Batch Differential Distillation

Distillation. Distillation separates volatile components from a waste stream by taking advantage of differences in vapor pressures or boiling points among volatile fractions and water. There are two general types of distillation, batch or differential distillation and continuous fractional or multistage distillation (see also Distillation). 

When the composition of the compounds in the still or bottoms changes significantly as the batch distillation progresses, an unsteady state condition will exist as for differential distillation (see discussion of this subject later). 

The results of the differential distillation end the same as the flash distillation, although the mechanism is somewhat different. This is a batch type operation distilling differentially. All sensible and latent heat are supplied separately from the steam or by superheat in the steam. Steam acts as an inert in the vapor phase, and quantity will vary as the distillation proceeds, while temperature and pressure are maintained. 

Batch Distillation, 45 Differential Distillation, 46 Simple Batch Distillation, 47 Fixed Number Theoretical Trays,... 

Batch with Constant Reflux Ratio, 48 Batch with Variable Reflux Rate Rectification, 50 Example 8-14 Batch Distillation, Constant Reflux Following the Procedure of Block, 51 Example 8-15 Vapor Boil-up Rate for Fixed Trays, 53 Example 8-16 Binary Batch Differential Distillation, 54 Example 8-17 Multicomponent Batch Distillation, 55 Steam Distillation, 57 Example 8-18 Multicomponent Steam Flash, 59 Example 8-18 Continuous Steam Flash Separation Process — Separation of Non-Volatile Component from Organics, 61 Example 8-20 Open Steam Stripping of Heavy Absorber Rich Oil of Light Hydrocarbon Content, 62 Distillation with Heat Balance,... 

The simplest example of batch distillation is a single stage, differential distillation, starting with a still pot, initially full, heated at a constant rate. In this process the vapour formed on boiling the liquid is removed at once from the system. Since this vapour is richer in the more volatile component than the liquid, it follows that the liquid remaining becomes steadily weaker in this component, with the result that the composition of the product progressively alters. Thus, whilst the vapour formed over a short period is in equilibrium with the liquid, the total vapour formed is not in equilibrium with the residual liquid. At the end of the process the liquid which has not been vaporised is removed as the bottom product. The analysis of this process was first proposed by Rayleigh(24). 

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. 

Operation of a batch distillation is an unsteady state process whose mathematical formulation is in terms of differential equations since the compositions in the still and of the holdups on individual trays change with time. This problem and methods of solution are treated at length in the literature, for instance, by Holland and Liapis (Computer Methods for Solving Dynamic Separation Problems, 1983, pp. 177-213). In the present section, a simplified analysis will be made of batch distillation of binary mixtures in columns with negligible holdup on the trays. Two principal modes of operating batch distillation columns may be employed ... 

Unlike continuous distillation, batch distillation is inherently an unsteady state process. Dynamics in continuous distillation are usually in the form of relatively small upsets from steady state operation, whereas in batch distillation individual species can completely disappear from the column, first from the reboiler (in the case of CBD columns) and then from the entire column. Therefore the model describing a batch column is always dynamic in nature and results in a system of Ordinary Differential Equations (ODEs) or a coupled system of Differential and Algebraic Equations (DAEs) (model types III, IV and V). 

Rigorous and stiff batch distillation models considering mass and energy balances, column holdup and physical properties result in a coupled system of DAEs. Solution of such model equations without any reformulation was developed by Gear (1971) and Hindmarsh (1980) based on Backward Differentiation Formula (BDF). BDF methods are basically predictor-corrector methods. At each step a prediction is made of the differential variable at the next point in time. A correction procedure corrects the prediction. If the difference between the predicted and corrected states is less than the required local error, the step is accepted. Otherwise the step length is reduced and another attempt is made. The step length may also be increased if possible and the order of prediction is changed when this seems useful. 

Accurately, a RCM is obtained by solving the differential equation describing the evolution in time of the liquid composition in a batch distillation still ... 

Figure 5.27. Cont d. (c) Composition control. Top product take-off and boil-up controlled by feed, (d) Packed column, differential pressure control. Eckert (1964) discusses the control of packed columns, (e) Batch distillation, reflux flow controlled based on temperature to infer composition.

A simple application for batch distillation is what is known as differential distillation. It consists of a boiler containing a load of liquid. The liquid is progressively vaporized, with the vapor flowing to a condenser, producing a liquid distillate. There is no reflux, so the only stage with vapor-liquid equilibrium is the boiler. 

EXAMPLE 17.1 BENZENE-TOLUENE DIFFERENTIAL BATCH DISTILLATION... 

A batch still contains 100 kmol of a benzene-toluene solution at 85°C and 100 kPa. The mixture is distilled with no reflux in the column, in a differential batch distillation process. Determine the equilibrium liquid and vapor compositions at 5°C increments up to 105°C. It is also required to find at each time interval the amount of solution in the still and the total distillate composition. 

In a binary batch distillation process with no reflux (differential distillation), constant relative volatility is assumed throughout the process, a = 2. If the initial liquid composition X° = 0.4, what is the initial distillate composition What is the composition of the liquid remaining in the boiler when 50% of the original liquid has been distilled When 99% has been distilled ... 

In a single-stage batch distillation with no reflux (differential distillation) at 100 kPa, the still is charged with 100 kmol of an equimolar binary mixture of hexane and heptane. The A -values are given by In A" = A, - B,/T, where T is in degrees Kelvin. 

An initial charge of a 100 kmol mixture of 40 mol% benzene (1) and 60 mol% toluene (2) is distilled by differential batch distillation with no reflux. The process is stopped when 70% of the benzene is distilled. Find the amount and average composition of the distillate and the amount and composition of the residue. The relative volatility of benzene to toluene is ai,2 = 2.5. 

The single-tray differential process will be discussed later in connection with batch distillation. 

Equation (12.52) for batch distillation is the same as the mass balance equation for continuous distillation except for the term on the left side of the eqnation, which is normally zero for continuous distillation. Thus, it is theoretically possible to employ the same approach for batch distillation as previously presented for continnons distillation, provided an accnmnlation term is introdnced. However, although apparently simple, it is actually very difficult in practice becanse of problems in solving the many simnltaneons differential eqnations involved. In any event, it is erroneons to neglect tray and column holdnp in stage compntations for batch distillation. 

Equations relating the flow rates and compositions of feed and product streams in differential separation processes, first derived by Lord Rayleigh [Rl] for batch distillation, are often called the Rayleigh distillation equation. We shall derive some of these relationships for type B differential stage separation, using the nomenclature shown in Fig. 12.11. 

Consider the binary differential distillation of Example 6.3. For this system, n-heptane with n-octane at 1 atm, the average relative volatility is a = 2.16 (Treybal, 1980). Using equation (6-117) derived in Problem 6.7, compute the composition of the residue after 60 mol% of the feed is batch distilled. 

The suitability of the different operating modes can be determined with the aid of programs for modeling batch distillations. The treatment of batch distillations is much more laborious than that for continuous distillations. However, the decision can be simplified by using Equations (2.3.2-29) and (2.3.2-30), which were determined for the different operating modes with the aid of differential equations. The minimum vapor quantity G is used for comparison ... 

A process that is closely related to sinple batch distillation is differential condensation fTreybal. 19801. In this process vapor is slowly condensed and the condensate liquid is rapidly withdrawn. A derivation similar to the derivation of the Raleigh equation for a binary system gives. 

In simple batch or differential distillation, liquid is first charged to a heated kettle. The liquid charge is boiled slowly and the vapors are withdrawn as rapidly as they form to a condenser, where the condensed vapor (distillate) is collected. The first portion of vapor condensed will be richest in the more volatile component A. As vaporization proceeds, the vaporized product becomes leaner in A. 

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