Boilup rate

Note that this equation holds for any component in a multi-component mixture. The integral on the right-hand side can only be evaluated if the vapor mole fraction y is known as a function of the mole fraction Xr in the still. Assuming phase equilibrium between liquid and vapor in the still, the vapor mole fraction y x ) is defined by the equilibrium curve. Agitation of the liquid in tire still and low boilup rates tend to improve the validity of this assumption. 

Assuming a specific boilup rate D , the compositions may now be calculated as a function of time ... 

Starting with an empty overhead receiver, the time Oj to condense D mols of vapor to fill the receiver, when the vapor boilup rate is G mols/hr. 

This is the boilup rate, which is approximately 3.3 ft vapor/sec. An approximately 1 ft 0 in. diameter column can handle this rate however, because it is in the usual size for a packed tower (or cartridge trays), the diameter must be checked using the packed tower calculations in Chapter 9 of this volume. 

P = Fugacity at reference standard condition f = Feed composition, i, or, = total mols of component, i, in distillate and bottoms G = Boilup rate, mols/hr... 

Repeat calculations, adjusting flow loop geometry if necessary, until assumed x gives the proper boilup rate. 

Investigate the response of the column to changes in the boilup rate, V. 

COLUMN FEEDRATE SATURATED LIQUID FEED FEED COMPOSITIONS REFLUX RATIO RELATIVE VOLATILITIES LIQUID HOLDUPS VAPOUR BOILUP RATE... 

The simulation is based on a fixed vapour boilup rate. Component balance equations are represented for benzene and toluene . The xylene concentrations are determined by difference, based on the sum of the mole fractions being equal to one. 

Theoretical trays, equimolal overflow, and constant relative volatilities are assumed. The total amount of material charged to the column is M q (moles). This material ean be fresh feed with composition Zj or a mixture of fresh feed and the slop cuts. The composition in the still pot at the begiiming of the batch is Xgoj. The composition in the still pot at any point in time is Xgj. The instantaneous holdup in the still pot is Mg. Tray liquid holdup and reflux drum holdup are assumed constant. The vapor boilup rate is constant at V (moles per hour). The reflux drum, eolumn trays, and still pot are all initially filled with material of eomposition Xg j. 

The reactor in Problem 13.14 is to be cooled by autorefrigeration. Determine the boilup rate in the reactor assuming that the condensate is returned to the reactor without subcooling. 

A liquid binary mixture with Bo = 10 kmol and xbo = <0.6, 0.4> molefraction is subject to conventional batch distillation shown in Figure 4.3. The relative volatility of the mixture over the operating temperature range is assumed constant with a value of (a=) 2. The total number of plates is, N = 20. The vapour boilup rate is, V = 5.0 kmol/hr and the reflux ratio is, r = 0.75. The condenser and total plate holdups are 0.2 and 0.2 kmol respectively. 

Kerkhof and Vissers and Mujtaba (1989) considered the operating cost Cj as constant, but in practice it may vary, say, with different boilup rates. More general expressions (Logsdon et al., 1990, Mujtaba and Macchietto, 1996) could also be used to evaluate the operating cost per hour. When C = 1.0, C2 = C3 = ts = 0, the maximum profit problem results in a maximum productivity problem (Mujtaba, 1989, 1999). 

Simple Model with Variable Boilup Rate... 

The boilup rate in actual columns is seldom kept constant but falls off as the distillation proceeds (as discussed in Chapter 3, also see Greaves et al., 2001 Greaves, 2003). Robinson (1969) assumed that the boilup rate is a linear function of the still composition (with boilup V0 at time t = 0 and kis a constant)... 

The model equations for multicomponent distillation under constant boilup rate (Robinson, 1969) are ... 

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). 

Case Boilup Rate Optimal Reflux Ratio at Minimum... 

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) ... 

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. 

Base Case Input Data The number of plates, N The vapour boilup rate, V moles/hr Column holdup = 15 = 250 = 0... 

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