Reboil Ratio

The dominance of distiHation-based methods for the separation of Hquid mixtures makes a number of points about RCM and DRD significant. Residue curves trace the Hquid-phase composition of a simple single-stage batch stiHpot as a function of time. Residue curves also approximate the Hquid composition profiles in continuous staged or packed distillation columns operating at infinite reflux and reboil ratios, and are also indicative of many aspects of the behavior of continuous columns operating at practical reflux ratios (12). 

Comp. Feed Distillate Bottoms 1. 0.1400 0.4295 0.0159 Case Reflux ratio Reboil ratio Feed composition Distillate composition Bottoms composition... 

The intersection of section profiles as illustrated in Figure 12.17 can be used to test the feasibility of given product compositions and settings for the reflux ratio and reboil ratio. However, the profiles would change as the reflux ratio and reboil ratios change, and trial and error will be required. 

Figure 12.18 For a given bottoms composition, a range of section profiles can be generated by varying the reboil ratio. (From Castillo F, Thong DY-C, Towler GP, 1998, Ind Eng Chem Res, 37 987 reproduced by permission of the American Chemical Society).

Bi in Figure 12.20. This means that there is some combination of settings for the reflux ratio and reboil ratio that will allow the section profiles to intersect and become a feasible column design. By contrast, bottoms composition B2 shows an operation leaf that does not intersect with the operation leaf of distillate D. This means that the two products D and B2 cannot be produced in the same column, and the design is infeasible. No settings of reboil ratio or reflux ratio can make the combination of B2 and D a feasible design. 

For a simple distillation column separating a ternary system, once the feed composition has been fixed, three-product component compositions can be specified, with at least one for each product. The remaining compositions will be determined by colinearity in the ternary diagram. For a binary distillation only two product compositions can be specified independently, one in each product. Once the mass balance has been specified, the column pressure, reflux (or reboil ratio) and feed condition must also be specified. 

S Entropy (kJ-K-1, kJkg-1-K-1, kJkmol-1-K-1), or number of streams in a heat exchanger network (-), or reactor selectivity (-), or reboil ratio for distillation (-), or selectivity of a reaction (-), or slack variable in optimization (units depend on application), or solvent flowrate (kg s-1, kmol-s-1), or stripping factor in absorption (-)... 

Select a reflux ratio R and determine the corresponding reboil ratio s from Eq. (45). 

A liquid binary mixture with B0 = 10 kmol (Hc) and xB0 = <0.6, 0.4> (xj) molefraction is subject to inverted batch distillation shown in Figure 4.12. The relative volatility of the mixture over the operating temperature range is assumed constant with a value of (a-) 2. The number of plates is, N= 10. The vapour boilup rate is, V = 10.0 kmol/hr. The total plate holdup is 0.3 kmol and the reboiler holdup is 0.1 kmol. The total batch time of operation is 4 hr with two time intervals. The first interval is of duration 1 hr and the column is operated with a reboil ratio of 0.8. The second interval is of duration 3 hrs when the column is operated with a reboil ratio of 0.9. The column operation is simulated with the type III model (section 4.3.2.1). 

The results in terms of the amount and composition in the condenser holdup tank and in the bottom product accumulator are presented in Tables 4.11 and 4.12 respectively. The condenser holdup tank and bottom product accumulator composition and reboil ratio profiles are shown in Figures 4.13 and 4.14 respectively. 

The optimal control of a process can be defined as a control sequence in time, which when applied to the process over a specified control interval, will cause it to operate in some optimal manner. The criterion for optimality is defined in terms of an objective function and constraints and the process is characterised by a dynamic model. The optimality criterion in batch distillation may have a number of forms, maximising a profit function, maximising the amount of product, minimising the batch time, etc. subject to any constraints on the system. The most common constraints in batch distillation are on the amount and on the purity of the product at the end of the process or at some intermediate point in time. The most common control variable of the process is the reflux ratio for a conventional column and reboil ratio for an inverted column and both for an MVC column. 

For single separation duty, Bernot et al. (1991) presented a method to estimate batch sizes, operating times, utility loads, costs, etc. for multicomponent batch distillation. The approach is similar to that of Diwekar et al. (1989) in the sense that a simple short cut technique is used to avoid integration of a full column model. Their simple column model assumes negligible holdup and equimolal overflow. The authors design and, for a predefined reflux or reboil ratio, minimise the total annual cost to produce a number of product fractions of specified purity from a multicomponent mixture. 

The input data defining column configurations, feed, feed composition, column holdup, etc. are given in Table 11.10. The reaction is modelled by simple rate equations (Table 11.10). The batch time is 12 hrs (ts). The objective of the study was to maximise the conversion (X) of the limiting reactant and to obtain the main product with purity of 0.7 molefraction by optimising the reboil ratio defined as V/L. The following optimisation problem (PI) was considered. Model type III was considered with chemical reaction. 

The solution of the problem PI results in the maximum conversion of 61.3% with 1.29 kmol of product C. The optimum reboil ratio was 0.96. Please see the original reference for further details. 

The column configurations and other parameters are defined in Table 11.11. Thirteen cases were considered using different initial charge compositions and different product purity specifications (same specifications for light and heavy product). The results are summarised in Table 11.11. The results clearly show the cases (shown in bold) when an IBD column is superior to a CBD column. The optimum reflux or reboil ratio profiles for 3 cases are shown in Figure 11.10. Refer to the original reference for further details. 

Figure 11,10. Optimum Reflux or Reboil Ratio Profiles for CBD and IBD Columns. [Sorensen and Skogestad, 1996] ...

Greaves et al. (2003) proposed a framework to optimise the operation of MVC columns with substantial reduction of the computational power needed to carry out the optimisation calculations. The framework relies on the use of NN based process model. The optimisation of a pilot-plant middle-vessel batch column (MVC) was considered to test the viability of the proposed framework. The maximum product problem was considered and solved by optimising the column operating parameters, such as the reflux and reboil ratios and the batch time. The NN based model is found to be capable of reproducing the actual plant dynamics with good accuracy, and that the proposed framework allows a large number of optimisation studies to be carried out with little computational effort. 

A certain amount of information has to be made available to the network which will be processed to obtain the output vector at the current time instant. The inputs can come either from direct measurements from the process, or from the network itself (i.e., NN outputs from previous time instants). The choice of the inputs should be made with engineering judgment. Too many inputs would overload the network and introduce unnecessary correlations among data, and can therefore disrupt the network performance on the other hands, too few inputs could be not enough for the network to learn the actual process behaviour. In Greaves et al. (2003), at time tk the following inputs were fed to the network tk, output vector Z0 at initial time (t0), and current values for the internal reflux and reboil ratios (Rd and RB, respectively), distillate rate (D), and bottoms rate (B). 

The results mostly show that the optimiser has been able to adjust the reflux and reboil ratios and the distillation time in such a way as to increase the total amount collected (i.e., the objective function), the capacity factor (productivity). Greaves et al. (2003) included another performance index (%Recovery of key component) in addition to CAP and the conclusions remained the same. 

Finally, to check the reliability of the simulation results provided by the NN model, the optimal reflux and reboil ratios were implemented into the detailed (i.e., deterministic) MVC simulator (Barolo et al., 1998). The broken lines in Figure 12.12 represent the relevant time profiles obtained with the detailed MVC simulator for an operation carried out using the optimal values of the reflux and reboil ratios as calculated by the NN. Greaves et al. (2003) noted that the actual process is indeed represented quite accurately by the NN model, which confirmed that the optimisation results were reliable. 

At minimum flows, pinch zones can be identified where the composition changes very little on successive stages. The profiles just intersect each other at the feed position. In Figure 3.23 (right-hand) a saddle pinch can be identified in the rectifying profile. This profile corresponds to the minimum reflux in a direct sequence, since the distillate is practically the pure component A. The minimum reflux is practically independent of the bottoms composition. Similarly, a minimum reboil ratio may be identified by simulation. The determination of the minimum number of stages is subtler, since the composition of the top distillate and bottoms are not independent, but the simulation may produce a reasonable estimation. 

Case Reflux ratio Reboil ratio Feed composition Distillate composition Bottoms composition... 

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