Batch distillation control

Spreadsheet Applications. The types of appHcations handled with spreadsheets are a microcosm of the types of problems and situations handled with fuU-blown appHcation programs that are mn on microcomputers, minis, and mainframes and include engineering computations, process simulation, equipment design and rating, process optimization, reactor kinetics—design, cost estimation, feedback control, data analysis, and unsteady-state simulation (eg, batch distillation optimization). 

The progress of batch distillation cau be controlled in several ways ... 

For a constant reflux ratio, the value can be almost any ratio however, this ratio affects the number of theoretical plates and, consequently, actual trays installed in the rectification section to achieve the desired separation. Control of batch distillation is examined in Reference 134. 

Sorensen (1999) has suggested a cyclic operation policy for batch distillation with repeated filling and dumping of the reflux drum. This configuration achieves the maximum attainable separation and requires minimal control. Furthermore, such a column can be operated very safely. 

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

Diwekar UM (1995) Batch Distillation - Simulation, Optimal Design and Control, Taylor Francis. 

Other synonyms for steady state are time-invariant, static, or stationary. These terms refer to a process in which the values of the dependent variables remain constant with respect to time. Unsteady state processes are also called nonsteady state, transient, or dynamic and represent the situation when the process-dependent variables change with time. A typical example of an unsteady state process is the operation of a batch distillation column, which would exhibit a time-varying product composition. A transient model reduces to a steady state model when d/dt = 0. Most optimization problems treated in this book are based on steady state models. Optimization problems involving dynamic models usually pertain to optimal control or real-time optimization problems (see Chapter 16)... 

Batch distillation with continuous control of distillate composition via the regulation of reflux ratio is illustrated in the simulation example BSTILL. In this an initial total reflux condition, required to establish the initial concentration profile with the column, is represented in the simulation by a high initial value of R, which then changes to the controller equation for conditions of distillate removal. 

The embedded model approach represented by problem (17) has been very successful in solving large process problems. Sargent and Sullivan (1979) optimized feed changeover policies for a sequence of distillation columns that included seven control profiles and 50 differential equations. More recently, Mujtaba and Macchietto (1988) used the SPEEDUP implementation of this method for optimal control of plate-to-plate batch distillation columns. 

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 ... 

Mujtaba, I. M., and Macchietto, S., Optimal control of batch distillation, presented at 12th IMACS World Congress, Paris, July (1988). 

A batch distillation plant consists of a still or reboiler, a column with several trays, and provisions for reflux and for product collection. Figure 13.10(c) is a typical equipment arrangement with controls. The process is applied most often to the separation of mixtures of several components at production rates that are too small for a continuous plant of several columns equipped with individual reboilers, condensers, pumps, and control equipment. 

Figure 13.10. Batch distillation McCabe-Thiele constructions and control modes, (a) Construction for constant overhead composition with continuously adjusted reflux rate, (b) Construction at constant reflux at a series of overhead compositions with an objective of specified average overhead composition, (c) Instrumentation for constant vaporization rate and constant overhead composition. For constant reflux rate, the temperature or composition controller is replaced by a flow controller.

Hence the reflux ratio, the amount of distillate, and the bottoms composition can be related to the fractional distillation time. This is done in Example 13.4, which studies batch distillations at constant overhead composition and also finds the suitable constant reflux ratio that enables meeting required overhead and residue specifications. Although the variable reflux operation is slightly more difficult to control, this example shows that it is substantially more efficient thermally—the average reflux ratio is much lower—than the other type of operation. 

Performance. So far, the deep-basin still has been operated only under batch-type control—that is, without continuous blowdown or heat exchange to the incoming sea water. In determining the performance of the still, incident solar radiation and distillate production are measured daily. From this information, the specific production in gallons per square foot per day and the thermal efficiency can be determined. In addition to the daily collection of performance data, hourly collections are made during periodic energy- and mass-balance runs. 

Dynamic Optimisation (Optimal Control) of Batch Distillation... 

Batch distillation is inherently a dynamic process and thus results to optimal control or dynamic optimisation problems (unless batch distillation task is carried out in a continuous distillation column). 

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. 

The minimum time problem is also known as the time optimal control problem. Coward (1967), Hansen and Jorgensen (1986), Robinson (1970), Mayur et al. (1970), Mayur and Jackson (1971), Mujtaba (1989) and Mujtaba and Macchietto (1992, 1993, 1996, 1998) all minimised the batch time to yield a given amount and composition of distillate using conventional batch distillation columns. The time optimal operation is often desirable when the amount of product and its purity are specified a priori and a reduction in batch time can produce either savings in the operating costs of the column itself or permit improved scheduling of other batch operations elsewhere in a process. Mathematically the problem can be written as ... 

The application of Equations P.1-P.7 to batch distillation enables the solution of time optimal control problems. 

Reprinted from Journal of Process Control, 6, Mujtaba, I.M. and Macchietto, S., Simultaneous optimisation of design and operation of multicomponent batch distillation column-single and multiple separation duties, 27-36, Copyright (1996), with permission from Elsevier Science. ... 

The batch distillation column consisted of 3 internal plates, reboiler and a total condenser. The reboiler was charged with a fresh feed of 5 kmol with Benzene molefraction 0.6. The total column holdup was 4 % of the charge. Half the holdup was in the condenser and the rest was distributed over the plates. The vapour load to the condenser was 3 kmol/hr. The required product purities were x oi = 0.90 and x B2 = 0.15. The solution of Equations 8.1-8.4 therefore gives DJ = 3.0 kmol and B2 = 2 kmol. This problem is same as case 3 shown in Table 8.1. Three reflux ratio (control) intervals were used to achieve (Dl, x Di) and one control interval to achieve (B2, x B2). 

The one level optimal control formulation proposed by Mujtaba (1989) is found to be much faster than the classical two-level formulation to obtain optimal recycle policies in binary batch distillation. In addition, the one level formulation is also much more robust. The reason for the robustness is that for every function evaluation of the outer loop problem, the two-level method requires to reinitialise the reflux ratio profile for each new value of (Rl, xRI). This was done automatically in Mujtaba (1989) using the reflux ratio profile calculated at the previous function evaluation in the outer loop so that the inner loop problems (specially problem P2) could be solved in a small number of iterations. However, experience has shown that even after this re-initialisation of the reflux profile sometimes no solutions (even sub-optimal) were obtained. This is due to failure to converge within a maximum limit of function evaluations for the inner loop problems. On the other hand the one level formulation does not require such re-initialisation. The reflux profile was set only at the beginning and a solution was always found within the prescribed number of function evaluations. 

As presented in the earlier chapters, the operating policy for a batch distillation column can be determined in terms of reflux ratio, product recoveries and vapour boilup rate as a function of time (open-loop control). Under nominal conditions, the optimal operating policy may be specified equivalently in terms of a set-point trajectory for controllers manipulating these inputs. In the presence of uncertainty, these specifications for the optimal operating policy are no longer equivalent and it is important to evaluate and compare their performance. 

Model predictive control in batch distillation (Fileti et al., 2000)... 

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