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Journal of Korea Technical Association of the Pulp and Paper Industry - Vol. 52 , No. 4

[ Article ]
Journal of Korea Technical Association of the Pulp and Paper Industry - Vol. 52, No. 4, pp.38-51
Abbreviation: J. Korea TAPPI
ISSN: 0253-3200 (Print)
Print publication date 30 Aug 2020
Received 08 Jul 2020 Revised 19 Aug 2020 Accepted 20 Aug 2020
DOI: https://doi.org/10.7584/JKTAPPI.2020.08.52.4.38

Sequential Modeling of Paper Drying Process to Reduce Thermal Energy Use, Part 1: Theoretical Model
Lingbo Kong1 ; Jingyi Zhao2 ; Jiahao Li2 ; Yuejin Yuan1,
1College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, Professor, People’s Republic of China
2College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, Student, People’s Republic of China

Correspondence to : † E-mail: yyjyuan1@163.com (Address: College of Mechanical and Electrical Engineering, Shaanxi University of Science & Technology, Xi’an, Shaanxi Province, 710021, People’s Republic of China)

Funding Information ▼

Abstract

Paper drying is one of unit operations that consume the most amount of thermal energy in papermaking machine. In this paper, the theoretical model for paper drying process was developed using sequential modeling method based on conservation laws of mass and energy. Aimed at reducing its thermal energy use, the overall structure of the paper drying model was proposed initially. It was composed of eight basic modules based on their different functions in paper machine drying process, i.e. cylinder group module, steam separation module, surface condensation module, fan module, heat recovery module, air heating module, paper sheet module and hood module. The models of above modules were also developed one by one in detailed, based on which, a theoretical model for a specific paper machine drying process could be constructed. It could use to simulate material and energy flow of each module and the whole drying process in a more comprehensive manner with integrated thermal energy use and drying performance information. In addition, the effect of operating conditions on thermal energy use in paper drying process could also be investigated.


Keywords: Paper machine, drying process, thermal energy, model

1. Introduction

Paper drying is a crucial process in paper and paperboard production with the purpose of dewatering efficiently and cost effectively while also achieving the requested paper physical properties. The drying operation is usually completed in the drying section of paper machine. It is the largest energy consumer compared with other processes for a paper machine. The share of energy consumption in drying process is as high as 80% for a paper machine and corresponding dewatering cost is about 78% of the total cost of dewatering process.1,2)

In general, optimization of paper machine drying process is based on mathematical model. In order to improve energy efficiency of the paper drying process, Sivill and Ahtila developed a thermodynamic simulation model to optimize the thermal recovery system of three paper machines in Finland.3) Laurijssen et al. conducted a thermal mechanics optimization study on the ventilation system of paper machine drying section in Dutch paper mills.4) Ekvall and Hägglund proposed a physical dynamic model that could optimized the drying cylinders in case of web breaks in a Sweden copy paper machine.5) In addition, Nilsson,6) Karlsson and Stenström,7) and Heo et al.8) constructed some paper drying models to describe heat and mass transfer in paper drying process from different perspectives, respectively. Lu and Shen also built a paper drying model based on the fundamental equation of heat and mass transfer in porous media.9) However, there were some input parameters in these models need to be obtained from field test, such as the surface temperature of cylinders. Besides, the developed models include some critical assumptions to simply the complicated transport phenomena. All the models describing heat and mass transfer processes contained several transport coefficients, which are difficult to obtain proper numerical values. As a result, they might be suitable for scientific theoretical research, but not conducive for enterprise operators to master and apply to instruct actual drying operation of paper machines.

In order to make a more comprehensive understanding about paper drying process thoroughly, some researchers also developed various drying model based on the principle of first law. Gong et al.10) and Tian et al.11) given a thermal balance calculation model that focused on the entire drying section of paper machine. Liu et al. simulated the paper machine drying section based on material and energy balance.12) Li et al. presented an optimization model for a paper drying machine with simultaneous modular approach.13) Zhou et al. proposed a general paper drying model integrated with material, energy and exergy flows analysis for a Chinese corrugated paper machine.14) Zhang et al. conducted a research on the energy model of drying section based on multi-agent system of paper machine.15) A steady-state model for the drying process in the paper machine which produces fluting paper was developed based on the mass and energy balances around the paper web, moisture, and air.16) Although these models can realize the purpose of overall analyzing the drying section of paper machine, the order of establishment and simulation of the models is still different from the process flow of the actual drying operation. This might lead to the deviation of simulation results from onsite or experimental data.

Based on the principle of mass and energy conservation, the sequential modeling method was used to develop the theoretical model for paper drying process according to the paper machine operational guidelines. The proposed model integrated energy use and drying efficiency information to present the incoming and outgoing logistics and energy flow of each module in a more comprehensive manner.


2. Methods and Assumptions

Sequential modeling method is a common method in the field of chemical process simulation as a result of its advantages of good modeling framework, simple algorithm design and reusable algorithm module. This section gives the general principles of model development, the division of drying modules, and general assumptions.

2.1 Modeling structure

The drying section of a paper machine is divided into eight basic modules as shown below according to the different functions of each operating unit, namely, the cylinder group module, steam separation module, surface condensation module, fan module, heat recovery module, air heating module, paper sheet module and hood module. Fig. 1 showed the modular diagram of a typical paper drying process with tri-stage steam-supplied drying section.


Fig. 1. 
Schematic modular diagram of a typical paper machine drying process.

Legends: ClyGro=cylinder group module; PapDry=paper sheet module; SteSep=steam separation module;SurCond=surface condensation module; CHR=conventional heat recovery module; AirHeat=air heating module.



In this work, the drying cylinders with the same operating steam pressure are usually regarded as one drying cylinder group module, then the whole drying section could be divided into three drying cylinder group modules (CylGro as shown in Fig. 1). Accordingly, the sheets entering and leaving each dryer group are also divided into three corresponding paper sheet modules (PapDry). After condensate in the cylinder group, the mixture of condensation and blow-through steam was sent to related steam separation module (SteSep). The flash steam out of each steam separation module was used as supply steam to the next cylinder drying group. The waste heat of flashed steam from the last separator (SteSep 3) was recovered to heat water via the surface condensation module (SurCond).

As regarding the ventilation system, the fresh air sent from the workshop through the fan module (Fan 1) has to be preheated by the conventional heat recovery (CHR) module firstly, and then heated by the air heating (AirHeat) module to required temperature for supply air. After captured the evaporated water from the paper sheets, the moisture air was collected in the hood module and exhausted to the conventional heat recovery for preheating fresh air. In this way, the entire paper machine drying process could be connected by various mass and energy flow as presented in Fig. 1. It is also based on this mutual relationship that it is beneficial to use the sequential modeling method to construct the theoretical model for a paper machine drying process.

2.2 Modeling methods

The input parameters of each module should be already known, while the output parameters should be determined by the developed model of each module, namely they are calculated results of the theoretical model. Only those parameters that can be accessed directly were used as inputs to the model. Some specific field-readable parameters, such as sheet dryness and steam flow, are generally used to validate the simulation results. For paper drying process, the known parameters as inputs to the model are the pressure and differential pressure of the main steam entering each cylinder drying group, initial steam flow rate, the dry solid content and temperature of the paper sheet that entering the 1st drying cylinder, the quantity and relative humidity of supply air. In fact, the supply air amount could be obtained through the power of related fans, so the fan power also should be the initial known input parameter.

In order to make the modeling process in line with the paper drying technique, we also first modeling the cylinder dryers, followed by ventilation and paper sheet module. At the beginning of paper drying, steam was vented into the cylinders and released latent heat, then the ventilation system was started to promote air circulation, and finally the wet paper was fed into the drying section from previous pressing section. All the basic modules were constructed based on the governing laws of mass and energy conservation.

The number of state parameters, known parameters, assumed parameters and intermediate parameters of each module should be analyzed and determined, and then the degrees of freedom (DOF) of each module could be calculated with Eq. 1. This also indicated the number of equations should be contained in each module.

Nd=Nt-Nk-Na-Nm[1] 

Among which, Nt, Nk, Na and Nm means the quantity of state parameters, known parameters, assumed parameters and intermediate parameters of each module, and Nd is DOF of related module.

2.3 Assumptions

The following assumptions were considered when constructing the theoretical model in paper drying process. The steam was assumed to be saturated since it was continuous condensate in the cylinder dryers. The pressure drop of steam and ventilation was ignored due to pipeline resistance. The heat and mass transfer between the paper sheet and supply air was mainly convective heat transfer, and it was supposed that the evaporation was absorbed by the supply air in the pocket area, and then mixed with leakage air in the hood. It was assumed that the heat loss from the cylinder was used to heat the mixed air in the hood. Finally, the radiation loss of cylinder dryers was also ignored in this work.


3. Mass and Energy Equations
3.1 Mass equations

The paper drying process involves the interaction of four basic materials such as fiber, steam, air and moisture. According to the principle of mass conservation, the mass of a certain material entering the drying system should equal to the mass of that material coming out of the drying system in unit time. Each of the four materials in the drying process has its specific mass balance equation.

The mass of fiber will keep constant after drying, so the mass equation of fiber should be,

Mof=Mif[2] 

Here, Mof is mass of fiber output and Mif is mass of fiber input.

The steam that enters the cylinder drying group is discharged in the form of condensate and blow-through steam, so the mass balance equation of steam is

Mc+Mb=Ms[3] 

Here, Mc, Mb, and Ms stand for mass of condensate, blow-through steam, and steam, respectively.

The air consumed by each drying cylinder group is composed of pocket supply air and leakage air of the hood. Thus, the amount of exhaust moist air (in terms of dry air) can be written as follows.

Mexh=Msup+Mleak[4] 

Here, Mexh, Msup, and Mleak stand for mass of exhaust air, pocket supply air, and leakage air, respectively.

The water evaporated from the paper drying is in the form of vapor absorbed by the supply air and turned into moist air exhaust from hood, therefore, the amount of evaporation (Mevap) is equal to the amount of water absorbed by the air, then the mass balance equation of water can be expressed as follows.

Mevap=MexhXexh-MsupXsup+MleakXleak[5] 
3.2 Energy equations

The general energy balance equation can be expressed with Eq. 6 base the first law of thermodynamics.

Qs-Qc=Qi[6] 

where Qs means thermal energy of the steam released in each drying group, Qc means the unavailable energy in the condensation, and Qi means various input thermal energy, e.g.: energy used for evaporating water (Q1), energy used for heating fiber and remaining water in the paper (Q2), energy used for heating supply air from preheated to required temperature (Q3), energy used for heating leakage air to exhaust temperature (Q4), and heat loss of each module (Q5). These different kinds of thermal energy can be obtained by Eqs. 7-11, where the symbol T is temperature, c is specific heat capacity, and H is enthalpy of each kind of material. u means moisture content of paper. The subscripts evap, exh, sup, leak, pre, ip, op, w, v and f stand for evaporation, exhaust air, supply air, leakage air, preheated air, input paper, output paper, water, vapor, fiber, respectively. Zi is coefficient of heat loss form each unit, which can be estimated from operator’s experience, usually between 5-10%.

Q1=MevapcwTevap-Tip+γ+cvTexh-Tev[7] 
Q2=Mfcf+MfuopcwTop-Tip[8] 
Q3=Msup Hsup-Hpre[9] 
Q4=Mleak Hexh-Hleak[10] 
Q4=QiZi[11] 

Drying efficiency of the paper drying process was evaluated with Eq. 12, which represent the ratio of energy used for evaporation (Q1) to total thermal energy supplied to the drying process (∑Qi).

η=Q1Qi×100%[12] 

4. Sequential Models of Paper Drying Process
4.1 Cylinder group module

The heat source for drying paper is come from the cylinder group module. It is used to provide heat for evaporating water through the latent heat of vaporization released from the condensation of steam in the cylinders. Fig. 2 presented the mass and energy flow and related state parameters of the cylinder group module.


Fig. 2. 
Modular diagram of the cylinder group.

As Fig. 2 shows, the available heat come from fresh steam Qmis_1 (m=1,3,5) and those from flash steam Qmis_2 (m=3,5) supplied the thermal energy for drying paper. Except the 1st cylinder group module which only use fresh steam, the rest modules use the mixture of fresh and flash steam. Most of the thermal energy released by the steam in the cylinder group (Qmsc) are transferred to the paper sheet (Qmcp) via the cylinder wall by conduction effect. In addition, there is also some thermal energy loss (Qmca) through convection with supply air in the pocket around uncovered part of the cylinders. The designed value of both the coefficient of heat loss from cylinders (Zmca) and ratio of blow-through steam to separator (Zmbt) are used in this model.

Based on the initial analysis of all the parameters involved with Eq. 1, the DOF of cylinder group module is eight. The mass and energy balance equations for fresh steam, flash steam, condensate and blow-through steam were developed and shown below.

Mmis=Mmis_1+Mmis_2Qmis=Qmis_1+Qmis_2Mmoc+Mmob=MmisMmob=MmisZmibPmob=Pmis-PsbPmoc=PmobQmcp+Qmca=Qmis-Qmoc-QmobQmca=Qmcp+QmcaZmca[13] 

Where Mmis_2 and Qmis_2=0 equal to zero for the 1st cylinder group or when m=1. The physical parameters, e.g. enthalpy of saturated steam and condensate at various temperature, were cited from the database developed by Zhou et al.17) According to the overall heat transfer mechanism from steam to cylinder surface, the surface temperature (Tc) could be determined by Eq. 14.

Tc=Ts-QschsctcAsc[14] 

Where the overall heat transfer coefficient was referred to the literature.18) The thermal energy obtained from the latent heat of steam (Qsc) is transferred to the paper sheet (Qmcp) and pocket air (Qmca), so we get Eq. 15.

Qsc=Qmcp+Qmca[15] 
4.2 Steam separation module

The blow-through steam and condensate come from related cylinder group module were sent to the steam separation module via the same pipeline. As a result of lower pressure in the separator, additional steam would be flashed from the condensate. The blow-through steam and new flashed steam will be reused for the next cylinder group in the cascading system. Fig. 3 presented the mass and energy flow and related state parameters of the steam separation group module.


Fig. 3. 
Modular diagram of the steam separator.

Based on the initial analysis of all the parameters involved in this module with Eq. 1, the DOF of steam separation module is equal to four. The mass and energy balance equations for flash steam, condensate (in and out), and blow-through steam were shown below.

Mnos+Mnoc=Mnib+MnicMnos=Mnib+MnicZnicQnos+Qnoc=Qnib+QnicTnoc=Tnos=fPnos[16] 

Where Znic is the ratio of flash steam and condensate as a result of the low pressure in the separator, which could be determined from the operating record of the separator.

4.3 Surface condensation module

The heat source for drying paper is come from the cylinder group module. It is used to provide heat for evaporating water through the latent heat of vaporization released from the condensation of steam in the cylinders. Fig. 2 presented the mass and energy flow and related state parameters of the cylinder group module.

As Fig. 4 shows, the DOF of this module is four. The mass and energy balance equations for flash steam, condensate, cold and warm water were shown below.


Fig. 4. 
Modular diagram of the surface condenser.

M7oc+M7ow'=M7is+M7iwM7oc=M7isQ7oc+Q7ow'=Q7is+Q7iwT7oc=To0[17] 

Where Toc is the temperature of condensate that was sent to the boiler house for reusing the waste heat. This temperature could be determined based on measured data. It is usually in the range of 70-80℃.

4.4 Fan module

Both supply air fan and exhaust air fan were included in the fan module. The role of the supply air fan is to maintain the mass transfer drive for evaporation from paper sheet surface by continuously feeding fresh air into the pocket. The exhaust air fan is used to absorb the vapor and exhaust out of the drying section to maintain high drying performance. As a result of the same working principle of supply and exhaust air fan. In this paper, the fan module is used to calculate the power consumption required by the supply or exhaust air fan in the paper drying process. The relationship between the power consumed (Efan) and volume flow was determined by Eq. 18.

Efan=KWfanPfan1000ηfan[18] 

Where K is capacity coefficient of the motor, generally between 1.2-1.3. Wfan is the volume flow of the fan in the operating conditions. Pfan is the full pressure of the supply or exhaust air fan. ηfan is the efficiency of fan at full pressure, which is usually set to 0.8.

4.5 Heat recovery module

The fresh air is commonly heat to the required temperature for increase the capacity of absorb vapor. It is firstly preheated in heat recovery module and then continuously heated in the next air heating module. The input and output information regarding heat recovery module was presented in Fig. 5.


Fig. 5. 
Modular diagram of the heat recovery.

As the parameters shown in Fig. 5, the DOF of heat recovery module was nine where Nt=21, Nk=6, Na=1, Nm=5. The mass and energy balance equations for fresh air, exhaust air (in and out), preheat air, condensate, and heat loss of this module were shown below.

M9oa=M9iaM9oa'=M9ia'M9oaX9oa+M9ca=M9iaX9iaM9oaX9oa'=M9iaX9ia'Q9oa+Q9oa'+Q9oc+Qhel=Q9ia+Q9oa'Qhel=Q9ia-Q9oa-Q9caηhelX9oa=Xa0T9oa=Ta0T9oc=Tc0[19] 

Where, ηfan is heat efficiency of conventional heat recovery (i.e. air-air heat exchanger). It is an assumed parameter based on the designed parameter.

4.6 Air heating module

The preheat supply air has be continuously heated by air heater before supplied to the pocket area. The input and output information regarding air heating module was presented in Fig. 6.


Fig. 6. 
Modular diagram of the air heater.

As the parameters shown in Fig. 6, the DOF of air heating module was six where Nt=16, Nk=5, Na=1, Nm=4. The equations for fresh steam, preheat air, supply air, condensate, and heat loss of this module were shown below.

M10oc=M10isM10oa=M10ia'M10oaX10oa=M10ia'X10ia'Q10oa+Q10oc+Qahl=Q10ia'+Q10isQahl=Q10is-Q10ocηahlT10oc=Tc0[20] 

Where, ηahl is heat loss of air heater (i.e. steam-air heat exchanger). It can be determined from the designed efficiency of steam-air heat exchanger.

4.7 Paper sheet module

The paper sheet module is one of the most important and complex modules in paper drying. In order to simplify the model, the moisture air was assumed as the mix of vapor and pocket air. This is just convenient for modeling so that the air mix is not displayed in Fig. 1. The input and output parameters were presented in Fig. 7.


Fig. 7. 
Modular diagram of the paper drying module.

The thermal energy used for drying paper Qkcp (k=11, 12, 13) is come from the heat transferred through the cylinder wall in the cylinder group module Qmcp (m=1, 3, 5). It is known for the paper sheet module but unknown for cylinder group module. This is also the reason why we should first calculate the cylinder group module which is in line with the paper drying techniques. Similarly, it is also required to calculate air heating module before the paper sheet module because the input values of supply air should be determined. According to the parameters shown in Fig. 7, the DOF of paper sheet module was eleven where Nt=25, Nk=7, Na=1, Nm=6. The balance equations as per ingoing and outgoing fiber, water, air, and heat loss of this module were shown below.

Mkof=MkifMkoa=MkiaMkoa'=MkoaMkoa'Xkoa'=MkiaXkiaM9oaX9oa'=M9iaX9ia'MkoaXkoa-Mk_evap=MkiaXkiaMkofukop-Mk_evap=MkifukipQkcp=Qkop-Qkip+Qk_evapl+QkpaQkpa=QkcpZkpaQkoa'-Qkia=QkpaTkoa=Tkoa'Qkop+Qkoa=Qkip+Qkia+Qkcp[21] 

The temperature of output paper, To,p, can be calculated with Eq. 22.

To,p=Tp-ΔTp[22] 

In which, the temperature difference (ΔTp) is the temperature drop as result of evaporation from paper sheet in the pocket with the form of convection heat transfer. Generally, it is 4-5℃ for high-speed paper machine, while 12-15℃ for traditional paper machine.18) The temperature of Tp is used to describe the paper that leave the cylinder surface, which can be determined by Eq. 23.

Qkcp=Qmcp=hcptpAcpTc-Tp[23] 

Where, tp is the drying time of paper sheet in the cylinder group module, Tc is the surface temperature of drying cylinder (Eq. 14), Acp is the contact area of heat transfer between cylinder and surface paper sheet, and hcp is coefficient of heat transfer between cylinder and surface paper sheet, see the literature for the values.19)

4.8 Hood module

The hood is used to remove the hot and moisture air that absorbs evaporated water so that maintain the high drying performance. In addition, the leakage air is also mixed in the hood with the moisture air from pocket due to the pressure difference inside and outside of the hood. Fig. 8 presented the involved total parameters of hood module. It should be noted that the moisture mix module is just used for simplifying the calculation. Because the evaporation was various according to different cylinder group module. This resulted in the various status of moisture air in the pocket. However, it’s assumed uniform in the hood. Therefore, there is additional moisture mix in Fig. 8. Under this condition, the total moisture air based on three different pocket supply air has to be determined firstly, then the unknown variables could be modeled.


Fig. 8. 
Modular diagram of the hood.

Base on the parameters shown in Fig. 8, the DOF of hood module was seven where Nt=27, Nk=13, Na=1, Nm=6. The balance equations of various air of this module were shown below.

M14ia=M14ia_1+M14ia_2+M14ia_3M14iaX14ia=M14ia_1X14ia_1+M14ia_2X14ia_2+M14ia_3X14ia_3Q14ia=Q14ia_1+Q14ia_2+Q14ia_3M14oa=M14ia+M14ia'M14oaX14oa=M14iaX14ia+M14ia'X14ia'Q14oa+Q14ha=Q14ia+Q14ia'+Q14caQ14oa=Q14oa+Q14haZha[24] 

In which, the relationship of leakage air flow and total exhaust air flow is,

M14ia'=ZleakM14oa[25] 

Where Zleak is the leakage coefficient of hood which defined as the ratio of leakage air to total exhaust air as a result of pressure difference. It usually in the range of 20-30% for closed hood, and even as high as 40-50% for semi-closed hood.20)


5. Conclusions

The theoretical model of paper drying process was constructed using sequential modeling method under the principle of first law according to the drying technique in this paper. The drying model was composed of eight basic modules based on their different function in paper drying process, i.e. the cylinder group module, steam separation module, surface condensation module, fan module, heat recovery module, air heating module, paper sheet module and hood module.

The models of the eight basic modules were presented in detail based on their specific functions after careful analysis of all the parameters involved. The drying model of a specific paper machine could be constructed or assembled with these basic modules according to the blueprint and field survey. The proposed theoretical drying model could be used to simulate the mass and energy flow of the whole drying process, which emphasize on energy consumption and drying performance. It could also use to evaluate the effect of some operating parameters on drying energy consumption with the purpose of reducing thermal energy use in paper machine drying process. The simulation results of the proposed model with a case study of newsprint paper machine drying process and the effect of operating parameters on thermal energy use will be presented and discussed in our next work.


Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 21808135) and the Key Project of International Science and Technology Cooperation Program of Shaanxi Province (No. 2020KWZ-015).


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