Distillation modeling

Verneuil et al. (Verneuil, V.S., P. Yan, and F. Madron, Banish Bad Plant Data, Chemical Engineering Progress, October 1992, 45-51) emphasize the importance of proper model development. Systematic errors result not only from the measurements but also from the model used to analyze the measurements. Advanced methods of measurement processing will not substitute for accurate measurements. If highly nonlinear models (e.g., Cropley s kinetic model or typical distillation models) are used to analyze unit measurements and estimate parameters, the Hkelihood for arriving at erroneous models increases. Consequently, resultant models should be treated as approximations. 

If necessary the hydraulic relationships, previously derived for batch distillation, are also easily implemented into a continuous distillation model. 

G.G. Podrebarac, F.T.T. Ng, G.L. Rempel, The production of diace-ton alcohol with catalytic distillation part II. A rate-based catalytic distillation model for the reaction zone, Chem. Eng. Sci. 53 (3) (1998) 1077. 

For a given Rexf, the vapour rate profile is averaged to obtain an average Vexp to be used in the batch distillation model developed by Greaves et al.. Figure 3.12... 

Robinson and Gilliland (1950), Abrams et al. (1987) and Hasebe et al. (1992, 1995), Sorensen and Skogestad (1996a), Barolo et al. (1998), Furlonge et al. (1999) reported simulation results using inverted, batch distillation columns with middle vessel and multi-effect batch distillation, respectively. Mujtaba (1997) simulated batch distillation operation using a continuous distillation model. 

Rigorous and stiff batch distillation models considering mass and energy balances, column holdup and physical properties result in a coupled system of DAEs. Solution of such model equations without any reformulation was developed by Gear (1971) and Hindmarsh (1980) based on Backward Differentiation Formula (BDF). BDF methods are basically predictor-corrector methods. At each step a prediction is made of the differential variable at the next point in time. A correction procedure corrects the prediction. If the difference between the predicted and corrected states is less than the required local error, the step is accepted. Otherwise the step length is reduced and another attempt is made. The step length may also be increased if possible and the order of prediction is changed when this seems useful. 

Bosley and Edgar (1994a,b) developed techniques to calculate directly dynamic distillation (DDD) derivatives (non iterative), which were then employed to integrate rigorous DAEs (index 2) based batch distillation model. 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

However, most of the batch distillation models (e.g. Mujtaba and co-workers Sorensen and Skogestad, 1996) relate the amount of distillate collected (Hamodei) with the vapour boil-up rate in the column (Vtomm), the internal reflux ratio (Rmodei) and the total operating time (tdig) by,... 

For each column, the recoveries of the light and heavy key components have been specified. Then, the minimum number of trays Nmill and the minimum reflux ratio Rmin have been calculated using the shortcut distillation model DSTWU with Winn-Underwood-Gilliland method in Aspen Plus. The reflux ratio was set to... 

Nonequilibrium methods (Sec. 4,2.13) tend to be global Newton methods extended to solve mass-transfer-inhibited systems. Nonequilibrium methods are not yet completely extended to more common systems, but these methods should see the greatest amount of development in distillation modeling. 

As was pointed out earlier, molecular distillation is normally used to fractionate mixtures of components of very low volatility. It is proposed that a supercritical fractionation process, as schematically shown in figure 6, can be used to produce fractions superior to that of molecular distillation. In order to test this, a molecular distillation model must be used. As a first approximation, the molecular distillation of high molecular weight alkanes is viewed as a simple flash. The vapour pressure data of Kudchadker et al[10] was used in the flash calculations. 

Figure 1 Plot of wt.% MnO versus radial distance in garnets from Kwoiek, British Columbia (Hollister, 1966) (reproduced by permission of American Association for the Advancement of Science from Science 1966, 154, 1647-1651). MnO can be fitted with a Rayleigh distillation model, with Mn 23 (O, analyzed points) (source Spear, 1993).

The operations needed include two reactors, splitting, mixing, cooling, condensing, recycle and distillation. The propylene and acrolein conversions and product yields are to be specified. These could be calculated if sufficient kinetic data were available. A sinpplified distillation model, such as the FUG method, could be used. Split and recoveries need to be estimated. 

Lagana, F., Barbieri, G., and Drioli, E. Direct contact membrane distillation Modeling and concentration experiments, J. Membr. Sci., 166, 1, 2000. 

Martinez, L., et al. Characterisation of three hydrophobic porous membranes used in membrane distillation Modelling and evaluation of their water vapor permeabilities, J. Membr. Sci., 203, 15, 2002. 

The commercial process simulators contain a range of distillation models with different degrees of sophistication. The design engineer must choose a model that is suitable for the purpose, depending on the problem type, the extent of design information available, and the level of detail required in the solution. In some cases, it may make sense to build different versions of the flowsheet, using different levels of detail in the distillation models so that the simpler model can be used to initialize a more detailed model. 

The simplest distillation models to set up are the shortcut models. These models use the Fenske-Underwood-Gilliland or Winn-Underwood-Gilliland method to determine the minimum reflux and number of stages or to determine the required reflux given a number of trays or the required number of trays for a given reflux ratio. These methods are described in Chapter 11. The shortcut models can also estimate the condenser and reboiler duties and determine the optimum feed tray. 

The minimum information needed to specify a shortcut distillation model is... 

The easiest way to use a shortcut distillation model is to start by estimating the minimum reflux and number of stages. The optimum reflux ratio is usually between 1.05 and 1.25 times the minimum reflux ratio, Rmm, so 1.15 x Rmin is often used as an initial estimate. Once the reflux ratio is specified, the number of stages and optimum feed stage can be determined. The shortcut model results can then be used to set up and initialize a rigorous distillation simulation. 

Rigorous distillation models can be used to model absorber columns, stripper columns, refluxed absorbers, three-phase systems such as extractive distillation columns, many possible complex column conflgurations, and columns that include... 

Several of the commercial simulation programs offer preconfigured complex column rigorous models for petroleum fractionation. These models include charge heaters, several side strippers, and one or two pump-around loops. These fractionation column models can be used to model refinery distillation operations such as crude oil distillation, vacuum distillation of atmospheric residue oil, fluidized catalytic cracking (FCC) process main columns, and hydrocracker or coker main columns. Aspen Plus also has a shortcut fractionation model, SCFrac, which can be used to configure fractionation columns in the same way that shortcut distillation models are used to initialize multicomponent rigorous distillation models. 

Other multistage vapor-liquid separations such as absorption and stripping can be modeled using variations of the rigorous distillation models, as can multistage liquid-liquid extraction. 

Component splitters are sometimes used in place of distillation columns when building simple models to provide initial estimates for processes with multiple recycles. There is little advantage to this approach compared with using shortcut distillation models, as the component splitter will not calculate the distribution of non-key components unless a recovery is entered for each. Estimating and entering the recoveries for every component is difficult and tedious, and poor estimates of recoveries can lead to poor estimates of recycle flows, so the use of component splitters in this context effectively adds another layer of iteration to the model. 

The column profiles for the rigorous distillation model are shown in Figure 4.51. The profiles do not show any obvious poor design of the column, although the design is not yet optimized. 

Figure 4.51. Column profiles for the rigorous distillation model.

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