_{1}

The effects of equipment parameters of batch distillation column on the yield proportion are discussed and analyzed, the relations between maximal yield proportion and the column equipment parameters are correlated, which not only can be used to appraise rationality of the design parameters of the columns being employed and which but also can be used to new batch distillation column design. Under the assistance of the separation difficulty defined in this paper, the minimum number of theoretical plates is determined by the limit loss proportion method given, and further the actual number of theoretical plates and the height for the batch distillation are calculated by using the redundancy coefficient found to complete the whole design of the batch distillation as shown in the computational sample. Research showed that the actual number of theoretical plates and the height of batch distillation column with the column diameter 0.6 m are 17 and 5.1 m in alcohol mixture separation system of the sample proposed. Moreover, the approach can be extended to the design of batch distillation column with a separation system of multi-component liquid mixture after those adjacent components are treated as numerous binary component systems.

Batch distillation as a significant and flexible separation approach is frequently employed in pharmaceutical, food, and petrochemical industries to acquire manifold high value-added and high-purity products. Generally batch distillation research can be divided into two classifications whereby they are operational type and design type. On the one hand, as a significant research branch, operational problems mainly involve modelling, simulation, optimization, control and so on [

A new operation mode for reactive batch distillation in middle-vessel columns was proposed, depending upon the characteristics of the reaction mixture [

Although all of above references showed achievements in operational aspects of batch distillation, investigators’ contributions to design type in batch distillation also circumvent touched problems within their research stages. A short-cut method as a replacement of simulated continuous distillation column design channels was mentioned and provided reasonably and effectively accurate solutions in designing batch distillation columns, evading much iterative procedures and considerable computational effort in rigorous models [

Abovementioned fruits regarding design types in batch distillation were better promotors whether in a generalized level or in an idiographic case, but their computations still were complex or were merely applicable to specific circumstances. As a result aim of this investigation is to propose a shortcut design technique to determine the theoretical and actual plate number of the batch distillation column and the height of the batch distillation column to solve the complexity problems that the batch distillation column was designed by referring to the continuous distillation column design theories or to overcome the uncertainty shortcomings that the design of the batch distillation column originated from the empirical method and the semi-empirical method and further set an example to lead the way that can guide the design of batch distillation column from binary system separation to multi-component system separation.

It is highly important for evaluating the rationality of the design of batch distillation column to study the effects of the established separation task and of the equipment parameters on the component yield of separation process in a batch distillation column. The effects of operating parameters such as reflux ratio, operating pressure and operating steam velocity on product recovery yield have been well known [

A certain number of theoretical plates are the guarantee to complete the separation task. Generally too few theoretical plate number not only can’t make the light component achieve a fixed concentration multiple like a continuous distillation, but also it can’t reach the concentration requirements. Moreover, too many theoretical plates have little effect on improving the light component recovery yield, and thus the investment in equipment will be greatly increased.

As shown curve φ_{1} in _{2} in _{12} in

Therefore, there must exist an optimal number of theoretical plates when a batch distillation column is designed.

The liquid holdup at column top is an important parameter for batch distillation, especially for the external reflux distillation equipment. On the one hand, it has storage effect on liquid discharge. On the other hand, it is also conducive to the regulation of reflux ratio. When some fluctuations occur in the operation, the concentration at column top is able to be stabilized and liquid holdup at column top existence has a great influence on the separation effect.

During the distillation process the “flywheel effect” is produced by the absorption or the release of volatile components with the increase or decrease of the concentration in the column. As an inertial effect, the “flywheel effect” makes the concentration change in the column slow, and encourages the trailing of the light component concentration. However, for the product distillation section that will be ended, high product concentration can be maintained at column top for a long time. Therefore, when the liquid holdup in column body is small, the increase of the liquid holdup in column body is beneficial to the increase of the recovery yields φ_{1} and φ_{2} of the light component product and the heavy component product as shown in

The increase of the liquid holdup in column body is beneficial to the increase of the recovery yields φ_{1}and φ_{2} of the light component product and the heavy component product as shown in _{12}, with the increase of liquid holdup in the column, which affects the yields φ_{1} and φ_{2} of the light component product and the heavy component product. Therefore, it is also important to control the liquid holdup in column body reasonably.

For a definite separation task which is completed on a fixed batch distillation column, the product recovery yield at column top is always less than 100% when the required concentration of the product at column top can’t be maintained, there is always a residual light component in the column and they will be treated as a transition product. The loss proportion in this section refers to the fraction of the residual light component in the total feed quantity of the component, which is determined by the separation requirements and the equipment parameters of the column. For different operation strategies, the values of recovery yield and loss proportion are different. Due to the existence of liquid holdup in the column, there is a theoretical maximum yield and a limit loss proportion. Obviously, the sum of the maximum yield and the limit loss proportion is equal to one. An analytical expression for calculating limit loss proportion is derived by indefinitely prolonging the operation time of constant concentration at column top. For the operation of constant concentration at column top, the product output at column top tends to be a limit value with the increase of time, which is assumed to be D y .

Thus, the limit loss proportion to the light component can be expressed as

e = H B 0 x B 0 − D y x D H B 0 x B 0 (1)

where e , H B 0 , x B 0 and x D are the limit loss proportion, the total feed quantity, the raw material concentration and the product concentration, respectively.

Assume the liquid holdup at column top and the liquid holdup per plate in column body are H c and H j and let η and x B , min be average mole fraction of the light component in column body and mole fraction of the light component at column bottom. Thus, the Equation (2) and the Equation (3) can be drawn by mass balance of the light component and by total mass balance.

e H B 0 x B 0 = H B x B + H j N η + H c x D (2)

H B = H B 0 − D y − H j N − H c (3)

Combining the Equation (2) and the Equation (3) output of the light component distillate product can be calculated from the Equation (4).

D y = H B 0 x B 0 ( 1 − e ) / x D (4)

The limit of constant concentration at column top must tend to total reflux operation and thus the minimum value of the concentration at column bottom, x B , min , can be obtained from the Fenske equation as shown the Equation (5).

x B , min = x D α N − 1 − x D ( α N − 1 − 1 ) (5)

where N is the number of the theoretical plate.

It is known from Fenske equation that the concentration of the light component on the first, the second and even the n^{th} plate can be obtained from the following the Equation (6)

x n = x D α n ( 1 − x D ) + x D (6)

where n is the code of the theoretical plate.

Thus, the average concentration of the light component in column body is

η = 1 N ∫ 1 N x n d n = 1 − 1 N ln α ln [ ( 1 − x D ) α N + x D ] α ( 1 − x D ) α + x D (7)

where η is average mole fraction of light component in column body.

Further, the limit loss proportion e can be calculated by the Equation (8) by combining the Equation (2), the Equation (3), the Equation (4) and the Equation (5).

e = e 1 + e 2 + e 3 (8)

where the three sub-items e_{1}, e_{2} and e_{3} are expressed as follows

e 1 = x D − x B 0 x B 0 ( α N + 1 − 1 ) ( 1 − x D ) (8-a)

e 2 = N H j H B 0 x B 0 [ η − x D − η ( 1 − x D ) ( α N + 1 − 1 ) ] (8-b)

e 3 = H c x D H B 0 x B 0 . (8-c)

From the mathematical expression of the limit loss proportion, it can be seen that the value of limit loss proportion is determined by the physical properties, separation requirements and equipment parameters of the separated object system for a specific separation task and the value is independent of the operating parameters. In

Although the limit loss proportion is derived from the binary component liquid mixture separation system, it is also applicable to the batch distillation process of the multi-component separation system. In this case, the product recovery yield of the multi-component batch distillation is further reduced by the effect of the trailing of the former component. But it hardly can affect the use of the approach of the limit loss proportion in the batch distillation design because the multi-component system can be simplified to become numerous binary adjacent component system. Therefore, the influence curve of the theoretical plate number on the limit loss proportion still can have guided the design of the batch distillation column.

By discussing the effect of operation parameters on the different component product recovery yield for a certain type batch distillation column, the main operating parameters that affect the recovery yield of the component product herein can be correlated into a new factor to simplify the design of the batch distillation design, which is called separation difficulty. Assume that a binary liquid mixture with an average relative volatility α is separated from an initial state x B 0 to a final state x D under the separation action of a batch distillation column. Considering Fenske equation expression and easy use the mathematical expression of the separation difficulty β employed is defined as:

β = lg [ ( x D 1 − x D ) ( 1 − x B 0 x B 0 ) ] / α (9)

where β , x D , x B 0 and α respectively are separation difficulty, mole fraction of the light component at column top, the initial mole fraction of the light component at column bottom and the average relative volatility of the light component relative to the heavy component.

For the task of a certain separating difficulty, the critical theoretical plate number N c is obtained from the limit loss proportion approach. In order to keep a certain margin, a redundancy coefficient ζ is given. Thus, the number of the theoretical plates determined is

N = ζ N c (10)

where N , N c and ζ are the actual number of the theoretical plates, the critical theoretical plate number and the redundancy coefficient, respectively.

Take different ζ values, a series of theoretical plates can be gotten. Afterwards, the minimum number of theoretical plates, which have little effect on the recovery yield increase of the component product by the algorithm [

Taking the separation difficulty β as the horizontal coordinate and the redundancy coefficient ζ as the longitudinal ordinate, the relation curve of separation difficulty β and redundancy coefficient ζ is drawn as shown in

For a separation task with a certain separation difficulty, the minimum number of theoretical plates is given according to the relationship between the limit loss proportion and the number of theoretical plates. And then the actual number of theoretical plates in batch distillation column is determined by the correction of the redundancy coefficient under the assistance of the separation difficulty.

The specific steps are shown as follows:

1) Select column diameter and packing type according to the requirement of processing capacity and estimate the liquid holdup each plate in column body H j and the liquid holdup at column top H c .

2) Draw the relation curve of N ~ e according to physical properties data of matter and separation requirements.

3) Find the critical number value of theoretical plates between the N ~ e sensitive area and the N ~ e flat area in the N ~ e relation curve.

4) Start to separate the next component taking the stock in the column bottom as a raw material, and the material quantity and the concentration of the components in the column bottom are calculated by material balance.

5) Repeat the steps 2, 3 and 4 until the required product indicators at column top are fully calculated.

6) Compare N c values for each component group and take the maximum critical number of theoretical plates N ′ c to become the minimum number of theoretical plates required.

7) See

N = ζ N ′ c (11)

By using following steps, the height of batch distillation column can be determined.

1) Identify design task. A raw liquid mixtures that are composed of ethanol, n-propanol and n-butanol with mass fraction ratio 0.4, 0.2 and 0.4 need to be separated by a batch distillation column. Calculate the column height that can make product concentration required of ethanol and n-propanol be 99 percent and 78 percent at column top and that can process 2.5 ton raw material per batch. Assume that there are two operational periods to the distilled products at column top. The first operational period refers to the time range that the first component product is being distilled off until the beginning of the first transition fraction product is being distilled off at column top. The second operational period refers to the time range that the second component is being distilled off until the beginning of the second transition fraction product is being distilled off at column top.

2) Select the BX type wire mesh corrugated packing with the column diameter 0.6 m. The height of equal plate ε is 0.3 m. The liquid holdup in packing is 5% of the volume of packing layer. By accounting, the liquid holdup each plate in column body H j is 3.4 kg and the liquid holdup H c at column top is 50 kg.

3) Plot the N ~ e relation curve in the first operation period that is from the first component product distilling off to the beginning of the transition fraction product distilling off at column top. Take common relative volatility between ethanol and n-propanol 2.08 as the value calculated. The curve a in

4) Get critical number of the theoretical plate. See

5) Find the initial conditions of the second operating period. The maximum

yield of ethanol product derived from the material balance is D y = H B 0 x B 0 ( 1 − e ) x D 1 , whose result is 941 kg.

Assume the amounts of transition fraction products are close to the sum of the liquid holdup at column top and the liquid holdup in column body, the ethanol mass lost in the first component product and the transition fraction product is

S 2 = [ ( H c + H j N c 1 ) − H B 0 x B 1 0 e ] − D y ( 1 − x D 1 ) ,

whose value is 30.3 kg by calculation.

Furthermore, the mass of solutions at column bottom is

H B = ( H B 0 x B 2 0 − S 2 ) + H B 3 0 x B 3 0 ,

whose value calculated is 1469.7 kg. Simultaneously concentrations of n-propanol and n-butanol calculated at column bottom are x B 2 = 0.3196 , and x B 3 = 0.6804 , respectively.

6) Calculate the number value of theoretical plates required for the second operational period. Take common relative volatility between n-propanol and n-butanol 2.19 as a calculated value. The curve b in

7) Compare their sizes for the critical numbers of the theoretical plate N c 1 and N c 2 . Since N c 1 is greater than N c 2 , then take the practical critical theoretical plate number N ′ c = N c 1 = 15 . Moreover, the separation difficulty in the system

is β = lg [ ( x D 1 1 − x D 1 ) ( 1 − x B 1 0 x B 1 0 ) ] / α , whose value is 1.044 after the verification is

completed. See

N = ζ N ′ c = 1.08 × 15 = 16.2

The actual number values of theoretical plates are rounded to become N = 17 , then the height of the batch distillation column can be drawn from the below.

Z = ε N = 0.3 × 17 = 5.1 m

Finally, the height of the batch distillation is 5.1 m.

By discussing the effects of equipment parameters such as the number of the theoretical plate, the liquid holdup at column top and the liquid holdup at column body in a batch distillation column on maximal yields of light component and of heavy component in a binary component separation system, change curves of the limit loss proportion of the light component and of the heavy component with the numbers of theoretical plate are built. The curves can become a requisite in this design tactic of a batch distillation column and can be used to guide equipment selection of batch separation system of liquid mixture of whether simple binary component or complex multi-component by using following procedures:

1) Compute the values of separation difficulty defined according to the known data between adjacent components in binary component or multi-component system.

2) Identify the value of redundancy coefficient in terms of the steps said in the design technique including the sample mentioned.

3) Get the actual number of theoretical plates and reduce the height of the batch distillation column.

4) In alcohol mixture separation system of the sample given, the actual number of theoretical plates and the height of batch distillation column with column diameter 0.6 m are 17 and 5.1 m, respectively.

To sum up, the design approach of the batch distillation column described in this paper is simple and feasible as shown in computational sample and it also will be able to be used to design multi-component batch distillation column when the adjacent components are regarded as numerous binary components. Moreover, some investigations such as a unity of separation difficulty to different systems needed to be separated; the augmentation of curve with regard to separation difficulty and redundancy coefficient for designing batch distillation column, novel operational control strategy and modified optimization algorithm in batch distillation simulation will become future investigation target after this work and synchronously novel research hotspots will come into being.

The financial support from the United Laboratory Construction Fund of China and of Liaoning Province (No. 2011), the Natural Science Foundation of Liaoning Province (No. 2013020150), the Program for Liaoning Excellent Talents in University (No. LJQ2011134), and the Science and Technology Fund from Shenyang Institute of Engineering (No. XNZD-1807) are gratefully acknowledged.

The author declares no conflicts of interest regarding the publication of this paper.

Hao, W.F. (2019) A Short-Cut Design Technique to Batch Distillation Column. Advances in Chemical Engineering and Science, 9, 263-279. https://doi.org/10.4236/aces.2019.93020

B: Column bottom (-)

c: Column top (-)

D: Output of light component distillate product (kg)

D: Distillate product (-)

e: Limit loss proportion (-)

H: Initial feeding quantity (mol)

H: Liquid holdup at column top, column plate, column body and column bottom (mol or kg)

N: Number of the theoretical plate (-)

n: Code of the theoretical plate (-)

S: Ethanol mass lost in the first component product and the transition fraction product (kg)

x: Mole fraction of different components raw material and mole fraction of the light component, heavy component and transition fraction product at column top, on column plate, in column body and at column bottom (-)

y: Yield amount expression (-)

Z: Actual height of the batch distillation column (m)

Special characters

α: Average relative volatility of the light component relative to the heavy component (-)

β: Separation difficulty of the separation system (-)

η: Average mole fraction of the light component in column body (-)

ε: Height of equal plate (m)

ζ: Redundancy coefficient (-)

φ: Recovery yield of the component product (mol/mol)

λ: Recovery yield of the transition fraction product (mol/mol)

Superscript

0: Initial State

Subscript

1, 2, 3: Component, numerical code or operational period

c: Critical value or column top

i: Column body

j: Column plate

min: Minimum value