contain enough information to convert into TBP curve using standard ASTM correlations. We must fit these data to a reasonable model to obtain estimates for the missing data points (see also Section 1.4). Sanchez et al. [53] have evaluated several different types of cumulative probability distribution functions to fit distillation curves of crudes and petroleum products. They conclude that the cumulative beta function (with four parameters) can represent a wide range of petroleum products [53]. We use this method to extend the measured partial distillation curve. 

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McCaffrey, W. C. Comparison of Probability Distribution Functions for Fitting Distillation Curves of Petroleum, Energy Fuels 2007, 21, 2955. 

Sinchez, S., Ancheyta, J., McCaffrey, W. 2007. Comparison of probabihty distribution functions for fitting distillation curves of petroleum. Energy Euels 21 2955-2963. 

Chapter 12 summarizes other important aspects of hydroprocessing such as correlations to predict product properties, hydrogen consumption, calculation of residue conversion, calculation of fresh-basis catalyst composition, and use of probability functions for fitting distillation curves. 

Step 1 Open Beta.xls. Cells B2 to B5 show the adjustable parameters in beta distribution funchon, the cells A8 to B16 require the input of the distillation curve, cells H8 to K16 and the graph indicate the fitted results. 

Figure 2.9 Data fit of the distillation curve as a function of liquid volume using the Beta function.

Table 2.14 contains the distillation curve and specific gravity (or density) from each cut If a complete distillation curve is not available, we recommend using the beta distribution fitting method to identify missing values (Section 1.4). The residue distillation curve may not be available routinely. We use the simple correlation outlined by Kaes [3] to identify key points on the distillation curve as a function of residue density. We can then use the same beta distribution fit to complete the entire required distillation curve. Finally, we also require the light gas composition (C1-C5) composition leaving with the naphtha and overhead products. 

Spreadsheet to fit distillation and density/specific gravity curves to beta distributions... 

Probability distribution functions. Many functions with different number of parameters are reported in the literature however, their fitting capability for the distillation curve of petroleum has not been determined. Knowing the best function for distillation data is helpful for modeling purposes. 

A comparison of the fitting capability of all functions reported in Tables 12.20 and 12.21 was performed by statistical methods. The procedure for parameter estimation is described below the four-parameter Beta-distribution function nsing a single distillation data set is taken as an example, which corresponds to a simnlated distillation curve of hydrocracked Maya crude oil ... 

Weibull Extreme, Weibull, and Kumaraswamy probability distribution functions are recommended for fitting distillation data, whose application for this purpose has not been previously reported. Further work is necessary to correlate the features of these best-ranked functions with the nature of the distillation curves of petroleum. 

Let us now consider a few examples for the use of this simple representation. A grand composite curve is shown in Fig. 14.2. The distillation column reboiler and condenser duties are shown separately and are matched against it. Neither of the distillation columns in Fig. 14.2 fits. The column in Fig. 14.2a is clearly across the pinch. The distillation column in Fig. 14.26 does not fit, despite the fact that both reboiler and condenser temperatures are above the pinch. Strictly speaking, it is not appropriately placed, and yet some energy can be saved. By contrast, the distillation shown in Fig. 14.3a fits. The reboiler duty can be supplied by the hot utility. The condenser duty must be integrated with the rest of the process. Another example is shown in Fig. 14.36. This distillation also fits. The reboiler duty must be supplied by integration with the process. Part of the condenser duty must be integrated, but the remainder of the condenser duty can be rejected to the cold utility. 

Figure 14.2 Distillation columns which do not fit against the grand composite curve. (From Smith and Linnhoff, Trans. IChemE, ChERD, 66 195, 1988 reproduced by permission of the Institution of Chemical Engineers.)...

Consider now a few examples of the use of this simple representation. A grand composite curve is shown in Figure 21.2a. The distillation column reboiler and condenser duties are shown separately and are matched against it. The reboiler and condenser duties are on opposite sides of the heat recovery pinch and the column does not fit. In Figure 21.2b, although the reboiler and condenser duties are both above the pinch, the heat duties prevent a fit. Part of the duties can be accommodated, and if heat integrated,... 

Muj taba, I. M. and S. Macchietto. Efficient Optimization of Batch Distillation with Chemical Reaction Using Polynomial Curve Fitting Techniques. Ind Eng Chem Res 36 2287-2295 (1997). 

A stock solution of NH4C1 dissolved in deionized-distilled water was prepared for calibration. Aliquots of this solution were further diluted to obtain the solutions for the calibration curve. Each solution was then subjected to the treatment just described. The calibration curve (Figure 2) was fit by the linear least-squares regression equation... 

Apparatus consists of a heating mantle, a 125 round-bottom reaction flask a three-way side-arm adapter, a 50 ml burette with a No 5 rubber stopper, a water-cooled condenser, a support with a clamp, a curved adapter and a 125 ml Erlen flask, serving as a receiver. Std tapered ground glass joints are used to connect the distilling flask side-arm adapter, condenser and curved adapter. The three-way side-arm adapter has a female joint, at its upper end,to which the burette is fitted with the No 5 rubber stopper. 

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