Distillation optimal reflux

Thus the optimal reflux ratio for an appropriately integrated distillation column will be problem-specific and is likely to be quite different from that for a stand-alone column. 

EXAMPLE 12.4 DETERMINATION OF THE OPTIMAL REFLUX RATIO FOR A STAGED-DISTILLATION COLUMN... 

In this example we illustrate the application of a one-dimensional search technique from Chapter 5 to a problem posed by Martin and coworkers (1981) of obtaining the optimal reflux ratio in a distillation column. 

Logsdon, J. S. and L. T. Biegler. Accurate Determination of Optimal Reflux Policies for the Maximum Distillate Problem in Batch Distillation. Ind Eng Chem Res 32 (4) 692-700 (1993). 

While the reduced SQP algorithm is often suitable for parameter optimization problems, it can become inefficient for optimal control problems with many degrees of freedom (the control variables). Logsdon et al. (1990) noted this property in determining optimal reflux policies for batch distillation columns. Here, the reduced SQP method was quite successful in dealing with DAOP problems with state and control profile constraints. However, the degrees of freedom (for control variables) increase linearly with the number of elements. Consequently, if many elements are required, the effectiveness of the reduced SQP algorithm is reduced. This is due to three effects ... 

Kerkhof and Vissers showed that for difficult separations an optimal reflux control policy yields up to 5% more distillate, corresponding to 20-40% higher profit, than either constant distillate composition or constant reflux ratio policies. 

Robinson (1969) considered the following example problem. A binary feed mixture with an initial amount of charge, B0 = 100 kmol and composition xB0 = <0.50, 0.50> molefraction, having constant relative volatility of 2.0 was to be processed in a batch distillation column with 8 theoretical stages. The aim was to produce 40 kmol of distillate product (D) with composition (xd) of 0.5 molefraction for component 1 in minimum time (tF) using optimal reflux ratio (/ ). 

The Hamiltonian, the adjoint equations and the optimal reflux ratio correlation will be same as those in Equations P.10-P.13 (Diwekar, 1992). However, note that the final conditions (stopping criteria) for the minimum time and the maximum distillate problems are different. The stopping criterion for the minimum time problem is when (D, xq) is achieved, while the stopping criterion for the maximum distillate problem is when t, xo) is achieved. See Coward (1967) for an example problem. 

Table 4.6 in Chapter 4 presents the simulation results for a quaternary batch distillation. The amount of product and the composition of key component of each cut were used by Mujtaba (1989) to formulate and solve a minimum time problem for each cut. Optimal reflux ratio in each operation step is obtained independently of other step with the final state of each step being the initial state of the next step. 

For single separation duty, Mujtaba and Macchietto (1993) proposed a method, based on extensions of the techniques of Mujtaba (1989) and Mujtaba and Macchietto (1988, 1989, 1991, 1992), to determine the optimal multiperiod operation policies for binary and general multicomponent batch distillation of a given feed mixture, with several main-cuts and off-cuts. A two level dynamic optimisation formulation was presented so as to maximise a general profit function for the multiperiod operation, subject to general constraints. The solution of this problem determines the optimal amount of each main and off cut, the optimal duration of each distillation task and the optimal reflux ratio profiles during each production period. The outer level optimisation maximises the profit function by... 

Figure 6.4. Optimal Reflux Ratio Profiles for Binary Distillation. [Mujtaba and Macchietto, 1993]e...

Two binary mixtures are being processed in a batch distillation column with 15 plates and vapour boilup rate of 250 moles/hr following the operation sequence given in Figure 7.7. The amount of distillate, batch time and profit of the operation are shown in Table 7.6 (base case). The optimal reflux ratio profiles are shown in Figure 7.8. It is desired to simultaneously optimise the design (number of plates) and operation (reflux ratio and batch time) for this multiple separation duties. The column operates with the same boil up rate as the base case and the sales values of different products are given in Table 7.6. 

Mayur et al. (1970) formulated a two level dynamic optimisation problem to obtain optimal amount and composition of the off-cut recycle for the quasi-steady state operation which would minimise the overall distillation time for the whole cycle. For a particular choice of the amount of off-cut and its composition (Rl, xRI) (Figure 8.1) they obtained a solution for the two distillation tasks which minimises the distillation time of the individual tasks by selecting an optimal reflux policy. The optimum reflux ratio policy is described by a function rft) during Task 1 when a mixed charge (BC, xBC) is separated into a distillate (Dl, x DI) and a residue (Bl, xBi), followed by a function r2(t) during Task 2, when the residue is separated into an off-cut (Rl, xR2) and a bottom product (B2, x B2)- Both r2(t)and r2(t) are chosen to minimise the time for the respective task. However, these conditions are not sufficient to completely define the operation, because Rl and xRI can take many feasible values. Therefore the authors used a sequential simplex method to obtain the optimal values of Rl and xR which minimise the overall distillation time. The authors showed for one example that the inclusion of a recycled off-cut reduced the batch time by 5% compared to the minimum time for a distillation without recycled off-cut. 

The results are summarised in Table 8.1 and Figures 8.4-8.8 which show the optimal reflux ratio profiles and the corresponding accumulated and instant distillate composition curves. The optimal reflux ratio profiles presented in Figures 8.4-8.8 are different from case to case. 

Figure 8.4. Accumulated and Instant Distillate Composition and Optimal Reflux Ratio Profiles (case 2). [Mujtaba, 1989]...

The value of q, the optimal batch time with and without recycle, the percentage time savings due to recycle and the optimal amount and composition of the recycle are presented in Table 8.7 for cases wherever it is applicable. The accumulated and instant distillate composition curves with and without recycle cases are shown in Figures 8.14-8.17. These figures also show the optimal reflux ratio profiles for each case. 

The minimum batch times for the individual cuts and for the whole multiperiod operation are presented in Table 8.8 together with the optimal amount of recycle and its composition for each cut. The percentage time savings using recycle policies are also shown for the individual cuts and also for the whole operation. Figure 8.18 shows the accumulated distillate and composition profile with and without recycle case for the operation. These also show the optimal reflux ratio profiles. Please see Mujtaba (1989) for the solution statistics for this example problem. 

Figure 8.18. Accumulated, Instant Distillate and Optimal Reflux Ratio (example 2) [Mujtaba and Macchietto, 1992 Mujtaba, 1989]b...

The chemical reaction scheme, kinetic data and other input data are given in Table 9.4. There are 2 control variables in each cut. These are the reflux ratio and the duration of the cut. The results of the optimisation are shown in Table 9.5 and Figure 9.14. The distillation column needs to be operated initially at low optimal reflux ratio to remove most of the water. 

In Greaves et al. (2001), a hybrid model for an actual pilot plant batch distillation column is developed. However, taking advantage of some of the inherent properties of batch distillation processes a simpler version (new algorithm) of the general optimisation framework is developed to find optimal reflux ratio policies which minimises the batch time for a given separation task. 

Optimum reflux can be in principle determined as a trade-off between investment and operation costs. The column cost is roughly proportional with the number of stages N. The cost of utilities depends on the vapour flow, proportional with the reflux plus distillate, 7 + l. Consequently, the optimisation of the function Fg =N(R + l) versus R leads to a convenient approximation of the optimum reflux. In practice, the optimal reflux takes values between 1.1-1.5, the most probable being 1.2-1.3. 

Optimal reflux ratio for a distillation column, for which the capital cost of the column and heat exchangers is balanced against the utility costs for cooling water in the condenser and steam in the reboiler. 

Optimal control of a batch distillation column consists in the determination of the suitable reflux policy with respect to a particular objective function (e.g. profit) and set of constraints. In the purpose of the present work, the optimisation problem is defined with an operating time objective function and purity constraints set on the recovery ratio (90%) and on the propylene glycol final purity (80% molar). Different basis fimctions have been adopted for the control vector parameterisation of the problem piecewise constant and linear, hyperbolic tangent function. Optimal reflux profiles are determined with the final conditions of the previous optimal reactions as initial conditions. The optimal profiles of the resultant distillations are presented on figure 2. 

Common examples include optimizing distillation column reflux ratio and reactor temperature. Consider the... 

Batch Distillation Chapter 4 is devoted to batch distillation. This is one of the most important and one of the most studied unit operations in batch industries. Separation is based on vapor-liquid equilibria. There are a number of configurations possible in conventional batch colmnn, namely, the constant reflux mode, the variable reflux mode, and the optimal reflux mode. There are a number of new configurations that have emerged in the literature for batch distillation. This chapter describes aU these operating modes and configurations. Various levels of models are available for different analysis. Different numerical integration techniques are needed to solve equations of these different models. Optimization and optimal control are well studied for this unit operation. 

As stated earlier, the two basic modes of batch distillation are (l)constant reflux, and (2)variable reflux, resulting in variable distillation composition and constant distillate composition of the key component, respectively. The third operating mode, optimal reflux or optimal control is the trade-off between the two operating modes. 

The optimal reflux mode is a reflux profile that optimizes the given indices of column performance chosen as the objectives. The indices used in practice generally include the minimum batch time, maximum distillate, or maximum profit functions. This... 

The constant Ci in the Hengstebeck-Geddes equation is equivalent to the minimum number of plates, Nmin, in the Fenske equation. At this stage, the variable reflux operating mode has Gi and R, the constant reflux has and Ci, and the optimal reflux has, Ci, and R as unknowns. Summation of distillate compositions can be used to obtain Gi for variable reflux and for both constant reflux and optimal reflux operation, and the FUG equations to obtain R for variable reflux and Gi for both constant reflux and optimal reflux operations. The optimal reflux mode of operation has an additional unknown, R, which is calculated using the concept of optimizing the Hamiltonian, formulated using the different optimal control methods. 

An efficient optimization approach for reactive batch distillation using polynomial curve fitting techniques was presented by [55]. After finding the optimal solution of the maximum conversion problem, polynomial curve fitting techniques were applied over these solutions, resulting in a nonlinear algebraic maximum profit problem that can be efficiently solved by a standard NLP technique. Four parameters in the profit function, which are maximum conversion, optimum distillate, optimum reflux ratio, and total reboiler heat load, were then represented by polynomials in terms of batch time. This algebraic representation of the optimal solution can be used for online optimization of batch distillation. 

The following example of batch distillation optimal control (optimal reflux policy problem illustrates this. 

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