Mathematical modelling and energy performance assessment of airimpingement drying systems for the production of tissue paper
Paolo Di Marco a, Stefano Frigo a, Roberto Gabbrielli b, *, Stefano Pecchia c
a Dipartimento di Ingegneria dell'Energia, dei Sistemi, del Territorio e delle Costruzioni, Universit�a di Pisa, Largo L. Lazzarino, 56126 Pisa, Italyb Dipartimento di Ingegneria Civile e Industriale, Universit�a di Pisa, Via Bonanno Pisano, 25/b, 56126 Pisa, Italyc Novimpianti Drying Technology, Via del Fanucchi, 17, 55014 Marlia Capannori, LU, Italy
a r t i c l e i n f o
Article history:Received 28 September 2015Received in revised form2 August 2016Accepted 3 August 2016
In this paper an original and exhaustive mathematical modelling of air impingement drying systems forthe production of tissue paper in the Yankee-hoods configurations is reported, which offers the possi-bility to optimize its energy performance. The model takes into account many detailed operative pa-rameters of the overall drying process with the aim to execute its energy and mass balance and toevaluate its energy performances. The validity of the mathematical model has been assessed by com-parison with actual data from an existing tissue paper mill. Finally, the energy performances of twodifferent layouts of the air system have been evaluated and compared. Changing the operative param-eters of the drying process, such as air jet temperature and speed and moisture content of the extractionair, it is possible to obtain the same paper production with an energy saving of about 4.5%. In average, thelayout with two parallel air circuits assure an energy saving of about 1% with respect to the layout with asingle air circuit.
The drying process consists of the moisture removal from wetmaterials thanks to heat and mass transfer mechanisms [1]. It re-quires large amount of energy due to the high latent heat of thewater that has to evaporate. So, it is essential to study in depth thethermodynamic conditions and plant layout of the drying in orderto minimize its energy consumption and its environmental impact.Using different configurations of the drying system, such as fluid-ized bed dryers, try dryers, dry tunnels, several heat and masstransfer mechanisms can be adopted to assure the water evapora-tion: hot air jets, microwave, vacuum, infrared,microwave-vacuum,hot air-infrared, thermal contact with high temperature surfaces. Inindustry the drying is required for many materials, such as fruits,vegetables, meat, sausages, wood, plywood, chemicals, paper. Thescientific literature about the studies on the drying processes isvery extensive in the energy sector due to their large energy im-plications. The most meaningful recent examples that be
mentioned are described briefly in the following. In Ref. [2] thedrying of apple slices on drying tray in a combined microwave-hotair flow dryer is experimentally studied in order to assess the ef-fects of the operative conditions on the drying process and toevaluate its specific energy consumption. In Ref. [3] an energy andexergy analysis of industrial fluidized bed paddy drying is pre-sented. Using the balance equations of energy and exergy of thedrying chamber, a model for the energy performance assessment ispresented and validated using experimental data from two testcampaigns. In Ref. [4] energy and exergy analyses of native cassavastarch drying in a tray drier is reported in order to assess the energyperformance of the process. Using the first law of thermodynamics,a simple model is proposed in order to assess the energy perfor-mances of the process from the experimental data. In Ref. [5] thedrying rate curves of the olive stone are experimentally obtained. In[6] the drying performances in terms of energy consumptions of amicrowave-assisted fluidized bed drying of soybeans are evaluatedusing a mathematical model that is validated using an experi-mentally activity. In Ref. [7] a mathematical framework, that isvalidated using experimental data, is developed to estimate thedrying performance of a mixed-mode solar dryer with potatoes.
In this paper the drying system of the sheets of tissue paper isconsidered and its energy performances are analysed. Indeed, the
b [m] width of the paper sheet that is wrapped on the Yankeecylinder
cpd [J/kg K] specific heat of the dry fibrecpv [J/kg K] specific heat of steamcpw [J/kg K] specific heat of watercp1 [J/kg K] specific heat of the impingement aircp1 [J/kg K] specific heat of the moist exhaust air at the
temperature averaged between T2 and Teacpinl [J/kg K] specific heat of the air from the milld [m] orifice diameter of the nozzlesD [m2/s] diffusion coefficientdA [m2] heat exchange surface of the tissue sheetdc [m] contracted orifice diameterdmev [kg/s] mass flow of vapor that is produced during the
drying process in dqdm1 [kg/s] mass flow of the air impinging the transversal stripe
of tissue sheetdT [K] infinitesimal temperature variation of the sheet during
the drying processdq [rad] infinitesimal angle of wrapE [�] Ackermann correction factore [�] air excess factor for the combustionF [�] LMTD correction factorf [�] open area fraction of the hoodfc [�] vena contracta fraction of the air nozzleshn [m] nozzle-to-sheet distanceh [kJ/kg] the mass enthalpy of the streamshfg [J/kg] latent heat of water at the sheet temperaturehs [J/kg] heat of sorptionLe [�] number of LewisLHV [J/kg] lower heating value of the fuelLMTD [K]logarithmic mean temperature difference_mcond [kg/s] mass flow of the steam that condensates inside the
Yankee cylinderMCw moisture content of the wet-end exhaust gasMCd moisture content of the dry-end exhaust gasmd [kg/s]mass flow of the dry fibre_mev [kg/s] mass flow of the water that is evaporated from the
tissue sheet during the drying_mfuel [kg/s] mass flow of the fuel in the burner of the
Monosystem configuration_mfuel_d [kg/s] mass flow of the fuel in the burner of the dry
circuit of the Duosystem configuration_mfuel_w [kg/s] mass flow of the fuel in the burner of the wet
circuit of the Duosystem configuration_minl [kg/s] air mass flow intake from the mill into the hoods in
the Monosystem configuration_minl_d [kg/s] air mass flow intake from themill into the dry hood
in the Duosystem configuration_minl_w [kg/s] air mass flow intake from the mill into the wet
hood in the Duosystem configurationmw [kg/s] mass flow of the water within the sheet_mwc [kg/s] water mass flow [kg/s] for the coating_m00drying [kg/m2 s] mass flow per unit area of the exhaust moist
air at q_mw_fuel [kg/s] mass flow of the water that is produced during
the fuel combustion in the Monosystemconfiguration
_mw_fuel_w [kg/s] mass flow of the water that is produced duringthe fuel combustion in the wet circuit of theDuosystem configuration
_mw_fuel_d [kg/s] mass flow of the water that is produced duringthe fuel combustion in the dry circuit of theDuosystem configuration
Nuimp [�] Nusselt number of the heat exchange between thetissue sheet and the impingement air
NuL [�] Nusselt number of the heat exchange between thetissue sheet and the air outside the hoods
ptot [Pa] total pressure of the impingement airpva [Pa] partial pressure of the vapor in the impingement airpvp0 [Pa] partial pressure of the vapor on the evaporating
surface of the sheetPrimp [�] Prandtl number of the heat exchange between the
tissue sheet and the impingement airPrL [�] Prandtl number of the heat exchange between the
tissue sheet and the air outside the hoods_Q [kW] thermal power of the air to air heat recuperatorQ
00c [W] overall heat that is provided to the tissue sheet by the
Yankee cylinder during the drying_Qloss [W]thermal power that is lost due to the thermal exchange
between the hoods and the mill environmentq
00c [W/m2] heat flux from the steam in the Yankee cylinder to the
tissue sheetq
00a[W/m2] heat flux from the air impingement to the tissue
sheet or from the surrounding air when the sheet isor not under the hoods, respectively
R [m] radius of the Yankee cylinderRttot [m2 K/W] overall heat transfer resistance per unit area
between the condensate steam of the Yankeeand the tissue sheet
Rv [J/kg K] gas constant of water vaporReimp [�]Reynolds number of the heat exchange between the
tissue sheet and the impingement airReL [�] Reynolds number of the heat exchange between the
tissue sheet and the air outside the hoodsRstoich [�] mass ratio between air and the fuel at the
stoichiometric conditionsS [m2] the surface of the recuperatorSoh [m2] lateral surface of the cylinder outside the hoodsSby [m2] overall surface of the two bases of the Yankee cylinderT [K] temperature of the tissue sheet along the wrap angle
above the Yankee cylinderTcyl [K] temperature of the condensate steam inside the
Yankee cylinderTea [K] bulk temperature of the exhaust air downstream the
drying process at the outlet of the hoodsTf [K] film temperatureTmill [K] temperature of the ambient air in the tissue millT1 [K] air impingement temperatureT2 [K] exhaust air temperature downstream the jetTlim [K] maximum allowable temperature at the inlet of the
burner due to its structural strengthTlim_w [K] maximum allowable temperature at the inlet of the
burner of the wet circuit due to its structural strengthTlim_d [K]maximum allowable temperature at the inlet of the
burner of the dry circuit due to its structural strengthTw temperature of the wet-end air impingementTd temperature of the dry-end air impingementX [kg water/kg dry air] moisture ratioU [W/m2 K] overall heat transfer coefficient of the air to air heat
recuperator
P. Di Marco et al. / Energy 114 (2016) 201e213202
Vw velocity of the wet-end air impingementVd velocity of the dry-end air impingementzr [kg water/kg fiber] moisture ratio of the tissue sheetaimp [W/m2 K] convective heat transfer between the tissue sheet
and the impingement airamill [W/m2 K] convective heat transfer between the tissue sheet
and the air outside the hoodsaby [W/m2 K] heat transfer coefficient between the two bases of
the cylinder and the environment within thetissue mill
aoh [W/m2 K] heat transfer coefficient between the lateralsurface and the environment inside the tissuemill
Dhevc [J/kg] evaporation heat of the water for the coatingDhevy [kJ/kg] condensation heat of the steam inside the Yankee
cylinderq [rad] generic wrap angleε [�] contraction coefficient of the flux in the nozzler1 [kg/m3] mass density of the impingement airl1 [W/m K] thermal conductivity of the impingement air4 [�] relative humidity of the air within the boundary layer
above the tissue sheet
P. Di Marco et al. / Energy 114 (2016) 201e213 203
production of tissue paper, that requires the evaporation of largeamounts of water, is a very intensive energy process. The averageconsumption of primary energy per ton of paper produced and perton of evaporated water is about 5800 MJ (about 1600 kW h) and4000 MJ (about 1100 kW h), respectively [8]. In modern tissuepaper mill the sheet drying is contemporarily assured by the steamheated Yankee cylinder, which is wrapped around by the tissuesheet, and by high temperature and speed air jets from two hoodsequipped with steam/oil heated air heaters (this configuration canbe found, at present, only in old small mills) or with fuel (mainlynatural gas) fired burners.
The Yankee-hood dryer is the crucial section of the paper ma-chine due to its large thermal energy consumption. As a conse-quence of continuously increasing energy costs, the determinationof operating conditions with the lowest energy consumption isessential in order to design and operate the tissue machine and theair drying system in the most efficient and economical way whileensuring the required paper quality and daily production. Evenenergy savings of few percentages correspond to large amounts ofenergy, considering that the annual thermal energy consumption ofa middle size tissue mill is about 50 GW h.
The overall energy performances of the sheet drying systemsdepend on many interdependent process parameters in a very com-plex way. So, this aspect implies that the assessment of the energyperformances both in design and operating phase is a very difficulttask. This is generally executedwithout a structured approach on thebasis of a very deep knowledge and practical experience of theoperative behaviour of the Yankee-hood drying systems.
In this context, a mathematical model for the reliable assess-ment of the energy performances of the overall drying system,during design phase and energetic diagnosis in existing tissuemills,can be considered an effective and useful tool for designers andplant managers in order to highlight operating conditions withminimum specific energy consumption.
In the scientific and technical literature, several examples ofmathematical models about Yankee-hood drying systems for theassessment of the energy performances of tissue sheet productionhave been proposed. In particular, in Ref. [9] a very comprehensivemodel, that was successively used as reference by several otherauthors, is reported. This model considers the Yankee hood con-figurations that are characterized by the presence of the steam coilsfor the introduction of thermal power into the air system. Thisconfiguration is not suitable to reach high temperature values ofthe impinging air jet. The modern air hoods for tissue sheet pro-duction are characterized by one or two fuel burners in order toreach air temperature up to 700 �C. In this case the process of heatandmass transfer between the air and the wet paper sheet requiresa particular modelling that is not taken into account in Ref. [9]. So,the results cannot be considered completely reliable for high airtemperature values.
In Ref. [10] mass and energy balances of a Yankee-cylinder with
a single hood, i.e. a very simple drying configuration, are reported.The modelling of the heat andmass transfer of water evaporation isneglected and the heat and mass transfer coefficients are simplydefined by the user as input data. The psychrometric Mollierenthalpy-air humidity chart is integrated in the model and thethermodynamic states on the chart of the wet air streams upstreamand downstream the hood nozzles are evaluated by the mathe-matical model. In Ref. [11], a mass and energy balance of an existingdrying duo parallel system with a black box approach is proposedas diagnosis tool. The measurement of the inlet and outlet streamsare used to evaluate the actual fuel consumption of the tissuedrying without taking into account the drying mechanism of thesheet. In Ref. [12] the same authors proposed an energy model of adrying duo parallel system taking into account also the heattransfer between the air and the sheet and neglecting the masstransfer in the drying process. The heat transfer coefficient is sim-ply calculated starting from a guess value and using a user-definedcorrection relation.
In Ref. [13], two mathematical models, which use some fieldmeasurements andmake it possible to determine the drying rate ofexisting hoods for a parallel duo drying system, are reported. Thesemodels do not take into account the detailed mechanism of heatand mass transfer during the air jet impingement.
In Ref. [14], the energy optimization of the Yankee-hood dryer isexecuted in order to assess the operative configuration with theminimum consumption of an existing paper mill. The mass andenergy balance of each system equipment is combined with a verysimple model of the drying process of the tissue sheet.
In the context described above, this paper presents an originaland exhaustive mathematical model for the simulation and energyperformance assessment of Yankee - hood drying systems for tissuepaper production. The limits of the methods, that are present inliterature, are overcome by the present model in an original way, asdescribed in the following. The heat and mass transfer mechanismsof the sheet drying are integrated within the mass and energy bal-ance of the overall air system in order to obtain reliable results aboutthe tissue production and its energy consumptions. In particular, thetemperature and moisture content of the tissue sheet during thedrying along the wrap angle and the temperature and pressure ofeach stream of the air system can be evaluated. The model uses themost updated relations for the reliable simulation of the tissue sheetdrying and takes into accountmany characteristics of the system thatare essential for the reliability of the performance assessment. Usingthe results of the model it is possible to obtain the best set of theoperative parameters, in order to minimize the specific energyconsumption. Hence, the effective use of the model here proposedhas meaningful practical implications in terms of tissue mill designand operation from the energy point of view.
In literature many detailed contributions concerning themathematical modelling of the production of high grammage paperin multi-cylinder configuration are present. This kind of
P. Di Marco et al. / Energy 114 (2016) 201e213204
production, where the paper is wrapped onmany internally heatedcylinders thanks to fabric felt, is largely and deeply investigated. Abrief description of the most relevant paper is reported below. InRef. [15] an analytical model based on a system of complex differ-ential equations describing the drying process of the paper duringthe contact with the wet web/internal heated cylinder is described.In Ref. [16] the temperature profile of multi-cylinder dryers alongthe drying process is calculated and validated with experimentaldata of a real paper mill using a modelling of the heat exchangebetween the paper and the cylinders. In Ref. [17] a very complexdifferential mathematical model for unsteady state conditions ofthe thermal contact between felt, paper and cylinder is proposedand numerically solved. The results of the model are comparedwith data obtained experimentally using infrared measurements ofthe surface temperature of the cylinders. In Ref. [18] a simple modelbased on the Mollier chart of the multi-cylinder dryers with closedhoods for the vapor suction and of the heat recovery system isproposed. In Ref. [19] a block approach for the assessment of theenergy consumption of a multi-cylinder newsprint paper machineusing the energy and mass balance equations is presented andvalidated with experimental test on a full scale tissue mill. InRef. [20] a comprehensive method, that is based on energy loadaudit and energy flow analysis and energy efficiency estimation, forassessing the energy performance of the dryer section isinvestigated.
The mathematical models of the multi-cylinder dryers cannotbe used for the energy assessment of the tissue paper productionbecause (i) the air system with the impingements in the hoods isnot present, (ii) the number of cylinders is higher than one as in thetissue production, (iii) a felt for the adhesion of the paper on theinternal steam heated cylinders is used, (iv) the thickness andgrammage of the paper is so high that the capillary phenomenacannot be neglected during the drying of the paper sheet.
Fig. 1. Duosystem configuration with pa
2. Configuration of the drying air system
The wet paper sheet wraps around the rotating internally steamheated Yankee cylinder. The heat transfer for the drying is assuredboth by the heated cylinder via conduction and by the hot airimpingement jets via convection. The configuration of the drying airsystem (Fig. 1) is composed by two parallel air circuits (duosystemconfiguration), each of them equipped with a gas fired burner thatassures the production of high temperature air. Then, the air is blowntowards the two hoods. After the impingement, the exhaust airmixed with the evaporated water from the tissue sheet is suckedfrom the gap between the Yankee cylinder and the hoods. The humidexhaust air is partially extracted both from the wet-end side and thedry-end side and then conveyed to the recuperator and finally to theatmosphere. The remaining part of the humid exhaust airs from thehoods is recirculated to the burners. In order to fulfil the mass bal-ance of the overall circuit, some make-up air enters the drying sys-tem together with the fresh air that is necessary for the combustionprocess. The make-up air feeds both air loops. The fresh air is pre-heated within a heat exchanger (hereafter called “recuperator”) us-ing the extracted humid air. Five fans assure the circulation of the airwithin the wet and dry loops, the feeding of the burners and theextraction of the humid air. The fans for the combustion airs arelocated downstream the recuperator. This fact implies that somefurther fresh air can be sucked through the valves S1 and S2 (seeFig. 1) in order to limit the temperature of the combustion air andconsequently ensure the structural integrity of the burners.
3. Mathematical model of the Yankee cylinder e hood dryingsystem
The mathematical model of the drying air system is divided insome parts starting from the following assumptions:
rallel weteend and dryeend hoods.
Fig. 2. Scheme of the Yankee-cylinder and two air hoods.
P. Di Marco et al. / Energy 114 (2016) 201e213 205
(i) the temperature and humidity profile within the thickness ofthe thin sheet is uniform and water is always available on thesheet surface. So, the phenomena of water diffusion, that aretypical of the high grammage paper, are neglected;
(ii) along the longitudinal direction of the Yankee cylinder, thehumidity profile and temperature are uniform neglecting theeffect of small differences of water content on the dryingprocess;
(iii) along the longitudinal direction of the Yankee cylinder, theair jets are supposed to be uniformly distributed so that theheat flux of the air impingement on the tissue sheet can beconsidered as a continuous function that depends only onthe wrap angle, neglecting the reciprocal interaction be-tween adjacent air jets;
(iv) the circumferential heat conduction within the Yankee cyl-inder is neglected due to its high rotational speed.
3.1. Drying process of the tissue sheet
The drying of the tissue sheet, that is attached to the Yankeecylinder along the wrap angle from the press to the doctor blade(from A to E in Fig. 2), is assured by two contributions: from oneside the sheet is heated by the internally heated Yankee cylinder(conduction) and from the other by the air jets (convection).
So, the energy balance of an infinitesimal piece of tissue sheet atthe generic wrap angle (Fig. 3) can be expressed with the followingequation:�q
00c þ q
00a
�bRdq ¼
�mccpd þmwcpw
�dT þ
�hfg þ hs
�dmev (1)
The heat flux from the Yankee can be evaluated with the
Fig. 3. Scheme for the energy balance of the infinitesimal piece of tissue sheet.
following equation:
q00c ¼
1Rttot
�Tcyl � T
�(2)
Rttot can be directly inserted in the model or, alternatively, canbe calculated as the summation of the single heat transfer re-sistances, such as the condensate layer on the internal wall, thefouling on the internal wall, the Yankee shell, the spray coating onthe external surface of the Yankee, the contact between the Yankeeand the tissue sheet [21].
Using the heat of sorption it is possible to take into account thatthe evaporation of the boundwater that is included inside the sheetrequires an extra amount of energy besides the latent heat ofvaporization for free water. In particular, the following expression[21] can be used for the evaluation of hs:
hs ¼ 0:10085 Rv1� f
fz1:0585r T2 (3)
When the tissue sheet is outside the hood, so after the last pressand between the outlet of the dry-end hood and the doctor blade(A-B and D-E as Fig. 4), q
00a can be evaluated as follows:
q00a ¼ amillðTmill � TÞ (4)
where a [W/m2 K] can be evaluated as follows assuming thegeometrical configuration of a laminar flow above a fixed surfacewith constant temperature (the sheet temperature is evidentlyconstant in each dq) [22]:
The thermophysical properties for the calculation of NuL, ReLand PrL shall be evaluated at the film temperature that is theaverage between Tmill and T.
When the tissue sheet is under the hoods (B-C and C-D as Fig. 2),the heat exchange is due to the high temperature air impingement.The convective heat transfer is strongly influenced by the masstransfer due to the vapor flow diffusing from the tissue sheet to thebulk air flow through the laminar boundary film. Indeed, the air jetsassure not only thewater evaporation from the tissue sheet but alsothe heating of vapor to the exhaust temperature from the hoods[21]. So, q
00a under the hoods shall be evaluated as follows [23]:
q00a ¼ aimp
EeE � 1
ðT1 � TÞ (6)
where E [�] can be evaluated as follows:
E ¼ dmev
dAcpvaimp
T2 � TT1 � T
(7)
where
dA [m2] can be evaluated as bRdqaimp is evaluated modifying the well-known expression ofMartin [24e29] in order to take into account the effects of thehigh temperature of the air jets on the heat transfer mechanism:
P. Di Marco et al. / Energy 114 (2016) 201e213206
Nuimp ¼
�fc
100
�0:9505�3:649�
�0:03455þ4:812 fc
100
�hndc
�1þ60:47 fc
100
,
2640:90
þ 0:10
1þ0:05693�T1�273:15
100
�3
375Re0:772imp Pr1=3imp
(8)where
fc ¼ f ε, f is the ratio between the overall cross section area of thenozzles and the overall internal surface of the hood ε is thecontraction coefficient of the flux in the nozzle [28], anddc ¼ d
ffiffiffiε
p.
For the calculation of (eq. (8)), it is necessary to evaluate thethermophysical properties of the air jet at the film temperature thatis the average between T1 and T. The dimensionless numbers, Nuimpand Reimp, should be calculated using dc as characteristic length ofthe heat transfer process. Moreover, the speed of the impinging airis used to calculate Reimp.
The vapor mass flow that is produced in the drying process(dmev) can be evaluated using the equation of Stefan [30]:
dmev ¼ a
r1cp1Le2=3
ptotRvT
ln
ptot � pvaptot � pvp0
!dA (9)
where
Le ¼ l1r1cp1D
D can be calculated using the following equation (10) [31]:
8>>>>><>>>>>:
D ¼ 1:87� 10�10T2:072f
9:872� 10�6ptot280K< Tf <450K
D ¼ 2:75� 10�9T1:632f
9:872� 10�6ptot450K< Tf <1070K
(10)
The energy balance of the impingement air can be expressed inthe following way:
ðT1 � T2Þdm1cp1 ¼ q00adAþ dmevcpvðT2 � TÞ (11)
Combining equations (6) and (7), it is possible to obtain theexplicit dependence of the exhaust air temperature on theimpingement and sheet temperature:
T2 ¼ T1 � ðT1 � T2Þ ¼ T1 �a EeEeE�1 ðT1 � TÞ
dm1dA cp1
(12)
The overall energy balance of the Yankee cylinder has to takeinto account the presence of some thermal losses, due to the heatexchange between the cylinder and the environment air across itsbases, where thermal insulation is sometimes mounted and theheat transfer across the lateral surface of the cylinder not coveredby the paper sheet (outside of the hoods) due to the injection of thecoating cold water solution. So, _mcond can be evaluated in thefollowing way:
Q00c þ _mwcDhevc þ Sbyaby
�Tcyl � Tmill
�þ Sohaoh
�Tcyl � Tmill
�¼ _mcondDhevy
(13)
where
aby [W/m2 K] is calculated using the reference geometry of therotating disk in a quiescent fluid [31]) and aoh is calculated using(eq. (5)).
Finally, the bulk temperature of the exhaust air downstream thedrying process at the outlet of the hoods (streams 2 and 3 in Figs. 1and 2) (Tea) can be evaluated as follows from the energy and massbalances of the mixing streams of drying air and air intake:
_minl enters into the hoods from the mill through the gap be-tween the Yankee cylinder and the hoods, because the pressureis slightly lower than the atmospheric valuecpinl [J/kg K] is calculated at an average temperature between T2and Tea
The mass and energy balance of the drying air system can beexamined in Appendix A.
4. Assessment of the energy performances of the dryingsystem of the duosystem configuration with parallel weteende dryeend hoods
4.1. Inputs and validation of the simulation model
The model has been implemented and iteratively solved usingMATLAB language [32]. Afterwards, it has been tested and cali-brated using actual operative data of an existing tissue mill (seeFig. 1 for the layout of the air drying system) as reported in Table 1,where also the main inputs of the model are summarized.
It is necessary to explain some specific features of the inputdata:
� The width of the tissue sheet on the Yankee cylinder is higherthan that on the pope reel due to the presence of the trimmedwasted on the Yankee cylinder.
� The tissue sheet is creped (i.e., its grammage changes from theoutlet of the Yankee cylinder and the pope) and, consequently,the peripheral speed of the Yankee cylinder is higher than thatof the pope.
� For simplicity, the overall heat transfer coefficient between thesteam inside the Yankee cylinder and the tissue sheet is directlyprovided as input of the model.
The most meaningful outputs from the energy point of view are:
Table 1Input data of the simulation model which are taken from to an existing tissue mill with duosystem configuration and parallelweteend e dryeend hoods.
Inputs
Wrap angle between the press and the inlet of the wet-end hood, � 15Wrap angle of the wet-end hood, � 125Wrap angle of the dry-end hood, � 125Wrap angle between the outlet of the dry-end hood and the doctor blade, � 15Yankee cylinder diameter, mm 4572Steam pressure inside the Yankee cylinder, bar 6Ambient temperature, �C 30Ambient absolute humidity, g/kg 10Ambient pressure, bar 1Air impingement temperature of the wet-end hood, �C 450Air impingement temperature of the dry-end hood, �C 450Air impingement speed of the wet-end hood, m/s 110Air impingement speed of the dry-end hood, m/s 110Percentage open area of the nozzles within the hoods, - 1.2Gap between the hoods and the tissue sheet, mm 20Diameter of the nozzles, mm 5.6Absolute humidity of the exhaust air from the wet-end hood, g/kg 500Absolute humidity of the exhaust air from the dry-end hood, g/kg 250Width of the dried sheet on the Yankee cylinder, mm 2850Width of the sheet on the pope, mm 2800Daily production at the pope, t/day 110Grammage at the pope, g/m2 18Coefficient di creping, % 20Percentage of the in-leaked air within the hoods, - 5Temperature of the pulp after the vacuum press at the inlet of the Yankee cylinder, �C 38Heat transfer coefficient of the Yankee cylinder, W/m2K 890Fibre content after the vacuum press, % 39Fibre content at the pope, % 95Temperature inside the paper mill near the Yankee cylinder, �C 30Lower heating value of the fuel, MJ/kg 39Air excess for the burner of the wet-end circuit, % 25Air excess for the burner of the dry-end circuit, % 25Maximum allowable temperature of the burner of the wet-end circuit, �C 200Maximum allowable temperature of the burner of the dry-end circuit, �C 200Inlet fuel temperature, �C 20
P. Di Marco et al. / Energy 114 (2016) 201e213 207
� The specific energy consumption is defined as the ratio betweenthe overall thermal power consumption, i.e. the summation ofthe gross thermal power of the Yankee cylinder and the termLHV _mfuel, and the hourly paper production. The specific energyconsumption can be evaluated using the hourly mass flow of theevaporated water in place of the paper production.
� The thermal power of the drying unit is the summation of thenet thermal power of the Yankee cylinder and the thermal po-wer that is provided to the tissue sheet by the air jets within thehoods.
In Table 2 the existing plant data and the outputs of the model
Table 2Comparison between the results of the simulation model and the real data of an existin
Outputs
Overall mass flow of evaporated water, kg/hSpecific evaporation rate (referenced to the lateral surface of the Yankee cylinder), kg/Thermal power of the drying unit, kWSteam mass flow of the Yankee cylinder, kg/hSpecific energy consumption, kWh/t paperSpecific energy consumption, kWh/t evaporated waterSheet velocity on the Yankee cylinder, m/minSheet velocity at the pope, m/minAir impingement mass flow at the wet-end hood, kg/sAir impingement mass flow at the dry-end hood, kg/sMass flow of the make-up air, kg/sMass flow of the exhaust air, kg/sTemperature of the exhaust air downstream the wet-end hood, �CTemperature of the exhaust air downstream the dry-end hood, �CTemperature of the exhaust air, �C
are summarized for the comparison. It is possible to note that thediscrepancy between them is always not higher than 5%. This factconfirms the reliability of the simulation model. It is important tonote that it is not possible to compare in a reliably way the pro-posed model with those that are present in literature, because theother models are not completed as the present one.
4.2. Assessment of the energy performance
After the validation of the model, the dependence of the energyand production performances of the tissue mill on some importantoperative parameters has been investigated. First of all, the effect of
g tissue mill with duosystem configuration and parallel weteend e dryeend hoods.
the overall heat transfer coefficient of Yankee cylinder is analysed(Fig. 4). This analysis is generally executed by Yankee cylindermanufacturer or by the tissue mill manager in order to better un-derstand and evaluate the cylinder performances. The decrease ofthe heat transfer coefficient, that could occur due during theoperative life due to straw pipes jamming or syphon damaging,induces a strong penalization of the overall drying performanceand energy efficiency, since the heat transfer via the Yankee cyl-inder is generally more efficient than the air impingement one.Consequently, increasing the plant life the latter has to be usedmore intensively in order to assure the required water evaporation.
Successively, we investigated how to define the best values ofthe moisture content of the exhaust air at the outlet of the dryinghoods (streams 5 and 10 in Fig. 1). The moisture contents of thesetwo streams are very important from the operative point of view,because they are directly managed by the tissue plant manager inorder to control the paper machine performances. This can beachieved adopting a suitable control on the extraction fan (V3 inFig. 1) and on shutters that are generally located in the extractionstreams (streams 5 and 10 in Fig. 1). The results of this analysis(Fig. 5) showed that the effect of the moisture content of the wet-end exhaust gas on the energy consumption is lower. So, it is bet-ter to reduce the moisture content of the wet-end extraction inorder to increase the paper production with a lower increase of theenergy consumption.
Fig. 5. Energy and production performance of the tissue mill in function of themoisture content of the exhaust air of a duosystem configuration with parallelweteend e dryeend hoods (MCw: moisture content of the wet-end exhaust gas).
Fig. 4. Energy and production performance of the tissue mill in function of the overallheat transfer coefficient of the Yankee cylinder of a duosystem configuration withparallel weteend e dryeend hoods.
If the moisture content of the extraction air is higher, the massflow of the dry air is lower and, consequently, also the make-up airflow rate is lower. It is interesting to note that the paper productiondecreases when the moisture content of the extraction air streamsincreases, because the evaporation rate is lower using impingementair with highermoisture content, in accordancewith the Stefan law.Indeed, if the extraction air has higher moisture content, also theimpingement air is moister. It is important to note that it isimpossible to decrease the moisture content of the exhaust airstreams below a minimum threshold value because the mass flowsof the recirculation streams (streams 6 and 11 in Fig. 1) tend to zerowhen the moisture contents become low.
A third analysis we performed concerns the effect of theimpingement temperature on the paper mill performance. In thelast years, all manufactures of tissue drying systems increasedlargely the operative temperature of the impingement jets in orderto obtain larger sheet velocity and, consequently, the paper pro-duction as denoted in Fig. 6. This procedure leads to a marked in-crease in the energy consumption. Passing from 150 �C to 550 �C, sofrom conventional steam heat exchangers to sophisticated gas-firedburners, the specific energy consumption increases in the range10e30% even if the installation of heat recovery steam generatorson hood exhaust line can mitigate this energy increase. The in-crease of the impingement temperature in the wet-end hood isgenerally more effective than in the dry-end hood in terms of paperproduction growth and specific energy consumption decrease.
Finally, the effect of the impingement velocity on the energy andproduction performances has been analysed (Fig. 7). In order toincrease the production with the lower energy consumptiongrowth, it is more effective to change the impingement velocity ofthe wet-end side. In fact, in the dry-end hood, the heat exchange isless effective due to the lower moisture content of the tissue sheetand to the larger role of the sorption heat. In general, higher ve-locities assure higher evaporation rates and, consequently, largerpaper production. Using the same geometry of the hoods, thisimplies higher mass flow of the air jets and, consequently, the in-crease of the specific energy consumption.
In Table 3, considering for example a daily paper production of110 t/d, as in the reference case, we report a summary of thesimulated results reported in Figs. 5e7. Changing the operativeparameters, the specific energy consumption can vary from1685 kW h/t to 1610 kW h/t, with a percentage saving of about 4.5%,that corresponds to a large amount of energy for a middle sizepaper mill.
Fig. 6. Energy and production performance of the tissue mill in function of the tem-perature of the air impingements of a duosystem configuration with parallel weteende dryeend hoods (Tw: temperature of the wet-end air impingement).
Fig. 7. Energy and production performance of the tissue mill in function of the speedof the air impingements of a duosystem configuration with parallel weteend e dry-eend hoods (Vw: velocity of the wet-end air impingement).
Table 3Comparison between the results of the simulation model and the real data of an existin
MCw, g/kg MCd, g/kg Specific energy consumption, kWh/
300 380 1685500 250 1632
Tw, �C Td, �C Specific energy consumption, kWh/
350 550 1658550 350 1610
Vw, m/s Vd, m/s Specific energy consumption, kWh/
100 120 1637120 100 1626
Fig. 8. Monosystem configuration.
P. Di Marco et al. / Energy 114 (2016) 201e213 209
5. Performance comparison with the monosystemconfiguration
Since the reliability of the mathematical model described abovehas been demonstrated, it is applied to a different layout of thedrying system after some modifications that are listed in AppendixA. After that the energy performances have been evaluated with asimilar simulation activity described above. The aim of this analysisis to evaluate how the energy performances of the drying processare affected by the layout of the air system. So, we compare thislayout with the duosystem configuration.
The layout that has been taken into account is the monosystemconfiguration (Fig. 8), whose peculiarities with respect to the pre-vious configuration are: (i) only one burner is adopted; (ii) there isonly one air circuit; (iii) the hot air stream is divided into twostreams that are blown towards the tissue sheet within both hoods;(iv) the humid exhaust air from the wet-end hood is partiallyrecirculated to the dry exhaust air stream and partially extractedand conveyed to the atmosphere.
g tissue mill with duosystem configuration and parallel weteend e dryeend hoods.
t paper Percentage reduction of the specific energy consumption, %
e
3.1
t paper
e
2.9
t paper
e
0.7
As the characteristics of the wet-end and dry-end hoods areidentical, the following inputs for the hoods for the reference casehave been adopted:
(i) the air impingement temperature of the wet-end (dry-end)hood is equal to 450 �C,
(ii) the air impingement speed of the wet-end (dry-end) hood isequal to 110 m/s,
(iii) the absolute humidity of the exhaust air from the wet-endside is 500 g/kg,
(iv) the air excess for the burner is 25%.
The results of the reference case are reported in Table 4. Thehighermoisture content of the air jets due to the higher humidity ofthe extracted air in the dry-end hood implies lower paper pro-duction (the drying rate is lower due to the higher moisture con-tent) (by about 3.6%) and lower energy consumption (by about1.5%) in comparison with the duosystem configuration in accor-dance with the results reported in Fig. 5.
The energy and production performances in function of theoverall heat transfer coefficient of the Yankee cylinder, themoisturecontent of the exhaust air, the temperature and speed of the airimpingement have been evaluated and reported in the followingFigs. 9e12, respectively. The performance of the monosystemlayout depends on the operative parameters in a similar way to thatof the duosystem layoutwith parallel configuration. In particular, incomparison with the duosystem layout:
Table 4Results of the simulation model applied to an existing tissue mill with monosystem configuration.
Outputs
Daily production at the pope, t/day 106.0Overall mass flow of evaporated water, kg/h 6457.6Specific evaporation rate (referenced to the lateral surface of the Yankee cylinder), kg/m2 h 70.1Thermal power of the drying unit, kW 4977Steam mass flow of the Yankee cylinder, kg/h 4145.3Specific energy consumption, kWh/t paper 1586Specific energy consumption, kWh/t evaporated water 1085Sheet velocity on the Yankee cylinder, m/min 1753.3Sheet velocity at the pope, m/min 1461.1Air impingement mass flow at the wet-end hood, kg/s 7.27Air impingement mass flow at the dry-end hood, kg/s 7.27Mass flow of the make-up air, kg/s 1.42Mass flow of the exhaust air, kg/s 6.1Temperature of the exhaust air downstream the wet-end hood, �C 275Temperature of the exhaust air downstream the dry-end hood, �C 275Temperature of the exhaust air, �C 275
Fig. 9. Energy and production performance of the tissue mill with monosystemconfiguration in function of the overall heat transfer coefficient of the Yankee cylinder.
Fig. 10. Energy and production performance of the tissue mill with monosystemconfiguration in function of the moisture content of the exhaust air.
Fig. 11. Energy and production performance of the tissue mill with monosystemconfiguration in function of the temperature of the air impingements.
Fig. 12. Energy and production performance of the tissue mill with monosystemconfiguration in function of the speed of the air impingements.
P. Di Marco et al. / Energy 114 (2016) 201e213210
1. For the monosystem configuration, the influence of the heattransfer coefficient of the Yankee cylinder on the performance isvery similar (Fig. 9).
2. For the monosystem configuration, the influence of the mois-ture content of the exhaust air on the performance is larger(Fig. 10). It is important to note that the minimum allowablevalue of the moisture content is about 330 g/kg because lower
values imply that the recirculation mass flow (stream 5 of Fig. 8)becomes equal to zero due to the high mass flow of theextraction flow. Further reductions of the moisture contentwould imply that the exhaust air extraction could occur alsofrom the dry-end hood (the flow of the stream 5 of Fig. 8 wouldbe from the outlet of the dry-end hood to that of the wet-end
Fig. 13. Comparison between the duosystem and monosystem layout.
P. Di Marco et al. / Energy 114 (2016) 201e213 211
hood). This operative condition is not usually adopted due to thelow energy efficiency.
3. For the monosystem configuration the influence of theimpingement temperature is much higher than in the duosys-tem configuration (Fig. 11).
4. For the monosystem configuration the influence of theimpingement speed is much higher than in the duosystemconfiguration (Fig. 12).
Comparing the performances of both configurations that weanalysed, we can conclude that, using similar operative parameters,the monosystem configuration is characterized by lower energyconsumption and lower paper production. If the comparison isexecuted with the same daily paper production (see Fig. 13, wherethe results of all simulations are summarized in a single view), inthe duosystem layout, thanks to its larger number of controllableoperative parameters, it is generally possible to find a particularoperative setting which corresponds to a lower specific energyconsumption than in the monosystem. Finally, it is possible toassess that, if the daily paper production increases thanks to anappropriate modification of the thermodynamic characteristics ofthe air jets and of the extracted air, the specific energy consumptionof the monosystem configuration tends necessarily to increase.
6. Conclusions and future developments
This paper presents an original and exhaustive mathematicalmodel of the drying process in tissue paper production in order toassess its energy consumption and paper productivity as a functionof the most important geometrical data and operative parametersof the drying system.
The results of the simulation model differ not higher than 5%from the experimental data of an existing paper mill, assuring itsvalidity as effective tool for the assessment of the energy perfor-mances. Then, the model has been applied to two configurations ofdrying air systems in order to evaluate the dependence of the en-ergy performances on the most meaningful operative parameters.
Keeping the paper production of the reference case, in theduosystem configuration it is possible to reduce the specific energyconsumption by about 4.5% changing the operative parameters intheir allowable range. Considering the typical energy consumptionsof a middle size tissue mill, this value of energy saving correspondsto large amount of energy. The most interesting results with gen-eral validity for both layouts that have been considered are: (i)keeping the same paper production, the lowest energy consump-tions of a tissue mill can be obtained when (a) a Yankee cylinder
with higher heat transfer coefficient is used, (b) the moisturecontent in the exhaust air is high, (c) the jet temperature and speedare low; (ii) on the contrary, in order to maximize the paper pro-duction it is necessary to have (a) high efficient Yankee cylinder, (b)exhaust air with low moisture content and (c) air jets with hightemperature and speed.
Considering the same paper production, the plant layout withduosystem configuration is characterized in average by lower en-ergy consumptions with respect to the monosystem layout byabout 1%.
The present model could be improved removing some simpli-fications that have been adopted. In particular, the interaction ofadjacent air jets could be considered for configurations with verynarrow holes. Moreover, in some existing old paper machines, thegap between the Yankee cylinder and the hoods can largely varyalong the wrap angle and the transversal direction due to con-struction imperfections. This feature should be considered in orderto better estimate the heat and mass transfer coefficient in theimpingement process.
The model that has been here proposed can be effectivelyapplied after some modifications to other different layouts of dry-ing systems in order to find less energy-intensive configurations.For example, it may be used for the analysis of a new plant layoutthat is becoming common in the last years, characterized by a gasturbine whose exhaust gas replaces the gas fired burner, obtaininga combined heat and power configuration.
Appendix 1. Mass and energy balance of the drying air system
Using the references of the streams as reported in Figs. 1 and 8,the mass and energy balance of the drying air system can beexpressed in the following way:
- Duosystem configuration (Fig. 1) (the pedices w and d refer tothe wet-end and dry-end hoods, respectively)
Mass balance of the air for the wet-end hood
_m7 þ _minl w þ _mfuel w þ _mev w ¼ _m5 (A1)
Mass balance of the air for the dry-end hood
_m12 þ _minl d þ _mfuel d þ _mev d ¼ _m10 (A1bis)
Mass balance of the water for the wet-end hood
_m7X7
1þ X7þ _minl w
Xinl1þ Xinl
þ _mev w þ _mw fuel w ¼ _m5X5
1þ X5
(A2)
Mass balance of the water for the dry-end hood
_m12X12
1þ X12þ _minl d
Xinl1þ Xinl
þ _mev d þ _mw fuel d ¼ _m10X10
1þ X10
(A2bis)
Note that X5 and X10 are inputs of the model as required by theoperation of the tissue paper mill.
Mass balance of the burner for the air circuit of the wet-end hood
_m20 ¼ Rstoichð1þ ewÞ _mfuel w (A3)
Mass balance of the burner for the air circuit of the dry-end hood
_m24 ¼ Rstoichð1þ edÞ _mfuel d (A3bis)
Energy balance of the air to air heat recovery
P. Di Marco et al. / Energy 114 (2016) 201e213212
_m17ðh17 � h25Þ ¼ _m16ðh15 � h16Þ (A4)
where the streams 21, 15 and 18 exit the recuperator at the sametemperature, because the air flux is split at the outlet of therecuperator.
Thermal performance of the air to air heat recovery
_Q ¼ _m17ðh17 � h25Þ ¼ U LMTD SF (A5)
Energy balance of the fuel fired burner for the air circuit of the wet-end hood
_m9h9 þ _m20h20 þ _mfuel whfuel w þ LHV _mfuel w ¼ _m1h1 (A6)
Energy balance of the fuel fired burner for the air circuit of the dry-end hood
_m14h14 þ _m24h24 þ _mfuel dhfuel d þ LHV _mfuel d ¼ _m4h4(A6bis)
Energy balance of the mixer D
_m7h7 þ _m6h6 ¼ _m8h8 (A7)
Energy balance of the mixer F
_m11h11 þ _m12h12 ¼ _m13h13 (A7bis)
Energy balance of the mixer A
_m10h10 þ _m5h5 ¼ _m17h17 (A8)
Mass balance of the splitter B
_m15 ¼ _m12 þ _m7 (A9)
Mass balance of the splitter C
_m2 ¼ _m5 þ _m6 (A10)
Mass balance of the splitter E
_m3 ¼ _m10 þ _m11 (A11)
Mass balance of the mixer H
_m18 þ _m27 ¼ _m19 (A12)
Energy balance of the mixer H
_m18h18 þ _m27h27 ¼ _m19h19 (A13)
_m27 ¼ 0 if T20 � Tlim w (A14)
Mass balance of the mixer G
_m21 þ _m23 ¼ _m22 (A15)
Energy balance of the mixer G
_m21h21 þ _m23h23 ¼ _m22h22 (A17)
_m23 ¼ 0 if T24 � Tlim w (A18)
- Monosystem configuration (Fig. 8)
Mass balance of the air
_m12 þ _minl þ _mfuel þ _mev ¼ _m6 (A19)
Mass balance of the water
_m12X12
1þ X12þ _minl
Xinl1þ Xinl
þ _mev þ _mw fuel ¼ _m6X6
1þ X6(A20)
Note that X6 is an input of the model, because it is established bythe plant manager during the operation of the tissue paper mill.
Mass balance of the burner
_m16 ¼ Rstoichð1þ eÞ _mfuel (A21)
Rstoich evidently depends on the type of fuel and e is an inputparameter that is selected in order to assure the complete com-bustion of the fuel respecting the emission limits about thepollutant.
Energy balance of the air to air heat recovery
_m6ðh6 � h17Þ ¼ _m12ðh8 � h12Þ (A22)
Note that the streams 8 and 13 are split downstream therecuperator.
Thermal performance of the air to air heat recovery
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