Fractionating columns material balances

Chapter 2 reviewed in detail how to choose methodologies and calculate fractionation column material and energy balances. Now it is time to develop the column internal design patterns and their configurations of good-practice industry design engineering. 

When collecting meaningful field fractionating column data, the column must not only have constant flow rates, but the flows must give a good material balance (no accumulation). In addition, a steady state condition must exist for the given flow rates. 

For ideal mixtures, or where over the concentration range concerned the relative volatility may be taken as constant, Rm may be obtained analytically from the physical properties of the system as discussed by Underwood(28). Thus, if x a and xnB are the mole fractions of two components A and B in the liquid on any plate n, then a material balance over the top portion of the column above plate n gives ... 

The case of a column with four ideal plates used to separate a mixture of ethyl alcohol and water may be considered. Initially there are Si moles of liquor of mole fraction xfl with respect to the more volatile component, alcohol, in the still. The top product is to contain a mole fraction xd, and this necessitates a reflux ratio R. If the distillation is to be continued until there are S2 moles in the still, of mole fraction xs2, then, for the same number of plates the reflux ratio will have been increased to R2. If the amount of product obtained is Db moles, then a material balance gives ... 

The performance of a given column or the equipment requirements for a given separation are established by solution of certain mathematical relations. These relations comprise, at every tray, heat and material balances, vapor-liquid equilibrium relations, and mol fraction constraints. In a later section, these equations will be stated in detail. For now, it can be said that for a separation of C components in a column of n trays, there still remain a number, C + 6, of variables besides those involved in the dted equations. These must be fixed in order to define the separation problem completely. Several different combinations of these C + 6 variables may be feasible, but the ones commonly fixed in column operation are the following ... 

A representative fractional distillation column of which there are thousands In use in the process industries, notably in the petroleum and petrochemical industries, is shown in Fig. 2. The material balance of the column is ... 

We study the separation of 77-hexane-ethyl acetate mixture by using acetonitrile as a heavy heterogeneous entrainer. The simulation of the process is performed with the batch process simulator ProSimBatch [10]. It enables to evaluate operational parameters like the entrainer amount that are not provided by the feasibility and synthesis analysis The column model consists of usual plate by plate Material balance, Equilibrium, Summation of fractions and Heat balance... 

Example 5.3 A mixture containing 50 moles each of benzene and toluene is to be distilled under conditions of constant reflux ratio until mole fraction of the residual benzene is less than 0.20. The column contains three theoretical stages. Calculate the material balance for this separation. 

Data were collected periodically for feed and solvent flow rates and amount of fractions from each separator and raffinate. A material balance check was performed at the end of each run. If the material balance was more than 90%, the samples were analyzed. The packed column was considered to be in steady state when the amount of fractions and flow rates (solvent and feed) obtained were constant for three successive time intervals. A typical run required one hour to reach steady state. 

The mole fractions of the feed, bottom product and the distillate determine the ratio of feed to product flow rates. In a control volume from the top of the column to any cross section b, as shown in the right hand picture in Fig. 1.56, the material balance is as follows, when the mole fraction of the volatile components in the vapour is represented by y, and the fraction in the liquid is indicated by x,... 

The material balance from (1.228) is once again the starting point for investigating the concentration profile in a packed column being used to rectify a gaseous mixture. In this case the mole fractions will be used instead of the mole ratios. The amount transferred from the gas to the liquid phase is —NGdy, wherein NG is now the molar flow rate of the gas mixture rather than that of the carrier gas as in (1.228). Equation (1.228) is therefore replaced by... 

Note that Equation 13.2 can be summed up over all the components, and then combined with equation set 13.3 in order to yield the overall material balances on each tray. The condition that the sum of the feed mole fractions, Zj must be equal to 1 follows from these balances. Further, the overall tray material balance, summed over trays 1 through N, results in a column overall material balance. 

At a given point in time, the amount of liquid in the reboiler is and its composition in terms of the mole fraction of the lighter component is The distillate rate and composition at time / are D mol/h and Xg, respectively. The internal liquid and vapor flows at the same instant areL and P mol/h, assumed constant from tray to tray. A material balance at / around an envelope that includes the condenser and a column section from the condenser to any tray gives the following operating line equation if the holdups are neglected ... 

When m varies significantly over the range of mole fractions x which exist in the column, then the integral in Eq. (13-79) may be evaluated either graphically or numerically. The value of x for any y in the interval yt to yN+1 is given by the component-material balance... 

Material-balance diagram for continuous fractionating column. 

Adjust the benzene product flow rate. This is the overhead product of the benzene distillation column and depends on the value of the feed flow rate. In the next section we will see how to adjust the overhead flow rate in order to maintain the desired benzene purity and fractional recovery by a material balance controller which manipulates the distillate to feed ratio (D/F control). 

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