Role of Holding Tank in Lime and Limestone Slurry Sulfur Dioxide Scrubbing S. Uchida," C. Y. Wen, and W. J. McMichael Department of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506
Studies on the role of complete mixing holding tanks in SO2 scrubbing processes by lime and limestone slurries have been made. Data obtained from various sizes of holding tanks under different operating conditions were analyzed and mathematical models for the holding tanks in lime and limestone slurry processes have been proposed. The dissolution of lime into weak acid solutions could be explained by a shrinking core model and the performance of the holding tanks in the limestone slurry process could be approximated by an equilibrium stage model in which the tank was assumed to be in dynamic equilibrium with the surroundings. Finally, these models were combined with venturi scrubbers to simulate venturi-holding tank systems with a closed-loop recycling of the liquor. The sensitivities of some operating variables such as the recycling liquor rate and the alkali make-up rate on the absorption efficiency were examined.
Introduction In recent years, considerable effort has been devoted to investigating the ever-growing problem of atmospheric pollution by sulfur dioxide emission. Therefore, many types of processes have been developed for removing the pollutant from waste gases. Among them the absorption of sulfur dioxide by a slurry of lime or limestone followed by discarding the loaded absorbent have the outstanding advantages of relative simplicity, lowest investment, and freedom of marketing a by-product etc. There are many types of scrubbers and process schemes combined with a holding tank for closed-loop recycling of the lime or limestone slurry. That is, due to practical, as well as economical, consideration, most commercial wet scrubbing processes must be based on a closed-loop system in which the loaded liquor from the scrubber is regenerated and recycled within the process and not discharged from the process. To accomplish this, the scrubber is combined with a mixing/holding tank which regenerates the degenerated liquor with fresh feeds of lime or limestone. The main objectives of this study are to elucidate the dissolution mechanisms of lime and limestone into recycling liquor in the lime or limestone slurry process and to develop mathematical models for the holding tanks to simulate and design an overall scrubbing process which consists of a venturi scrubber and a holding tank. Previous Studies A clear understanding of the dissolution mechanism of lime and limestone into recycling liquor in the SOz scrubbing process is essential in development and efficient operation of the wet scrubbing system. Lime's effectiveness as an alkali scrubbing liquor largely depends upon its ultimate solubility and the rate of dissolution. Haslam (1926) performed an experiment on the dissolution of lime into different solutions and explained the rate by the film model. Effects of particle size, the ultimate solubility, and different solvents on the rate of dissolution were examined. He also explained his experimental data by assuming the infinite rate of hydrolysis reaction between lime and wat,pr.
In the case of limestone, not only are a number of reactions taking place simultaneously but also its solubility is strongly dependent upon the partial pressure of CO2 over the solution or concentration of carbonate ions in the solution (Boynton, 1966; Seidell, 1958). A few studies on the dissolution rate of limestone into several acid solutions have been reported by Borgwardt (1973), Drehmel (1971, 1972), Hatfield et al. (1972), Phillips and Ottmers (1972-1973), Phillips et al. (1972-1973), and Uchida et al. (1974). Drehmel studied the dissolution rate of 12 naturally occuring limestones and dolomites using a constant pH titration technique. Although the measured activation energy for limestone dissolution was comparable to that expected for a diffusion limited mechanism (5-6 kcal/mol), the dissolution rates varied as much as 30 times with different limestone types. This behavior indicates a strong dependence on a surface characteristics of limestone. Hatfield et al. (1972) performed a series of experiments on the dissolution rate of limestone for the pH range of 4.5-5.5 and measured the rate of CO2 evolution and obtained an empirical correlation for the dissolution rate constant. This is applicable to the certain ranges of the operating conditions. Uchida et ai. (1974) performed an experiment using the same technique as Drehmel's and presented a model to be applied only to the lower pH ranges than those in practical cases. Phillips et al. (1972-1973) reported that the limestone dissolution rate could be expressed as a function of the particle area and carbonate and hydrogen ion activities, and obtained a correlation. Their correlation and Borgwardt's correlation (1973) have some discrepancies between data and the calculated values and do not give the reliable information on this problem yet. Data on the absorption of SO2 by limestone slurry have been reported by Borgwardt (1972-1973), Burklin and Phillips (1972), Berkowitz (1972), Skloss et al. (1971), and Epstein et al. (1972-1973) with various types and scales of scrubbers and holding tanks.
Reaction Mechanism When lime is dissolved into water, the following two reactions may occur around the solid lime
+ HzO F? Ca(OH)2
(1)
Ca(OH)2 F' Ca2+ + 20H-
(2)
CaO All correspondence should be sent t o this author a t the Department of Chemical Engineering, Shizuoka University, 3-5-1 Johoku Hamamatsu 432 Japan. 88
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
Since reaction 2 is an ionic reaction. it is considered as an
instantaneous reaction. The previous study on the rate of dissolution of lime (Haslam et al., 1926) shows that the hydrolysis reaction (1) is also very fast and the dissolution process into water may be controlled by the diffusion of the products from the lime particle. If the sulfur dioxide is absorbed into lime slurry, the following reaction occurs in the liquid phase
SOz + 20H- e S032- + HzO
Equilibrium concentration 150°C, M g = O l Equilibrium concentration (50'C, Mg.30 mgmole/ll
L /
A
Burklin and Philltps(1972l~5O0C.Mg~I-6 ma. ma k/l)
1
(3)
When limestone dissolves and SOz is absorbed into recycling liquor in a limestone slurry process, a number of reactions take place in the liquid phase. Among them, the key reaction for the dissolution of limestone will be (Borgwardt, 1973; Uchida et al., 1974): CaC03(s)
+ H+
-
+
Ca2+ HC03-
(4)
When SO2 is absorbed, the HC03- produced by the above reaction will react with it to give HS03- as (Bjerle et al., 1972; Nilsson et al., 1958)
SO2
+ HC03-
-
HS03-
+ COZ 1
4.5
(5)
The produced HS03- by this reaction will dissociate to supply the H + consumed by reaction 4 as follows and the pH of the solution, therefore, remains essentially constant as in most practical operations.
HS03-
H+
+ s03'-
(6)
Ca2+ and S032- produced by reactions 2 and 3 or 4 and 6 combine to produce CaS03, some of which will be oxidized to CaS04 if oxygen is present in the gas phase and absorbed in the slurry. The calcium sulfite and calcium sulfate have low solubilities and precipitate out of the liquid phase. As the equilibrium concentration of total SOs, which includes all molecular and ionic sulfites calculated by the equilibrium model (Lowell, 1970; Berkowitz, 1972a), decreases sharply with the increase in the pH value of the liquor (see Figure 1);if the actual concentration of these sulfites in the scrubbing liquor once exceeds the certain value, the crystallization of solid Cas03 takes place near the surface of the limestone where the pH value is considered to be locally high. Then the deposited Cas03 blinds the limestone particles and retards the dissolution rate of limestone, which results in the lower limestone utilization (Kelso et al., 1971; Potts et al., 1971). Therefore, to attain the smooth dissolution of limestone and recovery of the pH value of the outlet liquor from the scrubber in the holding/ delay tank according to reactions 4, 5, and 6, the operation must be undertaken in the certain range of the pH value. This blinding effect is assumed to be no problem in the following analysis. The scaling in the equipment in the process, which is the most serious problem unsolved so far in the practical operation, may also occur by a similar mechanism when the pH value is not uniform in the recycling liquor. A clear understanding of the mechanisms of the dissolution of solid limestone and the crystallization of sulfite and sulfate salts is necessary to have a scale-free, pH-stable operation of the lime or limestone SO2 scrubbing process. Reactions 3 and 5 are here considered to be instantaneous and irreversible and to determine the rate of SOz absorption into lime and limestone slurries (Bjerle et al., 1972; Uchida, 1973; Uchida and Wen, 1973). If very fine solid particles are present in the liquid phase, due to the dissolution of the solid, SO2 absorption is enhanced depending upon the solid concentration, particle size, SO2 partial pressure etc. In that case, the enhancement factor for the rate of absorption can be calculated by
5.0
5.5
6.0
6.0
70
pH of liquor
Figure 1. Equilibrium concentration of total sulfite at 5OoC and its concentration in outlet liquor from holding tank vs. liquor pH.
the mathematical model recently proposed by Uchida et al. (1975).
Development of Models for Complete Mixing/Holding Tank In this section, the development of mathematical models for holding tanks under complete mixing conditions in the lime and limestone slurry processes is discussed. Lime Slurry Process. When a solid lime is placed in contact with the liquid, the liquid-solid interface can be considered to be covered by the lime saturated solution. The solute diffuses from the solid particle into the main body of the liquid where it is uniformly distributed by the convective currents. In order to develop a model for the dissolution of lime in a holding tank, the following assumptions are made: (i) the concentration of Ca(0H)z at the interface of the solid is considered to reach the saturated concentration immediately; (ii) the dissolution reactions take place only on the surface of the particle rather than within the paticle; (iii) all particles are nearly spherical in shape and can be represented by a mean diameter when they are present in the tank; (iv) as the dissolution proceeds, the size of the particle shrinks. Applying the particle shrinking model (Levenspiel, 1962) to the particle in the holding tank, the following equation may be written on the rate of the dissolution (7) Introducing the molar density of the solid CaO, this relation, we obtain
PMB,
into
If the diffusion process in the liquid film around the particle is the controlling step and the relative velocity between the solid and the fluid is small, the following relation is applicable. k, = DB/rp
(9)
Then, eq 8 can be integrated as Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
89
Equilibrium Concentration 150'C, Mg.01 Equilibrium concenfralion 150°C, Mg.30 mgmole/ll
Therefore, the radius of the solid particle at time t is given by
A
Burklin and r n l i i i p ~ ~ ~ 9 7 2 ) ~ 5Mg=I-6 o0c, mg-moie/ll
0
Skloss et ai.(1971ll5O'C, Mg-25-32mgmole/ll
The time required for the complete dissolution, 7, is given by 7 =
R p 2 PMB
2DB(CBs - CBO)
(12)
If the holding tank can be considered as a complete mixing tank, the fraction of solid dissolved in the tank has the following relation with the tank characteristics 1 - XB =
4t
(1 - XB)E(t) d t =
21 4.5
From the material balance of total Ca(0H)Z which includes dissociated and undissociated calcium hydroxides around the holding tank, the followihg additional relation is obtained
M X B = F(CBO- C B ~ )
90
Ind. Eng. Chern., Process Des. Dev., Vol. 15, No. 1, 1976
5.5 6.0 pH of liquor
6.0
1I
7.0
Figure 2. Equilibrium concentration of total calcium at 5OoC and its concentration in outlet liquor from holding tank vs. liquor pH.
4
I
2-
(14)
Equations 12, 13, and 14 are solved for a given inlet concentration of total Ca(0H)Z to obtain the outlet concentration in the solution. Limestone Slurry Process. As in the case of the lime slurry process, in order to provide a model for simulation of the limestone slurry process, experimental data taken under practical conditions are needed. However, only a few studies on the dissolution rate of limestone into several acid solutions have been reported (Borgwardt, 1973; Drehmel, 1971-1972; Hatfield et al., 1972; Phillips and Ottmers. 1972-1973; Phillips et al., 1972-1973; Uchida et al., 1974). These data were obtained under limited conditions different from the conditions of practical interest. Therefore, it is questionable that these results are useful to simulate the holding tank in the limestone slurry process. In order to develop a kinetic model to estimate the rate of dissolution of limestone, it is necessary to know the key reactions contributing to the dissolution as well as the ultimate solubility of limestone into the slurry. In the case of limestone, however, not only are a number of reactions taking place simultaneously but also the limestone solubility is strongly dependent upon the partial pressure of COz over the solution and on the concentration of carbonate ions in the solution (Boynton, 1966; Seidell, 1958). Besides the complexity of the reaction mechanism, reactions seem to interact with each other making it practically impossible to limit the number of reactions to a single rate-controlling step. There is, however, a considerable amount of data on the total concentrations of the key components such as sulfite, sulfate, calcium, and carbonate in the recycling liquor obtained from various SO2 scrubbing plants (Epstein et al., 1972-1973; Borgwardt, 1972-1973; Bufklin, 1972; Skloss et al., 1971). It is believed that these components play main roles in the overall reaction in the SOZ-limestone slurry processes. In Figures 1, 2, and 3, comparisons of the outlet concentrations of total sulfite, total calcium, and total sulfate with calculated equilibrium values [calculated by computer programs originally developed by Lowell et al. (1970) and revised later by Berkowitz (1972)] are shown as func-
5.0
.-_ _ _concentration Equilibrium
I
150C, Mg=30
rng-mole/l I
Id0 s64-
Sorg~ardtI1972,19731143~C, Mg*35mgmole/l I
A
Burklin and phillips119721(504C,Mg=I-6 rng-mole/ll
1
-
Skloss et al.l197il15O0C, Mg.25-32mgmole/l I
2-
-
i
6t
4t
4
'4.5
5.0
5.5 6.0 pH of liquor
6.5
20
Figure 3. Equilibrium concentration of total sulfate at 5OoC and its concentration in outlet liquor from holding tank vs. liquor pH.
tions of the pH values of the liquor leaving the holding tank. From these figures, we can observe the following facts. In spite of the significant differences in the operating conditions and the design of the holding tanks such as residence time and area exposed to the atmosphere, the data seem to indicate that concentrations of each component in the liquor are very close to the equilibrium values (as for the operating conditions, see Table I). The effect of magnesium components on the equilibrium relations seems significant. Since MgS03 and MgS04 are both soluble, the magnesium fed with the limestone will inexorably build up in the scrubbing liquor. The rate of building up of magnesium depends upon the operating time, quality of limestone, etc. The dissolution mechanism of limestone into SO2 scrubbing liquor which may contain various salts and ions in addition to dissolved COz is rather complex and cannot be completely explained by the available data at the present time.
Table I. Experimental Conditions of Holding Tanks Simulated in This Study Experimenter Burklin and Gleason Borgwardt Phillips (1971) (1972-1973) (1972) Limestone Alkali Lime Limestone 2 27 00 Tank volume. 1900-5 600 1300 (6000) 1. (gal) (500-1 500) (350) Liquid rate, 5 70-1 840 l./min 30-60 32.2 ( 150-48 5) (GPM) (8-16) (8.5) Residence 12-40 time, min 30-150 4-40 Liquid. temp, 43 50 “C 40-50
x,=lcuco,’, Y3=1CaSO3), Z,=lCaS04~ T3= Y3tZ3
xz=lcaco3)~ Y, =LCaS03), Zz=lCaSO4Iz T2 = Y2t Z
In order to develop a model for simulation of a holding tank in a limestone slurry process, the following assumptions are made: (i) the tank is operated under steady-state conditions and is completely mixed; (ii) the tank is operated very closely as an equilibrium stage, that is, the outlet concentrations of each component are in “dynamic equilibrium” with the gas phase; (iii) there is no heat transferred between the tank and the surroundings, and heat of dissolution can be neglected. A flow diagram of the holding tank is shown in Figure 4. Conservation of calcium, sulfur, and carbon in the holding tank system requires that
+ T2 + X3 + T3 (15)
F[S]1+ Ti = F[S]2
+ T2 + Tz + T3
F[C]1+ XI + M = F[C]z
(115)
5.4
50
M=X3+T3 (21) Also, the assumption that the holding tank liquor is perfectly mixed requires that the fraction of calcium carbonate leaving the tank in the solid purge stream be equal to the fraction of calcium carbonate in the solid phase of the recycling slurry. Symbolically
Figure 4. Material balance around a holding tank.
F [ C a ] l + X I + T I + M = F[Ca]z + X2
435
scrL--er, the requirement that ca.,ium does not accumulate in the system can be stated as
’fed
X,=IcaCO~, Y, =(CaSO,), Z,=(CaS04)I TI -YI+ 2 ,
Skloss et al. (1971) Limestone 2350 (620)
+ X2 + X3 + Nco2
(16)
(17)
+
where Ti = Yi 2; for i = 1, 2,3. In addition to the assumption of “dynamic equilibrium” of the holding tank liquor with the gas phase, it is assumed that both solid calcium sulfite and sulfate are present in the tank, and that the temperature of the liquor in the tank is fixed. Then, the composition of the liquid stream existing in the holding tank is uniquely determined by the pH of the liquor in the tank (Lowell et al., 1970; Berkowitz, 1972). Thus [Cab = f l ( p W
(18)
[SIz = fz(pH)
(19)
[Clz = f3(pH)
(20)
where fl, f2, and f 3 denote the functional relationships between the compositions and the p H of the holding tank liquor. If the holding tank is to operate in closed-loop with a
If the rate a t which C02 is evolved from the holding tank, Nco2, is known, then the above eight equations (eq 15-22) will uniquely determine the eight unknowns, [Ca]z, [S]2, [C],, X2, TP, X3, T3, and pH. Theoretically it is possible to solve this set of equations. However, it can be shown that the pH of the holding tank liquor must satisfy the following consistency condition, and that consequently the pH can be calculated without solving the entire set of equations (See Appendix).
- A[Ca] + A[S] + A[C] = Ncon/F
(23)
where AX = [XI, - [X]2. The rate of C02 evolution from the holding tank, Nco2, may be approximated by N C O z = KGaV(P*COz
- P’COz)
(24)
Once the value of KGa, which is a function of the operating conditions and the design of the tank, is known, every term in eq 23 becomes a function of pH only. Usually, the partial pressure of CO2 in bulk gas phase, pocoz,is negligible compared with p*coZ.The pH of the liquor leaving the tank can then be calculated by this equation. The value of KGa is estimated from experimental data obtained from various investigations (Borgwardt, 1972-1973; Burklin and Phillips, 1972; Skloss et al., 1971) by the following equation
KGU = (- A[Ca] + A[S]
+ AIC])F/Vp*coz
(25)
The calculated values of KGa are shown in Figure 5 as a function of the liquor flow rate, F. It can be seen from this figure that KGa increases slightly with the liquor flow rate. The scatter of the data is probably due to the extent of agitation which causes different level of evolution of C02. The following correlation approximates the functional dependence of KGa on F
KGa = 0.000211F’.263
(26)
The pH value thus determined gives us all the concentrations of species in the recycling liquor from the equilibrium relation. Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 1 , 1976
91
0 Bargwardt(1972,1973)
A Burklin and Phillips(1972)
0
Borgwrdt(1972,1973) A Burklin and Phllllpsl1972)
Skloss et al.lI971l
0
0 Sktoss e t a l l 1 9 7 1 )
1
A
5.0
6.0
5.5
5.0
6.5
7.0
75
pH, experimental 1041
10
t
I
2
4
6
3
"
6810' 2 4 68103 liquid flow rate, F , I/min
2
(1
4
Figure 5. Mass transfer coefficient for CO2 evolution from the
Figure 7 . Comparison of the values of calculated pH of outlet liquor from holding tank with experimental data (limestone slurry process).
holding tank vs. liquor flow rate.
.
Toto1 sulfate &q*ardt(l972-19731 A Borktm md RwIltpr11972) 0 Sklorr el 01 (19711
W 1 0 v IO-'
'
2
total
0 0.8
1.0
1.2 8
1.4
1.6
8 1.8
experimental cwentmtion of Ca(OH&,gmck/l x1U2
Figure 6. Comparison of calculated concentration of Ca(OH)* in solution from holding tank with data obtained by Gleason et al. (1971).
Simulation of Performance of Complete Mixing Holding Tank Simulations of complete mixing tanks for lime and limestone slurry processes are discussed. Only a few data on the performance of the holding tanks are available. The operating conditions under which these data were taken are summarized in Table 1. Holding Tank for Lime Slurry Process. Only one series of experiments performed by Gleason (1971) fed lime directly to the holding tank and gave reliable data. The model for the dissolution of lime proposed has been used to simulate the performance of the tank. The results are compared with experimental data in Figure 6, showing good agreement. Holding Tank for Limestone Slurry Process. The amount of data available on the performance of holding tanks in the limestone slurry processes is substantially greater than that available on the holding tanks in the lime slurry processes. The holding tanks in the limestone slurry processes have been simulated based on the proposed model and the comparisons of calculated results with the experimental data are shown in Figures 7 and 8. In the simulations of the holding tank in the limestone slurry process, it is assumed that the holding tank is an equilibrium stage. Based on the favorable comparisons of 92
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
4
6
I
8 IO"
Skims et 01 11971)
2 4 6 soi,sQ,or CO;,experirnmtal,g-mde/i
~4
1 I
B 10.'
Figure 8. Comparison of calculated values of concentrations of total sulfite, sulfate, calcium, and carbonate in outlet liquor from holding tank with experimental data (limestone slurry process). the calculated pH and concentrations of key components with the experimental data, this assumption appears to be very reasonable. A model based on the equilibrium stage assumption is used to simulate venturi scrubber-holding tank systems in which the scrubber liquor is recycled.
Simulations of Venturi Scrubber-Holding Tank System with Closed-Loop Recycle of Scrubbing Slurry Simulations of a venturi scrubber with a holding tank and some other auxiliary equipments as shown in Figure 9 are discussed. Prior to the discussion, the following assumptions are imposed on the scrubbing system. (i) There is no dissolution of lime or limestone in the process except in the holding tank, (ii) The holding tank is considered to be under the same conditions as those in the previous section. (iii) Solid deposits and undissolved lime or limestone are removed from the clarifier. (iv) Make-up water is either not required or can be added without significant effect on the process performance. (v) The system is under steadystate condition. (vi) From the reaction kinetic point of view, one mole of SO2 absorbed produces one mole of COz in the limestone process. The amount of COz evolved in the tank is equal to the amount of SO2 absorbed in the venturi scrubber. (vii) The main absorption reaction for SOz-lime or limestone slurry systems is considered to be either reaction 3 or 5 , and the performance of the venturi scrubber is calculated by the model proposed by Uchida and Wen (1973).
Flue Gas in
I
60
-
50
-
A Clarifier
- 80
-60 P
Solid
L
Figure 9. Venturi scrubber-holding tank system with closed-loop recycle of scrubbing slurry.
Inlet SO2 conc = 2 2 2 G p p m Inlet gas temp =365'F1185TI Gas velocity a t throat=98ft/sec130m/sec) 10
40
80 I20 160 alkali make-up rate, g-CaG/min
200
Figure 11. Performance of a venturi scrubber-holding tank systern with closed-loop recycling of slurry (lime slurry process).
Figure 10. (a) Logic diagram for simulation of venturi scrubberholding tank slurry with closed-loop recycling of slurry (lime slurry process). (b) logic diagram for simulation of venturi scrubberholding tank system with closed-loop recycling of slurry (limestone slurry process).
Hence, with the knowledge of given conditions such as the flow rate of recycling liquor, the amount of gas scrubbed, the alkalihulfur ratio etc., the performance of the system under the steady-state conditions can be calculated. Logic diagrams for the simulations of venturi-holding tank systems are shown in Figure 10. Lime Slurry Process with Closed-Loop Operation. The momentum, heat, and mass balances describing the lime slurry process based on Gleason's experimental condition (1971) were solved. The dependences of the alkali efficiency (defined as the percentage of consumed alkali to make-up alkali), and the SO2 removal percentage on the liquid flow rate and the alkali feed rate are shown in Figure 11. From this figure, the following can be observed. (i) At low alkali feed rate, the percentage of SO2 removal increases proportionally with the alkali feed rate. (ii) An increase in the liquid flow rate reduces the percentage of SO2 removal and alkali efficiency under the conditions employed here since the residence time in the holding tank under the constant volume condition decreases. This result seems contradictory to practical data. In the
practical cases, the percentage of SO2 removal increases with the liquid flow rate (Shah, 1971). One of the reasons is that the holding tank used in this simulation is rather smaller than the practical ones and the solid lime is directly fed to the tank. T o avoid scaling and blinding problems and to attain better mixing of the solid, each of those practical processes usually uses a separate delay tank and a mixing tank which have much larger size, that is, much longer residence time, and therefore, every inlet concentration of alkali in the liquor to the scrubber is nearly the same as the saturated solubility of lime. As seen from Figure 11, the same results as in the practical case will be expected by increasing the alkali make-up rate or the tank volume. (iii) At low liquid rates and the alkali feed rates above 80 g of CaO/min, the percentage of SO2 removal does not improve as rapidly with the increase in alkali rate as in the case where the alkali feed rate is less than 80 g of CaO/min. The reason for this is that a t this flow rate the solubility limit of CaO in the recycling liquor is reached. Therefore, the alkali efficiency goes down rapidly from this point. Limestone Slurry Process with Closed-Loop Operation. An overall simulation of a venturi-holding tank system is based on the experimental conditions used by Epstein et al. (1972-1973). The dependence of SO2 removal percentage and the pH value of the liquor in the holding tank on the flow rate of the recycling liquor is shown in Figure 12. Examination of this figure reveals the following. (i) The SO2 removal percentage increases with the liquid rate and the decrease in the pH value of the inlet liquor to the venturi has little effect on the absorption efficiency. (ii) An increase in the liquor flow rate causes a decrease in the pH value of the liquor leaving the tank since COS evolution per unit liquor from the tank decrease with the increase in the liquor flow rate. The pH value of the recycling liquor increases with the COZ evolution. (iii) A comparison is also given in Figure 1 2 with the value calculated by the empirical equation obtained by Epstein et al. (1972-1973) for their test facility at the TVA Shawnee Power Plant which is
SO2 removal % = 9.4 + 0.01F + 0.35 APV
(27)
Although the applicable range of this equation is limited, the agreement is satisfactory. Ind. Eng. Chem.. Process Des. Dev., Vol. 15, No. 1 , 1976
93
,
60s
I
- Liquid rate
VL
SO, removol %
- - - - Liquid rate
v5
pH of liquor
644
&I
40 -
zz30-
E
B2 0 10-
Inlet po; temp.=305’F i152oC) Gas velocity at thrwt=l00ft/sec(30m/secl
Effect of Solid Dissolution in Venturi on SO0 Removal %. Bjerle et al. (1972) performed an experiment of the absorption of SO2 in limestone slurry in a laminar jet absorber which had the residence time of the same order of magnitude as that in a venturi scrubber, and observed no limestone dissolution. Here, in order to see the effect of the dissolution of lime or limestone in the venturi scrubber on the percent removal of SOz, the mathematical model proposed by Uchida et al. (1975) can be approximately used in the simulation. The percent SO2 removal in the limestone slurry process used by Epstein et al. (1972-1973) is negligibly enhanced when the dissolution is taken into consideration for 10% solid limestone concentration and 200 mesh-size particles in comparison with the results calculated with the assumption of no solid dissolution. When the solid % is increased from 10% to 20%, the SO2 removal % is at most improved by 3~4% which is less than practically observed (Shah, 1971). At present, it is very difficult to determine if the improvement in the percent SO2 removal in limestone slurry processes in pilot- or commercial-scale operation is due purely to the effect of the solid dissolution since the physical properties of liquid such as the viscosity, density, surface tension, etc., and its hydrodynamic conditions in the scrubber and the holding tank may change considerably. , The drop diameter produced by the atomization in the venturi scrubber may be significantly affected and the turbulence of the liquid inside the droplet may be increased by the presence of the solid in the liquid. Conclusion The mechanisms of the dissolution of lime and limestone in holding tanks in the SO2 scrubbing processes have been investigated and the design procedures of a venturi scrubber with a holding tank have been shown. The specific conclusions and recommendations resulting from this study are as follows. 1. The dissolution mechanism of lime into a weak acid solution in a holding tank can be explained by a kinetic model which expresses the rate of dissolution of lime by the shrinking core model. 2. The performance of a holding tank under a complete mixing condition in the limestone slurry process can be approximated by the “equilibrium stage model” in which the liquor in the holding tank is assumed to be in a “dynamic equilibrium” with the gaseous phase above the tank. The 94
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
rate of COz evolution in the holding tank plays an important role in the dissolution process and may control the attainable pH value of the limestone slurry in the holding tank. 3. The effect of the presence of magnesium species in the liquid phases on the equilibrium relation appear to be very important. T o use the equilibrium stage model for a holding tank successfully, an accurate estimate of the concentration of magnesium components accumulating in the liquid phase is needed. 4. In order to develop a kinetic model for a holding tank and a tubular reactor in a limestone slurry process, and to have a scale-free and pH-stable operation of SO2 scrubbing by limestone slurry, it is necessary to have more understanding of the mechanisms of the dissolution of limestone and the crystallization of calcium salts in the recycling liquor. 5. Further study on the effects of the solid presence in the liquid phase on the absorption and the hydrodynamic characteristics of the scrubbing liquor in the scrubber and the holding tank is required to explain the experimental fact that the increase in the alkali-sulfur stoichiometric ratio slightly enhances the rate of SO2 absorption.
Appendix Assume that the pH of the liquid leaving the tank is known. Then, [Calz, [S]Z,and [C], are determined by eq 18-20. Substitutions of these relations into eq 15-17 gives
XZ+ Tz + X3 + 7’3 = F([Ca]l- [Gala) + M + Xi
+ 7’1
+ T3 = FI[S]i - [S]z)+ Ti b2 Xz + X3 = F{[C]i- [C]z)+ M + X i - Ncoz
bl
Tz
(A-1) (-4-21
b3
(A-3)
These equations can be written in matrix form as
LT ~ J Elementary matrix operations from the left on the equation show
Therefore, if eq 15-17 are to be consistent and have to have a solution, the condition bl = b2 + b3 must be satisfied. In terms of the definitions of the b’s
- A[Ca] + A[S] + A[C] = Nco2/F where AX = [XI, - [XI,.
(A-6)
Nomenclature C B ~= inlet concentration of component B, g-mol/cm3 CBO= bulk concentration of component B, g-mol/cm3 C B ~= saturated concentration of component B, g-mol/ cm3 [C] = total concentration of carbon in recycling liquor, gmol/cm3 [Ca] = total concentration of calcium in recycling liquor, g-mol/cm3 D B = diffusivity of component B in liquid phase, cm2/sec E ( t ) = exit age distribution function, l/sec F = liquid flow rate, cm3/sec (in eq 26,l./min)
Kca = mass transfer coefficient in gas phase, g-mol/cm3 sec atm (in eq 26, g-molfl. min atm) k, = dissolution rate constant, cm/sec M = molar feed rate of solid lime or limestone, g-mol/sec N c o z = rate of C02 evolution from holding tank, g-mol/ sec Nso2 = rate of SO2 absorbed in venturi scrubber, g-mol/ sec N B = mole of component B, g-mol p*co2 = partial pressure of C 0 2 in equilibrium with liquid phase in holding tank, atm poco2 = partial pressure of C02 in bulk gas phase, atm R , = radius of solid particle at t = 0, cm r = radius of solid particle at t = t , cm = total concentration of sulfur in recycling liquor, gmol/cm3 t = time,sec 2 = mean residence time, sec V = volume of holding tank, cm3 or 1. X B = fraction of solid dissolved x g = mean fraction of solid dissolved X , = flow rate of solid limestone in recycling liquor, i = 1-3, g-mol/sec [XI. = total concentration of component X in recycling li. quor, g-mol/cm3 Y; = flow rate of solid calcium sulfite in recycling liquor, i = 1-3, g-mol/sec 2, = flow rate of solid calcium sulfate in recycling liquor, i = 1-3, g-mol/sec
fi]
~~
Greek Letters hp, = pressure drop in venturi scrubber, cm of HzO PMB = molar density of solid B, g-mol/cm3 T = time required for complete dissolution, sec Subscript 1 = inlet concentration to holding tank 2 = outlet concentration from holding tank 3 = outlet concentration of solid from holding tank B = component B, CaO or Ca(0H)Z W = waste Literature Cited Berkowitz, J. B., Progress Report to EPA, A. D. Little, Inc., Boston, Mass., 1972a. Berkowitz. J. B., private communication, A. D. Little, Inc., Boston, Mass., 1972b. Bjerle I., Bengtsson, S..Farnkvist, K., Chem. Eng. Sci,, 27, 1853 (1972).
Borgwardt, R. H.. Progress Reports No. 1-6, Environmental Protection Agency, N.C., 1972-1973. Borgwardt, R. H., Progress Reports No. 8 and 9, Environmental Protection Agency, N.C., 1973. Boynton, R. S.,"Chemistry and Technology of Lime and Limestone," Interscience, New York, N.Y., 1966. Burklin, C. E., Phillips, J. L., Technical Note 200-014-10, Radian Corporation, Austin, Texas, 1972. Drehmel. D. C., paper presented at Second International Symposium for Lime/Limestone Wet Scrubbing, New Orleans, La., Nov 8-12, (Proceedings issued by EPA, APTD-1161, 1, 167) (1971); paper presented at 65th Annual Meeting of APCA, Paper No. 72-105, June 18-22, 1972. Epstein, M. et al., Progress Report to EPA, EPA Alkali Scrubbing Test Facility at the TVA Shawnee Power Plant, Bechtel Corporation, Calif.. 1972-1973. Gleason, R. J., McKenna, J. D., Final Report of Pilot Scale Investigation of a Venturi-type Contactor for Removal of SO2 by the Limestone Wet-Scrubbing Process, Cottrell Environmental Systems, Inc., 1971. Haslam, R. T.. Adams, F. W.. Kean, R. H., Ind. Eng. Chem., 18, 19 (1926). Hattield, J. D., Kim, Y. K.. Deming, M. E., TVA Progress Report to EPA, Tennessee Valley Authority, Muscle Shoals, Ala., 1972. Kelso. T. M., Williamson, P. C., Schultz, J. J.. Moore, N. D., paper presented at Second International Symposium for LimelLimestone Wet Scrubbing, New Orleans, La., Nov. 8-12, (Proceedings issued by EPA. APTD-1161, 1, 437) (1971). Levenspiel. 0.. "Chemical Reaction Engineering, Wiley, New York, N.Y., 1962. Lowell, P. S.,et al., Final Reports for No. CPA-22-65-138, 1 and 2, Radian Corporation, Austin, Texas, 1970. Nilsson, G., Rengemo, T., Sillen, L. G., Acta. Chem. Scand., 12, 868 (1958). Olander. D. R., A.I.Ch.€. J., 6, 233 (1960). Phillips, J. L., Ottmers, D. M., Jr., Monthly Work Report to EPA, Radian Corporation, Austin, Texas, 1972-1973. Phillips, J. L.. et al., Technical Note 200-014-05 to 09, Radian Corporation, Austin, Texas, 1972-1973) Potts, J. M., Slack, A. V., Hatfieid. J. D., paper presented at Second International Symposium for Lime/Limestone Wet Scrubbing, New Orleans, La., Nov. 8-12, (Proceedings issued by EPA, APTD-1161, 1, 195) (1971). Seidel, A., "Solubilities of Inorganic and Metal Organic Compounds," p 538, American Chemical Society, 1958. Shah, I. S.,paper presented at Second International Symposium for Lime/ Limestone Wet Scrubbing, New Orleans, La., Nov 8-12 (Proceedings issued by EPA, APTD-1161, 1,345) (1971). Skloss. J. L., Wells, R. M.. Mekrole, F. B., Phillips, N. P., Thompson, C. M.. Hawn. W. C., Technical Note 200-010-02, Radian Corporation, Austin, Texas, 1971. Uchida, S.,Ph.D. Dissertation in Chemical Engineering, West Virginia University Morgantown, W. Va., 1973. Uchida, S.Koide, K., Shindo, M., Chem. Eng. Sci., 30, 644 (1975). Uchida, S.,Wen, C. Y., Ind. Eng. Chem.. Process Des. Dev., 12, 437 (1973). Uchida, S.,Wen, C. Y., McMichael, W. J., Progress Report to €PA, No. 21, Contract No. EHS-D-71-20 (1973); Ch.I.Ch.€. J., 5, 111 (1974). Received for review F e b r u a r y 3,1975 Accepted August 18,1975 T h e work u p o n w h i c h t h i s p u b l i c a t i o n is based was p e r f o r m e d pursuant t o Contract No. EHSD 71-20 w i t h t h e E n v i r o n m e n t a l Protection Agency for w h i c h we are grateful.
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
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