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Vol.50, n. 2 : pp.339-347, March 2007 ISSN 1516-8913 Printed in Brazil BRAZILIAN ARCHIVES OF BIOLOGY AND TECHNOLOGY AN INTERNATIONAL JOURNAL

Effect of Water Losses by Evaporation and Chemical Reaction in an Industrial Slaker Reactor

Ricardo Andreola 1, Osvaldo Vieira 2, Onélia Aparecida Andreo dos Santos 1 and Luiz Mario de Matos Jorge 1* 1Departamento de Engenharia Química; Universidade Estadual de Maringá; Av. Colombo, 5790 - Bloco D90; [email protected], 87020-900; Maringá - PR - Brasil. 2Klabin Paraná Papéis; Fazenda Monte Alegre; Bairro Harmonia; 84275-000; Telêmaco Borba - PR - Brasil

ABSTRACT

A dynamic model of the slaker reactor was developed and validated for Klabin Paraná Papéis causticizing system, responsable for white liquor generation used by the plant. The model considered water losses by evaporation and chemical reaction. The model showed a good agreement with the industrial plant measures of active alkali, total titratable alkali and temperature, without the need of adjustment of any parameter. The simulated results showed that the water consumption by the slaking reaction and evaporation exerted significant influence on the volumetric flow rate of limed liquor, which imposed a decrease of 4.6% in the amount of water in reactor outlet.

Key words: Slaker reactor, modeling and simulation, white liquor

INTRODUCTION Ca(OH) 2(s) . In turn, green liquor is a liquid solution with a large quantity of sodium carbonate that The causticizing reactor system from Klabin reacts with calcium hydroxide producing sodium Paraná Papéis produce white liquor used in hydroxide and calcium carbonate, according to the cellulose digesters. This system is composed by causticizing reaction: Na 2CO 3(aq) + Ca(OH) 2(s) → 2 one slaker reactor followed by nine causticizing NaOH (aq) + CaCO 3(s) . This reaction is slightly reactors in sequence. According to Fig. 1, green exothermic. liquor and lime are continuously introduced in the At the outlet of the slaker reactor, there are two stirred slaker reactor. The lime from lime kiln is distinct streams: limed liquor and grits. The limed mainly composed of a large quantity of calcium liquor is basically formed by a sodium hydroxide oxide and a small amount of inert solids. solution with calcium carbonate, calcium The calcium oxide instantaneously reacts with hydroxide, inert solids and eventually unreacted water from green liquor producing calcium calcium oxide in suspension. hydroxide, according to a highly exothermic reaction, called slaking reaction: CaO (s) + H 2O(l)

* Author for correspondence

Brazilian Archives of Biology and Technology 340 Andreola, R. et al.

Lime Green liquor

Grits

Stirrer Limed liquor

Figure 1 - Scheme of slaker reactor

In the sequence, the flow is fed in causticizing dm m q  PM   PM  reactors by gravity, while the grits are removed e = w − e −V  e r +V  e r dt e 0, V  PM  1  PM  2 from the reactor by a screw.  Na 2O   d  The main objective of this article was evaluate the (5) effect of water losses by evaporation and chemical dm m q  PM  reaction in Klabin Paraná Papéis slaking reactor. f = w − f +V  f r (6) dt f 0, V  PM  1  Na 2O  dm m q g = − g MATERIAL AND METHODS wg 0, (7) dt V

Mathematical Modeling Where: a = Na CO , b = NaOH, c = Na S, d = The mathematical model was developed by 2 3 2 CaO, e = Ca(OH) , f = CaCO , g = inert solids. Andreola (2001) from mass balances on each 2 3 component, Equations (1) to (7), and from energy The model predicted the actual concentration of balance, Equation (9), over the slaker reactor, considering perfect mixture and constant volume. each soluble component (Ci*, i= a, b, c); the mass The hypothesis of perfect mixture was based on of insoluble solids inside the reactor (m j, j= d, e, f, the research developed by Hypponen and Luuko g) and the reactor’s temperature (T). Volumetric (1984) that showed the same value of residence flow rate (q) and mass flow rates (w j) must be time distribution for solids and liquid in a known. For model purposes, Causticising (r 2) and causticizing reactor system. The assumption of Slaking (r 1) kinetics were corrected by molecular constant volume (V) was based on the fact that the weights (PM) ratios. volume of slaker reactor was constant. The salker The actual concentration of a generic component i reactor has an outlet for the liquor at the top of (C i) was determined from its apparent reactor, according to Fig. 1, that keeps the level of concentration (C i*), using Equation (8). This liquid constant. procedure was necessary because the apparent * concentration represented the mass of a specific dC 1 ∗  PM  a = ()q C − qC − r  a  (1) component dissolved per unit volume of reactor. dt V 0 a 0, a 1 PM   Na 2O  However, part of this volume was occupied by ∗ insoluble solids: CaCO 3, CaO, Ca(OH) 2 and inert dC 1 ∗  PM  b = ()q C − qC + 2r  b  (2) solids. Each volume of the solid compounds 0 b 0, b 1   dt V PM Na O = ρ  2  (V j m j / j , j = d, e, f, g ) must be subtracted ∗ dC 1 ∗ from the total volume (V) to obtain the effective c = ()q C − qC (3) dt V 0 c 0, c volume (Vr) and the real concentration of each dm m q component, Equation 8. d = w − d −Vr (4) dt d 0, V 2 = ∗  V  Ci Ci .  (8) Vr 

Brazilian Archives of Biology and Technology Effect of Water Losses by Evaporation and Chemical Reaction in an Industrial Slaker Reactor 341

 m m m m  While the reactor temperature (T) was lower than Where: Vr = V −  f + e + d + g   ρ ρ ρ ρ  the boiling temperature of the reacting mixture f e d g   (T eb ), water evaporation did not occur, therefore, qevap = 0. However, when the reactor temperature The operational reactor temperature was very close reached T eb, water evaporation occured at constant to the boiling temperature of the reacting mixture. temperature and the rate of evaporation could be Both reactions were exothermic and the reacting instantaneously evaluated from the solution of the mixture temperature increased until it reached the following equation: boiling point. Consequently, there was energy loss C1 - q evap C2 = 0. by evaporation. To take this energy loss into As mentioned previously, the limed liquor was account, this loss was included in Equation (9), composed of an aqueous solution of sodium admitting that the enthalpy and boiling hydroxide, calcium carbonate, calcium hydroxide, temperature (T eb ) of the solution were identical to inert solids and, eventually, calcium oxide that of pure water ( ∆Hevap ) at the same pressure, unreacted. Consequently, the volumetric flow rate because the reacting mixture was composed of a of limed liquor (q) was composed of five distinct diluted solution. Insoluble solids were dispersed in terms: water (q H2O ); calcium carbonate (q CaCO3 ); solution and jointly form a slurry that had distinct calcium hydroxide (q Ca(OH)2 ); inert solids (q inerts ) density ( ρslurry ) and heat capacity (Cp slurry ). The and calcium oxide (q CaO ), according to Equation reactor’s liquid phase was called liquor. Liquid (10).

(∆Hliquor ) and solid ( ∆Hsolids ) enthalpy changes were evaluated from heat capacities of solids (Cp ) q = q + q + q + q + q (10) j H 2O CaCO 3 Ca (OH 2) CaO inerts and dissolved compounds (Cp j). Where: dT = − C q C (9)  m f   m  dt 1 evap 2 q = q  ; q = q e  ; CaCO 3  ρ  Ca (OH 2)  ρ  Where: V f  V e  (∆ + ∆ + + − ) H liquor H solids Q1 Q2 Q3  m  =  md  g C1 q = q  ; q = q  . Vρ Cp CaO  ρ  inerts  ρ  slurry slurry V d  V g  = −∆ = −∆ = − Q1 ( H r1)Vr 1; Q2 ( H r 2 )Vr 2 ; Q3 UA (T Tamb ) ∆ = * + * + * ∆ Hliquor Cp [( Ca 0, Cb 0, Cb 0, )q 1 The volumetric water flow rate (q H2O ) could be GL 0 ; obtained from water mass balance, admitting − (C* + C* + C*)q∆ ]; a b c 2 unsteady-state behavior, where the consumption of

 md 0, q   m q   water was given by the slaking reaction (q r1 ) and ∆ =  0 ∆ −  d ∆ + H solids Cp d   1 2  by evaporation (q evap ), according to Equation (11).  V   V   q = q − q − q (11)  m q   m q   H 2O 0 r2 evap Cp  e 0, 0 ∆ −  e ∆ + e   1 2   PM  V V r V H 2O      Where: q = 2   r2 ρ  PM   m q   m q   H 2O  Na 2O   f 0, 0 ∆ −  f ∆ + Cp f  1 2   V   V       The volumetric flow rate of limed liquor, q, could be obtained from Equations (10) and (11),  mg 0, q0   mg q    ∆ −  ∆ ; Cp g   1   2  according to Equation (12).  V   V   ∆ = − ∆ = − ; V 1 (Tin Tref ); 2 (T Tref ) =  ( − − ) q   q qr2 q (12) ρ ∆H Vr  0 evap C = H 2O evap . 2 Vρ Cp slurry slurry The reaction rate equations for the slaking reaction

(r 2), CaO (s) + H 2O(l) → Ca(OH) 2(s) , and causticizing reaction (r 1), Na 2CO 3(aq) + Ca(OH) 2(s) 2NaOH (aq) +

Brazilian Archives of Biology and Technology 342 Andreola, R. et al.

CaCO , employed in this work were those 3(s) 1 1 ew 1 employed by Swanda (1994), given by Equations = + + (15) UA h A A k h A (13) and (14). Both reactions were exotheric and it ext lm w int took account in the model by heats of slaking Wall thermal conductivity (k w) was taken from the (∆Hr2 ) and causticizing ( ∆Hr1 ) reactions. literature, wall thickness (e w) and logarithmic  m  averaged area (A lm ) from design specifications. r = k  d  (13) The internal heat-transfer coefficient by 2 2 V   convection (h int ) was obtained from Equation (16),  m  presented by Lydersen (1979), using physical = e { − 2 } r1 M 1Ca,o   k1Ca M 1 k '1 [EA ] (14) properties of pure water because the reacting V   mixture was composed of a diluted solution. = − ∆ − k1 k 0,1 exp[ .0 095 3 27190 / RT ] ; ρ 2 3/2 k = k exp[ − .0 0604 ∆ − 23004 14. / RT ] ; h D  nD agitator  3/1 '1 0,2 3 int = C  ()Pr (16) = + + k  µ  TTA Ca M 1 Cb M 2 Cc M 3 ;   = + where Pr is the fluid Prandtl number; D is the EA Cb M 2 5,0 Cc M 3 ; reactor inner diameter; D is the stirrer ∆ = TTA −112 33. ; stirrer 3 diameter; ρ, µ, k are density, viscosity and PM Na O PM Na O PM Na O conductivity of the fluid and n is the stirrer M = 2 ; M = 2 ; M = 2 1 PM 2 PM 3 PM rotation in rps. a b c Heat dissipation to ambient occured by free

convection from reactor walls to the surrounding Parameters Evaluation air. Hence, the external heat transfer coefficient The dynamic model had one thermal parameter U, (h ) was obtained from Equation (17), presented and three kinetic parameters: k , k e k . In this ext 2 1,0 2,0 by Kreith (1973), which took into account work, the overall heat transfer coefficient U was Grashoff number (Gr) and Prandtl number. obtained from equations (15) to (17) and the kinetic parameters used were similar to those h D given by Swanda (1994). ext = 13.0 ()Gr Pr 3/1 (17) As the slaker reactor was not insulated and the k temperature of the reacting mixture was greater Heat transfer coefficients were calculated from than the ambient temperature, heat flux occured Equations (15), (16) and (17). External heat from the reacting mixture to the environment. This transfer coefficient is h = 6.28 J/(m 2 o C s) and, heat loss was governed by an overall heat transfer ext h =1.95 10 5 J/(m 2 o C s). Then, the three thermal coefficient, U, that represented an equivalent int resistances related to the process were calculated: thermal resistance (R = 1/UA), composed by eq R = 4.89 10 -6 o C s/J; R = 2.31 10 -5 o C s/J and association of three distinct thermal resistances, on int W R = 2.53 10 -3 o C s/J, indicating that the heat the reaction mixture (R = 1/h A); on the wall of ext int int transfer between the reactor walls and the ambient reactor (R ) and externally (R = 1/h A), as w ext ext air was the limiting step (98.9% of R ). Thus, R Equation (15). eq eq ≈ R and UA = 394.38 J/( oC s). The values of the ext thermal and kinetics parameters used in simulations are shown in Table 1.

Table 1 - Parameters of the model UA 394.38 J/( °C s) -3 -1 k2 5.55 10 s -2 3 3 -1 k1,0 6.18 10 (m /kg Na2O ) (m /kg Ca(OH)2 ) s -5 3 2 3 -1 k2,0 2.41 10 (m /kg Na2O ) (m /kg Ca(OH)2 ) s

Brazilian Archives of Biology and Technology Effect of Water Losses by Evaporation and Chemical Reaction in an Industrial Slaker Reactor 343

RESULTS AND DISCUSSION state conditions, without the need of further parameter adjustment. The mathematical model was composed of seven The concentrations of NaOH, Na 2CO 3, Na 2S and ordinary differential equations, Equations (1) to mass of CaO and CaCO 3 reached steady-state in (7), and Equation (9), two kinetic equations for approximately 15 minutes, except mass of Slaking and Causticizing reactions, Equations (13) Ca(OH) 2 that took about 40 minutes, according to and (14) and, additionally, Equation (12) to Fig 3, 4 and 5. The concentration of Na 2CO 3 and calculate the volumetric flow rate of limed liquor the mass of CaO showed a significant decrease in the exit of reactor. This model was numerically initially, tending to constant values of 50.62 3 solved by SDRIV2 subroutine available in kg Na2CO3 /m and 379.84 kg of CaO. While the Kahaner et al (1989), with initial conditions concentration of Na 2CO 3 and mass of CaO presented in Table 2. The reactor simulation, on decreased in the system, the concentration of the first instants of simulation, was not real; it was NaOH and mass of CaCO 3 naturally increased in a hypothetical situation that resulted in a real the same proportion, because they were products condition of operation in steady-state conditions. of the causticizing reaction, tending to values of The operational conditions and reactor dimensions 85.54 kg/m 3 and 3772.1 kg, respectively, in used in model simulations, are shown in Table 3. steady-state conditions (Figs. 3 and 4). Contrary to According to Figs. 2, 6 and 7, the dynamic model the behaviour mentioned above, the Na 2S did not satisfactorily described the steady-state behaviour react, and its concentration was practically of the industrial slaker reactor, with respect to the constant at 31.40 kg/m 3 during the entire temperature, active alkali (AA) and total titratable simulation. alkali (TTA), measured at exit of reactor in steady-

Table 2 - Model initial conditions 3 Ca 145.30 kg/m 3 Cb 7.69 kg/m 3 Cc 29.79 kg/m

md 2639.5 kg

me 0.0 kg

mf 0.0 kg

mg 342.3 kg T 88.0 °C

Table 3 - Dimensions of Slaker reactor and operation conditions Total volume 41.60 m 3 Internal diameter of reactor 4.80 m Height of reactor 3.19 m Agitator diameter 1.75 m Agitation speed 0.93 rps Heat transfer area 62.83 m 2 Green liquor flow rate 3.89 10 -2 m3/s Green liquor temperature 88.0 ºC Lime addition rate 2.79 kg/s Lime temperature 300.0 ºC Lime availability 88.52 % Ambient temperature 20.0 ºC

Brazilian Archives of Biology and Technology 344 Andreola, R. et al.

105

100

95 T (ºC)T 90 model experimental 85 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 2 - Temperature as a function of time

) 160 3 3 120 NaOH 80 Na 2CO 3 40 Na 2S Concentration(kg/m 0 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 3 - Concentration as a function of time.

While the mass of inert solids in the reactor stayed in 91.15 kg/m 3 in the first 15 minutes (Fig. 6), practically unchanged along the time, and was while the total titratable alkali (TTA) stayed 3 equal to 337 kg, the mass of Ca(OH) 2 grew practically constant (120.78 kg/m in steady-state quickly initially, reaching a maximum of 300 kg condition) for the simulated period (Fig. 7). This and decreasing slowly soon after reaching the behaviour was expected since for each molecule of value of 149.69 kg at steady-state (Fig. 5). This consumed Na 2CO 3, two molecules of NaOH were behaviour revealed that initially the rate of formed, consequently there was a compensation generation of Ca(OH) 2 by the Slaking reaction was between the mass of Na 2O that was generated and higher than the rate of consumption of this the one that was consumed in the forms of NaOH component by the Causticizing reaction; however, or Na 2CO 3. this was reversed over time. At the first instant of simulation, the temperature The active alkali (AA) presented a fast growth in of the reactor quickly increased because of the the first minutes, due to the increased development of the strongly exothermic slaking concentration of NaOH in the reactor, and it reaction, taking around 3.5 minutes to reach the reached the concentration of steady-state condition boiling temperature of the reacting mixture, 100

Brazilian Archives of Biology and Technology Effect of Water Losses by Evaporation and Chemical Reaction in an Industrial Slaker Reactor 345

o C, and stayed constant until the end of the carbonate (q CaCO3 ) quickly increased and reached simulated period (Fig. 2). the maximum value of 2.12 10 -3 m 3/s, in the first Although the volumetric flow rate of limed liquor twelve minutes (Fig. 8). Simultaneously, the in the exit of the reactor (q) was composed of five volumetric flow rate of water (q H2O ) also reached -2 3 different terms: q CaCO3 , q H2O , q Ca(OH)2 , q CaO and the maximum value of 3.71 10 m /s, being 4.6% -2 3 qinerts , only the terms corresponding to the water smaller than the feed (3.89 10 m /s). However, and to the calcium carbonate, exerted significant qH2O suffered great oscillation in the first instants influence on this flow, corresponding to 94.2 and due to the high consumption of water by the 5.4% of the total, respectively. Because of that the slaking reaction (q r2 ) and by the evaporation behaviour of q was determined by the term (q evap ), and it reached steady-state after 210 corresponding to the water volumetric flow rate seconds (Fig. 9). Both, q evap and q r1 showed -3 -3 3 (q H2O ). On the other hand, when the exit maximum values of 2.78x10 and 3.45 10 m /s, volumetric flow rate, q, was compared to the respectively in the first 210 seconds, and decreased feeding volumetric flow rate, q 0, a small difference slowly until they reached constant values of between them was observed at steadystate: 1.3% in 1.15x10 -3 and 6.42x10 -4 m 3/s, respectively after relation to q 0 (Fig. 8). 900 seconds. Owing to the development of the causticizing reaction, the volumetric flow rate of calcium

5000 4000 CaCO 3000 3 2000 Mass (kg) 1000 CaO 0 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 4 - Mass of CaO (m d) and CaCO 3 (m f) as a function of time.

400

300 Inerts

200 Ca(OH) 2

Mass (kg) 100

0 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 5 - Mass of Ca(OH) 2 (m e) e inert solids (m g) as a function of time.

Brazilian Archives of Biology and Technology 346 Andreola, R. et al.

140 120 )

3 100 80 60

AA (kg/m 40 model 20 experimental 0 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 6 - Active alkali (AA) as a function of time.

140 120 ) 3 100 80 60 40 model TTA (kg/m 20 experimental 0 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 7 - Total titratable alkali (TTA) as a function of time.

0.05 0.04 /s) 3

0.03 qH2O qo q 0.02 qCaCO3 qCa(OH)2 qCaO qinerts

Flow rate (m 0.01 0 0 800 1600 2400 3200 4000 4800 Time (s)

Figure 8 - Volumetric flow rates as a function of time.

Brazilian Archives of Biology and Technology Effect of Water Losses by Evaporation and Chemical Reaction in an Industrial Slaker Reactor 347

0.05

/s) 0.04 3

0.03 qH2O qo 0.02 qr2 qevap

Flow rate (m 0.01 0 0 800 1600 2400 3200 4000 4800 Time (s)

= − − Figure 9 - Volumetric flow rate of water as a function of time, ( q H 2O q0 qr2 qevap )

ACKNOWLEDGEMENTS

The authors thank the State University of REFERENCES Maringá / DEQ and Klabin Paraná Papéis - Telêmaco Borba - PR for the technical and Andreola, R. (2001), Modeling, Simulation and financial support. Analysis of Klabin Paraná Papéis Causticizing Reactor System. M.S. Thesis (in Portuguese), State University of Maringá, Maringá, Brazil. Hypponen, O. and Luuko A. (1984), The residence RESUMO time distributions of liquor and lime mud flows in the recausticizing process. Tappi Journal , 67(7) , Foi desenvolvido e testado um modelo dinâmico 46-48. do reator de apagamento do sistema de Kreith, F. (1973) , Principles of Heat Transfer . Intext caustificação da Klabin Paraná Papéis, Press, New York. responsável pela geração do licor branco Kahaner, D. Moler, C. Nash, S. (1989), Numerical utilizado na planta. O modelo contempla perdas methods and software. Prentice Hall Series in de água por evaporação e por reação química e Computational Mathematics, New Jersey. apresentou boa concordância com dados Lydersen, L. A. (1979), Fluid flow and heat transfer. industriais de álcali ativo, álcali total titulável e John Wiley and Sons, New York. Swanda, A.P.(1994), Process modeling and control temperatura, sem a necessidade de ajuste de system evaluation for the pulp and paper nenhum parâmetro. Os resultados obtidos a recausticizing process. M.S. Thesis, University of partir de simulações revelam que o consumo de California, USA. água pela reação de apagamento, bem como pela evaporação, exercem uma influência significativa sobre a vazão volumétrica na saída Received: May 05, 2005; do reator, impondo uma diminuição de 4,6% Revised: March 08, 2006; sobre o teor de água na corrente de saída do Accepted: October 18, 2006. reator em relação à alimentação.

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