Design and Control of the Cryogenic Distillation Process for

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Design and control of the cryogenic distillation process for purification of synthetic natural gas from methanation of coke oven gas Xingxing Li, Jiageng Li, and Bolun Yang Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 24 Nov 2014 Downloaded from http://pubs.acs.org on November 24, 2014

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Industrial & Engineering Chemistry Research

1

Design and control of the cryogenic distillation process for purification of

2

synthetic natural gas from methanation of coke oven gas

3

Xingxing Li, Jiageng Li, Bolun Yang*

4

Department of Chemical Engineering, State Key Laboratory of Multiphase Flow in Power Engineering,

5

Xi’an Jiaotong University, Xi’an Shaanxi 710049, P.R. China

6 7

Abstract:

8

A cryogenic distillation process for upgrade of synthetic natural gas (SNG) from methanation

9

of coke oven gas (COG) is designed and controlled using the method of gradually reducing

10

independent variables. Freedom analysis is performed to decide independent variables of the

11

cryogenic

12

Peng-Robinson-Boston-Mathias (PR-BM) thermodynamics method, parameters sensitivity

13

analysis is implemented to obtain the optimal operation conditions using Aspen Plus software.

14

After supplying the physical dimensions and control variables (reflux flow rate and reflux

15

ratio) of the distillation column, three control structures that involve fixed reflux flow rate,

16

fixed reflux ratio and dual-composition controllers are developed to control the cryogenic

17

distillation process. Under the significant disturbances of feed flow rate and feed composition,

18

evaluation results shows that the dual-composition control system displays the best effect for

19

maintaining the mole percent of CH4 in column bottoms and gas distillates, which are 99.87%

20

and 0.43%, respectively.

distillation

column.

Based

on

the

equilibrium

stage

model

and

21 22

Keywords: Synthetic natural gas; Cryogenic distillation; Freedom analysis; Fixed reflux flow

23

rate; Fixed reflux ratio; Dual-composition control

To whom correspondence should be addressed. Tel.: +86-29-82663189. Fax: +86-29-82663189. E-mail: [email protected]

ACS Paragon Plus Environment


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1. Introduction

2

The research of alternative fuel has been highly attractive with the concern of

3

environmental protection and growing energy demand. Natural gas, mainly containing

4

methane, is considered as one of the most promising alternative fuels because of its excellent

5

combustion characteristics such as high octane number, good antiknock property and less

6

emission.1 However, it is reported that natural gas will be exhausted in the range of 40-60

7

years, thus a sustained effort has been made to convert various feedstock into synthetic

8

natural gas.2-5 Nowadays, synthetic natural gas (SNG) is mainly produced from coal, and is

9

usually upgraded though chemical or physical adsorption to remove the small amount of CO2,

10

H2O, H2S and some phenols.6

11

As a by-product in coke production, the coke oven gas (COG), can be considered as an

12

important hydrocarbon resource to the synthesis of natural gas through the methanation

13

process.7 In this case, the SNG from COG methanation is constituted of CH4, N2 and H2 due

14

to the high proportion of H2 in COG,8 although the pressure swing adsorption method can be

15

adopted for purification of this kind of SNG, the close polarizability between CH4 and N2 may

16

induce the selection of adsorbent difficult.9,10 Therefore, the refrigeration distillation can be

17

developed as a favorable approach because of the wide different boiling temperatures among

18

CH4, N2 and H2. After distillation, the product from column bottom is the well purified

19

liquefied natural gas (LNG) with the mole percent of CH4 larger than 99.5%, which can

20

greatly save the storage space and transportation cost compared to the gaseous fuel. The

21

whole process for purification of SNG from methanation of COG is depicted in Figure 1.

22 23

Figure 1. Cryogenic distillation process for purification of synthetic natural gas

24

from methanation of coke oven gas.

25 26

Previous research of cryogenic distillation mainly focused on manufacturing large


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quantities of high-purity nitrogen, oxygen and argon for the steel and food processing

2

industries.11-14 In addition, cryogenic distillation in demethanizer and depropanizer is still the

3

dominant technology to provide many chemical products,15,16 then the carbon and hydrogen

4

isotope separation is as well explored using cryogenic distillation columns in recent years.17-19

5

However, few reports have been found concerning about CH4/N2/H2 system to SNG

6

purification in cryogenic distillation column.20

7

Moreover, owing to the changeability of COG from different coke ovens, two typical

8

disturbances including the variation of feed flow rate and feed composition are especially

9

noted in this SNG purification, thus the implementation of suitable control strategy is

10

essential to the successive stable operation of the cryogenic distillation column, and as well to

11

maintain the purity of the separated LNG. Up to now, on the basis of various control

12

mechanisms such as feedback, feed forward, decoupling and cascade control,21-24 many

13

control methods with varying degrees of simplifications have been developed for application

14

of different cryogenic distillation systems. A few examples are the multivariable model

15

predictive control for air separation process, the internal model control for the carbon isotope

16

separation process and the optimal control of an industrial depropanizer using the

17

non-dominated sorting genetic algorithm.25-27 Nevertheless, there have been few discussions

18

about rigorous nonlinear control of cryogenic distillation column.

19

Aspen Dynamics is a powerful tool for rigorous nonlinear dynamic simulation and control

20

of processing industries, which is tightly integrated with the corresponding steady state

21

simulator Aspen Plus. In this work, the method of gradually reducing independent variables is

22

developed to optimal design and control of the cryogenic distillation column in SNG

23

purification.

24

Peng-Robinson-Boston-Mathias equation of state (PR-BM EOS) method is established by

25

Aspen Plus for steady state simulation of the cryogenic distillation column. Then based on the

Firstly,

equilibrium

stage

model


combined

with

the


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column independent variables, parameters sensitivity analysis is done for going more into the

2

optimal conditions. Finally, the control variables among the independent variables are decided,

3

and three control structures with fixed reflux flow rate, fixed reflux ratio and

4

dual-composition controllers are proposed using Aspen Dynamics for rigorous nonlinear

5

dynamic control. Their performances for maintaining the CH4 purity in column bottoms and

6

CH4 impurity in gas distillates are observed and evaluated. The whole work will contribute to

7

the process design and optimal control of the cryogenic distillation column for SNG

8

purification.

9

2. Process Optimization of the Cryogenic Distillation

10

2.1. Model of Cryogenic Distillation Column

11

The SNG after COG methanation mainly contains CH4 59%, N2 5.9%, H2 35.1%, then it is

12

fed into the cryogenic distillation column where highly purified LNG can be obtained from

13

the column bottoms. During the optimal design of the column, the equilibrium stage model is

14

employed to the steady state simulation. To develop the equilibrium stage model, two

15

assumptions are indispensable: (1) Theoretical plate hypothesis, the compositions of vapor

16

and liquid streams leaving the stage are in equilibrium with each other; (2) Complete mixing

17

hypothesis, the liquid on the tray and the gas between two trays are completely mixed, they

18

have uniform temperature, pressure and compositions.28 For every column tray including

19

condenser and reboiler, the corresponding molar balance equation, vapor-liquid equilibrium

20

equation, component summation equation and enthalpy balance equation are as follows:

21

Molar balance equation:

22

Ls −1 xi , s −1 + Vs +1 yi , s +1 + Fs zi , s − Ls xi , s − Vs yi , s = 0

23

Vapor-liquid equilibrium equation:

24

yi , s = K i , s xi , s

25

Component summation equation:

(1)

(2)


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c

1

∑x

i, s

−1 = 0

(3)

−1 = 0

(4)

i =1

c

2

∑y

i, s

i =1

3

Enthalpy balance equation:

4

Ls −1hL , s −1 + Vs +1HV , s +1 + Fs H F , s − Ls hL , s − Vs HV , s − Qs = 0

5

2.2. Thermodynamics Method

(5)

6

The cryogenic distillation is under low temperature and high pressure, and the gas mixture

7

of CH4/N2/H2 system has the nonpolar characteristic, thus the Peng-Robinson equation of

8

state with Boston-Mathias modified function (PR-BM EOS) can be adopted to describe the

9

vapor liquid equilibrium by calculating the fugacity coefficient,29 which is expressed in

10

Appendix section 1.

11

According to the PR-BM thermodynamics method, the necessary parameters built in Aspen

12

Plus are listed in Table 1. Then the residual curve map for the CH4/N2/H2 system can be

13

generated, as shown in Figure 2. The points of feed, gas distillates and column bottoms have

14

been labeled in Figure 2, which lie on a straight line, as required by the overall component

15

balances. Furthermore, the gas distillates composition and the column bottoms composition

16

lie on the same residue curve, and this relationship demonstrates that the cryogenic distillation

17

is feasible for the CH4/N2/H2 system.30

18 19

Table 1. PR-BM Thermodynamic Parameters for the CH4/N2/H2 System

20 21

Figure 2. Residual curve map for the CH4/N2/H2 system (3 MPa).

22 23 24

2.3. Freedom Analysis To determine the distillation process completely, a set of specifications needs to be



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1

provided. Normally, for a simple distillation problem, the degree of freedoms is C+6 where C

2

is the number of feed components.31 So for this cryogenic distillation in separating CH4 from

3

H2 and N2, the number of independent variables is 9 and the selected independent variables

4

are listed in Table 2.

5 6

Table 2. Independent Variables of the Cryogenic Distillation Column for CH4/N2/H2 System

7 8

During deciding the independent variables, the flow rate and temperature of the feed is

9

hypothetically specified as 1 kmol/s and 100 K, respectively. Furthermore, the condenser

10

pressure is set close to the methanation pressure (3 MPa) and the feed composition is already

11

known (H2: 35.1%, N2: 5.9%, CH4: 59%). Therefore, the design of the cryogenic distillation

12

column depends on the remaining four independent variables: total number of trays, feed tray

13

location, flow rate of column bottoms and reflux ratio (Table 2). The objective of our work is

14

to separate methane, thus the following constraint condition is defined and parameters

15

sensitivity analysis can be implemented to obtain the optimal parameters:

16

xB ,CH 4 ≥ 0.995 , yD ,CH 4 ≤ 0.005

17

where xB ,CH 4 is the mole fraction of CH4 in column bottoms and yD ,CH 4 is the mole fraction

18

of CH4 in gas distillates.

19

2.4. Parameters Sensitivity Analysis

20

The influence of the total number of stages, feed tray location, column bottoms rate and

21

reflux ratio on mole fraction of CH4 in column bottoms and gas distillates are shown in Figure

22

3. It can be seen in Figure 3(a) that the mole fraction of CH4 in column bottoms is

23

monotonously increasing along with the increase of total number of trays, while the mole

24

fraction of CH4 in gas distillates displays an obviously opposite trend. Figure 3(b) shows that

25

the mole fraction of CH4 in column bottoms increases initially but decreases later when the


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feed tray location changes from stage 2 to stage 22, the change trend of CH4 mole fraction in

2

the gas distillates is just the opposite. Figure 3(c) reveals that an increase in the column

3

bottoms rate gives rise to a monotonous decrease in mole fraction of CH4 in gas distillates and

4

column bottoms concurrently. However, when the mole flow rate of column bottoms is larger

5

than 0.589 kmol/s, the mole fraction of CH4 in gas distillates declines slowly but the mole

6

fraction of CH4 in column bottoms falls quickly. It is found in Figure 3(d) that the CH4

7

concentration of column bottoms increases with the increasing of the reflux ratio, and that of

8

gas distillates shows a descending trend. Considering the constraint conditions to be satisfied,

9

the optimal total number of stages, feed tray location, column bottoms rate and reflux ratio

10

could be chosen as 23, 5, 0.589 kmol/s and 0.09, respectively, where the mole percent of CH4

11

in the gas distillates and column bottoms are 0.43% and 99.87%.

12 13 14

Figure 3. Effect of (a) total number of trays, (b) feed tray location, (c) column bottoms rate and (d) reflux ratio on distillates impurity and product purity.

15 16

Based on the parameters sensitivity analysis, the appropriate values of the independent

17

variables are determined. The simulation results using Aspen Plus tool for the cryogenic

18

distillation under these optimized conditions are summarized in Table 3. Figures 4(a) and 4(b)

19

are the composition profiles of CH4, N2 and H2 in gas phase and liquid phase along the

20

column height. The compositions have a wide change on stage 5 because it is the feed tray.

21

Due to the lower temperature of rectifying section (before stage 5), the mole fraction of light

22

component H2 in gas phase and liquid phase decreases quickly, correspondingly the mole

23

fraction of heavy component CH4 increases quickly. However, due to the higher temperature

24

of stripping section, the variation for mole fraction of H2 and CH4 in both gas phase and liquid

25

phase becomes slowly. Thus the mole fraction of N2 in gas phase and liquid phase could have

26

a local maximum value. Furthermore, in the gas phase, there is nearly no CH4 on stage 1, so a



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1

sudden variation for the compositions of N2 and H2 occurs on stage 1 (Figures 4(a)). Figure 5

2

shows the temperature profile of the column. The temperature along with stage 1 (condenser)

3

to stage 23 (reboiler) varies from 88.9 K to 171.7 K, which is close to the actual result

4

(78~163 K).

5 6 Table 3. Optimized Conditions and Simulation Results of the Cryogenic Distillation for SNG Purification 7 8

Figure 4. Composition profiles of (a) gas phase and (b) liquid phase along the cryogenic distillation column.

9 10

Figure 5. Temperature profile of the cryogenic distillation column.

11 12

3. Control of the Cryogenic Distillation Column

13

3.1. Control Strategy

14

Due to the changeability of COG from different coke ovens, there could be two kinds of

15

disturbances occurring in the distillation column. One is the feed flow rate change, and the

16

other is the feed composition change. After the successful calculation of equipment

17

dimensions (see Appendix section 2) and pressure checked, the steady state simulation in

18

Aspen Plus can be exported to Aspen Dynamics for rigorous nonlinear dynamic control of the

19

cryogenic distillation column.

20

Here, it is worth mentioning that, during the process optimization and control of the

21

cryogenic distillation, the strategy of gradually reducing independent variables is developed,

22

which is illustrated by Figure 6. Among nine independent variables describing the distillation

23

column, the feed flow rate, feed temperature, feed composition (2 independent variables) and

24

condenser pressure could be known and fixed. Next when the optimal design of the column is

25

completed, the total number of trays and feed tray location are fixed, thus only column

26

bottoms rate (or reflux flow rate) and reflux ratio have significant influence on the distillation


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1

results, which are determined as the control variables. Therefore, three control strategies can

2

be developed to control the distillation system: (1) reflux flow rate is fixed and reflux ratio is

3

adjusted to control the mole fraction of CH4 in gas distillate and column bottom; (2) reflux

4

ratio is fixed and reflux flow rate is adjusted to control the mole fraction of CH4 in gas

5

distillate and column bottom; (3) both reflux flow rate and reflux ratio are manipulated to

6

control the mole fraction of CH4 in gas distillate and column bottom.

7 8

Figure 6. Strategy of gradually reducing independent variables in the optimal design and control of the

9

cryogenic distillation process.

10 11

The three control structures are called CS1, CS2 and CS3, respectively, which are shown in

12

Figure 7. The former two control structures belong to single-end control strategy, and the last

13

control structure with two composition controllers belongs to dual-end control strategy

14

(dual-composition control). The same modules involved into the three control structures and

15

the differences are analyzed below.

16 17

Figure 7. Control structure with (a) fixed reflux flow rate (CS1); (b) fixed reflux ratio (CS2); (c) two

18

composition controllers.

19 20

The three control structures (Figure 7(a), 7(b) and 7(c)) have five same modules, and their

21

parameter specializations are listed in Table 4. Undoubtedly, there are several pairing

22

schemes among these control variables and the manipulated variables, and the presented

23

pairing scheme is one of these cases, which is referred to literature [30].

24 25

Table 4. Comparison of the Three Control Structures

26



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1

(1) Controller FC: Flow rate of feed to the column is controlled by manipulating the open

2

percentage of valve V1. Gain and integral time of the controller are 0.5 and 0.3 min,

3

respectively. If the feed flow rate increases, valve V1 needs to be turned down, so the

4

controller action is configured reverse.

5

(2) Controller LC1: Reflux drum level is controlled by manipulating condenser heat removal.

6

Condenser heat duty can be manipulated to change the distillate flow rate, which in turn

7

controls the level of the reflux drum. Gain and integral time of the controller are 20 and 12

8

min, which work pretty well in most column simulations.30 Furthermore, more heat needs to

9

be removed from the condenser if the liquid level decreases. Notice that the condenser heat

10

removal is negative, so the controller action should be direct.

11

(3) Controller LC2: Reboiler level is controlled by manipulating the flow rate of column

12

bottoms. It is defined as a proportional-only controller and installed to be direct acting. The

13

controller gain is set equal to 2.

14

(4) Controller PC: Condenser pressure is controlled by manipulating the distillate flow rate,

15

because the pressure will be changed as the variation of distillate flow rate. When the pressure

16

goes up, valve V2 needs to be turned up, so the controller action is set to be direct. The

17

proportional-only controller can also satisfy the control requirement, and the gain is the same

18

as the controller LC2.

19

(5) Controller TC: The temperature of a selected stage is controlled by adjusting the reboiler

20

heat input, which is set to be reverse acting. It can be seen in Figure 8 that the temperature of

21

11th stage is most sensitive to the variation of the reboiler heat duty, so the temperature of

22

11th stage is regarded as the controlled variable.32 Controller TC is tuned by the

23

relay-feedback test to determine the ultimate gain and integral time constant. As presented in

24

Figure 9, the gain and the integral time by the Tyreus-Luyben tuning rule are 283.8093 and

25

2.64 min, respectively.


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1

Figure 8. Tray temperature sensitivity to variation of reboiler heat duty.

2 3

Figure 9. Tuning results using the relay-feedback test for the tray temperature controller.

4 5

The differences of the three control structures (Figure 7(a), 7(b) and 7(c)) are explained as

6

follows:

7

CS1: In Figure 7(a), the reflux flow rate is controlled by manipulating the valve V4. In Aspen

8

Dynamics, the variable of “reflux flow rate” is set to be “fixed”, thus the reflux flow rate can

9

be not change.

10

CS2: In Figure 7(b), the variable of “reflux flow rate” is set to be “free”, and the fixed reflux

11

33 × on the flowsheet. The input of the Multiplier ratio is realized by a Multiplier block □

12

block is connected from the mass flow rate of the gas distillates (2.367 kg/s), and the output

13

of the Multiplier block is connected to the mass flow rate of reflux (0.853 kg/s). Therefore,

14

the parameter of the Multiplier block is equal to 0.360 (2.367 × 0.360 = 0.853), which

15

represents the reflux ratio. The specification of the Multiplier block is set to be “fixed” in

16

Aspen Dynamics, thus the reflux ratio can be not change.

17

CS3: In Figure 7(c), both reflux flow rate and reflux ratio are set to be “free”, but two

18

composition controllers are added. One controls CH4 impurity in the gas distillates (Controller

19

CCxD) and the other controls CH4 purity in column bottoms (Controller CCxB). The

20

manipulated variable of the CCxD controller is the reflux ratio, and it is tuned using the

21

relay-feedback test and Tyreus-Luyben rule (KC = 1.05 and Ti = 60.14 min). The manipulated

22

variable of the CCxB controller is the setpoint of the 11th stage temperature, and in turn

23

changes the reboiler heat input, which is a cascade control. It is also tuned by the

24

relay-feedback test to give the constants (KC = 45.20 and Ti = 20.78 min).



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1

The structural block diagrams for the three control strategies are shown in Figure 10. As the

2

structural block diagrams described, the main control objective function of the three control

3

strategies is mole fraction of CH4 in column bottoms. CS1 and CS2 belong to the temperature

4

control, but CS3 belongs to the temperature-concentration cascade control.

5 6

Figure 10. Structural block diagrams of the three control strategies.

7 8

3.2. Evaluation of the Control Performance

9

The purpose of the three control structures is to see how well they perform in face of the

10

two disturbances, specifically how close the variables of composition and temperature are

11

maintained to the desired specifications.

12

Disturbance in feed flow rate are firstly imposed on the system with three control structures.

13

At time equal to 0.5 h, feed flow rate is perturbed from 1 to 1.1 kmol/s; at time equal to 4.5 h,

14

the feed flow rate is then perturbed from 1.1 to 0.9 kmol/s. Figure 11 gives the closed loop

15

responses of column tray temperature (stage 11) and CH4 mole fraction in gas distillates and

16

column bottoms. It shows that all the control structures give stable regulatory control.

17

However, the bottoms CH4 purity and distillates CH4 impurity have different response gains

18

with the three control structures. The deviation values to the desired specifications can be

19

ranked in the order of CS1 > CS2 > CS3 (Figure 11(a), 11(c) and 11(e): at 4.5 h,

20

1.08E-05>1E-06>0, 4.67E-05>4.5E-05>0; at 8.5 h, 1.61E-04>8E-06>0, 6.8E-04>6.6E-04>0).

21

That is to say, as for the two single-end distillation control structures, the inherent ability to

22

handle feed flow rate disturbance is better for fixed reflux ratio than for fixed reflux flow rate.

23

Table 5 is the required changes of reflux flow rate and reflux ratio to satisfy the constraint

24

conditions under feed flow rate disturbance. That is to say, when the feed flow rate is

25

increased, the reflux flow rate will have large variation in the distillation system.34 In this

26

case, reflux ratio should be slightly decreased to make the mole fraction of CH4 in column


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1

bottoms and gas distillates satisfy the specified constraint conditions ( xB ,CH ≥ 0.995 ,

2

y D ,CH 4 ≤ 0.005 ). Therefore, fixed reflux flow rate may be inappropriate for maintaining the

3

CH4 mole fraction under this condition. Conversely, fixed reflux ratio will possess the better

4

effect. Furthermore, as described in Figure 11(e), the CH4 mole fraction in both gas distillates

5

and column bottoms are driven back to their desired specifications and tightly controlled by

6

the dual-composition control structure, this is because the reflux ratio can be slightly adjusted

7

by the top composition controller (CCxD) and the reflux flow rate can also be changed by the

8

tray temperature through the composition-temperature cascade controller (CCxB). Variation

9

of the 11th stage temperature by CS3 can be found in Figure 11(f), compared to the

4

10

temperature with no change by CS1 and CS2 (Figure 11(b) and 11(d)).

11 12

Figure 11. Closed loop responses of CH4 mole fraction in gas distillates, column bottoms and 11th stage

13

temperature by the control structure with (a) and (b) fixed reflux flow rate (CS1); (c) and (d) fixed reflux

14

ratio (CS2); (e) and (f) two composition controllers: At 0.5 h, feed flow rate is perturbed from 1 kmol/s to

15

1.1 kmol/s; at 4.5 h, feed flow rate is perturbed from 1.1 kmol/s to 0.9 kmol/s.

16 17

Table 5. Required Changes of Reflux Ratio and Reflux Flow Rate under Feed Flow Rate Disturbance

18 19

The control performances under disturbance of the feed composition are shown in Figure

20

12. CH4 and H2 are important fuel and chemical materials, which are the objective products

21

during the utilization of coke oven gas, so the feed composition of CH4 and H2 are only

22

perturbed. At time equal to 0.5 h, the feed composition of CH4/N2/H2 is perturbed from

23

0.59/0.059/0.351 to 0.58/0.059/0.361; at time equal to 4.5 h, it is perturbed from

24

0.58/0.059/0.361 to 0.60/0.059/0.341. Similarly, stable control is obtained by the three control

25

structures. Nevertheless, the deviation values to the desired specifications are in the order of

26

CS2 > CS1 > CS3 (Figure 12(a), 12(c) and 12(e): at 4.5 h, 2.33E-05>3E-06>0,

27

7.3E-05>5.57E-05>0; at 8.5 h, 2.3E-05>1E-05>0, 3.6E-05>3.4E-05>0), which is different

28

from the case under feed flow rate disturbance. The results display a preference for the control



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

structure with fixed reflux flow rate under feed composition disturbance. From another angle,

2

this reveals the significance of changed reflux ratio in dealing with feed composition

3

disturbance because reflux ratio changes more sensitive to feed composition perturbation than

4

reflux flow rate (Table 6), according to William L. Luyben’s explanation.35 Moreover,

5

disturbance in feed composition not only requires change in reflux ratio, but also requires

6

change in tray temperature (reflux flow rate will be changed) to hold the CH4 mole fraction at

7

the specified value, just as the results controlled by the dual-composition control structure

8

(Figure 12(e) and 12(f)), while the temperature of tray 11 by the two sing-end control

9

structures has nearly no change (Figure 12(b) and 12(d)).

10 11


12


13

ratio (CS2); (e) and (f) two composition controllers: At time 0.5 h, feed composition of CH4/N2/H2 is

14

perturbed from 0.59/0.059/0.351 to 0.58/0.059/0.361; at time 4.5 h, feed composition of CH4/N2/H2 is

15

perturbed from 0.58/0.059/0.361 to 0.60/0.059/0.341.

16 17

Table 6. Required Changes of Reflux Ratio and Reflux Flow Rate under Feed Composition Disturbance

18 19

4. Conclusion

20

In this work, the cryogenic distillation process for upgrade of SNG from COG methanation

21

was investigated thoroughly. From the viewpoint of freedom analysis, nine independent

22

variables describing the CH4/N2/H2 distillation system are decided. Using the equilibrium

23

stage model and the PR-BM thermodynamics method, the optimal operating conditions are

24

obtained according to the results of parameters sensitivity analysis and actual requirement.

25

The final CH4 purity in bottom product is 99.87% and the CH4 impurity in gas distillates is

26

0.43%.

27

After calculating the size of the reflux drum, reboiler and the column base, three control

28

strategies including fixed reflux flow rate, fixed reflux ratio and the dual-composition control


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1

are implemented on the cryogenic distillation column. The Tyreus-Luyben tuning rule for

2

proportional integrator (PI) controller configuration is involved in the nonlinear dynamic

3

control. The closed loop test results demonstrate that the proposed dual-composition control

4

structure can be regarded as the best control structure and successfully keep the column stable

5

operation with both product purity and distillates impurity at their specifications despite the

6

disturbances of feed flow rate and feed composition. Furthermore, as for the single-end

7

distillation control structure, the ability to handle feed flow rate disturbance is better for the

8

fixed reflux ratio than for fixed reflux flow rate, but to handle feed composition disturbance,

9

the fixed reflux flow rate is always preferred.

10 11 12 13 14

Acknowledgements The authors are grateful for the Major Research Plan of National Natural Science Foundation of China (91334101), National Natural Science Foundation of China (21276203).

15

Appendix

16 17 18

1. PR-BM EOS The Peng-Robinson equation of state with Boston-Mathias modified function are expressed

19

as follows:29

20

p=

21

where

22

a = ∑∑ xi x j aij

(7)

b = ∑ xi bi

(8)

RT a (T ) − Vm − b Vm (Vm + b) + b(Vm − b)

i

23

(6 )

j

i

24

ai = f (T , Tci , pci , ωi ) = 0.45724α i

R 2Tci2 pci


(9 )


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

RTci pci

Page 16 of 41

1

bi = f (Tci , pci ) = 0.07780

2

aij = (ai a j )0.5 (1 − kij )

(11)

3

kij = k ji

(12)

4

(10)

In BM modification of PR EOS, α i is given by:36

5

α i (T ) = {exp[ci (1 − Trd )]}2

6

where

7

d i = 1 + mi / 2

(14)

8

ci = 1 − 1 / d i

(15)

9

mi = 0.3764 + 1.5422ωi − 0.26992ωi

10 11 12

(13)

i

i

2

(16)

Tri = T / Tci

(17)

Based on the PR-BM thermodynamics method, the fugacity coefficient is calculated in the following form:37 c

A bi ( Z − 1) − ln( Z − B) − ×( b 2 2B

2∑ x j aij j =1

bi Z + 2.414 B ) ln( ) b Z − 0.414 B

13

ln φi =

14

where

15

Z = pV / RT

(19)

16

A = ap /(RT ) 2

(20)

17

B = bp / RT

(21)

18

So the vapor liquid equilibrium constant is calculated by:

19

Ki =

20

2. Equipment Sizing of Cryogenic Distillation Column

a

−

φiL φiV

(18 )

(22)


Page 17 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

If there are N stages in the column, the real number of trays is N − 2 because the reflux

2

drum is assumed to be the first stage and the reboiler is assumed to be the last stage. The

3

typical distance between two trays is 0.61 m.30 Besides, more space is needed to satisfy the

4

liquid holdup if surge occurs. Therefore, a design heuristic is made to provide an additional

5

20% more height, thus the length of the column can be estimated from the following equation:

6

L = 1.2 × 0.61× ( N − 2) = 1.2 × 0.61× (23 − 2) = 15.4 m

7

(23)

The diameter of the column is determined by the hydraulics parameters using the following

8

equation:

9

D=

4Vmax πu

(24)

10

where Vmax is the maximum volumetric flow rate of gas phase. u is the gas velocity and

11

can be estimated by:

12

u = 1 / ρV

13

where ρV is the gas density, and F factor should be close to 1. Using the Tray Sizing tool

14

in Aspen Plus, the column diameter is estimated to be 1.70 m.

15

(25)

Assuming that a length to diameter ratio is 2, the diameter of the condenser and the reboiler

16

could be calculated by eq 26:

17

d  Vc = π  c  × ( 2d c )  2

18

where Vc is the total volume of the condenser or reboiler. It is assumed that 50% of the

19

vessel volume is allowed for 5 min of liquid holdup entering or leaving the vessel. Hence, the

20

total volume can be estimated by eq 27:

21

Vc = Vr × 60 × 5 / 50%

22

where Vr is the volumetric flow rate of liquid phase. The volumetric flow rate of liquid in

23

the condenser (stage 1) and the reboiler (stage 23) are 0.002 m3/s and 0.018 m3/s,

2

(26)

(27)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

respectively. So the condenser is 0.914 m in diameter and 1.828 m in length, while the

2

reboiler is 1.902 m in diameter and 3.804 m in length, respectively.

3 4

NOMENCLATURE d c = diameter of condenser or reboiler, m

D = column diameter, m F = mole flow rate of feed stream, kmol/s hL ,S = enthalpy of liquid stream, kJ/kmol H V ,S = enthalpy of vapor stream, kJ/mol kij = binary interaction coefficient K i ,S = gas liquid equilibrium constant L = column length, m LS = mole flow rate of liquid stream, kmol/s N = total number of trays pc = critical pressure, MPa QS = removed heat, kJ/s

R = mole gas constant, J/(mol K) Tc = critical temperature, K Tr = reduced temperature

u = gas velocity, m/s Vc = volume of condenser or reboiler, m3 Vm = standard mole volume, m3/mol Vmax = maximum volumetric flow rate of gas phase, m3/s

Vr = volumetric flow rate of liquid phase in condenser or reboiler, m3/s VS = mole flow rate of vapor stream, kmol/s xB , CH 4 = mole fraction of CH4 in column bottoms xi ,S = mole fraction of component in liquid phase yD , CH 4 = mole fraction of CH4 in gas distillates

yi ,S = mole fraction of component in vapor phase Z = compressibility factor

Greek Symbols

α = correction factor φ = fugacity coefficient


Page 18 of 41

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ω = acentric factor ρV = gas density, kg/m3 Subscripts i = component of CH4, H2 or N2 s = stage number

1 2

References

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Behaviors of a Direct-injection Engine Operating on Various Fractions of Natural

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Distillation Columns based on Nonlinear Wave Phenomenon. Sep. Purif. Technol. 2001, 24,

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Modeling of Nitrogen Purification Columns. Sep. Purif. Technol. 2005, 46, 95.

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Optimum Design of Cryogenic Air Separation Plant by Packed Columns with Structured

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Application of Cryogenic Distillation Hydrogen Isotopes. Nucl. Tech. 2010, 33, 201.


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2012, 22, 798.

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Four-Component Mixtures. Chem. Eng. Res. Des. 2005, 83, 1145.

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Column. Chem. Eng. Commun. 1997, 159, 105.

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Control for a Binary Distillation Column. Int. J. Fuzzy Syst. 2004, 6, 53.

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(24)

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Composition-Temperature Control of Binary Distillation Columns. Ind. Eng. Chem. Res.

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2006, 45, 9010.

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Multivariable Control of a Cryogenic Distillation Process. Comput. Chem. Eng. 2000, 24,

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111.

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Processes in a Multivariable Carbon Isotope Separation Unit. Chem. Eng. Sci. 2012, 80, 205.

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Non-Dominated Sorting Genetic Algorithm - II. J. Loss Prevent. Proc. 2011, 24, 25.

Castellanos-Sahagun,

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Alvarez-Ramirez,

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Alvarez,

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Two-Point


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Columns. Comput. Chem. Eng. 2000, 24, 1843.

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BTEX Emission in Natural Gas Dehydration Using PR and RKS Equations of State with

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Different Predictive Mixing Rules. Environ. Modell. Softw. 2004, 19, 957.

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(30) Luyben, W. L. Distillation Design and Control using Aspen Simulation; Wiley: New

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York, 2006.

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(31) Mutalib, M. I. A.; Smith, R. Operation and Control of Dividing Wall Distillation

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Columns - Part 1: Degrees of Freedom and Dynamic Simulation. Chem. Eng. Res. Des. 1998,

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76, 308.

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(32) Hori, E. S.; Skogestad, S. Selection of Control Structure and Temperature Location for

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Two-Product Distillation Columns. Chem. Eng. Res. Des. 2007, 85, 293.

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(33) Luyben, W. L. Method for Evaluating Single-End Control of Distillation Columns. Ind.

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Eng. Chem. Res. 2009, 48, 10594.

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(34) Luyben, W. L. Unusual Control Structure for High Reflux Ratio Distillation Columns.

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Ind. Eng. Chem. Res. 2009, 48, 11048.

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(35) Luyben, W. L. Effect of Feed Composition on the Selection of Control Structures for

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High-Purity Binary Distillation. Ind. Eng. Chem. Res. 2005, 44, 7800.

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1


List of Figure Captions:

2 3

Figure 1. Cryogenic distillation process for purification of synthetic natural gas from methanation of coke

4

oven gas.

5


6

Figure 3. Effect of (a) total number of trays, (b) feed tray location, (c) column bottoms rate and (d) reflux

7

ratio on distillates impurity and product purity.

8

Figure 4. Composition profiles of (a) gas phase and (b) liquid phase along the cryogenic distillation

9

column.

10


11


12


13


14


15


16


17


18


19


20


21


22


23


24


25


26


27 28 29

List of Table Captions:

30 31

Table 1. PR-BM Thermodynamic Parameters for the CH4/N2/H2 System

32

Table 2. Independent Variables of the Cryogenic Distillation Column for CH4/N2/H2 System

33

Table 3. Optimized Conditions and Simulation Results of the Cryogenic Distillation for SNG

34

Purification

35

Table 4. Comparison of the Three Control Structures

36

Table 5. Required Changes of Reflux Ratio and Reflux Flow Rate under Feed Flow Rate Disturbance

37

Table 6. Required Changes of Reflux Ratio and Reflux Flow Rate under Feed Composition

38

Disturbance



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4 5 6 7 8 9 10

11 12

Figure 1. Cryogenic distillation process for purification of synthetic natural gas

13

from methanation of coke oven gas.

14 15 16 17 18 19 20


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1 2 3 4 5 6 7 8 9

10 11


12 13 14 15 16 17 18



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4 5 6 7

8 9 10

Figure 3. Effect of (a) total number of trays, (b) feed tray location, (c) column bottoms rate and (d) reflux ratio on distillates impurity and product purity.

11 12 13 14 15


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1 2 3 4 5 6 7 8

9 10

Figure 4. Composition profiles of (a) gas phase and (b) liquid phase along the cryogenic distillation column.

11 12 13 14 15 16 17 18 19 20



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4 5 6 7

8 9


10 11 12 13 14 15 16 17 18


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1 2 3 4 5

6 7


8


9 10 11 12 13 14 15 16 17 18 19 20



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4

5 6


7


8 9 10


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1 2 3 4 5 6 7 8

9 10


11 12 13 14 15 16 17 18



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4 5 6 7

8 9


10 11 12 13 14 15 16 17 18 19


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1 2 3 4 5 6 7 8 9 10 11 12

13 14


15 16 17 18 19 20 21 22 23 24 25 26 27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 2 3 4

5 6


7


8


9


10 11 12 13


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1

2 3


4


5


6


7


8 9 10 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 41

1 2 3 4 5 6 7 8 9 10

Table 1. PR-BM Thermodynamic Parameters for the CH4/N2/H2 System Critical pressure pc /MPa

Critical temperature Tc /K

CH4

4.599

190.56

N2

3.400

H2

1.313

Acentric factor

Binary interaction coefficient kij

ω

CH4

N2

H2

0.0115478

—

0.0311

0.0156

126.20

0.0377215

0.0311

—

0.1030

33.19

-0.215993

0.0156

0.1030

—

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25


Page 37 of 41

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1 2 3 4 5 6 7 8 9 10

Table 2. Independent Variables of the Cryogenic Distillation Column for CH4/N2/H2 System Independent variables

Number of independent variables

Specification

Total number of trays Feed tray location Feed flow rate Feed composition Feed temperature Condenser pressure Column bottoms rate Reflux ratio Total

1 1 1 C-1=2 1 1 1 1 9

Unknown Unknown Known Known Known Known Unknown Unknown

11 12 13 14 15 16 17 18 19 20 21



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1 2 3 4 5 6 7 8 9 Table 3. Optimized Conditions and Simulation Results of the Cryogenic Distillation for SNG Purification Operation conditions

Simulation results

Actual results

Total number of trays

23

Feed

CH4

N2

H2

Feed tray location

5

Feed composition

0.590

0.059

0.351

1 kmol/s

Bottom product (×102)

99.870

0. 129

0.001

Feed temperature

100 K

Top distillates

0.004

0.142

0.854

Condenser pressure

3 MPa

Reboiler heat duty

3092.1 kW

Column bottoms rate

0.589 kmol/s

Condenser heat duty

-412.1 kW

Reflux ratio

0.09

Reboiler temperature

171.7 K

Condenser temperature

88.9 K

Feed flow rate

10 11 12 13 14 15 16 17 18 19 20


Total number of trays

10~40

Distillation temperature

78~163 K

Operating pressure

0.12~3 MPa

Mole fraction of CH4 in column bottoms

≥ 99.5%

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Table 4. Comparison of the Three Control Structures Differences of CS1, CS2 and CS3

Same modules of CS1, CS2 and CS3 Controller type

Gain (Kp)

Integral time (Ti /min)

Controller action

PI

0.5

0.3

Reverse

Condenser heat removal

PI

20

12

Direct

LC2

Reboiler level

Column bottom flow rate

P

2

▁

Direct

PC

Condenser pressure

Distillate flow rate

P

2

▁

Direct

TC

Temperature of stage 11

Reboiler heat duty

PI

283.8093

2.64

Reverse

Control variable Feed flow rate

Manipulated variable Open percentage of valve V1

LC1

Reflux drum level

Controller FC

14 15 16 17 18 19 20 21


CS1: Reflux flow rate is fixed.

CS2: Reflux ratio is fixed.

CS3: Two composition controllers are added.


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Table 5. Required Changes of Reflux Ratio and Reflux Flow Rate under Feed Flow Rate Disturbance Feed flow rate /kmol/s

Reflux ratio

Reflux flow rate /kmol/s

0.9

0.091

0.0337

1

0.09

0.0370

1.1

0.089

0.0402

20 21 22 23 24 25 26 27 28 29 30 31 32


Satisfied constraint conditions

xB ,CH 4 ≥ 0.995

y D ,CH 4 ≤ 0.005

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Table 6. Required Changes of Reflux Ratio and Reflux Flow Rate under Feed Composition Disturbance Feed composition CH4/N2/H2

Reflux ratio

Reflux flow rate /kmol/s

0.580/0.059/0.361

0.082

0.0345

0.590/0.059/0.351

0.09

0.0370

0.600/0.059/0.341

0.097

0.0386

21 22 23


Satisfied constraint conditions

xB ,CH 4 ≥ 0.995

y D ,CH 4 ≤ 0.005

Design and Control of the Cryogenic Distillation Process for

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