Dissolution Kinetics of Western Deseret Phosphate … · Dissolution Kinetics of Western Deseret Phosphate Rocks, ... energy equals to 14.46kJ ... The purpose of this work is to investigate

Arab Journal of Nuclear Science and Applications 46(5) (1-16) 2013

1

Correspondence e-maildr_moh_helmyyahoocom DrMHTaha

Dissolution Kinetics of Western Deseret Phosphate Rocks Abu Tartur with

Hydrochloric Acid

HF Aly1 MM Ali2 MH Taha2 1Atomic Energy Authorityi Cairo Egypt

2Nuclear Materials AuthorityPO Box 530 El Maddi Cairo Egypt

Received 1062013 Accepted 2762013

ABSTRACT

The dissolution kinetics of the Abu-Tartur phosphate rock using dilute

hydrochloric acid has been investigated The influence of acid concentration

liquidsolid ratio particle size and temperature was studied to explore the dissolution

kinetics of phosphate rock It was found that the leaching rate increases with

increasing the acid concentration liquidsolid ratio temperature and decreases with

increasing particle size of the phosphate rock The kinetic data showed that the

leaching process can be described by a shrinking-core model with apparent activation

energy equals to 1446kJmol The low activation energy supported the findings that

the phosphate ore leaching rate is controlled by the diffusion of reactants and

leaching products through a porous ore Based on this model and the experimental

results the dissolution rate can be expressed by the following semi-empirical

equation[1 minus 3(1 minus α)23 + 2(1 minus α)]= 3 x 10-9C 099(L S) 208ro-216eminus 1448 RT t The

experimental results was tested graphically and statically and found that the above

model fits satisfactorily the experimental results

Key Words Abu Tartur phosphate Dissolution kinetics activation energy

Leaching Modeling

INTRODUCTION

Phosphate ore is an important economic deposit in Egypt Three main mine areas are found in

Egypt namely the western desert between El-Karga and El-Dakhla Oases the Nile valley near Idfu

and along the red sea between Safaga and Quesir The total phosphate reserves in Egypt are estimated

to exceed 3 billion tons Notholt (1985)Abu Tartur phosphate deposit is one of the largest phosphates

mining area (1000 million tons and 200 million tons proved) in the Middle East The mining area is

located in the western desert of Egypt about 60 Km from El-Karga City and 10 Km from the main

road between El-Karga and El-Dakhla Oases Phosphate ores in this area is of sedimentary origin and

of the apatite group of which the most commonly encountered variants are Fluor apatite

26410

OHFPOCa and Franco lite xOHFx

POCaX

CO 26410 3

European Fertilizer

Manufacturers Association (2000)

Dissolution of phosphate rocks to obtain phosphoric acid fertilizers is carried out by acidulation

using mineral acids These acids are sulfuric nitric or hydrochloric acid While sulfuric acid

acidulation is the most popular industrial process developed yet it suffers from the disadvantage of

producing enormous amount of phosphogypsum contaminated with radioactive radium Becker

(1989)

Two main tasks were addressed in the literature for treatment of phosphate rocks with HCl

The first is concerned with the reduction of calcareous materials to upgrade low grade ore to higher

P2O5 grade This task was found to be limited since HCl will dissolve some P2O5 with the calcium

carbonate materials which reduce the beneficiation efficiency Zafar et al(2006)used dilute

hydrochloric acid solution to dissolve calcareous material in low-grade phosphate rock The results


2


indicated that the acid concentration favors the dissolution of more phosphate element rather than that

of carbonates in the sample

On the other hand upgrading phosphate rocks containing calcareous materials using weak

acids was found to be more successful Zafar et al( 1996)Formic acid was used to upgrade Abu

Tartur calcareous phosphate from around 25 up to28Malash and Khodair( 2005)Other organic

carboxylic acids used are lactic acid Zafar and Ashraf (2007)acetic acid Gharabaghiaet al

(2009)and succinic acid Zafar et al( 2007)the mechanism of these reactions was found to be

chemically controlled with activation energy in the range 40-64 kJmol

The second main task is to use HCl for complete acidulation of the phosphate ore where by

hydrochloric acid produces phosphoric acid in a similar manner as sulfuric acid except that in this

case the product calcium chloride is very soluble in water according to the following equation

Ca10 (PO4)6F2 + 20HCl harr 6H3PO4 + 10CaCl2 + 2HF helliphelliphellip (1)

Following the separation of the solid impurities the obtained solution could be treated by two

ways in the first way the solution is contacted with water immiscible solvent such as amyl alcohol to

extract phosphoric acid and leaves the CaCl2 in the aqueous PhaseEl-Shall et al (1999) Abdel-Aal

and El-Sayed A( 2000) In the second way phosphoric acid is generally precipitated in phosphate

salts which are used as fertilizers Calcium salt is used to precipitate phosphoric acid in dicalcium

phosphate form (DCP) De Waal( 2001) Also Na2CO3 and or NaOHare used to precipitate sodium

monohydrogen phosphates and sodium dihydrogen phosphate from the acidulate solution Takhim

(2005) Takhim (2007)

Within this merits the kinetics and mechanism of dissolution of synthetic apatite (as amodel for

phosphate rock) in HCl was studied by Calmanovici et al (1997)They found that the activation

energy of this reaction equals about 14 kJmol and the kinetic model for dissolution was assumed as

shrinking particle behavior controlled by diffusion Olanipenkun et al (1994) studied the

acidulation of Nigerian phosphorite by dilute HCl They found that the experimental results fit the

diffusion kinetic model Similar findings and conclusions was reported by Olanipekun(2003)

The dissolution kinetics of phosphate ore in HNO3and H2SO4solutions has been investigated

The global dissolution rates have been found to be first order and the activation energy has been

calculated as 995 and 2966kJmol respectively Bayramoglu et al 1995 F Sevimet al( 2003 )

The effect of ultrasound on the dissolution kinetics of phosphate rocks in acidic medium

(HNO3HCl) have been investigated According to the results of the study it was observedthat

ultrasound enhances the attack of H+ on cationic sites on the rock and thisfacilitates the migration of

PO4-3 ions to the liquid medium The reaction is chemically controlled in both cases and the activation

energy are 16and 18 kJmol respectively Tekinet al( 2001 and 2002)

The purpose of this work is to investigate the effect of different factors on the kinetics of the

dissolution of Abu-Tartur phosphate rock in HCl solution in order to assess the dissolution

mechanism and establish an empirical equation relating the rate constant of phosphate rock leaching to

the particle size leaching temperature acid concentration and liquid to solid ratio for the purpose of

process design

Experimental procedure

The working sample was collected from the experimental mine of Abu Tartur plateau located in

the Western Desert of Egypt where the New Valley project is constructed The chemical analysis of

the phosphate rock is as shown in Table 1Four different size fractions (0063-015 025-0315 05-

06 and 07-075 mm) were obtained by sieving through ASTM standard sieves


3


Table (1) Chemical analysis of Abu-Tartur phosphate concentrate

Constituent Constituent

P2O5 301 SO3 150

CaO 444 MgO 090

Fe2O3 38 Al2O3 046

F 28 Na2O 028

SiO2 23 K2O 004

LOI 51

LOI = Loss of ignition

XRD of the sample indicated that the main mineral of the phosphate rock is Francolite together

with minor amounts of Dolomite and Calcite as shown in Fig (1)

For reaction kinetic studies hydrochloric acid concentration was varied between 005 and 020

M In a typical experiment 150 ml of hydrochloric acid solution was poured into a thermo- static

vessel 005 ndash 025 g amount of phosphate rock (0063-0150mm) fraction was added and stirred

mechanically After the desired reaction time the leach slurry was immediately separated by filtration

The P2O5 content in the leach solution was determined spectrometrically by means of the vanado

molybdo phosphoric acid colorimetric method Gilbert and Moreno (1965)

The dissolution fraction (α) of P2O5 was calculated by the following equation

α (P2O5) exp = Amount of P2O5 in the sample

Total amount of P2O5 in the original sample

Fig (1) The XRD pattern of original sample


4


RESULTS AND DISCUSSION

1- Effect of parameters

A number of experiments were carried out to follow the effect of reaction time on the phosphate

rock dissolution in HCl in terms of P2O5 fractional conversion at different leaching parameters

namely effect of mechanical stirring speed temperature particle size hydrochloric acid concentration

and liquid solid ratio

11- Effect of Stirring Speed

Stirring speed effect on the phosphate rock dissolution process was studied for the different

stirring speed 200 400 and 600 rpm however the other parameters were fixed at 01 M hydrochloric

acid concentration particle size 150 - 63 microm temperature of 20oC and L S mass ratio of 150 ml 01

g The experimental results given in Figure (2) as a relation between P2O5conversion fraction α and

time show that as the stirring speed increased from 200 to 600 rpm the P2O5conversion fraction

αincreased from 00629 to 0674 at 16 min This increase is within the experimental error of the

results Thus the change in stirring speed has no effect on the phosphate ore dissolution by diluted

hydrochloric acid process This indicates that the dissolution process does not seem to be controlled by

mass transfer through the liquid film Therefore in all proceeding experiments the stirring speed was

kept at 400 rpm

Fig (2) Effect of stirring speed on the P2O5conversion fraction (α) (particle size

150-63 microm LS mass ratio 150 ml01 g [HCl] 01 M temperature

20 oC)

0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

200 rpm

400 rpm

400 rpm


5


12- Effect of Particle Size

The effect of phosphate rock particle size on the phosphate rock dissolution process was

studied for the different particle size fractions 750- 700 microm 600- 500 microm 315- 250 microm and 150- 63

microm however the other parameters were fixed at 01 M hydrochloric acid concentration stirring speed

of 400 rpm temperature of 20C and L S mass ratio of 150 ml 01 g The experimental results given

in Figure (3) as a relation between P2O5conversion fraction α and time show that as the phosphate

rock particle size decreased from 750- 700 to 150- 63 microm the P2O5conversion fraction αincreased

from 0261 to 0652 at 16 min This means that the P2O5conversion fraction α is inversely

proportional to the phosphate ore particle size which may be due to the increase in the active surface

area Therefore150- 63 microm is the preferred phosphate particle size for the other experiments of the

phosphate ore dissolution process

Fig (3) Effect of particle size on the P2O5conversion fraction (α) ([HCl] 01 M

LS mass ratio 150 ml01 g rpm 400 temperature 20 oC)

13 Effect of Hydrochloric Acid Concentration

The effect of hydrochloric acid concentration ranging from 005 to 02 M on the dissolution of

phosphate rock was studied using L S mass ratio of 150 ml 01 g at a temperature of 20oC with

stirring speed of 400 rpm and 150- 63 microm particle size fraction The results obtained in

Figure (4) as a relation between P2O5conversion fraction α and time indicate that as the hydrochloric

acid concentration increases from 005 to 02 M the P2O5 conversion fraction α increased from about

0563to 0788 This may be due to the increase of the H+ ions in the solution Therefore 01 M

hydrochloric acid is the choice acid concentration used for the other experiments of the dissolution of

Abu Tatur phosphate ore

0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

gt 700 microm

gt 500 microm

gt 250 microm

gt 63 microm


6


Fig (4) Effect of hydrochloric acid concentration on the P2O5conversion

fraction (α) (particle size 150-63 microm LS mass ratio 150 ml01 g

rpm 400 temperature 20 oC)

14- Effect of Hydrochloric Acid to Phosphate Ore Mass Ratio

To study the effect of hydrochloric acid to phosphate ore mass ratio on the phosphate ore

dissolution by 01 M hydrochloric acid several experiments were carried at different hydrochloric

acid to phosphate ore mass ratio from 150 ml 01 g to 150 ml 025 g at a reaction temperature of 20

C stirring speed of 400 rpm and a particle size 150 - 63 microm The experimental results are given in

Figure (5) as a relation between P2O5conversion fraction α and time From the figure it is clear that as

the hydrochloric acid to phosphate ore mass ratio increases from 150 ml 01 g to 150 ml 025 g the

P2O5conversion fraction αdecreased from about 0652 to 0301which mean that the P2O5conversion

fraction α is inversely proportional to the hydrochloric acid to phosphate ore mass ratio This may be

due to the increase of solution bulk density which causes decrease in the migration of different ions to

the liquid medium Therefore150 ml 01 g hydrochloric acid to phosphate ore mass ratio represents

the preferred condition for the other phosphate ore dissolution experiments

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

versa

tion

Fracti

on

(α

)

005 [M]

010 [M]

015 [M]

020 [M]


7


15- Effect of Temperature

To study the effect of temperature on phosphate ore dissolution by diluted hydrochloric acid 01

M several experiments were carried out at different temperature from 20 to 50oC at stirring speed of

400 rpm L S mass ratio of 150 ml 01 g and a particle size 150-63 microm The experimental results are

given in Figure (6) as a relation between P2O5conversion fraction α and time From the figure it is

clear that as the temperature increases from 20 to 50 oC the P2O5conversion fraction αincreases from

0652 to 0801 at 16 min which indicates that the temperature has a slight effect on the P2O5

conversion fraction α Therefore 20 oC represents the preferred temperature for the other factors

experiments

Fig (6) Effect of temperature on the P2O5conversion fraction (α) ([HCl] 01 M

LS mass ratio 150 ml01 g rpm 400 particle size 150-63 microm)

0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o

Fig (5) Effect of hydrochloric acid to phosphate ore mass ratio on the

P2O5conversion fraction (α) (particle size 150-63 microm [HCl] 01 M



8


Dissolution Kinetics and Mechanism

To describe the dissolution of Abu Tartur phosphate rocks by hydrochloric acid the shrinking

core model (SCM) was used In the development of the SCM the general reaction below is used

F(fluid) + bS (solid) rarr C (Product in fluid) + porous residue

Where b is the moles of S consumed per mole of F reacted

In this reaction the solid reactant is considered to be non-porous and initially surrounded by a

fluid film through which mass transfer occurs between the solid particle and the bulk of the fluid As

the reaction proceed an ashinert layer form around the unreacted core Thus at any time there is an

unreacted core of material which shrinks in size during reaction Based on this model the rate

determining step slowest step which controls the system can be mainly one of the following

Levenspiel ( 1999)

a- Film diffusion control where F andor C diffuse through the stagnant liquid film

surrounding the solid particle

b- Surface chemical reaction where the chemical reaction occurs at the surface of the

unreacted core at the sharp interphase between the solid and the reaction product and

c- Internal diffusion process where the fluid F andor C diffuse through the porous ash

layer of the solid residue

Under the conditions used in this work external diffusion has been found not to apply to the

experimental fact that rate of stirring do not affect the fraction of the dissolved material and its effect

therefore will not be analyzed

On the assumption that the phosphate particles are spherical detailed mathematical analysis are

given by Levenspiel( 1999)In this concern when the reaction is controlled by chemical reaction at

the surface of particles the following relation is valid

1 minus (1 minus α)13 = KR t (2)

Where

KR = b ks C [ρ Rp]-1 (3)

and KR is a kinetic parameter for chemical reaction control(ms-1) b is stoichiometric coefficient ks

first order rate constant (ms-1) C is the concentration of F in the bulk of the fluid (mol m3) ρ is the

molar density of S (molm3) Rp is the radius of solid particle (m) t is time (s) and α is the fraction of

S reacted

When the reaction is controlled by internal diffusion through the ash layersolid residue product the

reaction obeys the following relation

1 minus 3(1 minus α)23 + 2(1 minus α) = Kd t (4)

Where

Kd = 6 b Def C [ρ Rp2]-1 (5)

and Kd is the kinetic parameter for product diffusion control and Def is the effective diffusion

coefficient of F through the product layer (m2 s-1 )


9


To experimentally verify equation 2 a plot of the relation between 1 minus (1 minus α)13 obtained for the

different parameters investigated and time t should give a straight line which passes through the origin

A similar verification of equation 4 can be obtained if a plot of the relation between 1 minus 3(1 minus α)23 +

2(1 minus α) vs time gives a straight line passing through the origin

To determine the most probable rate determining step and the mechanism of the dissolution

reaction of Abu-Tartur phosphate rocks by hydrochloric acid the experimental results given in Figs

234and 5 when plotted as a relation between1 minus (1 minus α)13 and t do not give straight lines which pass

through the origin These figures are not given for brevity This finding excluded that the chemical

reaction on the surface of unreacted solid is the factor controlling the dissolution reaction under study

On the other hand when the values of 1 minus 3(1 minus α)23 + 2(1 minus α)experimentally obtained and

given in Figs 234and 5 are plotted against t as given in Figs 789 and 10 straight lines which pass

through the zero point were obtained Further these figures revealed that these results are of high

accuracy with correlation coefficients (R2) for these relations are very close to 10 (ge 099) Therefore

equation 4 fit satisfactory the experimental results and we can propose that the dissolution of Abu

Tartur phosphate is controlled by diffusion through the ash layer of the product

To further verify this proposal the activation energy Ea was determined using the following

Arrhenius equation

k = A expminusEa RT (6)

Or

ln k = ln A ndash (Ea RT) (7)

Where k is the overall rate constant (m sminus 1) A is the frequency factor (sminus1) Ea is the activation energy

(J molminus1) R is the universal gas constant (8314 J Kminus1molminus1) and T is the reaction temperature (Kelvin)

Fig (7) Phosphate rock leaching kinetics under different temperature ([HCl]

01 M LS mass ratio 150 ml01 g rpm 400 particle size 150-63 microm)

K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10


The variations in the rate constants with temperature were obtained from the slopes of Fig (7)

plotted as a relation between ln k against 1T Figure 11 The relation is found to be linear with a

correlation coefficient of 099 and slope equals ndashEaR The activation energy of the dissolution of

phosphate rocks in hydrochloric acid solution was calculated from the slope of Fig11 and found to

be1448 kJmol This low activation energy value is consistent with the proposed ash diffusion

controlled mechanism In their work on the dissolution of pure hydroxyapatite in nitric acid

Calmanovici et al (1997) found that the activation energy of this reaction equal about 14kJmol

These findings excluded the possible mixed surface chemical reaction and product layer controlled

process since the activation energy of surface chemical reaction is usually greater than 40kJmol

Fig (8) Phosphate rock leaching kinetics under different particle size ([HCl] 01

M LS mass ratio 150 ml01 g RPM 400 room temperature)

K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (gt 700 microm)





11


Fig (9) Phosphate rock leaching kinetics under different acid concentration (LS

mass ratio 150 ml01 g RPM 400 room temperature)

Fig (10) Phosphate rock leaching kinetics under different liquidsolid ratio

([HCl] 01 M room temperature RPM 400 room temperature)

K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (150 ml010 g)





12


Fig (11) Arrhenius plot for phosphate rock leaching kinetics ([HCl] 01 M LS

mass ratio 150 ml01 g rpm 400)

Dissolution modeling

The Ash Layer Diffusion Controlled model may be used to describe the dissolution of

phosphate rock by hydrochloric acid according to eq (4) However its applicability is limited by the

specific values used for different reaction parameters of temperature particle size acid concentration

and liquidsolid ratio According to the Ash Layer Diffusion controlled model equations 4 amp 5the

value of kd depends on various reaction parameters The relation between different reaction parameters

and reaction rate constant kd could be written as follows

kd= ko Ca (LS) b Dc eminus E aRT (8)

Or

[1 minus 3(1 minus α) 23 + 2(1 minus α)] = ko Ca (LS)b R p ceminus E aRTt (9)

Where ko is the reaction rate constant the acid concentration L S the liquidsolid ratio T the

reaction temperature Ea the activation energy and R ko a b c are constants The stirring speed was

omitted as the results given in Fig (6) show that the change in the stirring speed has a negligible

effect on the dissolution of phosphate rock by hydrochloric acid

The effect of the particle size acid concentration and liquid to solid ratio on the reaction rate

constant k can be estimated by plotting the relations between log k and log Ro log C and log (LS)

respectively which give the values of a b and c constants as shown in Fig(12-14)

1- K 1T X 1000


13


Fig (12) Relation between log k and log [M]

Fig (13) Relation between log k and log ro


14


Fig (14) Relation between log k and log LS

The results show that the constants a b and chave the following values 099 208 and

-216 respectively The mathematical treatment for these results shows that kO has a value of

3 x 10-9Therefore equation (9) can be written as follows

kd=3 x 10-9C 099(L S) 208ro-216eminus 1448 RT (10)

Accordingly the following semi empirical equation can represent the dissolution of Abu

Tartur phosphate rock by hydrochloric acid

[1 minus 3(1 minus α)23 + 2(1 minus α)]= 3 x 10-9C 099(L S) 208ro-216eminus 1448 R Tt (11)

To verify this equation the calculated conversion fraction α cal was calculated under

different conditions at different interval times using equation 11 and compared with that

experimentally obtained α expThe results are presented in Fig(15) as a linear relation between α exp

and α cal The results indicated that the agreement between the experimental and calculated values is

good with a correlation coefficient of 104 and standard deviation of plusmn00496 which means that the

degree of scattering of the observed values about the regression line is small

Log LS


15


Fig (15) Agreement between experimental and calculated conversion values

Using the statistical analysis with 128 numbers of experimental data by Eq (12) give a relative

mean square of errors of 00678 which means that the semi empirical model can be used to express

the dissolution of phosphate ore by hydrochloric acid with nearly no significant random error

ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION

Hydrochloric acid can be used to leach phosphate rock The effective parameters on the

dissolution rate are reaction temperature particle size acid concentration and liquidndashsolid ratio with a

constant stirring speed of 400 rpm The results showed that by increasing all effective parameters the

leaching process increases except for solid particle size where its increase leads to decrease of the

leaching process

Analysis of the kinetic data by different kinetic models indicates that the leaching of phosphate

rock with hydrochloric acid is ash layer diffusion controlled process The mathematical treatment for

the results shows that the phosphate ore dissolution by hydrochloric acid activation energy is1448 kJ

M and the dissolution process could be expressed by the following semi-empirical kinetic equation

[1 minus 3(1 minus α)23 + 2(1 minus α)] = 3 x 10-9C 099(L S) 208ro-216eminus 1448 RT t

This equation indicates that both LS and particle size of the mineral play important role in the

dissolution kinetics Further this relation can be used to calculate the phosphate rock conversion

fraction for the different dissolution parameters The agreement between experimental and calculated

conversion fractions was achieved with a relative mean square of errors equals to 00678

y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES

(1) A J G Notholt (1985) Phosphorite resources in the Mediterranean Tethyan Phosphogenic

Province A progress report Sciences Geologiques Memoir 77 9ndash21

(2) European Fertilizer Manufacturers Association (2000) Booklet No 4 of 8 Production of

phosphoric acid Belgium

(3) P Becker Phosphates and Phosphoric Acid Raw Materials Technology and Economics of the

Wet Processes Marcel Decker Inc New York 1989

(4) ZI Zafar T M Ansari M Ashraf and A M ibid (2006) Effect of Hydrochloric Acid on

Leaching Behavior of Calcareous Phosphorites Iranian Journal of Chemistry amp Chemical

Engineering 25 (2) 47-57

(5) ZI Zafar M M Anwar and D W Pritchard (1996) Innovations in beneficiation technology

for low grade phosphate rocks Nutrient Cycling in Agroeco systems 46 135-151

(6) G F Malash S M Khodair (2005) Beneficiation of Abu Tartur phosphate rock by partial

acidulation with formic acid Alexandria Engineering Journal 44 487ndash492

(7) ZI Zafar and M Ashraf (2007) Selective leaching kinetics of calcareous phosphate rock in

lactic acid Chemical Engineering Journal 131 41-48

(8) M Gharabaghi M Noaparast M Irannajad (2009) Selective leaching kinetics of low-grade

calcareous phosphate ore in acetic acid Hydrometallurgy 95 341ndash345

(9) M Ashraf ZI Zafar and T M Ansari (2007) Selective leaching kinetics and upgrading of

low-grade calcareous phosphate rock in succinic acid Hydrometallurgy 80 286ndash292

(10) El-Shall H Abdel- Aal E A and Moudgil B (1999) Cost-Effective reagents as defoamers

and crystal modifiers to enhance the filtration of phosphogypsum USA Florida Institute of

Phosphate Research (FIPR) Florida University

(11) Abdel-Aal EA (2000) Recovery of phosphoric acid from Egyptian Nile Valley phosphate

tailings Minerals Engineering Journal 13(2) 223-226

(12) De Waal J C (2001) Production of dicalcium phosphate or monocalcium phosphate from

calcium phosphate US Patent 6183712 B1

(13) Takhim M (2005) Method for the production of phosphoric acid andor a salt thereof and

products thus obtained US Patent 20050238558 A1

(14) Takhim M (2007) Method for etching phosphate ores US Patent 20070122326 A1

(15) C E Calmanovici B Gilot and C Laguerie (1997) Mechanism and kinetics for the

dissolution of apatitic materials in acid solutions Braz J Chem Eng 14 (2)

(16) E O Olannipekun EO Orderinde RA and O K Okurumeh (1994) Dissolution of

phosphorite in dilute hydrochloric acid solution Pak J Sci Ind Res 37 183

(17) EO Olanpekun (2003) Kinetics of acidulation reaction in nitrophosphate process

IntJMinerProcess 69 1

(18) M Bayramoglu N Demircilblu and T Tekin (1995) Dissolution kinetics of Mazidagl

phosphate rock in HNO3 solution International Journal of Mineral Processing 43 249-254

(19) F Sevim H Saraccedil M M Kocakerim and A Yartaş (2003) Dissolution Kinetics of Phosphate

Ore in H2SO4 Solutions Industrial amp Engineering Chemistry Research 42 (10) 2052-2057

(20) T Tekin D Tekin and M Bayramoglu (2001) Effect of ultrasound on the dissolution kinetics

of phosphate rock in HNO3 ultrasonicss on chemistry 8 373-377

(21) T Tekin (2002) Use of ultrasound in the dissolution kinetics of phosphate rock in HCl

Hydrometallurgy 8 187-192

(22) R L Gilbert E CMoreno (1965) Dissolution of phosphate rock by mixtures of sulfuric and

phosphoric acids Ind Eng Chem Process Des Dev 4 368-371

(23) O Levenspiel (1999) Chemical Reaction Engineering second ed JohnWileyamp Sons Inc

New York


2


indicated that the acid concentration favors the dissolution of more phosphate element rather than that

of carbonates in the sample

On the other hand upgrading phosphate rocks containing calcareous materials using weak

acids was found to be more successful Zafar et al( 1996)Formic acid was used to upgrade Abu

Tartur calcareous phosphate from around 25 up to28Malash and Khodair( 2005)Other organic

carboxylic acids used are lactic acid Zafar and Ashraf (2007)acetic acid Gharabaghiaet al

(2009)and succinic acid Zafar et al( 2007)the mechanism of these reactions was found to be

chemically controlled with activation energy in the range 40-64 kJmol

The second main task is to use HCl for complete acidulation of the phosphate ore where by

hydrochloric acid produces phosphoric acid in a similar manner as sulfuric acid except that in this

case the product calcium chloride is very soluble in water according to the following equation

Ca10 (PO4)6F2 + 20HCl harr 6H3PO4 + 10CaCl2 + 2HF helliphelliphellip (1)

Following the separation of the solid impurities the obtained solution could be treated by two

ways in the first way the solution is contacted with water immiscible solvent such as amyl alcohol to

extract phosphoric acid and leaves the CaCl2 in the aqueous PhaseEl-Shall et al (1999) Abdel-Aal

and El-Sayed A( 2000) In the second way phosphoric acid is generally precipitated in phosphate

salts which are used as fertilizers Calcium salt is used to precipitate phosphoric acid in dicalcium

phosphate form (DCP) De Waal( 2001) Also Na2CO3 and or NaOHare used to precipitate sodium

monohydrogen phosphates and sodium dihydrogen phosphate from the acidulate solution Takhim

(2005) Takhim (2007)

Within this merits the kinetics and mechanism of dissolution of synthetic apatite (as amodel for

phosphate rock) in HCl was studied by Calmanovici et al (1997)They found that the activation

energy of this reaction equals about 14 kJmol and the kinetic model for dissolution was assumed as

shrinking particle behavior controlled by diffusion Olanipenkun et al (1994) studied the

acidulation of Nigerian phosphorite by dilute HCl They found that the experimental results fit the

diffusion kinetic model Similar findings and conclusions was reported by Olanipekun(2003)

The dissolution kinetics of phosphate ore in HNO3and H2SO4solutions has been investigated

The global dissolution rates have been found to be first order and the activation energy has been

calculated as 995 and 2966kJmol respectively Bayramoglu et al 1995 F Sevimet al( 2003 )

The effect of ultrasound on the dissolution kinetics of phosphate rocks in acidic medium

(HNO3HCl) have been investigated According to the results of the study it was observedthat

ultrasound enhances the attack of H+ on cationic sites on the rock and thisfacilitates the migration of

PO4-3 ions to the liquid medium The reaction is chemically controlled in both cases and the activation

energy are 16and 18 kJmol respectively Tekinet al( 2001 and 2002)

The purpose of this work is to investigate the effect of different factors on the kinetics of the

dissolution of Abu-Tartur phosphate rock in HCl solution in order to assess the dissolution

mechanism and establish an empirical equation relating the rate constant of phosphate rock leaching to

the particle size leaching temperature acid concentration and liquid to solid ratio for the purpose of

process design

Experimental procedure

The working sample was collected from the experimental mine of Abu Tartur plateau located in

the Western Desert of Egypt where the New Valley project is constructed The chemical analysis of

the phosphate rock is as shown in Table 1Four different size fractions (0063-015 025-0315 05-

06 and 07-075 mm) were obtained by sieving through ASTM standard sieves


3




P2O5 301 SO3 150

CaO 444 MgO 090

Fe2O3 38 Al2O3 046

F 28 Na2O 028

SiO2 23 K2O 004

LOI 51















4


















kept at 400 rpm



20 oC)

0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

200 rpm

400 rpm

400 rpm


5
























0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

gt 700 microm

gt 500 microm

gt 250 microm

gt 63 microm


6

















0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

versa

tion

Fracti

on

(α

)

005 [M]

010 [M]

015 [M]

020 [M]


7










experiments



0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o





8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


3




P2O5 301 SO3 150

CaO 444 MgO 090

Fe2O3 38 Al2O3 046

F 28 Na2O 028

SiO2 23 K2O 004

LOI 51















4


















kept at 400 rpm



20 oC)

0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

200 rpm

400 rpm

400 rpm


5
























0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

gt 700 microm

gt 500 microm

gt 250 microm

gt 63 microm


6

















0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

versa

tion

Fracti

on

(α

)

005 [M]

010 [M]

015 [M]

020 [M]


7










experiments



0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o





8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


4


















kept at 400 rpm



20 oC)

0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

200 rpm

400 rpm

400 rpm


5
























0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

gt 700 microm

gt 500 microm

gt 250 microm

gt 63 microm


6

















0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

versa

tion

Fracti

on

(α

)

005 [M]

010 [M]

015 [M]

020 [M]


7










experiments



0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o





8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


5
























0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

ver

sati

on

Fra

ctio

n (

α)

gt 700 microm

gt 500 microm

gt 250 microm

gt 63 microm


6

















0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

versa

tion

Fracti

on

(α

)

005 [M]

010 [M]

015 [M]

020 [M]


7










experiments



0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o





8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


6

















0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

on

versa

tion

Fracti

on

(α

)

005 [M]

010 [M]

015 [M]

020 [M]


7










experiments



0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o





8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


7










experiments



0

01

02

03

04

05

06

07

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

150 ml010 g

150 ml015 g

150 ml020 g

150 ml025 g

0

01

02

03

04

05

06

07

08

09

0 200 400 600 800 1000 1200

Time sec

P2O

5 C

onve

rsat

ion

Fra

ctio

n (

α)

20 C

30 C

40 C

50 C

o

o

o

o





8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


8












Levenspiel ( 1999)














Where

KR = b ks C [ρ Rp]-1 (3)




S reacted




Where

Kd = 6 b Def C [ρ Rp2]-1 (5)




9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


9


















Arrhenius equation


Or






K1 = 00004x

R2 = 09913

K2 = 00005x

R2 = 099

K3 = 00006x

R2 = 09904

K4 = 00007x

R2 = 09903

0

002

004

006

008

01

012

014

016

018

0 50 100 150 200 250 300

Time sec

1-3(

1-α)

23 +

2(1

-α)

Linear (20 C)

Linear (30 C)

Linear (40 C)

Linear (50 C)

o

o

o

o


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


10













K1 = 7E-06x

R2 = 099

K2 = 1E-05x

R2 = 09924

K4 = 00004x

R2 = 09913

K3 = 5E-05x

R2 = 09901

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


11






K2 = 00004x

R2 = 09913

K3 = 00006x

R2 = 09902

K4 = 00008x

R2 = 09932

K1 = 00002x

R2 = 09907

0

002

004

006

008

01

012

014

016

018

02

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)

Linear (01 [M])

Linear (015 [M])

Linear (02 [M])

Linear (005 [M])

K1 = 00004x

R2 = 09913

K2 = 00002x

R2 = 09964

K3 = 00001x

R2 = 09909

K4 = 6E-05x

R2 = 0992

0

002

004

006

008

01

012

0 50 100 150 200 250 300

Time sec

1-3

(1-α

) 2

3 +

2(1

-α)






12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


12












Or









1- K 1T X 1000


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


13





14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


14
















Log LS


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


15






ER =

21

12

2exp1

N

i cal

cal

N

(12)

CONCLUSION





leaching process










y = 10459x + 00082

R2 = 09504

0

02

04

06

08

1

0 01 02 03 04 05 06 07 08 09

α exp

α c

al


16


REFERENCES















































New York


16


REFERENCES















































New York

Documents

Dissolution Kinetics of Western Deseret Phosphate … · Dissolution Kinetics of Western Deseret Phosphate Rocks, ... energy equals to 14.46kJ ... The purpose of this work is to investigate