Abstract:Kraft lignin has the potential to replace traditional fossil resources for the preparation of high-value chemicals because it is rich in aromatic rings and active functional groups.An effective method for the pyrolysis of kraft lignin into chemicals/fuels is microwave-assisted depolymerization.A simulation model is urgently needed to illustrate the coupling effect and mechanism of lignin conversion during the depolymerization process.In this study,COMSOL Multiphysics was used to simulate the microwave-assisted depolymerization process.The results showed that microwave power had a significant effect on the electric field and temperature distribution in the microwave cavity,while the reaction time had little effect on the electric field.The effect of the nitrogen flow rate on the electric field and temperature was negligible.The intensity of the electric field,heating rate of lignin,and final temperature of lignin depolymerization increased with increasing microwave power.

Keywords:microwave depolymerization; numerical simulation; kraft lignin;COMSOL Multiphysics

1 lntroduction

Due to the excessive exploitation of traditional fossil fuels and the subsequent serious environmental pollution,renewable and abundant energy sources are urgently required. Lignocellulose, composed of cellulose,hemicellulose,and lignin,is a potential alternative source of renewable energy,and has attracted considerable attention in various areas[1-2].Lignin is a natural renewable resource,similar to cellulose,in terms of yield.Kraft lignin produced from kraft pulp has a global annual production of more than 50 million tons.It has the potential to replace traditional fossil resources for the preparation of highvalue chemicals(monophenolic compounds)due to the proliferation of aromatic rings and active functional groups(hydroxyl groups)within the structure.Kraft lignin is commonly burned to obtain energy because of its complex structure and high accessibivity,but is still underutilized.Therefore,the conversion of kraft lignin into high-value-added products has become a very topical research area[3-4].There are many methods for lignin utilization,including combustion,carbonization,and depolymerization. Microwave-assisted depolymerization is a new type of conversion technology that converts lignin into biofuels and chemicals having the advantages of selective heating,easy control,and environmental protection[5-6].

The process is a complicated process[7-8]and comprises a multidisciplinary approach pertaining to the core physics fields involved in the microwave heating process.These fields include electromagnetics,heat,fluid flow,and reaction kinetics.Currently,the mechanism of microwave-assisted depolymerization of kraft lignin remains obscure.It is important to develop a model that can simulate the microwave-assisted lignin depolymerization process[9].One method showing potential for visualizing and quantifying the microwave heating process is numerical simulation[10].However,there are few numerical simulation studies on the microwave-assisted depolymerization of kraft lignin because of the complexity of lignin degradation.There are also gaps remaining in the research,for example,some research ignores heat loss,caused by heat flux and fluid heat transfer,which affects the accuracy of the simulation results.Ma et al[11]simulated the process of oleic acid pretreatment during microwave-assisted biodiesel generation,and studied the effects of size,pores,and materials on the efficiency of oleic acid absorption of microwaves.Li et al[12]simulated the process of microwave-assisted degradation of coal and established a coupling model for electromagnetic-heat-transfer-porous media.The results showed that the absorption of microwaves by coal caused the electric field distribution in the cavity to form high-energy and low-energy regions.The microwave process produces inhomogeneous electromagnetic fields and selective heating[13].In this study, the electromagnetic-temperature-fluid Multiphysics model was developed using COMSOL Multiphysics software,and the heat loss caused by heat flux and fluid heat transfer was considered.The effects of changing microwave power,nitrogen flow rate,and reaction time on the electric field in the microwave cavity and the temperature field distribution of kraft lignin were investigated.

2 Geometric model and experimental process

2.1 Geometric model and mesh division

COMSOL Multiphysics software was used to simulate the microwave heating process. COMSOL Multiphysics is a simulation platform designed to simulate the physics of a device[14].It was designed to incorporate a wide range of core physics fields,including solid mechanics,acoustics,fluid flow,heat transfer,chemical transfer,and electromagnetism.This software was deemed suitable for studying the effect of the interaction of the different physical parameters on the microwave heating process[15].

The microwave model used in this study was modified based on the microwave reactor(HYZG1512) developed for lignin conversion.The microwave device consists of a microwave cavity,waveguide,insulating layer,and quartz reactor.The frequency of the microwave system was 2.45 GHz.The microwave energy enters the cavity through a rectangular waveguide at a maximum power of 1200 W,operating in the TE10 mode[16].The geometric model of the microwave-assisted depolymerization device based on COMSOL Multiphysics simulation software is shown in Fig.1.The waveguide was a rectangular port located behind the furnace chamber.The furnace chamber and waveguide were made of copper.Lignin was placed in a glass tube and placed on the right side of the cavity.COMSOL Multiphysics version 5.4 was used in this study.The geometric model was meshed using the finite element method,and the quality of the mesh was calculated(Fig.1).The geometric model was a complete grid composed of 9141 domain units,338 boundary units,and 30 vertex units[17-19].Geometric parameters of the microwave model are shown in Table 1.

Fig.1 (a)Geometric model for microwave-assisted depolymerization;(b)finite-element meshed geometric model

Table 1 Geometric parameters of the microwave model

2.2 Governing equations

2.2.1Electromagnetic field

Maxwell's equations are used to accurately calculate the electromagnetic field.The calculation equation is shown in Equation(1)[20]:

where∇is the intensity of the vortex source of the vector field at each point;μis the permeability of medium,H/m;Eis the electric field intensity,V/m;ωis the angular frequency of electromagnetic wave;ε0is the vacuum dielectric constant,8.85×10-12F/m;εris the relative dielectric coefficient of the sumple,3.04-0.12j;k0is the wavenumber of free-space electromagnetic waves,51.31 rad/m;jis the current density,A/m2;andσis the conductivity,S/m[21].

2.2.2Heat transfer equation

The Fourier energy balance equation was used to calculate the heat transfer in the microwave field.The calculation equation is shown in Equation(2)[22].

whereρis the density of the medium,kg/m3;Cpis the heat capacity of the medium,J/(kg·K);tis the time,s;kis the thermal conductivity of the medium,W/(m2·K);uis the speed vector,m/s;Tis the temperature,K;andQis the total heat supplied to the sample,J[23].

2.3 Boundary conditions

In this microwave model,the walls of the microwave cavity and waveguide are assumed to be made of copper.Thus,the electric field only penetrates a short distance outside the boundary and is calculated in the frequency domain.The calculation equation is shown in Equation(3)[24].

whereμ0is the vacuum permeability,4π×10-7N/A2;μris the relative permeability,1;nis the refractive index and the unit is 1[25].

2.4 Experimental process

The kraft lignin used in the experiment was purchased from the TCL(Shanghai)Development Co.,Ltd.The experimental equipment was connected to a dynamic nitrogen flow system as well as a rapid condensation device.10 g of kraft lignin was homogeneously mixed with MoS2at 1:2(w/w),and the mixtures were placed in a quartz reactor.Then,nitrogen at a flow rate of 600 mL/min for 10 min was used to drain the air in the reactor.At this stage,the desired microwave power was applied.After reaching the reaction time,the product vapor of lignin was cooled and collected by rapid condensation at(35±1)℃with the cooling medium of ethanol[26].The residual solid mass in the glass tube was collected when the reactor was cooled to below 200℃.

In the microwave-assisted depolymerization simulation,a single-factor experiment method was used to study the effects of microwave power(400,600,800,1000 W),pyrolysis time(100,200,300,and 400 s),and nitrogen flow rate(300,600,900,and 1200 mL/min)on the electric field distribution for the microwave cavity and the distribution of the temperature field of lignin.

3 Results and discussion

3.1 Effect of microwave power

Dielectric properties play an important role in microwave heating.Commonly,biomass/lignin has poor absorptivity for microwave energy.Absorbent was widely used for assisting the heating up of lignin[27].The effect of microwave power on kraft lignin microwave-assisted depolymerization was studied.As shown in Fig.2(a1)-Fig.2(a4),the temperature distributions of kraft lignin were uneven.The uneven temperature distribution was caused by the distribution of the electric field.With the increase in microwave power from 400 to 1000 W,the maximum depolymerization temperature changed from 662℃to 1580℃.This is because the higher microwave power can provide a stronger electric field,and lignin can absorb more energy and convert it into internal energy.The high-temperature region and depolymerization temperature reached their highest values when the microwave power was 1000 W.The electric field distribution changed significantly with the increase in microwave power.It can be observed from Fig.2(b1)-Fig.2(b4)that the electric field intensity increased from 3.42×104V/m to 5.5×104V/m as the microwave power increased from 400 Wto 1000 W.

Fig.2 Distribution of electric field and temperature field with different microwave power

3.2 Effect of nitrogen flow rate

The effect of nitrogen flow rate on kraft lignin microwave-assisted depolymerization was studied.The results are shown in Fig.3.The temperature and electric field intensity remained almost unchanged when the nitrogen flow rate increased from 300 to 1200 mL/min.Although the nitrogen flow rate increased fourfold,and the electric field intensity remained constant at 4.84×104V/m.This indicated that nitrogen absorbed some energy and flowed through the system.The nitrogen flow rate had a negligible effect on the depolymerization temperature and the conversion efficiency of lignin.

Fig.3 Distribution of electric field and temperature field with different nitrogen flow rate

3.3 Effect of reaction time

The influence of the reaction time on the microwaveassisted depolymerization of kraft lignin is shown in Fig.4.The depolymerization temperature rose rapidly with the increase in reaction time as seen in Fig.4(a1)-Fig.4(a4).When the reaction time increased from 100 s to 400 s,the average depolymerization temperature increased from 413℃to 1280℃.The electric field intensity remained constant at 4.84×104V/m when the reaction time changed from 100 to 400 s,as shown in Fig.4(b1)-Fig.4(b4).This result indicates that the reaction time had no effect on the microwave field.During the reaction process,the lignin/absorbers maintained a constant dielectric property as the temperature increased[28].Consequently,the heating rate and lignin conversion efficiency can be adjusted by varying the reaction time.

Fig.4 Distribution of electric field and temperature field with different reaction time

3.4 Variation of average depolymerization temperature

The average depolymerization temperature was obtained from the domain probe,which was defined by COMSOL Multiphysics software.The average depolymerization temperature of kraft lignin was obtained from Fig.5,which reflects the effects of microwave power,reaction time,and nitrogen flow rate during the microwave-assisted lignin depolymerization process.The microwave power and reaction time had a significant influence on the average depolymerization temperature of kraft lignin; however, the average depolymerization temperature was almost unchanged at different nitrogen flow rate.

As shown in Fig.5(a)and Fig.5(c),the average depolymerization temperature increased linearly with the increase in microwave power and reaction time.A higher microwave power results in a higher electric field intensity,which in turn renders a quicker temperature rise for the same reaction time.A faster heating rate and suitable depolymerization temperature could lead to high yields of liquid depolymerization products[29].It can be seen from Fig.5(b)that the average depolymerization temperature decreased from 576.75 to 570.03℃as the nitrogen flow rate increased from 300 to 1200 mL/min.Nitrogen flow rate had a negligible effect on lignin microwave-assisted depolymerization owing to the influence of low temperature.It can be concluded that when the same depolymerization temperature is required,the reaction time can be greatly shortened by choosing the appropriate microwave power.

Fig.5 Variation of average depolymerization temperature with microwave power(a),nitrogen flow rate(b),and reaction time(c)

4 Conclusions

In this study,COMSOL Multiphysics software was successfully used to simulate the variation of the electromagnetic field and temperature field with reaction time,microwave power,and nitrogen flow rate during microwave-assisted depolymerization of kraft lignin.The heat flux and heat loss caused by the fluid heat transfer were considered when constructing the microwave model.Microwave power had a significant effect on the cavity electric field and kraft lignin depolymerization temperature distribution.The electric field intensity,heating rate of kraft lignin,and average depolymerization temperature of kraft lignin improved with an increase in microwave power.The reaction time had little effect on the cavity electric field distribution,while it had a significant influence on the kraft lignin depolymerization temperature distribution.Nitrogen flow rate had no influence on the cavity electric field and kraft lignin depolymerization temperature distribution.Overall,the reaction time and microwave power are the key factors affecting the heating rate and conversion efficiency of kraft lignin,which can be used to enrich target products such as monophenols.

Acknowledgments

This work was supported by the Foundation of Key Laboratory of Pulp and Paper Science and Technology of the Ministry of Education of China(No.KF201917),and the National Natural Science Foundation of China(31800497).