Modeling and Simulation of Drying Cylinders in Paper Processes

Korean Chem. Eng. Res., Vol. 45, No., February, 007, pp. 7-4 os o o m ml Ç içii k 39-79 ne 7 (006 o 7p r, 006 o 3p }ˆ) Modeling and Simulation of Drying Cylinders in Paper Processes Eun Ho Lee, Ki-Young Kwak and Yeong-Koo Yeo Department of Chemical Engineering, Hanyang University, 7 Haengdang-dong, Seongdong-gu, Seoul 33-79, Korea (Received 7 November 006; accepted 3 December 006) k l p rp rv rl s e p p p l rp p p p. p p er qp nr p l m s rl e v p k p tn. v p kp ƒ d p lr e o p l r m nr p l e ep ˆ ppp r. e p r o m pn l v mp s rp kr p e lp r p m. h Abstract The purpose of the present study is to identify the drying cylinder model in paper plants and to analyze characteristics of process responses for changes in input variables. The model developed in this work is based on actual plant operation data where the steam pressure applied to the cylinder behaves as the major variable. It is found that heat transfer coefficients from the condensate to the canvas could be represented as empirical relations based on heat conductivities and operation data. The effectiveness of the cylinder model is demonstrated by the measured moisture contents and web temperature. Stability of the drying process is analyzed based on the transfer functions derived from the cylinder model. Key words: Paper Process, Drying Cylinder, Heat Transfer Coefficient, Simulation, Stability. rv rl s rp r rp rp s o l e p rp p p l q p ep p l m. rv rp s rl e p, v l, v v p, lr tn p. s rl s e v p k p q tn p p. Depoy[] s rl l e, v, p rp l ep p e mp Mori [] p p lr pr v p m m p l v pp p Iron [3] m. Karlsson [4]p v p m l v p p s e rl p rp l m. Karlsson [5]p v edšp o rn To whom correspondence should be addressed. E-mail: ykyeo@hanyang.ac.kr l s r t e l r p m. s e p l e v k p, e pp lr r rp r p ep pn l ˆ p p rp. kn s rp l pl v p m l m p p tn pq p p m p p tn. v p m l m p p tn pq v, e, n m,, p p. v kl p e m v p m l q m p v k e m mp ˆ p. l l r p pn l t e l p p lr m. p p p l e v p l p p p. s e p n m tp d p p v p m l m p tn pqp p. rv rl v s ~e tn r ˆl p p p bone-dry(ash)p l sn v l l 7

8 pp Ë mëlm p, v p v p m. kn r ˆ ˆ ep o p l m p ˆ r }k l rp nrl n r k rp l kr p Ž p m. l p t r p r š s e p p m l p. lr rl p s r v m pn l sr mp lr,, p rp rn l rp p o l ˆ l.. o om in Š s e rp s single-tierm double-tier p. s rl pre-dry l single-tierm double-tier s after-dry p double-tier sq. s o p Fig. ~4m p l p. Fig. p lp e -o-ƒ d p s o p p p, Fig. e m e pl op p p n ˆ p. Fig. 3p op ƒ dm r v k e p p p, Fig. 4 lp e -ƒ d-o p o p ˆ p. Fig. ~4l p m p single-tier e, Fig. 3. Drying configuration C. Fig. 4. Drying configuration D. Fig.. Drying configuration A. open-run(web + canvas), vaccum roll, open-run, doubletier e, free-run(web) p l p. e v tp lp p, e, v, ƒ d ~ e n r. lr p rp ep ˆ l pl rn r p p. ) pl p m p m t p tkp tp. ) pp lr l r p p p tk pr p tk v lp r. 3) p p pr ov. 4) bone-dry pr. 5) e l v p k p pr. r~ s r p p p lv l p v k p rl. l pl v p e m r n e k e v leˆ rp p m. s e p l pn lr Table, Table Table 3l p m. lr ~ H = f(l, V )p a ˆ rr tlv p r [4, 5]. Table l t lvv kp H, H, H 6 p nr p Š p p rep o l pn m. H = 685 0 6 + ----- L 0 3 76 + 0.675 ( V 60).79 + 0.0486 L 0 3 ( V60 ) 3.39 Fig.. Drying configuration B(free-run). o45 o 007 k / (486 / ) ()

rv r s e p 9 Table Heat transfer coefficients of configuration A Description Thick [mm] Thermal conductivity [Kcal/m/h/ o C] Heat transfer coefficient [Kcal/m /sec/ o C] (web~air) Specific heat capacity [Kcal/kg/ o C] Density [kg/m 3 ] H 6 Canvas.5 0.045 0.36 0.8 0 3 H 5 = 0.0678 Web 0. 0.3.3 0 3 H 4 = 0.3380 Cylinder 5/ 37. 0.3 7.8 0 3 = 0.867 Cylinder 5/ 37. 0.3 7.8 0 3 H Condensate 3.0 0 3 H Table Heat transfer coefficients of configuration C Description Thick [mm] Thermal conductivity [Kcal/m/h/ o C] Heat transfer coefficient [Kcal/m /sec/ o C] Specific heat capacity [Kcal/kg/ o C] Density [kg/m 3 ] H 9 Cylinder 5/ 37. 0.3 7.8 0 3 = 0.867 Cylinder 5/ 37. 0.3 7.8 0 3 H Condensate 3.0 0 3 H Table 3 Heat transfer coefficients of configuration D Description Thick [mm] Thermal conductivity [Kcal/m/h/ o C] Heat transfer coefficient [Kcal/m /sec/ o C] Specific heat capacity [Kcal/kg/ o C] Density [kg/m 3 ] Web 0. 0.3 0.3 0 3 H 5 = 0.0678 Canvas.5 0.045 0.36 0.8 0 3 H 8 = 0.7 vacuum 5 37. 0.3 7.8 0 3 / H = ------- --- + ----- H = 0.000074 V 0.78 () (3) ) p = H Ts T T T L D C ( ( ) H (5) H 6 = ----- + ----- ----- + ----- H 5 H 4 3. o m s e l l vp r p p, e, v ƒ d l p l v. p l p l v v p (Fig. ~4 s). (4) ) e 3 = H T T T L ---- D C ( ( ) = T L ---- D C ( ( ) H 4 (6) (7) Korean Chem. Eng. Res., Vol. 45, No., February, 007

0 pp Ë mëlm 3) v 4 = --- m T 6 --- 0.3.366 0.+ 000 00 [( H 4 ( T 3 ) H 5 ( T 5 )) m ev H ev ] (8) H ev = h vap + h s h vap = 505.3747( T r ) 0.354 + 69.658 T r T T r ---- 4 = = ------- 373.95 T c ϕ h s R -- ϕ.0585 = 0.0085 T 6 ( ) 0.456 (9) (0) () () Ms( y+ y) = Ms y ( ) dms( y) -- g ------- m ev = = ------- Bw m Stefan e (4)p m ev ------- A β = g ------- t Bw β P tot P ----- total P va R v T ln - β P total P vpo R v α a p = ---- ρ a c a Le 3 m ev ------- A α = ---- ρ a c a Le 3 ---- P va T ( ) () () (3) (4) P tot P ---- tot P va R v T ln ----- P α C total P va P tot P ln - vpo P total P vpo (5) 0.354 H ev = 505.3747 ------- + 69.658 ------- 373.95 373.95 0.465 P va = 097 0 5.4 690 ----- T aw + 30 +0.04 R --- + 73.5.0585 T 6 ( ) (3) C = 7.03 0 4 kg water o C Ws (6) 4) ƒ d = 097 0 690 5.4 -- + 30 ϕ (7) 5 = H 5 T 5 T 5 T a L 3 D 3 C 3 ( ( ) H 6 (4) m ev r pi 3 360 - w C 486 log P tot P = va ----- 00 P tot (8) 5) e : m r v v r v k o(fig. 3) 3 = T L ---- D C 6) v : (Fig. 4) 7 ( ( ) H 9 = T 7 T 5 L D C ( ( )) (5) (6) v p p v kp p p v p m m p ˆ p. = P sat ( T) R, M s ( ) (7) l d (R) p p rep e p [5]. ϕ e 47.58 T 6 =.877.0585 + 0.0085 T 6 ( ) p p p sep llv. = 097 0 5.4 690 --- + 30 ϕ (8) (9) 6 = 00 m ev 000 m (9) p l o ep p s o A(Fig. ), B(Fig. ), C(Fig. 3), D(Fig. 4) s l s e p mp, p e l p m kk p o p qs m. lr H 5m p r v p m s l p r v kl m ˆ e p p lp pl. p e l tp v p m m p p p o Cl p rp s ol lp p p, e, H 9p r p lp p. p e m v p r e vrl p k r ˆl p e m p m ov rp ˆp p. ol lp v p m,, p, e p p pn l A, B, C, Dp qs p p lv s rp m. p p Fig. 5m p nk p. o ep eˆ p Laplace p l r pp ep ˆ ˆ p. p 30Í l d m p v, p 30Í p p nl ~ ϕ =p. Bone-dry r l pr v p r p p p p t m. v v p ep lp p. ( Ms( y+ y) Ms( y) )Bw L y = g L y t o45 o 007 k (0) Fig. 5. Input and output variables in drying process.

rv r s e p Table 4 The combination of drying configurations Description Pre-dryer After-dryer Pre-dryer After-dryer Pre-dryer After-dryer Cylinder A+C A+C A A A+C A+C Ratio Web A A A+B+D+B A+B A+B A+B 4. y q r p lr v p m l m p lr H 5 pre-dryer afterdryerp l p m p pn l sr l pn mp, er r m m l s p sr m. p pn pre-dryerm after-dryer p 5Í, 3Í p. p m e /n p m rp r ˆp n e p p v e p n m orl p m l eq r l rp m s }k l. p e m p p ln p 0. t m. e p r l (, p )p m p pr m. Table 4l p o p s l l Fig. 6l Fig. vl ˆ l. Fig. 6 Fig. 7p predryerm after-dryerl p s e l vrp p k vrl p op m ˆ p. p p e m v p r p v p m m p e v r v k p e v l v vrl e r vr v l l p p. Fig. 6p pre-dryer 3 w s e p m, Fig. 7p after-dryer 47 w s e p m e p. Fig. 8 Fig. 9 v p m, Fig. 0 Fig. p e m v p m el ˆ p. Fig. 8 Fig. 9 e m r vrl eq v p open-run free-run v p kp m pre-dryer p n v vp v p m v, e v r Fig. 6. Drying section of cylinder contacting with web (cylinder no.3). Fig. 7. Drying section of the cylinder contacting with web (cylinder no.47). p m ˆ p. Fig. 0 Fig. p e m v p r vrl eq l e p kp, v p open-run free-run v el p. l ratio e n l webp e r p pp p. Fig. 6 Fig. 7p e kp p tp Fig. 8 Fig. 9 v p e m r l p e l r vp p tp l ratio r mp, Fig. 0 Fig. p e p m v p p (Vaccum roll pr v) tp ratio ˆ l. pre-dryl after-dryl p v p m p p k p. p p lr p rnp v k n m l p v el m p p. ~rp pre-dryer v p freewater p v bond-water. After-dryer v p bond-water sizingl k l rp pre-dryer v after-dryer v p lr p pp k p. v dryer r l p lr r n r l s l sr tl l after-dryerl p lr r p. v k m p d m tlr p l after-dryer v p m p ˆ p. kl lp s e p ˆ ˆ p. pp ˆ el Am B ep eˆ ll v p. Korean Chem. Eng. Res., Vol. 45, No., February, 007

pp Ë mëlm Fig. 8. Drying section of the cylinder and vacuum contacting with web (cylinder and vacuum roll no.3). Fig.. The drying cylinder contacting with web (cylinder no.47). X = AX + BU Y= CX+ DU Y = GU (30) T X = Y = T T 3, U = U U T 5 U 3 T 6 Fig. 9. Drying section of cylinder contacting with web (cylinder no.47). T G G G 3 T T 3 T 5 T 6 = G G G 3 G 3 G 3 G 33 G 4 G 4 G 43 G 5 G 5 G 53 G 6 G 6 G 63 U U U 3 (3) Fig. 0. The drying cylinder contacting with web (cylinder no.3). o45 o 007 k r G ij l ˆ l. er rl D 0p, C p p ˆ l t p. p p l l m p t p v kk o l Fig. l p p Ul p l p p p k. kn ol lp s rp l kr l Ž l k. Fig. 3l k p m p pole p p p kr rpp k p. G p n p zero p p kp p v. Fig. 4 e rp p, e e n p l m er nr q l p. lp p er s rp q ˆ ppp k p. p vs ~e pr s l p (,, v k)p l (v p m )p p pp, er rp nrl r l r

rv r s e p 3 ˆl p e p m lp p. 5. Fig.. Step responses (steam: 00 o C, speed:,000 m/min, BW: 50 g/m ). rv r s e p p o l k s o p k e p m. e p v p, e q~l p lr re l p llv p pn mp v k p pr n p p s r k e p p m p r k. pvp s er v p m pn l v mp lr sr mp, l bone-dry pr r l v p r m. e p m v p m m l qn m. v kl p m m p p p er e p m m l v k e m mp Žk l k. s rp m er nr q l lp p er s rp q ˆ ppp k pl. kn s o l l p m kp o r l kr p p m. k Fig. 3. Stability of the drying process(ë: zero, Ë, x: pole). Fig. 4. Simulation of web temperature and moisture content in the dryer process(pre-dryer, after-dryer). A : Evaporation area [m ] Bw : Basis weight [kg/m ] c a : Heat capacity of air [kcal/kg o C] C : Heat capacity of condensate [kcal/kg o C] C : Heat capacity of cylinder [kcal/kg o C] C 3 : Heat capacity of canvas [kcal/kg o C] D : Density of condensate ] [kg/m3 D : Density of cylinder [kg/m 3 ] D 3 : Density of canvas [kg/m 3 ] g : Evaporation rate [kg/m ] H : Heat transfer coefficient between condensate interface and cylinder [kcal/m sec o C] H : Heat transfer coefficient between condensate and cylinder interface [kcal/m sec o C] : Heat transfer coefficient between cylinder and cylinder interface [kcal/m sec o C] H 4 : Heat transfer coefficient between cylinder and web interface [kcal/m sec o C] H 5 : Heat transfer coefficient between web and canvas interface [kcal/m sec o C] H 6 : Heat transfer coefficient between canvas and air [kcal/m sec o C] : Heat transfer coefficient between web and air [kcal/m sec o C] H 9 : Heat transfer coefficient between cylinder and air [kcal/m sec o C] L : Thickness of condensate [m] L : Thickness of cylinder [m] L 3 : Thickness of canvas [m] Le : Lewis number m : Basis weight [kg/m ] Korean Chem. Eng. Res., Vol. 45, No., February, 007

4 pp Ë mëlm m ev Ms r R v P va P tot : Evaporation rate [kg/m sec] : Moisture content [kg/kg] : Radius of cylinder [m] : Gas constant of water vapor [46.5 J/Kgwater/K] : Vapor pressure [bar] : Total pressure [bar] : Partial vapor pressure at the surface of web [bar] T : Temperature of condensate [ o C] T : Temperature of the st cylinder interface [ o C] T 3 : Temperature of the nd cylinder interface [ o C] : Temperature of pulp [ o C] T 5 : Temperature of web [ o C] T 6 : Temperature of web interface [ o C] T 7 : Temperature of vacuum cylinder [ o C] T aw : Temperature of wet bulb [ o C] Ts : Temperature of steam [ o C] V : Operation speed [m/min] w : Wih of web [m] m m α H ev : Heat transfer coefficient between web and air [kcal/m sec] : Heat of evaporation [kcal/kg] h s : Heat of absorption [kcal/kg] h vap : Latent heat [kcal/kg] ρ a : Density of air [kg/m 3 ] : n G ij (s) y. Depoy, J. A., Analog Computer Simulation of Paper Drying A Workable Model, Pulp & Paper M. Canada., 73(), 67-75(97).. Mori, Y., Shimizu, H., Takao, K., Ikari, T. and Nambu, T., Development of A New Automatic Grade Change System for Paper Machine, Proceedings from Control Systems 000, Victoria. B. C., Canada, 3(000). 3. Berrada, M., Tarasiewicz, S., Elkadiri, M. E. and Radziszewski, P. H., A State Model for the Drying Paper in the Paper Product Industry, IEEE Trans. Indust. Electronics., 44(3), 579-586(997). 4. Karlsson, M., Papermaking Science and Technology Book 9, Fapet Oy., 55(000). 5. Karlsson, M., Stenstrom, S. and Baggerud, E., Dynamic Simulation of the Steam Supply System for a Multi-cylinder Dryer, Nordic Pulp and Paper Res. J., 7(), 66-74(00). o45 o 007 k