_{2}Removal in Flue Gas via Venturi Scrubber

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This paper investigates the problem of gas-liquid flow SO_{2} removal in nonquiescent flue gas. Using venturi scrubber as the prototype, the population balance model (PBM) combined with the CFD is implemented to characterize the droplets behaviors. Discrete methods as class model (CM) and various quadrature-based moment models (QBMMs) are applied to numerically solve the population balance equations (PBEs). Taking NaOH solution as the reaction kinetics, the sulfur removal efficiency simulation with CM and different QBMMs methods is validated through the operation measurements. The comparison results show that the CM can achieve better accuracy with more bins, which showed the minimal error 3.6%, consisting 30 bins. However, the computational time of the CM is approximately 19.3 times as long as QBMMS. Among the QBMMs, the ECQMOM approach enjoys the best balance between the simulation efficiency and accuracy, while EQMOM shows the least computational load and CQMOM wins the minimal calculation precision. This result will provide sufficient reference for engineers working in the field of the droplets distribution in the venturi scrubber design.

As the main pollutant in the petroleum industry, exhaust gas from fuel contains a significant amount of SO_{2} owing to the sulfur contained in fossil fuels [_{2} severely cause atmosphere pollution and ecosystem damage, which significantly threatens the human life. Also, the increase of the emission is one of the principal causes of the acid rain [_{2}, the improvement of currently used methods is essential. Currently, wet flue gas desulfurization coupled with selective catalytic reduction is popular for the simultaneous SO_{2} removal [

The venturi that is investigated in this paper is a device used to absorb sulfur dioxide, which is installed at the end of production line as an equipment to clean the flue gas. Venturi scrubber is a two-phase reactor with low-energy input and good-mixing effect. Now most of the relevant studies are based on experiments, which require a long time and a lot of cost to verify the correctness of the designs. The flow field inside venturi is complex, and the fluid velocity is fast, which make the experiment difficult to observe. These above make numerical simulation indispensable in venturi’s research. So this paper aims at finding the most suitable simulation method of the venturi. Due to the high ratio of gas to liquid, the result of CFD with multiphase model cannot meet the rate measured in factory. Thus, PBM is needed to compute a correct result. And most reactors use low-density medium as the discrete phase to study the dynamics characteristics of particles. Besides, the discrete phase of the venturi selected in this paper is liquid. In this case, the behavior of particles such as growth, breakup, and aggregation is more affected by its own stress, which is different from the situation of gas as the discrete phase. So the paper studies the condition of the internal flow field and adaptability of different discrete methods to the venturi firstly. The condition of the flow can show the process of the mass and energy transfer, which could indicate the direction of redesigns. And the choices of the discrete methods should consider both accuracy and time cost, which could provide the basement with subsequent investigations and designs.

As for energy transfer between two phases, Bhutada et al. [

The mass transfer coefficient

Schematic of dynamic evaluation of particles.

In the simulation of the multiphase flow, the population balance model (PBM) have a good performance to describe the process of reaction and the Sauter Mean Diameter (SMD) of droplets, which can be used to analyze the behavior of the population of droplets from the single droplet in their local environment [

To simulate the discrete phase distribution, the population balance equation (PBE) is used to describe the particles behaviors as breakage and aggregation. Several numerical methods are commonly applied, such as the class method (CM) [

To extend the area adopted by the MOM, McGraw [

In this contribution, four type of QBMMs, as QMOM, CQMOM, EQMOM and ECQMOM as well as the CM, have been presented to solve the multiphase reaction with multivariate SMD and mass transfer, which are described in

The sulfur dioxide content before and after the flue gas passes through the venturi scrubber with the NaOH solution injection, where the mass transfer efficiency of wet desulfurization is simulated throughout the venturi scrubber chamber [

The population balance model is adopted for modeling the droplets behaviors in the venturi scrubber, which describes the processes of the natural growth and decrease of droplets and the birth and death of particles occur due to aggregation and breakage. And the breakup kernel which was presented by Hengel et al. [

The equations for PBM model.

Name | Equations | Equ. num. |
---|---|---|

Bubble source equation | (1) | |

(2) | ||

Bubble growth equation | (3) | |

(4) | ||

Aggregation equation [_{ij} is the distance ratio of the bubble and its turbulence path length; | (5) | |

(6) | ||

(7) | ||

(8) | ||

(9) | ||

Breakage equation [_{e} is particle eddy size; | (10) | |

(11) | ||

(12) | ||

QMOM model equation [ | (13) | |

(14) | ||

(15) | ||

(16) | ||

(17) | ||

CQMOM [ | (18) | |

(19) | ||

(20) | ||

(21) | ||

(22) | ||

EQMOM [ | (23) | |

(24) | ||

(25) | ||

(26) | ||

(27) | ||

ECQMOM [ | (28) | |

(29) | ||

(30) |

After the procedure given above, the SMD is worked out by the simulation, which is used to calculate the contact surface between gas and liquid phases. Then the removal rate of sulfur dioxide is reckoned based on the mass transfer equation, which are shown in Table

The equations for mass transfer.

Name | Equations | Eq. Number |
---|---|---|

Mass transfer equation (_{1} is the volume fraction of the liquid phase; | (31) | |

(32) | ||

(33) | ||

(34) | ||

(35) | ||

(36) |

This section may be divided into subheadings. It should provide a concise and precise description of the experimental results and their interpretation as well as the experimental conclusions that can be drawn.

In this work, a sulfur removal scrubber with a capacity of 4000 tons/year is taken as the prototype (refer to Figure _{1}, which is 750 mm. The diameter of the liquid sparger is _{2}, which is designed by requirement of spray. The convergence has a diameter of dcon, which is 1.3 times as long as _{1}, with a length of l2 (1.9_{1}). The throat has a diameter of dthroat (0.85_{1}), and a length of l4 (0.48_{1}). The diameter of the outlet of the diffusion section is dout, which is the same length as _{1}. The contraction angle from the convergence to the throat is _{1}, and the expansion angle after the throat is _{2}.

(a) Schematic diagram. (b) Meshing diagram.

In field equipment, SGA94-SO_{2} flue gas analyzer made by KANE corporation (refer to Figure

SGA94-SO_{2} flue gas analyzer.

Field data of the venturi scrubber.

Venturi scrubber measurement data | |||
---|---|---|---|

Liquid flow rate | 33 m^{3}/h | Gas flow rate | 4000 Nm^{3}/h |

Liquid temperature | 58.3°C | Gas temperature | 155°C |

Liquid pressure | 0.72 MPa | SO_{2} concentration | 765 mg/Nm^{3} |

NaOH concentration | 0.125 mol/l | Sulfur removal efficiency | 48.76% |

In this section, the model in the previous section is simulated and verified. Three-dimensional transient and steady simulations are carried out with the commercial CFD software Ansys FLUENT 18.0. The iteration time step is set to be 1

On the basis of the simulation, the PBM model is adopted to use the CM. According to Kazakis et al. [_{32} is the mean Sauter diameter and _{s} is the diameter of sparger. And the distribution of particle is calculated as follows:

When the atomized medium is water,

In the above simulation model, sodium hydroxide is added to absorb sulfur dioxide, and the reaction model proposed by Uchida [

As the results of simulation, the concentration of sulfur dioxide is compared with the measure value of experiment to obtain the errors of different models and the simulation model of venturi reactor which is the most suitable for the working environment mentioned in the paper is found by the comprehensive consideration of calculation time and calculation accuracy.

In this section, the results of above experimental and simulation are introduced, and the results are compared and analyzed to draw relevant conclusions.

Firstly, this paper discusses the influence on the results by mesh size, which compares the simulation results of velocity under different sizes of mesh. In the simulation, more accurate results need the smaller mesh, which would increase the computation and prolong the simulation time. Bhutani et al. firstly applied mesh adaptivity to population balance equation for modeling the multiphase flow and presented the mesh at two-phase mixing area should be smaller [

The results of velocity in different mesh size.

After determining the mesh size, the process of reaction mass transfer is added on the basis of the cold mode flow field to calculate the concentration of sulfur dioxide, and the PBM is also added to investigate the distribution of droplet size. The velocity and pressure distribution of the flow field in the reactor is shown in Figure

The velocity of different part in the venturi scrubber.

Figure _{2} in venturi, which can directly reflect the simulation of mixing. It can be seen that the liquid is atomized and vaporized under high pressure after entering venturi and the mixing begins to occur at the interface of gas-liquid. In the contraction section, due to the dramatic change of pressure and velocity, the gas distribution tends to be uniform rapidly. When the liquid accelerates, the break frequency of droplets would increase. It is easier to mix the gas with dispersed droplets. So, there is only a little difference in concentration because of the reaction. In the throat, the fastest speed and the effect of negative pressure make the turbulence intensity stronger and the flow field more complex. And under the influence of the above reasons, the droplets are broken more violently and dispersed more evenly. So the throat is where most of the reaction happens in venturi. Finally, the flow entrances the diffuser. In the process of pressure and velocity change, the velocity around the pipeline decreases fast and the velocity in the center decreases slowly due to the influence of friction on the reactor wall. The difference in velocity would create the difference in pressure, which was called collapse pressure by Zhang [

(a) concentration of liquid in venturi; (b) concentration of SO_{2} in venturi.

In the experiment, because the venturi reactor mentioned in this paper is a working equipment, it is impossible to directly obtain the state of the internal flow field by using PIV and other devices. Therefore, only the measured value of sulfur dioxide can be used to verify the correctness of the simulation. So sulfur dioxide concentrations at different locations in the reactor are measured using the sensors mentioned in Figure _{2} is measured on the inlet, throat, and outlet sections of the venturi scrubber in 10 groups. Each group is measured for 10 minutes, and the average value of the meter reading is calculated within 10 minutes as the measurement result. According to the results, the amounts of mean concentration at inlet, throat, and outlet are 633,550 and 392 mg/Nm^{3}, respectively. It indicates that the removal reaction of sulfur dioxide mainly occurs in the convergence and throat, while the interaction between the two phases in the contraction section is mainly dominated by collision and mixing. In the convergence, the concentration of sulfur dioxide decreases by 132 mg/Nm^{3}, which may be because the two phases have higher concentrations of sulfur dioxide and sodium hydroxide at the beginning of the reactor entry, so the reaction happening is larger. In the contraction section, the concentration of sulfur dioxide dropped by 83 mg/Nm^{3}, but the mixture is more uniform. In the throat, where the reaction is most concentrated due to the degree of mixing and the intensity of turbulence, the concentration of SO_{2} drops by 158 mg/Nm^{3}. Because of the other component in the gas (e.g., H_{2}S and CO) and the accuracy of sensor, there is a 5% error in the measurement. The removal rate by measurement is 48.76%. And the sulfur dioxide is removed 20.66% during the throat (refer Figure

The value of measurement.

In this paper, venturi is simulated by CM and QBMMs, respectively. And the results of simulation are compared with those of experiment to obtain the most suitable method (refer to Figure

(a) The results of simulation by CM in different bins. (b) The results of simulation by QBMMs.

As for the CM, the quantity of bins would influent on the accuracy and time cost consumption. Bannari [

Computational time and error of simulation in different models.

Model | CM (5 bins) | 10 bins | 20 bins | 30 bins |
---|---|---|---|---|

Error (%) | 14.99 | 11.54 | 7.63 | 3.2 |

Cost | 3.2 | 8.7 | 12.3 | 19.3 |

As for the QBMMs, the most significant advantage is the fast and accurate potential, which becomes more important as the number of bins used in the CM is increased [

Computational time and error of simulation in different models.

Model | CM (30 bins) | QMOM | EQMOM | CQMOM | ECQMOM |
---|---|---|---|---|---|

Error (%) | 3.2 | 7.75 | 4.05 | 6.34 | 5.28 |

Cost | 19.3 | 1 | 1.5 | 0.8 | 1.2 |

The SMD of droplets plays a fundamental role in the CFD study of multiphase flow via venturi scrubber under industrial operating conditions. PBM is coupled with CFD simulations to account for dispersed phase behavior. The results of velocity, pressure, and volume faction can illustrate the accuracy of the simulation. And it also can be seen that the CM and QBMMs approaches can predict the gas/liquid flow dynamics, mass transfer, and the SO_{2} removal rate in the venturi scrubber.

The CM can compute SMD of droplets in venturi and describe the distribution about diameter of droplets. And the accuracy of CM heavily depends on the quantity of bins. There is 3.2% gap between the results of experiment and simulation by the CM with 30 bins, while the simulation by CM with 5 bins has an error of 14.99%.

However, the QBMMs do not pay attention to the process of aggregation and breakage of each droplet, which are effectively able to save the time consumed in the simulation of multiphase, which only costs about 5% of time spent by CM. Among the various QBMMs, the CQMOM computes the result of simulation in a shortest time and the EQMOM adapts venturi most satisfactorily. The ECQMOM can calculate the result of simulation fast under a higher accuracy (5.28%). So the ECQMOM can become the best choice for the optimization design.

The application of QBMMs to simulate the condition of flow in the venturi could be an important evolution of investigation in this work. And the QBMMs methods could calculate an accurate result under a faster speed, especially ECQMOM. But this method cannot calculate the distribution of the particle size. So if you want to study quantitatively the size of particles, such as the size of the daughter particle after breakup or the proportion of small particles in the discrete phase, it could not be used. And the error of the QBMMs can be accepted in engineering projects. However, if a higher accuracy is required in the experimental study, the CM method with a large number of bins would be the only choice. In this paper, the PBM-CFD is proved to predict the flow field in venturi at different methods and provide a basis for optimization. A comparison on cost and accuracy between CM and QBMMs in this paper and the reduction of high gas-liquid ratio flow field would be useful, in order to highlight advantages and drawbacks.

(1) The data used to support the findings of Table

The authors declare that they have no conflicts of interest.

All authors have read and agreed to the published version of the manuscript. Shuo Zhang and Wenyue Cui were responsible for numerical model. Shuo Zhang and Wenyue Cui provided the experimental device. Shuo Zhang and Wenyue Cui performed simulation. Shuo Zhang and Wenyue Cui performed validation. Tao Wu and Xiaohang Zhao performed data analysis. Shuo Zhang performed investigation. Wenyue Cui wrote the original draft. Shuo Zhang reviewed and edited the article. Shuo Zhang supervised the study. Wenyue Cui performed project administration. Shuo Zhang was responsible for funding acquisition.

The validation measurements were provided by CNPC Northeast Refining & Chemical Engineering Co. Ltd in a certain CNPC refinery plant CFF boiler. This research was funded by National Natural Science Foundation of China (Grant no. 61803071), China Postdoctoral Science Foundation (Grant nos. 2018M631786 and 2019T120205).

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