Hu Yuqi; Li Xiaoran; Li Chunli

(National-Local Joint Engineering Laboratory for Energy Conservation of Chemical Process Integration and Resources Utilization, School of Chemical Engineering and Technology, Hebei University of Technology, Tianjin 300130)

Abstract: A new vapor distributor based on the Coanda effect is added to the Dividing Wall column (DWC), and the multiphase flow simulation is performed using ANSYS Fluent by this model. The results show that with the addition of the liquid phase, the new vapor distributor still follows the Coanda effect. Hereby, the vapor is ejected from the slits of the distributor to take away the surrounding vapor, and a negative pressure is formed under the distributor, so as to achieve the purpose of regulating Rv. Analogously to the working principle of vapor distributor, a certain amount of vapor is drawn out from a position of prefractionator, which is equivalent to the vapor ejected by the distributor. The same amount of vapor is fed into the main column, which corresponds to the gas phase at the inlet of the distributor. The Rv is adjusted by changing the speed of the input or output vapor. Simulation results show that adding this control mechanism on the basis of temperature or concentration control structure can better achieve the effect of vapor distribution.

Key words: Aspen Plus; ANSYS fluent; DWC; simulation optimization; control mechanism

1 Introduction

Distillation, as a most mature and widely used separation technology in the chemical industry, consumes a great deal of energy. With the advancement of technology, the energy consumption of the distillation process has been improved, but it still has a long way to go to solve this problem. Therefore, reducing the energy consumption of the distillation process is still a hot research topic.

The DWC is based on a distillation column, and a dividing wall is added inside the distillation column to divide the distillation column into four parts, as shown in Figure 1. They are the prefractionator, the main column,the public rectification section, and the public stripping section.

The actual process of mass transfer in the DWC is extremely complicated, and there are many adjustable parameters, such as vapor distribution ratio Rv, liquid distribution ratio RL, feed location, the position of the side-draw, and the number of trays for each part, among which RLand Rvare two very important parameters.Compared with the conventional distillation column, upon facing the disturbance of the feed or composition, the parameters of the DWC will fluctuate more and the time required for returning to the steady-state will be longer,thus increasing the difficulty of control[1].

Figure 1 The principle of DWC

In terms of the control strategy of DWC, Wolf and Skogestad[2]first proposed a three-point control structure for the DWC, offering the idea of studying the control of the DWC. Dwivedi, et al.[3]have found that only the modified component control strategy can resist the interference of feed concentration by an extra single temperature controller, but it also shows the negative effect on the product purity. Then, Avila, et al.[4], by taking the ethanol dehydration extraction process with the trainer of ethylene glycol as an example, designed and controlled the extractive distillation DWC (EDWC).At the same time, two control schemes were proposed,one was a temperature control structure with adjustable Rv, and the other was a temperature control structure without adjustable Rv. Through simulation, it is found that the temperature control structure with adjustable Rvhas a better control effect, and both the residual difference of product purity and stabilization time are significantly reduced, which can improve the stability of the system.

Obviously, there are many controllable parameters in the DWC, which makes the control strategies have a wide variety and show different performance. Among them,RLand Rvare two very important parameters. During the experiment or pilot operation, RLcan be controlled by installing electromagnetic relays, etc., which are easy to implement, but the control of Rvis more difficult to achieve. The optimizable direction of the operating point in the replaced model is also different from that of the actual operating point[5], as shown in Figure 2.Therefore, the model in the previous study did not truly reflect the DWC. Neglecting Rv, which is one of the many influencing factors of the DWC, in the alternative model will cause a deviation from the real one.

Figure 2 Optimized direction of model operating points and real operating points

In China, Hu Yuqi[6], has put forward a new vapor distribution device based on the Coanda effect. Through a large number of ANSYS Fluent simulations and experiments, the device can effectively adjust the Rvby adjusting the velocity of the inlet. Multiphase flow simulation[7-12]has been widely used in many fields of engineering, but relevant researches on the simulation inside the DWC has not been popularized. Based on the vapor distributor proposed by the Hu Yuqi’s group of the Hebei University of Technology mentioned above, this paper deeply studies the multiphase flow simulation and dynamic control process inside the DWC. Inspired by the working principle of the vapor distributor, this paper proposes a control mechanism for substituting Rvbased on a new method that the amount of vapor extracted from the prefractionator and the amount of vapor introduced into the main column, through which the device can achieve the same effect as Rvdevice without adding an external device.

2 Steady-State Simulation of Four-Column Model

2.1 Basic structure of four-column model

This paper, by taking the separation of the n-hexane-nheptane-n-octane system as an example, carried out the simulation with Aspen Plus (v8.8), in which the molar fraction of n-hexane, n-heptane and n-octane accounts for 20%, 60%, and 20%, respectively, under operating conditions covering a feed temperature of 50 °C, and a feed flow rate of 11.6 kmol/h. The thermodynamic equation with NRTL, which is suitable to process nonpolar mixture, is selected as the physical property method.The process flow is shown in Figure 3.

Figure 3 Flowsheet of process

2.2 Optimized parameters

After the rigorous simulation, the optimized parameters in Table 1 are obtained.

Table 1 Rigorous simulation and optimization results of DWC

By optimizing the simulation, the molar purity of all three substances reaches 0.98, and the steady-state model is obtained.

3 CFD and ANSYS Fluent Simulation

3.1 Principle of vapor distributor

Figure 4 shows a schematic diagram of the vapor distributor structure. Figure 4(a) shows the inlet and outlet of the distributor, and Figure 4(b) is the side and bottom view. The upper surface (① in Figure 4(a)) of the vapor distributor is connected with the lower edge of the wall;it is a three-dimensional device and its inlet position is on one side (② in Figure 4(b)) of distributor, while on the opposite side (③ in Figure 4(a)) there is a very narrow slit, which is the vapor outlet position of the device.

The vapor distributor takes advantage of the Coanda effect.The Coanda effect refers to the tendency of a fluid to change from the original flow direction to the other surface along with the object under the action of a force. When there is surface friction between the fluid and the surface of the object, the fluid will continue to flow along the surface of the object under the action of adhesion as long as the curvature of the surface is small enough. As the vapor passes through the vapor distributor, a Coanda surface is formed at the vapor outlet of the vapor distributor, creating a Coanda effect. Figure 5 shows a schematic diagram of the principle of the vapor distributor.

Figure 4 Schematic diagram of vapor distributor

Figure 5 Schematic diagram of the principle of the vapor distributor

In order to better study the actual flow of the fluid in the column, this paper uses CFD and ANSYS Fluent (v15.0)simulation software to build the physical modeling, obtain a solution, and analyze the post-processing.

3.2 Physical model

In order to be closer to the fluid flow process occurring in the DWC during the actual production process, this paper uses ANSYS ICEM CFD simulation software for modeling and meshing. A complete DWC model with a vapor distributor device is modeled, as shown in Figure 6.In this model, the column height is 3 m and the diameter is 0.6 m. The principle of the vapor distributor in the column is shown in Figure 7.

Figure 6 DWC model with vapor distributor

Figure 7 Principle of vapor distributor in column

3.3 Mesh division

This paper uses an unstructured mesh as shown in Figure 8.

Figure 8 Model mesh

3.4 Selection of calculation method and model

3.4.1 Mass conservation equation

The flow conditions in the column must meet the law of conservation. The mass conservation equation is obtained according to this law:

Among them, Smis called the source term, which is the mass (such as the evaporation of droplets) added to the continuous term from the dispersed secondary term. For the simulation used in this paper, a cold model is used,which only considers the distribution of the gas-liquid phase in the DWC. It does not consider mass transfer and phase transition, so Smis 0, in which i = 1, 2, 3, ...,,and ρ is the density, with uiequating to the speed in the i direction.

3.4.2 Momentum conservation equation

The conservation of momentum is also one of the basic laws that must be satisfied for fluid flow in a column.The law can be expressed as: the rate of change of the momentum of a fluid in a micro-body to time is equal to the sum of the forces acting on the micro-body. That is Newton’s second law, and the momentum equation is:

in which P refers to the static pressure, and τijrepresents the stress tensor.

The solver type selects the Pressure-Based solver, the time type is a steady state, and the speed equation selects the absolute speed, while the operating pressure is 101325 Pa.This experiment uses water and air to represent the vaporliquid two phases, regardless of reaction and heat transfer.Mohammad, et al[13]. used the Multi-Fluid VOF model to numerically simulate conditions in water pipes. This flow condition is the intersection of gas and liquid phases,which is similar to the flow condition in this paper. The article states that the maximum error of the Multi-Fluid VOF model relative to the experimental value is 8.17%,while the error of the VOF model is 22.01%. Therefore,the Multi-Fluid VOF model can significantly reduce the simulation error and makes the simulation results closer to reality. Therefore, this paper chooses the Multi-Fluid VOF model. The standard k-ε model is selected as the turbulence model in this paper, and its equation can be expressed as:

where: Gkis a turbulent energy term produced by a laminar velocity gradient; Gbis a turbulent energy term produced by buoyancy; YMis the contribution of the turbulent pulsation expansion to the dissipation rate in the global flow in the compressible flow; C1, C2, C3are constant; Sk, Sεare the defined kinetic energy term and the turbulent dissipation term source term; σk, σεare k equation and ε equation turbulence Prandtl number,respectively.

3.4.3 Setting of boundary conditions

As regards the setting of boundary conditions, the inlet of the vapor distributor is set as a vapor inlet, the top of the column is set like a liquid inlet, and the initial velocity of the liquid is set at 0. Then the liquid falls down because of gravity, and the bottom of the column is set as a liquid outlet for convenient observation and processing of vapor distribution on both sides of the device. The upper stage of the vapor distributor is divided into left and right parts and is set as the inner surface, and the rest is set as the wall surface.

3.5 Calculation and post-processing

3.5.1 Relationship between the distribution ratio of vapor and amount of vapor extracted

When the condition is set, the operation is performed.After the operation is finished, the data are imported into the CFD-post for data post-processing, and the speed vector diagram is obtained, as shown in Figure 9. It can be seen from Figure 9 that the vapor also follows the Coanda effect when there is liquid phase flow. ① can indicate that the vapor ejected from the slit will continue to flow upward along the wall surface and will form a vortex after encountering the tray. ② indicates that due to the rising vapor, a negative pressure zone will form under the vapor distributor.

Figure 9 The vapor distributor speed vector

Figure 10 Relationship between Rv and the vapor velocity at the vapor inlet of the distributor■—F=1.0 m/s (kg/s)0.5, Liquid Phase;●—F=1.5 m/s (kg/s)0.5, Liquid Phase;▲—F=1.0 m/s (kg/s)0.5, No Liquid Phase;▼—F=1.5 m/s (kg/s)0.5, No Liquid Phase

In order to better illustrate the vapor distribution of the device under multiphase flow conditions, it is compared and analyzed with the previous single-phase flow conditions (i.e., only vapor input is considered and no liquid is involved). It can be seen from Figure 10 that in the simulation process under single-phaseflow conditions, when the kinetic energy factor of the empty column is 1.0 m/s (kg/s)0.5and 1.5 m/s (kg/s)0.5,the vapor distribution ratio of the device is uniform and it increases with an increasing amount of introduced vapor Vm. In the multiphase flow model with the liquid,a similar conclusion can be obtained, denoting that in the actual industrial production, the device can still achieve the effect of distributing vapor in the case of vaporliquid -phase. Upon taking the kinetic energy factor of the empty column as 1.0 m/s (kg/s)0.5as an example,with the increase of the introduced vapor volume, the vapor phase flow rate of the prefractionator gradually increases, while the vapor phase flow of the main column gradually decreases. As shown in Figure 11, this fact is consistent with the distribution trend when the liquid is not concerned.

Figure 11 Relationship between the vapor distribution on both sides of the distributor and the inlet rate of the device when F0=1.0■—prefractionator; ■—main column

3.5.2 Comparison of pressure cloud maps

After importing the data into the CFD-post for data postprocessing, the partial pressure cloud maps are obtained,as shown in Figures 12 and 13.

Figure 12 is a cloud diagram of the pressure around the vapor distributor without the liquid, and Figure 13 is the one after the liquid is added. By comparison, it can be seen that when no liquid is concerned, the overall pressure in the column is less than that after the liquid is added. And the pressure at the corners of the inlet nozzle of the vapor distributor, at the corners of the top of the distributor, and at the slit of the outlet vapor is slightly larger, as shown in ①, ②, ③ in Figure 13. After addingthe liquid phase, the pressure is slightly larger besides the above partial pressure value, while the upper left corner of the first stage above the vapor distributor also has a larger pressure value. This is due to the Coanda effect,which causes the vortex formation at the mouth of the device. Judging from the previous velocity vector diagram(Figure 9), we can see that during the mixing of the liquid and the vapor, a large amount of vapor is concentrated at④ in Figure 12, so that the partial pressure is increased.Reinforcement measures should be taken at the column body within a larger pressure area to ensure the safety of the production process.

Figure 12 No liquid phase partial pressure cloud

Figure 13 Liquid phase partial pressure cloud

4 Dynamic Control Simulation and a New Type of Control Mechanism for Regulating Rv

Through a series of dynamic simulation, the importance of Rvin the control process of the DWC is confirmed through four control structures. Fang, et al.[14]have proved that the optimal operating area under the two operating conditions of heat transfer and non-heat transfer between the wall is different, denoting that heat transfer also affects Rv. In summary, many factors can affect Rv, making it difficult to control. From the principle of the vapor distributor mentioned in Section 3.1, it can be known that the vapor distribution effect in that device is caused by the Conada effect, denoting that when the vapor blows out from the slit at a high speed, the surrounding vapor and the vapor under the distributor are sucked and entrained together and are finally flowed out from that narrow slit.Inspired by this idea, this paper proposes an Rvcontrol device serving as the vapor distributor, with the method of extracting vapor and inputting vapor. Among them,the vapor extracted from the side of the prefractionator corresponds to the vapor flowing out from the slit of the vapor distributor. The vapor input from the side of the main column corresponds to the vapor added from the inlet of the vapor distributor. This method is easier to operate and can be realized in actual production. Figure 14 is a schematic diagram of the operation of its fourcolumn model. The inner part of the red dotted line is the control mechanism.

Figure 14 Schematic diagram of the operation

4.1 Sensitive stages selection

In addition to the amount of vapor extracted, another variables that have a large impact on the simulation process are the locations of the extracted vapor and the input vapor. Upon considering that the temperature at every stage of the DWC can represent the difference of the vapor and liquid concentration at various locations,the issue on how to specify the locations of the extracted and input vapor needs to find some stages in which their temperature is the most sensitive to the external interference. Since the heat load of the reboiler is sensitive to the change of R, a change of R within ±0.1% is given and the ratio of the temperature change of each stage to the change of R-value is observed, so as to find the tray with the largest value, which should be the sensitive tray.Figure 15 and Figure 16 show the relationship between the gain and the number of the theoretical trays. It can be ascertained that the sensitive stage in column 1 is the 7thstage, and the sensitive stage in column 2 is the 20thstage.

Figure 15 Diagram of the relationship between the gain of column 1 and the number of theoretical stages■—-10%; ●—10%

Figure 16 Diagram of the relationship between the gain of column 2 and the number of theoretical stages■—-10%; ●—10%

4.2 Steady-state simulation of control mechanism

By combing the four-column model with the DWC, this paper regards the rising vapor flow rate above the 7th tray of the column 1 as the actual vapor volume distributed to the prefractionator, and considers the rising vapor volume above the 20th tray of the column 2 as the actual vapor volume distributed to the main column. The ratio of the two vapor volumes is regarded as the true Rvof the DWC.By taking Vm= 38 m/s as an example, the amount of vapor drawn from the left side of the column 1 is calculated to be 0.075 m3/s. The simulation process has converged after being debugged. At this time, the rising vapor volume of the 7th stage of column 1 is 12.713 kmol/h,the rising vapor volume of the 20th stage of column 2 is 5.524 kmol/h, and the Rvis 0.7, which corresponds to the relationship between the amount of vapor extracted and Rvin Figure 10. Through simulation, it is found that the relationship between the velocity of the extracted vapor and Rvis basically consistent with that of Figure 10.Therefore, it is concluded that the vapor distribution can be achieved by adjusting the amount of vapor withdrawn from the column 1 and the amount of vapor introduced into the column 2.

4.3 Basic control principle and effect

The basic control structure is shown in Figure 17. An external vapor extraction structure is added above the 7th stage of column 1, and a stream having the same flow rate with the one extracted from column 1 is introduced above the 20th stage of column 2. The remaining control structures are the same as the control structure without the vapor distribution mentioned above. In order to facilitate the study of the basic principles of this control mechanism, this paper does not consider the composition of the system temporarily, and only considers the changing quantity. Then, the controller and control parameters are presented in Table 2.

Table 2 Controller and control parameters

4.4 Disturbance curve of feed flow and composition

Figure 17 Rv temperature control structure based on the extracted and introduced vapor volume

Figure 18 Response curve of Rv control structure based on extracted and introduced vapor volume

It can be seen that when a ±10% disturbance in feed flow rate and a ±10% disturbance of feed compositions are given, respectively, the results are satisfactory, as shown in Figure 18.It can be seen from the above disturbance curve that the temperature control structure with this special control plan, in which the external vapor extraction is achieved in column 1 and the external vapor introduction is achieved in column 2, has attained a well control effect.In this control strategy, the overshoot value and the residual difference are further reduced. Concretely, in the temperature control structure, whena±10% disturbance in feed flow rate is given, this control system could restore stability in 3 hours, while the control structure without vapor distribution did not reach stability within 10 hours.In addition, the residual difference in product purity decreased by 40%, and the maximum overshoot is reduced from 0.002 to 0.000 7, which is by 65% lower than the original control scheme. When a ±10% disturbance of feed composition is given, the control system starts to stabilize in 3.5 hours. However, the original control system did not reach a stable level within 10 hours. The residual difference of product purity is reduced by 0.001 6,and the maximum overshoot is reduced from 0.005 8 to 0.000 45, which is by 92% lower than the original control scheme. From the above data analysis, it can be seen that the temperature control structure slightly increases the overshoot value under a disturbance of ±10% compared with the control strategy without vapor distribution. This is because the temperature control itself is fast, but it cannot keep the purity of the product constant. However,as a whole, this control scheme is significantly better than the original control scheme (without vapor distribution).That is to say, the control system with this special vapor distribution device and its corresponding control plan is feasible.

5 Conclusions

(1) In this paper, the ANSYS Fluent is used to simulate the multiphase flow of the DWC with the new vapor distributor. The simulation results show that in the presence of liquid phase, Rvincreases with the increase of the vapor velocity at the inlet, denoting that there is a corresponding relationship between the introduced vapor velocity and Rv.

(2) Based on the working principle of the vapor distributor, this paper proposes a new control mechanism for controlling DWC. This mechanism aims to extract a certain amount of vapor from a specific position in the prefractionator, and at the same time intends to extract the same amount of vapor from a specific position in the main column. The control mechanism can better achieve the purpose of regulating Rvand can achieve the same effect as the vapor distributor without adding an external device. The control performance is verified by the Aspen Dynamics software, and its controllability is confirmed.

Acknowledgments: This work was supported by the National Natural Science Foundation of China (21878066).