• 沒有找到結果。

Dissolution rates of limestones of different sources

N/A
N/A
Protected

Academic year: 2021

Share "Dissolution rates of limestones of different sources"

Copied!
13
0
0

加載中.... (立即查看全文)

全文

(1)

www.elsevier.nlrlocaterjhazmat

Dissolution rates of limestones of different sources

Shin-Min Shih

)

, Jyh-Ping Lin, Gwo-Yuan Shiau

Department of Chemical Engineering, National Taiwan UniÕersity, Taipei, 106 Taiwan

Received 20 January 2000; received in revised form 26 April 2000; accepted 1 May 2000

Abstract

The dissolution characteristics of limestones from six sources in Taiwan have been studied by using the pH-stat method in a stirred tank at 608C, pH values of 4 and 6, stirrer speeds of 500–1000 rpm, and a particle size of 75–125 mm aperture width. The dissolution rates of the limestones were found to be controlled by the mass transfer of hydrogen ions with chemical reactions in the liquid film surrounding the limestone particle. The measured value of mass transfer coefficient increases with an increasing pH value and stirrer speed and remains constant with particle size. For the six limestones at the same particle size, the measured dissolution rates per unit area are the same due to the mass-transfer control kinetics; however, the time taken to reach a certain fraction of dissolution is proportional to the molar concentration of the soluble species in the limestone and the initial particle size. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Limestone; Dissolution; Flue gas desulfurization

1. Introduction

The wet type limestone scrubbing process is the most commonly used flue gas

Ž .

desulfurization FGD process for thermal power plants. In this process, limestone slurry is used to absorb SO from the flue gas. Limestone particles in the slurry dissolve and2 react with the absorbed SO to from solid products. Accurately evaluating the dissolu-2 tion rate of limestone is important in the development and the efficient operation of the SO wet scrubbing system.2

Ž .

The main constituent of limestone is calcite CaCO . Many studies on the dissolu-3

tion of calcite or limestone have been carried out so far. The most significant previous

)

Corresponding author. Tel.: q886-2-23633974; fax: q886-2-23623040.

Ž .

E-mail address: smshih@ccms.ntu.edu.tw S.-M. Shih .

0304-3894r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.

Ž .

(2)

work on calcite dissolution has been done under seawater conditions by geochemists.

w x

Plummer et al. 1 reviewed this work and concluded that the rates were controlled by hydrogen ion diffusion below pH 5 and by surface reaction kinetics above pH 5.

w x

Plummer et al. 1 introduced no factors to account for the specific geological character-istics of the limestone samples. However, some studies under conditions typical of FGD

w x

have given apparent effects of limestone type and particle size. Drehmel 2 measured the dissolution rates of various types of limestone in acid media and showed the considerable differences in their dissolution rates. He also found a strong effect of

w x

particle size. Chan and Rochelle 3 measured the dissolution rate of reagent calcite as a function of pH, temperature, CO2 partial pressure, and solution composition. They modeled the dissolution rate by mass transfer with equilibrium acid–base reactions and a

w x

finite-rate homogeneous reaction of CO and H O. Toprac and Rochelle 4 extended2 2

Ž .

the work of Chan and Rochelle 1982 to commercial limestones of different types and grinds by modifying the mass-transfer model to account for the effect of solution turbulence on large particles. They found that particle size distribution is the most important reactivity characteristic of a ground limestone of reasonable purity. The work

w x

by Gage and Rochelle 5 showed that in the presence of sulfite and other inhibitors of limestone dissolution, the dissolution rate is not simply mass transfer controlled and it

w x

can be a strong function of limestone type. Ukawa et al. 6 reported that their experimental results for the dissolution of limestones of different compositions and size distributions are in good agreement with the predictions of the model proposed by

w x

Toprac and Rochelle. Ahlbeck et al. 7,8 proposed a sequential method for measuring the reactivity of limestone.

Since the dissolution of a limestone may be affected by its geological origin and composition, there is a need to study the dissolution characteristics of local limestones to provide the basic data for the design and operation of local FGD facilities.

In this study, the dissolution rates of limestones from six major sources in Taiwan were measured and compared for particles of the same initial size range without the presence of sulfite and other inhibitors by using the pH-stat method.

2. Mathematical model

When a strong acid is added to a stirred limestone slurry, the acid completely dissociates and hydrogen ions are formed. The limestone in water dissolves to a low degree according to

CaCO3|Ca2qqCO2y3 .

Ž .

1

y

Ž . Ž .

The carbonate ions react with the hydrogen ions to form HCO , CO3 2 aq and CO2 g as follows CO2yqHq |HCOy 2

Ž .

3 3 HCOy qHq|CO aq qH O

Ž

.

Ž .

3 3 2 2 CO2

Ž

aq

.

|CO g .2

Ž .

Ž .

4

(3)

Ž .

When carbonate ions are consumed by reaction 2 , more limestone dissolves. Most

Ž .

researchers found that reaction 1 is very fast, and some reported that the rate depends

w x Ž . w x

on the property of limestone 2,7,8 . Reaction 2 is instantaneous 9 ; its equilibrium constant is very large, 2.27 = 1010 m3rkg mol at 298 K, thus almost all the carbonate

ions are converted by this reaction in acidic solution.

Since the rates of the reactions involved are fast, the dissolution rate of limestone is affected by the mass transfer of the reacting species. A complete mass transfer model

w x

involving the diffusion of all possible species was presented by Wallin and Bjerle 10 . Their results showed that the diffusion of hydrogen ions is the dominant process. Toprac

w x w x

and Rochelle 4 and Ukawa et al. 6 found that the dissolution rate is primarily controlled by the mass transfer of hydrogen ions from the liquid bulk to the limestone

w x

surface through the boundary layer surrounding the limestone particle. Ahlbeck et al. 8 proposed that the dissolution rate is controlled by the mass transfer of the hydrogen ion and its reaction at the limestone surface.

Assuming that the limestone particle is nonporous and spherical and dissolves according to shrinking-core behavior, the rate per unit surface area of the particle can be expressed by

dR

)

yrm sk C y C

Ž

b s

.

Ž .

5

dt

where rm is the molar concentration of CaCO and MgCO in the limestone, R is the3 3 particle radius, t is the time, k is the dissolution rate constant, Cb is the bulk concentration of hydrogen ions, C)

is the surface concentration of hydrogen ions if the

s

surface reaches equilibrium. The dissolution rate constant k is defined by

1 1 1

s q

Ž .

6

k kL kr

where kL is the mass transfer coefficient and k is the rate constant of the surfacer reaction. For limestone dissolution in acidic solution, C is much greater than C)

, and

b s

)

Ž . w x

Cs can be taken as zero in Eq. 5 8 . At constant C , if the mass-transfer coefficientb

kL is independent of particle size or for the period in which the particle size change is

Ž .

not appreciable, Eq. 5 can be integrated to yield

r Rm 0 R

t s

ž

1 y

/

Ž .

7

kCb R0

where R is the initial particle radius. The independence of k0 L on particles size under the experimental conditions of this study is justified by subsequent discussion in Section 4.

The particle radius R is related to the fraction of dissolution X of the particle by

1

R 3

s

Ž

1 y X

.

Ž .

8

(4)

Ž . Ž .

Substituting Eq. 8 into Eq. 7 yields

1

r Rm 0 3

t s 1 y 1 y X

Ž

.

.

Ž .

9

kCb

If the limestone sample is composed of particles of uniform size, both the dissolution rate per unit surface area and the fraction of dissolution of the sample should be the same as those of a single particle at the same dissolution time, i.e.,

1 dm dR srm

Ž

10

.

AS dt dt m 1 y sX

Ž

11

.

m0

where m0 and m is the total moles of CaCO3 and MgCO3 in the sample before dissolution and at dissolution time t, respectively; and A is the total surface area of theS

sample. A can be calculated from its initial value, AS SO, by

2r3

m

A s AS SO

ž /

.

Ž

12

.

m0

3. Experimental

Batch dissolution rates for various limestones were measured at constant pH by using a pH–stat apparatus. The pH was automatically controlled to "0.02 units by titrating with 0.1 M HCl. The limestone dissolution rate was related to the titration rate by the stoichiometry

CaCO q 2HCl3 |CaCl qH OqCO .2 2 2

Ž

13

.

The relative change of calcium concentration in the reactor was minimized by dissolving 0.15 g of CaCO3 in 0.25 l of 0.1 M dissolved CaCl . The cumulative2 dissolution was determined directly from a recording of HCl volume added vs. time. The fraction of dissolution X was obtained by the ratio of the HCl volume added to that required for complete dissolution.

The experimental apparatus is shown in Fig. 1. Agitation was provided by a three-blade propeller rotating at 500–1100 rpm to fully fluidize the sample. The reactor temperature was controlled to "0.28C by a water jacket. The experiments were performed at 608C and pH 4 and 6.

Natural limestones from six different mines in Taiwan were provided by cement companies. The contents of CaCO in these limestones are from 74 to 95 wt.%, and3

(5)

Ž . Ž . Ž . Ž .

Fig. 1. Schematic of experimental apparatus. 1 Autotitrator, 2 HCl bottle, 3 pH probe wire, 4 HCl titrant

Ž . Ž . Ž . Ž . Ž . Ž .

line, 5 temperature compensation electrode wire, 6 stirrer, 7 reactor, 8 valve, 9 microtube pump, 10

Ž .

water bath, 11 copper coil.

Ž .

MgCO from 0.8 to 3.2 wt.% Table 1 . The percent available for dissolution in a given3

sample was taken to be the sum of CaCO and MgCO contents.3 3

The raw sample were crushed, ground, and sieved to different size ranges. Samples obtained between 75 and 125 mm apertures were used in this study. These samples were washed with ethanol to remove adhered fine particles. Their size distributions were measured by using a Coulter LS-230. The results showed that the portion of fine particles is negligible. The volume-mean particle diameters of these six samples were

Ž .

not exactly the same, but varied from 102.4 to 127.6 mm Table 1 .

The bulk density, porosity, and BET surface area of each type of limestone were measured and are listed in Table 1. The total molar concentration of CaCO and MgCO3 3

for each limestone, r , is also shown in Table 1, which was calculated from the bulkm

density and the weight fractions of CaCO3 and MgCO3 for the limestone. The

Ž .

limestomes from eastern part of Taiwan Shin-Cherng, Tay-Bair Mt., Her-Pyng have

Ž .

higher rm than those from western part Dah-Gang Mt., Chyh-Ke Mt., Bann-Pyng Mt. .

Table 1

Soluble contents and physical properties of limestones

Source CaCO3 MgCO3 d rb e Sg rm

3 2 3 Žwt.%. Žwt.%. Žmm. Žgrcm. Žm rg. Žmolrcm. Tay-Bair Mt. 94.8 1.1 102.4 2.579 0.05 0.4 0.02478 Her-Pyng 92.7 2.7 112.2 2.497 0.09 0.7 0.02395 Shin-Cherng 95.0 3.2 118.2 2.619 0.04 0.2 0.02586 Chyh-Ke Mt. 77.5 1.1 125.4 2.603 0.05 0.7 0.02051 Dah-Gang Mt. 81.0 0.8 117.5 2.516 0.08 1.6 0.02060 Bann-Pyng Mt. 74.0 1.1 127.6 2.452 0.10 2.5 0.01846

(6)

4. Results and discussion

Ž .

As can be seen from Table 1, the limestones have very small porosities F 0.1 and thus can be considered as nonporous. Their BET specific surface areas, varying from 0.2 to 2.5 m2rg, are much larger than that calculated for a nonporous spherical particle with

the same diameter. The larger measured specific surface area is attributed to the adhered fines, the irregular particle shape, and the uneven and rough particle surface, as can be seen from the SEM micrograph of limestone particles.

During the dissolution experiment, the fine particles and the rough surface layer dissolved first and gave a short initial period of high dissolution rate. The HCl volume added during this period was not included in the HCl volume added vs. time data for dissolution rate calculation. This initial HCl volume was very small compared to the total volume required for complete dissolution. As the dissolution proceeded, the particle shape became rounder and the particle surface became smoother.

4.1. Dissolution at pH 4

Fig. 2 shows the data of HCl volume added vs. time at 608C and pH 4 for Tai-Bair Mt. and Bann-Pyng Mt. Other types of limestone gave similar plots. It can be observed that the dissolution rate is higher at higher stirrer speed. This indicates that the dissolution rate was affected by mass transfer.

w Ž .1r3x

Fig. 3 shows the plot of 1 y 1 y X vs. time for Tai-Bair Mt. limestone. One can see that the data points for each stirrer speed can be represented by a straight line up to the corresponding X value of about 0.97 or the RrR value of about 0.3. This result0

Ž .

indicates that Eq. 9 is valid not only for the early period of dissolution, but also for the latter period in which the reduction of particle size is appreciable. This result also implies that the dissolution rate constant k is insensitive to particle size.

Ž .

According to Eq. 6 , k is a function of kL and k . Thus the insensitivity of k tor

particle size is due to either that k , which is independent of particle size, is a lot smallerr

than kL and k f k or that kr L is a weak function of particle size. Since kL is also a function of stirrer speed and the slope of the straight line in Fig. 3 increases with increasing stirrer speed, the insensitivity of k to particle size is due to the fact that kL is a weak function of particle size.

The liquid phase mass transfer coefficient for particles suspended in stirred tanks has been measured by many investigators. Correlation given by Calderbank and Moo-Young

w11 shows kx to be independent of particle size if the mass transfer is due to turbulence

L

in the surrounding fluid. According to the terminal velocity–slip velocity theory,

w x

Harriott 12 found that the mass transfer coefficient must increase with decreasing diameter for very small particles, but should be nearly independent of particle size over

w x

the range of 100–1000 mm. Correlations presented by Brian et al. 13 and Levins and

w x

Glastonbury 14 show that kL is affected by particle diameter, specific agitation power, and Schmidt number and that kL increases as particle diameter decreases, but the effect of particle diameter on kL is small at high values of particle diameter, specific agitation power, and Schmidt number.

(7)

Ž .

Fig. 2. Titration curves for limestones at pH 4 and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl . a2

Ž .

Tai-Bair Mt., b Bann-Pyng Mt.

In the present study, the stirrer speed, being in the range of 500–1000 rpm, is high, the particles were fully suspended, and the particle size considered, being in the range of

Ž . Ž .

about 100 initial diameter to 30 mm final diameter , is not small; thus the agitation condition should be in the range where the effect of particle size on mass transfer is rather small.

Ž .

According to Eq. 9 , the value of k can be calculated from the slope of the straight line in Fig. 3. The value of k obtained for each stirrer speed, v, is shown in Fig. 4. It is seen that there is a linear relation between ln k and ln v and k varies as the 0.43 power of the stirrer speed. This result is in accordance with the correlation between kL and v

w x

(8)

Ž .1r 3

Fig. 3. Plot of 1y 1y X vs. time for Tai-Bair Mt. limestone dissolution at pH 4 and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl .2

is in the range of 0.3–0.5. According to the correlation given by Levins and Glastonbury

w14 , kx is proportional to the 0.21 power of the specific agitation power. Since the

L

w x

specific agitation power increases as the two to three power of the stirrer speed 15 , the exponent of v can be estimated to be in the range of 0.41–0.62.

Fig. 4. Rate constant k vs. stirrer speed for Tai-Bair Mt. limestone dissolution at pH 4 and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl .2

(9)

Table 2

Ž

Dissolution rate constants for limestones of different sources mean particle diameters: 102–128 mm, sample weight: 0.15 g, liquid volume: 250 ml 0.1 M CaCl2 solution, stirrer speed: 1100 rpm, pH: 4.0 and 6.0,

.

temperature: 608C

Ž .

Source Rate constant k cmrs

pH s 4.0 pH s6.0 Tay-Bair Mt. 0.223 0.846 Her-Pyng 0.246 0.940 Shin-Cherng 0.253 0.688 Chyh-Ke Mt. 0.223 0.836 Dah-Gang Mt. 0.208 0.908 Bann-Pyng Mt. 0.195 0.981 Average 0.225 0.867 SD 0.022 0.103

Basing upon the observed behavior of k in response to the changes of particle size and stirrer speed, one may conclude that k is essentially equal to kL and the dissolution of limestone is controlled by the mass transfer of hydrogen ions. The same conclusion holds for other types of limestone.

Table 2 gives the values of k measured at pH 4 and a stirrer speed of 1100 rpm for the six limestones. The k values vary from 0.195 to 0.253 cmrs among the six limestones. The variation in k value, however, has no consistent relation with the limestone property; therefore, it is attributed to the experimental errors. The average value of k for the six limestones is 0.225 cmrs with a standard deviation of 10% of the average k value.

4.2. Dissolution at pH 6

The dissolution rates of the limestones at pH 6 and 1100 rpm stirrer speed were very slow. Less than 20% of limestone was dissolved in 140 min. The corresponding

Ž .

particle-size change was estimated to be less than 7%. Therefore, Eq. 9 can be employed to describe the dissolution of limestone. As shown in Fig. 5, where the data

Ž .1r3

are plotted in terms of 1 y 1 y X vs. time, the data for each limestone can be represented by a straight line.

The value of k calculated from the slope of the straight line corresponding to each limestone is also show in Table 2. The k values for limestone also differ somewhat from one another; but the variation in k value also shows no relation with the limestone property or the value obtained at pH 4, and therefore is caused by the experimental error. The average value of k for the limestones is 0.867 cmrs with a standard deviation of 12% of the average k value. The independence of k value on the source of limestone indicates that the dissolution of limestone at pH 6 is also controlled by mass transfer.

Ž .

According to Eq. 9 , the time taken for a limestone to reach a certain fraction of dissolution is proportional to its r R if kC is kept constant. This relationship can bem 0 b

confirmed by comparing the experimental data for all types of limestone. As can be seen from Fig. 5, except for Her-Pyng limestone, the limestone with larger value of r Rm 0

(10)

Ž .1r 3

Fig. 5. Plot of 1y 1y X vs. time for limestone dissolution at pH 6, 1100 rpm, and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl .2

Žsee Table 1 takes longer time to reach the same fraction of dissolution. The exception.

of Her-Pyng limestone may be due to the fact that the actual r R is smaller than thatm 0

calculated from Table 1.

4.3. Analysis on the effect of pH

As can be seen from Table 2, the k value at pH 4 is smaller than that at pH 6. This indicates that the mass transfer coefficient measured in the limestone dissolution experiment is not the physical mass transfer coefficient. The reason for such effect of pH on the k value is that the mass transfer of Hq

ions was accompanied by chemical reactions in the mass transfer boundary layer, as a number of investigators have pointed out. Although the actual processes involved are complex, an approximate analysis can be made to explain the effect of pH on the k value.

Ž .

We may assume that reaction 1 reaches equilibrium at the surface of limestone and

Ž .

reaction 2 is replaced by the following two reactions CO2yqH O|HCOy qOHy

Ž

14

.

3 2 3 Hq qOHy|H O2

Ž

15

.

q Ž .

due to the low concentration of H in the vicinity of the surface. Since reaction 14 is

Ž .

instantaneous and water is already available on the surface, reaction 14 can be also

Ž .

(11)

equilibrium constant is very large, but Hq

has to move into the boundary layer from the bulk solution or OHy

has to move outward from the surface for their reaction to take

Ž . Ž .

place. Thus the actual rate of reaction 15 and the place where the reaction 15 occurs depend on the inward diffusion of Hq

and the outward diffusion of OHy

. Since the reaction of Hq

with OHy

is faster than that with HCOy

, we may assume that at pH ) 4,

3

the Hq

ions diffusing into the boundary layer are consumed entirely by the reaction with OHy

ions and that the dissolution rate equals the rate of Hq

or OHy

consumption in the boundary layer. Thus, for mass transfer of Hq

across the boundary layer accompanied

Ž . Ž . w x

with reaction 15 , the rate constant k in Eq. 9 can be expressed as 16

w

y

x

y DOH OH s 0 q k s kH

ž

1 q

/

Ž

16

.

q DH Cb

where k0q is the physical mass transfer coefficient for H q

; D y and D q are the

H OH H

y q

w y

x

diffusivities of OH and H , respectively; OH s is the equilibrium concentration of

y

Ž . q

OH at the surface of limestone. Eq. 16 implies that the penetration depth of H is smaller than the boundary layer thickness due to the instantaneous reaction between Hq

and OHy

, thus the apparent mass transfer coefficient k is larger than the physical mass transfer coefficient which is defined by assuming the penetration depth to be the boundary layer thickness. It is obvious that the enhancement factor, the terms in the

Ž .

bracket of Eq. 16 , increases with increasing pH, while other experimental variables are kept constant.

The value of k0q and enhancement factors can be estimated for the present H

experimental conditions. According to the diffusivity data given by Chan and Rochelle

w x w yx

y q

3 , D rD was determined to be 0.57. The value of OH can be estimated from

OH H s

w x Ž .

the solubility product of calcite, Ksp 17 , and the equilibrium constant of reaction 14 ,

w x K rKw 2 18 : log K s y8.03 y 0.01183 T y 273sp

Ž

.

Ž

17

.

Kw 1568.6 log s y y0.4105 q 0.00673T .

Ž

18

.

K2 T w yx

At 608C and 0.1 M CaCl2 solution, the value of OH s was estimated to be

y6 Ž .

4.9 = 10 M. Thus, according to Eq. 16 , the enhancement factors estimated for pH 4 and 6 are 1.03 and 3.79, respectively. The ratio of these two values, 0.27, agrees very well with the ratio of the two average measured values of k, 0.26. The average value of

0 Ž .

q

kH calculated from the two average measured values of k using Eq. 16 is 0.224 cmrs. These results indicate that under the present experimental conditions, the dissolution rate at pH 6 is greatly enhanced by the chemical reaction of Hq

with OHy

within the boundary layer, whereas the enhancement at pH 4 is small and the dissolution rate approximates the physical mass transfer rate.

5. Conclusion

At the experimental conditions of this study, the dissolution rate of limestone is controlled by the mass transfer of hydrogen ions accompanied with chemical reactions

(12)

in the liquid film surrounding the limestone particle. The dissolution rate constant, being equal to the mass transfer coefficient, increases as the pH value and the stirrer speed increase, and remains constant as the particle size decreases. The dissolution rate is enhanced mainly by the reaction of Hq

with OHy

within the liquid film; but at pH 4, the enhancement effect is small and the measured rate constant approximates the physical mass transfer coefficient. A model which assumes that the limestone particle dissolves according to shrinking-core behavior, and the mass transfer coefficient is independent of particle size well describes the dissolution kinetics. Although the six limestones have different geological properties and soluble contents, the dissolution rates per unit surface area at the same particle size are the same, i.e. independent of the source of limestone, due to the mass-transfer control kinetics. However, the time taken to reach a certain fraction of dissolution depends on the source and the particle size of limestone since the required time is proportional to the molar concentration of CaCO and MgCO3 3

in the limestone and the initial particle size.

Notation

AS Ž

2.

total surface area of limestone particles m

ASO Ž

2.

initial value of As m

Cb Ž

3.

bulk concentration of hydrogen ion kg molrm

C)

s Ž

3.

equilibrium surface concentration of hydrogen ion kg molrm

d diameter of limestone particle mŽ .

D q

H Ž

2 .

diffusivity of hydrogen ion m rs

D y

OH Ž

2 .

diffusivity of hydroxyl ion m rs

e porosity of limestone

k dissolution rate constant mrsŽ .

k0q

H physical mass transfer coefficient for hydrogen ion mrsŽ .

kL mass transfer coefficient mrsŽ .

kr rate constant of surface reaction mrsŽ .

K2 the second ionization constant for carbonic acid kg ionrmŽ 3.

Ksp solubility product kg ionrmŽ 3.2

Kw Ž

3

.2

ion product for water kg ionrm

m total moles of CaCO and MgCO in solid phase kg mol3 3 Ž .

m0 initial total moles of CaCO and MgCO in solid phase kg mol3 3 Ž .

R radius of limestone particle mŽ .

R0 initial radius of limestone particle mŽ .

Sg specific surface area of limestone m rkgŽ 2 .

t time sŽ .

T temperature KŽ .

X fraction of dissolved limestone

Greek letters

rb bulk density of limestone kgrmŽ 3.

rm molar concentration of CaCO and MgCO in limestone kg molrm3 3 Ž 3. v stirrer speed rpmŽ .

(13)

References

w x1 L.N. Plummer, D.L. Parkhurst, T.M.L. Wigley, ACS Symp. Ser. 93 1979 538.Ž .

w x2 D.C. Drehmel, Proceedings of the Second International LimerLimestone Wet-Scrubbing Symposium vol.

11972, pp. 167–194, US EPA, APTD-1161.

w x3 P.K. Chan, G.T. Rochelle, ACS Symp. Ser. 188 1982 75.Ž . w x4 A.J. Toprac, G.T. Rochelle, Environ. Prog. 1 1982 52.Ž .

w x5 C.L. Gage, G.T. Rochelle, J. Air Waste Manage. Assoc. 42 1992 926.Ž . w x6 N. Ukawa, T. Takashina, N. Sinoda, Environ. Prog. 12 1993 238.Ž . w x7 J. Ahlbeck, T. Engman, M. Vihma, Chem. Eng. Sci. 48 1993 3479.Ž . w x8 J. Ahlbeck, T. Engman, M. Vihma, Chem. Eng. Sci. 50 1995 1081.Ž . w x9 P.V. Danckwerts, Gas–Liquid Reactions, McGraw-Hill, New York, 1970. w10 M. Wallin, I. Bjerle, Chem. Eng. Sci. 44 1989 61.x Ž .

w11 P.H. Calderbank, M.B. Moo-Yang, Chem. Eng. Sci. 16 1961 39.x Ž . w12 P. Harriott, AIChE J. 8 1962 93.x Ž .

w13 P.L.T. Brian, H.B. Hales, T.K. Sherwood, AIChE J. 15 1969 727.x Ž . w14 D.M. Levins, J.R. Glastonbury, Trans. Inst. Chem. Eng. 50 1972 132.x Ž . w15 A.S. Foust, Principles of Unit Operations, 2nd edn., Wiley, New York, 1980.x w16 D.R. Olander, AIChE J. 6 1960 233.x Ž .

w17 O. Sohnel, J. Garside, Precipitation: Basic Principles and Industrial Applications, Butterworth–Heine-x ¨

mann, Oxford, 1992.

w18 H.S. Harned, B.B. Owen, The Physical Chemistry of Electrolyte Solutions, 2nd edn., Reinhold, Newx

數據

Fig. 1. Schematic of experimental apparatus. 1 Autotitrator, 2 HCl bottle, 3 pH probe wire, 4 HCl titrant
Fig. 2. Titration curves for limestones at pH 4 and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl
Fig. 3. Plot of 1y 1y X vs. time for Tai-Bair Mt. limestone dissolution at pH 4 and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl
Fig. 5. Plot of 1y 1y X vs. time for limestone dissolution at pH 6, 1100 rpm, and 608C for 0.15 g limestone in 250 ml 0.1 M CaCl

參考文獻

相關文件

In this paper, we would like to characterize non-radiating volume and surface (faulting) sources for the elastic waves in anisotropic inhomogeneous media.. Each type of the source

Results for such increasing stability phenomena in the inverse source problems for the acoustic, electromagnetic, and elastic waves can be found in [ABF02, BLT10, BHKY18, BLZ20,

You are given the wavelength and total energy of a light pulse and asked to find the number of photons it

Wang, Solving pseudomonotone variational inequalities and pseudocon- vex optimization problems using the projection neural network, IEEE Transactions on Neural Networks 17

Define instead the imaginary.. potential, magnetic field, lattice…) Dirac-BdG Hamiltonian:. with small, and matrix

incapable to extract any quantities from QCD, nor to tackle the most interesting physics, namely, the spontaneously chiral symmetry breaking and the color confinement.. 

(Another example of close harmony is the four-bar unaccompanied vocal introduction to “Paperback Writer”, a somewhat later Beatles song.) Overall, Lennon’s and McCartney’s

 Create and present information and ideas for the purpose of sharing and exchanging by using information from different sources, in view of the needs of the audience. 