Boilup ratio variable

The column may be operated to meet various performance specifications within certain ranges. The variables that can be specified in multi-component separation include all the component compositions, rates, or recoveries in the two products as well as the product rates, properties, and temperatures, the reflux and boilup ratios, the condenser and reboiler duties, and the tray temperatures and liquid and vapor rates. 

Instead of regarding all of the reflux and boilup ratios as fixed, let one of them be varied, say VNi/Bu as required to satisfy the condition that QRl = QC2. The new variable VNi/Bx is added to the set of variables and the variable QC1 is removed from the set of variables and functions by replacing QC2 by QRi. Thus, to solve this problem, the variables are taken to be... 

On the basis of an assumed value for VNl /Bl, one complete trial is made on column 1. The set of bottom flow rates bi% j so obtained is used as the feed to column 2. The reboiler duty QRl found for column 1 is taken to be the assumed value QC2 for making the trial on column 2. Then the capital 0 method is applied and a new value of Vsi/Bi is obtained. This value of the boilup ratio is used in making the second trial on column 1. Also, in the application of the IN Newton-Raphson method to column 1, the assumed values of Qcl and QRl are set equal to the most recent set of values found by use of the capital 0 method. In the application of the IN Newton-Raphson method to columns 1 and 2, the independent variables are taken to be Qcl, QRl, 7, Lj/Vj, for column I and Qc2 > Qr2 > Tfh Lj/Vj for column 2. 

In the specifications given by set 2 of Table 7-2, the reflux ratios and boilup ratios are fixed and the capital 0 method again consists of 14 functions in 14 independent variables. If the reflux rates Ll u Lx 2 and the total flow rates Dx and B2 are specified instead of the reflux ratios and boilup ratios, the capital 0 method reduces to two functions in two independent variables 0t and 02 see set 3 of Table 7-2. In this case the g functions for the capital 0 method are given by... 

For the case where the reflux ratio L /D and the boilup ratio Vs/B are specified in lieu of the reflux rate Lt and the distillat rate D for a conventional distillation column having a partial condenser, formulate the g funct ns of the 0 method where the variables x are taken to be... 

Before delving into the feed rearranging control structure, we first construct the fundamental control configuration for the reactive distillation with two feeds. Recall that, unlike the control of conventional distillation systems, we need to control the internal composition (or temperature) to maintain stoichiometric amounts of the two fresh feeds. For the purpose of illustration in this work, we choose to control the composition of reactant A on tray 13 where a large change in the composition of A is observed (Fig. 18.5b). Thus, we have three compositions to be controlled top composition of C, bottoms composition of D, and composition A on tray 13. For the manipulated variables, the ratio scheme is used these three ratios are reflux ratio, boilup ratio, and feed ratio. Figure 18.12 shows the control structure. 

Figure 18.12 Control structure of reactive distillation using feed ratio, reflux ratio, and boilup ratio as manipulated variables with fixed feed locations.

The result of the RGA indicates that we should pair the internal composition with the feed ratio, pair the top composition with the reflux ratio, and pair the bottoms composition with the boilup ratio (xa - T oA/-f oB> d,c - R/D, and Xb,d - ys/R)- After the variable pairing, the basic control loops are in place. Figure 18.12 shows the control configuration for the reactive distillation without feed rearrangement. 

Avoid saturation of a manipulated variable. A good example of saturation is the level control of a reflux drum in a distillation column that has a very high reflux ratio. Suppose the reflux ratio (R/D) is 20, as shown in Fig. 8.10. Scheme A uses distillate flow rate D to control reflux drum level. If the vapor boilup dropped ouly 5 percent, the distillate flow would go to zero. Any bigger drop in vapor boilup would cause the drum to run dry (unless a low-level override controller were used to pinch back on the reflux valve). Scheme B is preferable for this high reflux-ratio case. 

Example 16.5. Yu and Luyben (Ind. Eng. Chem. Process Des. Dev., 1986, Vol. 25, p. 498) give the following steadystate gain matrices for three alternative choices of manipulated variables reflux and vapor boilup (R — V), distillate and vapor boilup (D — V), and refiux ratio and vapor boilup (RR — V). 

Table 5.2 summarises the results for two cases (i) constant vapour boil-up rate, (ii) variable vapour boilup rate. The initial and final time optimal reflux ratio values are shown in Table 5.2 for both cases. The optimal reflux ratios between these two points follow according to Equation P.13 for each case. See details in the original reference (Robinson, 1969). 

Equality constraints h(D°, D°) = 0 may include, for example, a ratio between the amounts of two products, etc. Inequality constraints g(u, D°) < 0 for the overall operation include Equations 7.14-7.18 (the first two of which are easily eliminated when m and H are specified) and possibly bounds on total batch time for individual mixtures, energy utilisation, etc. Any variables of D° and D° which are fixed are simply dropped from the decision variable list. Here, Strategy II was adopted for the multiple duty specification, requiring B0 to be fixed a priori. Similar considerations hold for V, the vapour boilup rate. The batch time is inversely proportional to V for a specified amount of distillate. Also alternatively, for a given batch time, the amount of product is directly proportional to V. This can be further explained through Equations 7.24-7.26) ... 

This leaves four variables to be controlled by manipulating five streams. The fifth stream, often termed the "free stream, is usually flow controlled. If the free stream is the boilup rate, it is sometimes controlled by differential pressure. This technique is discussed in Chap. 19. At other times, the free stream is controlled by ratio control (often reflux to feed) or by a detuned composition controller (above). 

In addition, there are four degrees of freedom that are adjustable during design and are also adjustable during operation of the column reflux flow rate (/ ), vapor boilup (V), sidestream flow rate (5), and the liquid split ratio (jSl = i-p/i-R)- The variable Lp is the liquid flow rate fed to the prefractionator side of the wall, and Lp is the total liquid leaving the bottom tray in the rectifying section. Of course, the rest of the liquid coming from the bottom of the rectification section is fed to the sidestream side of the column. Distillate and bottoms flow rates are used to maintain liquid levels in the reflux drum and column base, respectively. 

These three controlled variables require three manipulated variables. There are four available reflux flow rate, sidestream flow rate, vapor boilup, and liquid split. Vapor boilup has an immediate and strong effect on all compositions throughout the system, and therefore, in theory, could be used to control any of the three product compositions or a composition in the prefractionator. Reflux affects all compositions, but the only composition that it affects quickly is the distillate composition. Its effect on products lower in the column can take considerable time because of the liquid hydraulic lags. Therefore, it seems logical to control distillate composition with reflux. Reflux-drum level is then controlled by manipulating distillate. This choice is for situations in which the reflux ratio is not high. If the reflux ratio is greater than about 3, conventional distillation control wisdom says to control composition with distillate and control the reflux-drum level with reflux. 

For the unconstrained degree of freedom the suggested control variables tested were one of the following boilup in the HP column, fixed boilup to feedrate ratio (Qb/F), the pressure in the HP column, reflux ratio in the HP column, fixed reflux to feedrate ratio, distillate flow in HP column, bottom flowrate in HP column, temperatures in the HP column, temperatures in the LP column, distillate composition in the HP column and bottom composition in HP column. 

Table 3.7 provides the optimum design results for the conventional process over a range of temperature-dependent relative volatilities. Because the column relative volatilities are only slightly lower than those of the constant relative volatility case, we assume that the three design optimization variables are the same as in the constant relative volatility case. The slightly lower relative volatilities produce small increases in the number of trays, the reflux ratios, and the vapor boilups in both columns. There is a small increase in the recycle flowrate (D2). 

A two-temperature control structure is considered first. Selecting the vapor boilup and reflux ratio as manipulated variables, the control problem then is to find the best locations for the two temperature control trays. Figure 12.50 shows the steady-state changes in tray temperatures throughout the column for several small changes in vapor boilup and reflux ratio. 

Using the reflux ratio and vapor boilup as the manipulated variables, the two-temperature control structure is shown in Figure 12.80. Two temperature control trays, tray 85 and tray 5, are selected based on SVD analysis. Using relay-feedback tests, values of ultimate... 

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