STATIC SIMULATION PROGRAM OF COPPER SOLVENT EXTRACTION CONFIGURATIONS USING MICROSOFT EXCEL SOLVER

Transcription

1 STATIC SIMULATION PROGRAM OF COPPER SOLVENT EXTRACTION CONFIGURATIONS USING MICROSOFT EXCEL SOLVER Joseph Kafumbila This textbook provides the proedure for design stati simulation programs using Exel Solver for optimization on an Exel worksheet. This proedure will allow the design of a stati simulation program for all opper solvent extration onfigurations. The stati simulation program will be designed to size a new plant or trak performane of an old plant. K afumbila K asonta Joseph P r o e s s d e s i g n e r

2 Design of simulation program of opper solvent extration onfiguration using Mirosoft Exel Solver 06 Joseph Kafumbila

3 Contents. INTRODUCTION EQUILIBRIUM LINE SIMULATION MODELS EXTRACTION STEP STRIPPING STEP EQUILIBRIUM LINE AND MACCABE THIELE DIAGRAM EQUILIBRIUM LINE MACCABE THIELE DIAGRAM CONSTRAINTS OF COPPER SX-EW PLANT EQUILIBRIUM CONSTRAINTS BETWEEN EXTRACTION AND STRIPPING STEPS MAXIMUM VALUE OF EXTRACTANT VOLUME PERCENTAGE FREE ACID CONCENTRATION IN PLS MAXIMUM FREE ACID CONCENTRATION IN SPENT ELECTROLYTE MINIMUM COPPER CONCENTRATION IN SPENT ELECTROLYTE MAXIMUM COPPER CONCENTRATION IN ADVANCE ELECTROLYTE OPTIMUM VALUE OF RATIO OF ORGANIC TO AQUEOUS OF EXTRACTION STEP SATURATION RATIO SR SIMULATION PROGRAM USING EXCEL SOLVER PROGRAM DESCRIPTION STATIC SIMULATION PROGRAM DESIGN BIBLIOGRAPHY... 74

4 . Introdution Copper prodution tehnology hanges drastially in the last 5 years with introdution of solvent extration-eletrowinning iruit as a opper prodution method. The tehnology of opper solvent extration produes the most eonomial opper from low-grade opper ore. Copper solvent extration tehnology onsists of two iruits onneted by a ommon organi phase. In the first step, alled extration step, metal is extrated from aqueous phase by organi phase. In the seond step, alled stripping step, metal is reovered from organi phase. The seond aqueous phase is more pure and onentrated. At the beginning, opper solvent extration onfiguration operating on dilute aqueous phases were onstituted with two stages respetively to extration and stripping steps. Design of this ExS onfiguration was simple and based on the value of opper transfer per extratant volume perentage of 0. (g/l/% v/v). This value gives opper extration effiieny greater than 98% and opper stripping effiieny of 60%. Afterwards, understanding that opper extration effiieny was not the most important parameter than the ost of opper prodution plant, one stage of stripping step was removed and the value of opper transfer was inreased to 0.6 (g/l/%v/v). Design of this ExS onfiguration was based on the expeted value of opper extration effiieny of 90%. MaCabe Thiele method was introdued in design of opper solvent extration onfiguration when opper solvent extration tehnology started to be used for high-grade opper ore. A large number of laboratory tests were required before obtaining the optimal onfiguration by using MaCabe Thiele method. It was at this level that a simulation model of equilibrium line of extration and stripping steps was introdued. Several simulation models of equilibrium line of opper solvent extration using helating reagents were made. These simulation models were based either on equilibrium onstant of opper solvent extration hemial reation [] or on extrapolation urves of equilibrium lines of extration and stripping steps []. Simulation model based on hemial reation equilibrium onstant was required knowledge of phenomenology of hemial reation. Currently, most of stati simulation programs of opper solvent extration onfiguration use equilibrium line simulation models based on hemial reation equilibrium onstants beause it is easy to simulate impat of iron o-extration to extration step and temperature to stripping step. Design of this stati simulation program requires a ertain level of knowledge in omputer programming. This bloks innovation in design of new reagent or omplex opper solvent extration onfigurations beause stati simulation programs are developed by extratant suppliers far from plant designers. Equilibrium line simulation model based on hemial reation equilibrium onstant requires knowledge of all intermediate hemial reations. Example of intermediate hemial reations ourring during opper solvent extration with MOC- 45 is the following []: Cu + + HR CuR + H + (a) 3

5 Cu + + (HR) CuR + H + (b) HR (HR) () HR and (HR) are the moleular forms of MOC- 45 extratant in organi phase. (3). Equilibrium onditions of eah hemial reation are given by mathematial expressions (), (), and K a = [CuR ]x[h+ ] [Cu + ]x[hr] () K b = [CuR ]x[h+ ] [Cu + ]x[(hr) ] () K = [(HR) ] [HR] (3) where K a, K b, and K are respetively hemial reation equilibrium onstants of hemial reations (a), (b), and (). Stati simulation model will be defined by finding the equilibrium onstants values using experimental data of equilibrium lines. It must involve the following mathematial expressions giving mass balanes. - Copper mass Balane: [Cu + ] i = [Cu + ] f + V o V a x [CuR ] (5) - Oxime radial R mass balane: [HR] t = [HR] + x [(HR) ] + x [CuR ] (6) - Hydrogen ion mass balane: [H + ] f = [H + ] i + x V o V a x [CuR ] (7) Where the indies i, f and t respetively mean initial, final and total. V o and V a respetively mean volume of organi and aqueous phases. 4

6 One the values of hemial reation equilibrium onstants are obtained, the equilibrium line simulation model will use these mathematial expressions from () to (7) to predit the value of opper onentration in organi phase from the value of opper and free aid onentrations in aqueous and the values of V a and V o. This design method of equilibrium line simulation model is used by reagent suppliers and its design is omplex. For dynami modeling used in industrial opper solvent extration plant, plant metallurgists use extrapolation urves of equilibrium lines []. In most ases, the onditions for using these extrapolation equations are limited to this opper solvent extration plant. The goal of this textbook is to give a simple proedure for designing a stati simulation program of opper solvent extration onfiguration. This simple proedure will allow designers to quikly have a stati simulation program for omplex onfiguration or new produt that have not yet simulation program developed by supplier. It will also allow plant metallurgists to have a stati simulation program for heking plant performanes. This stati simulation program uses Exel solver program for optimization. Exel Solver is the Mirosoft add-in program used for what-if analysis. Exel solver program allows finding the optimum value for a formula in one ell. Knowledge of the use of Exel Solver is not suffiient. The textbook also gives advie that prevents stati simulation programs to rash when initial data hange. In the seond hapter, the textbook offers equilibrium line simulation models of extration and stripping steps not requiring knowledge of intermediate hemial reations. Equilibrium ondition of global hemial reation is resulted on the assumption that ioni strength varies very little only in aqueous phase. On the other hand, the ioni strength varies in organi phase. The textbook gives results of experimental tests. Extration and stripping equilibrium lines were generated by ontating a series of different volumes of aqueous phase and stripped organi phase by mehanial stirring. Following attainment of equilibrium after 5 min, phases were allowed to separate. After phase disengagement, opper was analyzed in raffinate by AAS, whereas free aid was determined by titration. After more than 0 years of researh, the new theory of equilibrium ondition of opper solvent extration hemial reation begins to be lear. In the third and fourth hapters, the textbook also gives theoretial onepts of opper solvent extration and industrial onstraints whih allow, together with equilibrium line simulation models, to design a stati simulation program of simple or omplex opper solvent extration onfiguration. In the fifth hapter, the textbook gives the design proedure of the stati simulation program of opper solvent extration onfiguration from an example. The proedure involves two options. The first onerns the designers and the seond onerns the plant metallurgists. The simulation program alled SimSXCu Full version.0 gives stati simulation programs of eighteen opper solvent extration onfigurations. 5

7 . Equilibrium line simulation models.. Extration step... Equilibrium ondition Extration step is guided by thermodynami disequilibrium between aqueous and organi phases. Copper mass transfer is stopped when thermodynami property reahes equilibrium ondition in both phases. Global opper solvent extration hemial reation with Lix984N extratant is followed hemial reation (d) [3]. LIX 984N reagent, a : volume blend of LIX 860N-I and LIX 84N-I, is a mixture of 5- nonylsaliylaldoxime and -hydroxy-5-nonylaetophenone oxime. Cu + + HR CuR + H + (d) where Cu + and H + are opper and hydrogen ioni speies in aqueous phase, HR is aid form of Lix984N extratant, and CuR is opper omplex form in organi phase expression (8) [4]. Thermodynami equilibrium ondition of global hemial reation (a) is given by the mathematial μ CuR + μ H + - μ Cu + - μ HR = 0 (8) where μ ρ is hemial potential of speies ρ Chemial potential of speies ρ is given by the mathematial expression (9). μ ρ = RTln(β ρ x γ ρ x C ρ C ρ 0) (9) where β ρ is standard-state ativity of speies ρ and is a funtion of solvent nature and temperature, 0 γ ρ is hemial ativity oeffiient of speie ρ, C ρ is molar onentration of speies ρ, C ρ is referene molar onentration whih by onvention is molar onentration, R is the perfet gas onstant, and T is the temperature The substitution of the mathematial expression (9) for all speies in the mathematial expression (8) gives the mathematial expression (0) whih is the thermodynami equilibrium ondition. 6

8 [Cu e or ] x [H e aq ] [Cu e aq ] x [HR or β CuR x β H x γ Cu x γ HR e ] = β Cu x β HR γ CuR x γ H = K e (0)... Value of K e from molar onentration... Definition The value of thermodynami equilibrium ondition K e from molar onentrations alled K e is given by the mathematial expression (). K e = [Cu or e ]x[h e aq ] () e e ] [Cu aq ]x[hr or... Copper molar onentrations in organi and aqueous phases The values of opper molar onentrations at the steady-state in organi and aqueous phases are respetively given by the mathematial expressions () and (3). [Cu e or ] = Cu e or () [Cu e aq ] = Cu aq e (3) e e where Cu aq and Cu or are respetively opper onentrations (g/l) in aqueous and organi phases The mathematial expression (4) gives opper mass balane at the steady-state. e i i e Cu or = Cu or + (Cu aq - Cu aq ) x V aq (4) V or i i where Cu aq and Cu or are respetively initial opper onentrations (g/l) in aqueous and organi phases. V aq and V or are respetively volumes of aqueous and organi phases Free extratant molar onentration in organi phase expression (5). The value of free extratant molar onentration in organi phase is given by the mathematial [HR e V% x 0.9 x 000 or ] = 00 x 70 - x Cuor e (5) 7

9 where v% is extratant volume perentage (v/v) in organi phase. 0.9 is the density of Lix984N extratant. 70 is the mass molar of Lix984N extratant Hydrogen ion molar onentration in aqueous phase The value of hydrogen ion molar onentration in aqueous phase omes from sulfuri aid dissoiation reation. Sulfuri aid dissoiation reation has followed hemial reations (e) and (f). H SO 4 HSO 4 + H + K a = 0 4 (e) HSO 4 SO 4 + H + K a =.5 0 (f) If C is free sulfuri aid molar onentration in aqueous phase and C is molar onentration of anion SO 4 assoiated with opper and buffers in aqueous phase. Sulfuri aid dissoiation reation (e) is omplete a beause the value of hemial reation equilibrium onstant K is big. Following mass balane omes from sulfuri dissoiation reation (e). H SO 4 HSO 4 H + Initial state C 0 0 Final state -C C C Mass balane 0 C C Sulfuri aid dissoiation reation (f) is not omplete beause the value of hemial reation equilibrium onstant K a is not big enough. Following mass balane omes from sulfuri aid dissoiation reation (f). Y is molar onentration of anion HSO 4 whih goes into dissoiation. HSO 4 SO 4 H + Initial state C C C Final state -Y Y Y Mass balane C -Y C +Y C +Y Thermodynami equilibrium ondition of sulfuri aid dissoiation reation (f) is given by the mathematial expression (6). Resolution of the mathematial expression (6) gives seond-degree equation. Hydrogen ion molar onentration in aqueous phase is given by the mathematial expression (7). The value of molar onentration Y is given by the mathematial expression (8) and the values of onstants A and B are given by the mathematial expressions (9) and (0). K a = (C +Y)(C +Y) (C Y) (6) 8

10 [H e aq ] = C + Y (7) Y = ( A+ A 4 x B) (8) A = C + C + K a (9) B = C x (C - K a ) (0) From the mathematial expression (8), the value of molar onentration Y beomes zero when the value of molar onentration C is equal to the value of hemial reation equilibrium onstant K a. When the value of molar onentration C is greater than the value of hemial reation equilibrium onstant K a, the value of molar onentration Y is lower than zero. In this ondition, the value of molar onentration Y in the mathematial expression (7) is zero. When the value of molar onentration C is lower than the value of hemial reation equilibrium onstant k a, the value of molar onentration Y is greater than zero...3. Value of K e from hemial ativity oeffiients..3.. Definition The value of thermodynami equilibrium ondition K e from hemial ativity oeffiients of speies alled K e is given by the mathematial expression (). β CuR x β H x γ Cu x γ HR K e = β Cu x β HR γ CuR x γ H () The value of K e is multipliation of two ratios. First ratio is the ratio of standard state ativities of speies whih is a onstant and seond ratio is the ratio of hemial ativity oeffiients of speies. The seond ratio of hemial ativity oeffiients also is multipliation of ratios of hemial ativity oeffiients in organi and aqueous phases respetively Ratio of hemial ativity oeffiients in aqueous phase Depending on molar onentrations of speies in aqueous phase, three ases are possible [5]: - Aqueous phase very diluted. In this ondition, the values of hemial ativity oeffiients tend to. - Ioni strength in aqueous phase varies very little. In the ondition, the value of ratio of hemial ativity oeffiients is a onstant. - Ioni strength in aqueous phase varies. In this ondition, the value of ratio of hemial ativity oeffiients is a variable. 9

11 The assumption is that ioni strength varies very little. So, ratio of hemial ativity oeffiients is a onstant in aqueous phase Ratio of hemial ativity oeffiients in organi phase In organi phase, the study done on the extratant Kelex 00, whih is helating opper solvent extration reagent, shows that ratio of hemial ativity oeffiients of speies in organi phase is a funtion of opper onentration in organi phase [4]. The assumption is that this thermodynami property is also true for helating opper extratant...4. Observations Conlusion from preeding observations is that the value of thermodynami equilibrium ondition K e is a funtion of opper onentration in organi phase...5. Mathematial relationship between the values of thermodynami equilibrium ondition and opper onentration in organi phase..5.. Pure opper sulfate aqueous phase Test onditions of lab test done with pure opper sulfate aqueous phase are the following: - Initial opper onentration in aqueous phase: 8 g/l. - Initial free aid onentration in aqueous phase: 5 g/l. - Extratant: Lix984N. - Extratant volume perentage in organi: 0%. Table gives equilibrium line data of lab test from whih the values of thermodynami equilibrium ondition K e of eah steady-state position are alulated. Data of steady-state position having the value of opper onentration in aqueous of 0.79 g/l are derived from ondition that the value of molar onentration C is equal to the value of hemial reation equilibrium onstant K a. Corresponding opper onentration in organi phase is obtained by extrapolation on equilibrium line. Figure gives the values of thermodynami equilibrium ondition K e versus the values of opper onentration in organi phase. Results show that: - The values of thermodynami equilibrium ondition K e are not the same for steady-state positions of equilibrium line. - The value of thermodynami equilibrium ondition K e is a linear funtion of the value of opper onentration in organi phase. 0

12 - The values of line slope are not the same in the ranges (0.8 to 5.75 g/l Cu) and (5.75 to 0.8 g/l Cu) where molar onentration Y is greater or lower than zero respetively. Table : Value of K e from equilibrium line data of lab test Lab test Organi Aqueous Aq Org Cu Cu Cu Free Lix984N Cu Y C C H K e g/l g/l moles/l moles/l moles/l moles/l moles/l moles/l moles/l Figure : Values of K e versus values of opper onentrations in organi phase of lab test..5.. Industrial opper sulfate aqueous phase Test onditions of lab test done with industrial opper sulfate aqueous phase are the following: - Elements grade of industrial opper sulfate aqueous phase is given in Table. - Extratant: Lix984N. - Extratant volume perentage in the organi: 8%. Table 3 gives equilibrium line data from whih the values of thermodynami equilibrium ondition K e of eah steady-state position are alulated. Figure gives the values of thermodynami equilibrium ondition K e versus the value of opper onentration in organi phase.

13 Table : Element grades of industrial opper sulfate aqueous phase of lab test Cu Co Al Fe Mg Mn Zn Ni Aid g/l g/l g/l g/l g/l g/l g/l g/l g/l Table 3: Value of K e from equilibrium line data of lab test Lab test Organi Aqueous Aq Org Cu Cu Cu Free Lix984N Cu Y C C H K e g/l g/l moles/l moles/l moles/l moles/l moles/l moles/l moles/l Figure : Values of K e versus values of opper onentration in organi phase of lab test Results show that: - In the industrial aqueous phase ontaining various sulfate buffers, molar onentration C is greater than the value of hemial reation equilibrium onstant K a. So, molar onentration Y is lower than zero.

14 - The value of thermodynami equilibrium ondition K e also is a linear funtion of the value of opper onentration in organi phase Observations In order to get loser to industrial onditions, only the range where molar onentrations Y are lower than zero will be taken in simulation model. Hydrogen ion onentration in aqueous phase is given now by the mathematial expression (). The mathematial expression (3) gives sulfuri aid onentrations in aqueous phase after opper solvent extration. [H or e ] = AC aq e 98 () e i i A aq = A aq + (Cu aq - Cu e aq ) x,54 (3) e i where A aq is sulfuri aid onentration (g/l) in aqueous phase at the steady-state and A aq is initial sulfuri aid onentration (g/l) in aqueous phase...6. Equilibrium line simulation model of extration step The substitution of the mathematial expressions (), (3), (5) and () in the mathematial expression () gives the mathematial expression (4) whih gives the value of thermodynami equilibrium ondition K e as a funtion of extratant volume perentage in organi phase, free aid onentration in aqueous phase and opper onentrations in organi and aqueous phases. K e = Cu e org [A Cue x e aq ] aq [ x V% x Cu org e ] (4) The value of thermodynami equilibrium ondition K e obtained from the mathematial expression (4) is plotted versus the values of opper onentration in organi phase in the range where the value of molar onentration Y is lower than zero using pure opper sulfate aqueous phase. Table 4 gives equilibrium line data of lab test, 3, 4 and 5. Figure 3 gives the value of thermodynami equilibrium ondition K e versus the values of opper onentration in organi phase. Results show that: - Initial free aid onentration does not affet the value of line slope. - The value of line slope is a funtion only of extratant volume perentage in organi phase. Line mathematial expression of thermodynami equilibrium ondition obtained from equilibrium line data has a shape given by the mathematial expression (5). 3

15 K e =D x Cu e or + E (5) Table 4: Equilibrium line data of lab tests, 3, 4 and 5 of extration step Lab test Lab test 3 Lab test 4 Lab test 5 i Cu aq 8 g/l i Cu aq 8 g/l i Cu aq 8 g/l i Cu aq 8 g/l i A aq 5 g/l i A aq 5 g/l i A aq 0 g/l i A aq 0 g/l V% 0 % V% 0 % V% 5 % V% 5 % e e Cu aq Cu or e e Cu aq Cu or e e Cu aq Cu or e e Cu aq Cu or Figure 3: Values of K versus the values of opper onentrations in organi phase from equilibrium line data of lab tests, 3, 4, and 5 The values of onstants D and E are funtions of extratant volume perentage. Mathematial expressions giving the values of onstants D and C are extrapolation urves of the value of onstants D and C obtained at different values of extratant volume perentage in the range of 8-3%. Equilibrium line simulation model of extration step is given by the mathematial expression (6). Thermodynami equilibrium onditions of K e and K e given by the mathematial expressions (6) and (4) are equals for eah steady-state position of equilibrium line. K =(-8.5 x v% (.746) ) x Cu e or +.7 x v% ( 0.646) (6) 4

16 .. Stripping step... Equilibrium ondition Stripping step is guided by thermodynami disequilibrium between aqueous and organi phases. Copper mass transfer is stopped when thermodynami property reahes equilibrium ondition in both phases. Copper stripping hemial reation with Lix984N extratant is followed hemial reation (g) whih is the reverse reation of opper extration hemial reation. CuR + H + Cu + + HR (g) The mathematial expression (7) gives the thermodynami equilibrium ondition. [Cu e or ] x [H e aq ] [Cu e aq ] x [HR or β CuR x β H x γ Cu x γ HR e ] = β Cu x β HR γ CuR x γ H = K s (7)... Simulation with equilibrium line model of extration step Thermodynami equilibrium ondition of extration and stripping steps are similar. Equilibrium line simulation model of extration step is used to simulate equilibrium line of stripping step. Test onditions of lab test 6 of stripping step are the following: - Initial opper onentration in aqueous phase: 35 g/l - Initial free aid onentration in aqueous phase: 80 g/l. - Copper onentration in loaded organi: 5.98 g/l. - Extratant: Lix984N. - Extratant volume perentage in organi: 3%. Table 5 gives equilibrium line data and the values of opper onentration in organi phase from equilibrium line simulation model of extration step. Figure 4 gives the values of opper onentration in aqueous phase from equilibrium line data and Extration step simulation model versus the values of opper onentration in organi phase Results show that there is a gap between the values of opper onentration from experimental data and equilibrium line simulation model of extration step. The gap is due probably to the differene of ioni strength between extration and stripping aqueous phases. 5

17 Table 5: Copper onentration in organi simulated with extration step simulation model Equilibrium line data Model Aqueous Organi Aqueous Cu (g/l) Cu (g/l) Cu (g/l) Figure 4: Copper onentration from equilibrium line data and Extration step simulation model in aqueous phase versus opper onentration in organi phase of lab test Equilibrium line simulation model of stripping step Table 6 gives equilibrium line data and the values of thermodynami equilibrium ondition K s of lab test 6. Figure 5 gives the value of thermodynami equilibrium ondition K s versus the values of opper onentration in organi phase. Results show that: - The value of thermodynami equilibrium ondition K s is a linear funtion of the values of opper onentration in organi phase. 6

18 - Auray of the value of thermodynami equilibrium ondition K s depends on auray in hemial analysis of opper onentration in aqueous phase. - The value of molar onentration Y is lower than zero. So, line slope is a funtion of extratant volume perentage only. The values of K s is given by the mathematial expression (8). K s = Cu e org [A Cue x e aq ] aq [ x V% x Cu org e ] (8) Table 6: Value of K s from equilibrium line data of lab test 6 Lab test Organi Aqueous Aq Org Cu Cu Cu Free Lix984N Cu Y C C H K s g/l g/l moles/l moles/l moles/l moles/l moles/l moles/l moles/l Figure 5: Values of K s versus the values of opper onentration in organi phase of lab test 6 Line mathematial expression of thermodynami equilibrium ondition obtained from equilibrium line data has a shape given by the mathematial expression (9). K s =F x Cu e or + G (9) 7

19 The values of onstants D and E are funtions of extratant volume perentage. Mathematial expressions giving the values of onstants D and C are extrapolation urves of the value of onstants D and C obtained at different values of extratant volume perentage in the range 8-3%. Equilibrium line simulation model of stripping step is given by the mathematial expression (30). Thermodynami equilibrium onditions of K s and K s given by the mathematial expressions (30) and (8) are equals for eah steady-state position of equilibrium line. K s =( x 0 3 e x v% ) x Cu or x v% ( 0.85) (30) 8

20 3. Equilibrium line and MaCabe Thiele diagram 3.. Equilibrium line 3... Desription Equilibrium line gives the distribution of dissolved omponent, between two phases. In the ase of opper solvent extration, it shows how opper distributes between aqueous and organi phases under the different onditions experiened in the proess. Equilibrium line data are obtained from lab test or by omputer modeling Computer modeling of equilibrium line Thermodynami equilibrium onditions given by the mathematial expressions (4) and (6) for extration step and by the mathematial expression (8) and (30) for stripping step are used for omputer modeling of extration and stripping equilibrium lines respetively. Copper and free aid onentrations in initial aqueous phase and also extratant volume perentage in organi phase are data whih must be known for omputer modeling of equilibrium lines. Thermodynami equilibrium onditions K e and K e for extration step and K s and K s for stripping step are rearranged to have opper onentration in aqueous phase on one side and opper onentration in organi phase on the other side. It appears two news equilibrium orretions α and α for extration step and π and π for stripping step. The mathematial expressions of news equilibrium orretions are given by the mathematial expressions (3) and (3) for extration step and (33) and (34) for stripping step. At the steadystate, the equilibrium orretions α and α are equals for extration step and π and π are equals for stripping step. α = [A aq i +(Cui aq Cu e aq ) x.54] Cue aq α = [ 8.5 x v%(.746) x Cu e or +.7 x v% ( 0.646) ] x (3.303 x V% x Cu e or ) Cue or π = [A aq i +(Cui aq Cu e aq ) x.54] Cue aq (3) (3) (33) π = [( x 0 3 x v% 0.983) x Cu e or x v% ( 0.85) ]x(3.303 x V% x Cu e or ) Cue or (34) 9

21 There are two ways for omputer modeling of equilibrium line. The first way is started from the known value of opper onentration in aqueous phase from whih opper onentration in organi phase is alulated. Grouping of equilibrium orretions α and α of extration step or π and π of stripping step gives a ubi equation as a funtion of opper onentration in organi phase. The seond way is started from the known value of opper onentration in organi phase from whih opper onentration in aqueous phase is alulated. Grouping of equilibrium orretions α and α of extration step or π and π of stripping step gives a seond-degree equation as a funtion of opper onentration in aqueous phase. For extration step, the value of opper onentration in aqueous phase is given by the mathematial expression (35) where the values of onstants H and J are given by the mathematial expression (36) and (37). e Cu aq = H H 4 x J (35) i i H = -.99 x A aq x Cu aq 0.4 x α (36) i J = (0.644 x A aq i + Cu aq ) (37) For stripping step, the value of opper onentration in aqueous phase is given by the mathematial expression (38) where the values of onstants L and M are given by the mathematial expressions (39) and (40). e Cu aq = L L 4 x M (38) i i L = -.99 x A aq x Cu aq 0.4 x π (39) i M = (0.644 x A aq i + Cu aq ) (40) Maximum loading Maximum loading (ML) is the value of opper onentration in organi phase orresponding to the value of initial opper onentration in aqueous phase on equilibrium line at the steady-state. Maximum loading is a funtion of the values of opper and free aid onentrations in aqueous phase and also extratant volume perentage in organi phase. The value of maximum loading is given by the first away method for omputer modeling of equilibrium line in whih the value of opper onentration in aqueous i phase at steady-state is the value of initial opper onentration Cu aq. The value of equilibrium orrelation α is hanged to α ML. The value of equilibrium orrelation α ML is given by the mathematial expression (4). 0

22 ML α = [A aq i ] Cui aq (4) Absolute maximum loading Absolute maximum loading is the value of maximum loading when the value of initial free aid onentration in aqueous phase is zero. Therefore, the values of equilibrium orrelations α and α are also zeros. The value of absolute maximum loading (AML) omes from equilibrium orrelation α and is given by the mathematial expression (4). The value of absolute maximum loading is not a linear funtion of extratant volume perentage. AML = x (V%). (4) 3.. MaCabe Thiele diagram 3... Stage sheme of extration and stripping steps Extration and stripping steps of opper solvent extration are frequently arried out at industrial sale with mixer-settlers. This equipment inludes a mixer in one stage or two stages in series to disperse one phase into other to provide interfaial ontat for mass transfer, followed by a settler to allow phases to oalese and separate Extration step Figure 6 gives sheme of stage of rank n of extration step in asade onfiguration. Stage of rank n of extration step reeives aqueous phase E n aq from stage of rank n- and organi phase E n+ or from stage of n rank n+. Stage of rank n produes aqueous phase E aq and organi phase E n or. Figure 6: Sheme of stage of rank n of extration step

23 For asade onfiguration ontaining m stages, stage of rank reeives PLS (E o aq ) and produes Loaded organi LO e (E or ). Stage of rank m reeives stripped organi SO e (E m+ or ) and produes raffinate Raf (E m aq ) Stripping step Figure 7 gives sheme of stage of rank n of stripping steps in asade onfiguration. Stage of rank n of stripping step reeives aqueous phase S n+ aq from stage of rank n+ and organi phase S n or from stage of n rank n-. Stage of rank n produes aqueous phase S aq and organi phase S n or. For asade onfiguration ontaining p stages, stage of rank reeives loaded organi LO s (S 0 or ) and produes advane eletrolyte AD (S aq ). Stage of rank p reeives spent eletrolyte SP (S p+ aq ) and produes stripped organi SO s (S p or ). Figure 7: Sheme of stage of rank n of stripping step 3... Parameters and designation 3... Stage of rank n Eah aqueous phase leaving stage of rank n of extration or stripping step is haraterized by the following independent parameters: n - V aq n - Cu aq : Flowrate (m 3 /h). : Copper onentration (g/l). n - A aq - : Free aid onentration (g/l). Eah organi phase leaving stage of rank n of extration or stripping step is haraterized by the following independent parameters:

24 n - V or n - Cu or : Flowrate (m 3 /h). : Copper onentration (g/l). - v% n : Extratant volume perentage in organi phase (%). The important parameters of stage of rank n of extration and stripping are: - Ratios R e n and R s n are ratios of organi to aqueous flowrates of extration and stripping stage of rank n respetively. - Parameters Mef e n and Mef s n are respetively mixer effiieny of stage of rank n of extration and stripping steps Casade The important parameters of asade onfiguration are: - Ratios R e and R s are respetively ratios of organi to aqueous flowrates of extration and stripping asade. - Parameter v% is extratant volume perentage in organi phase (%) of asade. - Parameters Eff e and Eff s are respetively extration and stripping effiieny of asade. - Parameter Cu t is net opper transfer from organi phase to opper eletrolyte per % of extratant volume perentage of stripping asade Mass balane Extration step Stage of rank n Conservation of opper mass flowrate at stage of rank n is given by the mathematial expression (43). The value of ratio R e n of stage of rank n is given by the mathematial expression (44). The value of free aid onentration in outlet aqueous phase of stage of rank n is given the mathematial expression (45). n n n n+ n n V aq x Cu aq + V or x Cu or = V aq x Cu aq + V n n or x Cu or (43) R n e = V n or V aq n = Cu aq n Cun aq Cu n+ or Cu or n (44) n n n A aq = A aq + (Cu aq - Cu n aq ) x.54 (45) 3

25 Casade Conservation of opper mass flowrate of asade is given by the mathematial expression (46). The value of ratio of R e of asade is given by the mathematial expression (47). The value of free aid onentration in outlet aqueous phase of asade is given by the mathematial expression (48). Copper extration effiieny of asade is given by the mathematial expression (49). V aq x PLS + V or x SO e = V aq x Raf + V or x LO e (46) R e = V or V = PLS Raf aq LO e SO e (47) m 0 A aq = A aq + (PLS-Raf) x.54 (48) Eff e = (PLS Raf) PLS x 00 (49) Stripping step Stage of rank n Conservation of opper mass flowrate of stage of rank n is given by the mathematial expression (50). The value of ratio R s n is given by the mathematial expression (5). The value of free aid onentration in outlet aqueous phase of stage of rank n is given by the mathematial expression (5). n n n n+ n n n n V or x Cu or + V aq x Cu aq = V or x Cu or + V aq x Cu aq (50) n R s = V n or V aq = Cuaq n Cun+ aq n Cu n or Cu or n (5) n n+ n+ A aq = A aq + (Cu aq - Cu n aq ) x.54 (5) Casade Conservation of opper mass flowrate of asade is given by the mathematial expression (53). The value of ratio R s is given by the mathematial expression (54). The value of free aid onentration in outlet aqueous phase of asade is given by the mathematial expression (55). Copper stripping effiieny of asade is given by the mathematial expression (56). Net opper transfer from organi phase to aqueous phase is given by the mathematial expression (57). 4

26 V or x LO s + V aq x SP = V or x SO s + V aq x AD (53) R s = V or V = AD SP aq LO s SO s (54) A aq = A p+ aq + (Cu p+ aq - Cu aq ) x.54 (55) Eff s = (LO s SO s ) LO s x 00 (56) Cu t = (LO s SO s ) V% = AD SP V% x R s (g/l/v%) (57) MaCabe Thiele diagram Extration step MaCabe Thiele diagram of stage of rank n of extration step is shown in Figure 8. The Point A n gives feed oordinates, the Point B n gives outlet oordinates and the Point C n gives outlet equilibrium oordinates. Triangle E n B n B n D n D n E n gives MaCabe Thiele diagram of stage of rank n of extration step. Slope of line E n D n is given by the mathematial expression (58). Slope of line A n B n is given by the mathematial expression (59). Slope E n D n = Cu or n Cun+ or n = Rn (58) e Cu n aq Cu aq Slope A n B n = Cu or n Cun+ or n = - Rn (59) e Cu n aq Cu aq Copper onentrations in aqueous and organi phases, leaving stage of rank n are given by the mathematial expressions (60) and (6). Cu n n aq = Cu (aq/e) x Mef e n + Cu 00 aq n x (- Mef e n ) (60) 00 Cu or n n = Cu (or/e) x Mef e n 00 + Cu or n+ x (- Mef e n 00 ) (6) 5

27 Figure 8: MaCabe Thiele diagram of stage of rank n of extration step Stripping step MaCabe Thiele diagram of stage of rank n of stripping step is shown in Figure 9. The Point A n gives feed oordinates, the Point B n gives outlet oordinates and the Point C n gives outlet equilibrium oordinates. Triangle D n B n B n E n E n D n gives MaCabe Thiele diagram of stage of rank n of stripping step. Slope of line E n D n is given by the mathematial expression (6). Slope of line A n B n is given by the mathematial expression (63). Slope E n D n = Cu or n Cun or n+ = Rn (6) s Cu n aq Cu aq Slope A n B n = Cu or n Cun or n = - Rn (63) s Cu n+ aq Cu aq Copper onentrations in aqueous and organi phases, leaving stage of rank n are given by the mathematial expressions (64) and (65). Cu n n aq = Cu (aq/e) x Mef s n + Cu 00 aq n+ x (- Mef s n ) (64) 00 Cu or n = Cu (or/e) n x Mef s n 00 + Cu or n x (- Mef s n 00 ) (65) 6

28 Figure 9: MaCabe diagram of stage of rank n of stripping step 7

29 4. Constraints of opper SX-EW plant 4.. Equilibrium onstraints between extration and stripping steps In opper solvent extration plant having extration step ontaining one or more asades and stripping step ontaining one or more asades, equilibrium onstraints between extration and stripping steps are given by the mathematial expressions (66) and (67). LO e = LO s (66) SO e = SO s (67) 4.. Maximum value of extratant volume perentage Organi phase is onstituted with extratant and diluent. Extratant is organi ompound whih extrats metal from aqueous phase. Diluent is organi liquid in whih extratant is dissolved. In the industrial praties, the maximum value of extratant volume perentage in organi phase in opper solvent extration is between 30 33% [6]. Organi phase visosity inreases with inreasing of extratant volume perentage in organi phase Free aid onentration in PLS from 0.5 to 80 g/l. Free aid onentration in PLS depends on leahing tehnique. Free aid onentration in PLS an go 4.4. Maximum free aid onentration in spent eletrolyte The value of maximum free aid onentration in spent eletrolyte is 80 g/l. This value of maximum free aid onentration is fixed by anode orrosion rate in EW iruit. It has been observed that inreasing of free aid onentration in opper eletrolyte inreases disonnetion of PbO to Pb metalli. Therefore, it inreases anode orrosion rate [7] Minimum opper onentration in spent eletrolyte In opper EW iruit, limiting urrent density is urrent density beyond whih opper powder is produed. The value of limiting urrent density inreases with inreasing opper onentration in opper 8

30 eletrolyte. Critial urrent density is urrent density beyond whih opper athode struture starts to be granular. It has been observed that the value of ritial urrent density is 35% of limiting urrent density [8]. The maximum value of urrent density in opper EW iruit is fixed by anode orrosion rate due to oxygen evolution on anode. Evolution of oxygen gas on anode inreases with inreasing urrent density. Inreasing of oxygen evolution on anode also inreases unhooking of PbO on anode. The maximum value of urrent density, whih allows to anodes to have a life of 5 years is 30 A/m. In the presene of obalt in opper eletrolyte at the level of 00 mg/l (obalt stabilizes PbO on anode), the maximum value of urrent density an reah 370 A/m. The value of maximum urrent density must be lower than ritial urrent density of opper onentration in spent eletrolyte. It has been observed that the minimum value of opper onentration in spent eletrolyte whih respets this onstraint is 30 g/l. In the industrial pratie, the value of opper onentration in spent eletrolyte is varied between 30 and 35 g/l Maximum opper onentration in advane eletrolyte In the past time, ratio R s /R e was fixed. This ratio is the enrihment fator of opper onentration from leah solution to opper eletrolyte. Under this ondition, opper onentration in advane eletrolyte inreases with inreasing amount of opper transferred. The value of maximum opper onentration in advane eletrolyte is reahed when opper onentration in loaded organi reahes the value of maximum loading (ML). Copper onentration in advane eletrolyte is given by the mathematial expression (68) AD = SP + R s R e x (PLS Raf) (68) Currently, opper tankhouse onsists of two parts; the first, alled savenger ells, is treating advane eletrolyte to oxidize soluble organi phase oming with advane eletrolyte. The seond, alled ommerial ells, is treating mixture of outlet eletrolyte from savenger ells and reyled eletrolyte from ommerial ells. Design of opper tankhouse is done suh as flowrate of opper eletrolyte to ommerial ells is 4 times greater than advane eletrolyte flowrate to savenger ells. This means that 0% of ells in opper tankhouse work as savenger ells. Maximum opper onentration drop aross ell is fixed at 3 g/l beause opper eletrolyte flowrate in onventional ell is fixed by athode fae veloity for a better quality of opper athode surfae. In the industrial pratie, athode fae veloity is 0.0 m 3 /hrs. per m of total athode area in the ell [9]. Copper onentration in spent eletrolyte is fixed at 35 g/l. In this ondition, opper onentration drop between spent and advane eletrolytes is 5 g/l and maximum opper onentration in advane eletrolyte is 50 g/l. These onditions give smallest size of opper tankhouse. The value of ratio R s is given by the mathematial expression (69). R s = R e x (AD SP) (PLS Raf) (69) 9

31 4.7. Optimum value of ratio of organi to aqueous of extration step Ratios R e and R s are external ratios. Internal ratio is ratio of volume flowrates inside of mixer. When the value of internal ratio (O/A) is greater than., aqueous phase is dispersed in organi phase. Mixer works in organi ontinuity regime. On the other side, when ratio (A/O) is greater than., organi phase is dispersed in aqueous phase. Mixer works in aqueous ontinuity regime. It has been observed that rud formation dereases when mixer works in organi ontinuity regime [0]. Therefore, all mixers of extration and stripping steps work in organi ontinuity regime and the optimum value of ratio R e is now. whih gives smallest size of mixer and settler without any organi or aqueous stage reyle Saturation ratio SR Currently, saturation of organi phase with opper (high value of (LO/ML) is important parameter in design of opper solvent extration plant. This parameter takes into aount good use of organi phase (high value of Net opper transfer) and also rejetion of iron from organi phase. In opper solvent extration, iron is transferred to opper eletrowinning iruit by physial entrainment. In addition, Ferri is transferred by hemial entrainment. Studies on iron transfer show that the average of iron hemial entrainment is between 35 to 60% of total entrainment []. Iron presene in opper eletrolyte auses redution of urrent effiieny. Maximum iron onentration in opper eletrolyte is.5g/l whih will give urrent effiieny greater than 90%. Copper eletrolyte bleed is used to maintain this iron level in eletrolyte. Inreasing of flowrate of opper eletrolyte bleed inreases ost of obalt reagent whih is added to opper EW iruit. In all opper solvent extration plants having asade onfiguration with two stages to extration step, it has been observed that iron onentration in loaded organi out of stage of rank is lower than iron onentration in partially loaded organi out of stage of rank. This effet is alled rowding []. The value of ratio ( LO ) is a new onstraint alled saturation ratio SR. This onstraint is appliable to ML all opper solvent extration onfigurations (ExS, ExS, 3ExS, series-parallel, interlaed, double seriesparallel and others). The mathematial expression (70) gives the value of saturation ratio. SR = LO x 00 (%) (70) ML 30

32 5. Simulation program using Exel solver program 5.. Desription Simulation program is done on Exel spreadsheet in format of Exel solver program. Exel solver is the Mirosoft add-in program used for what-if analysis. Exel solver program allows finding the optimum value for a formula in ell alled the objetive ell. First step of stati simulation program design is reation of simulation program table on Exel spreadsheet. Simulation program table is made with three small tables whih are table of extration step, table of stripping step, and table of simulation program onstraint. In simulation program table, data have red olor, solver onstraints have blue olor and solver onstraints have green olor. There are two stati simulation program options for eah opper solvent extration onfiguration. For eah option of eah opper solvent extration onfiguration, there is a stati simulation program table. Two options are: - Option : Unknown parameter in opper solvent extration simulation program is extratant volume perentage in organi phase. This stati simulation program is for designer of opper solvent extration onfiguration. - Option : Unknown parameters in opper solvent extration simulation program are extratant volume perentage, saturation ratio, and mixer effiienies of extration and stripping steps for existing plant. This simulation program is for plant metallurgist. 5.. Stati simulation program design 5... General In this book for good understanding, stati simulation program design will be done step by step using a onventional onfiguration ontaining two stages in asade to extration step and two stages in asade to stripping step as an example. 3

33 5... Option. In this option, unknown parameter is extratant volume perentage. Table 7 gives data of hosen example for explanation of simulation program oneption. Table7: Data of hosen example of opper solvent extration onfiguration Desription Symbol Unity Value Extration step PLS Flow PLS Flow m 3 /h 400 Copper onentration in PLS PLS Cu g/l 7 Aid onentration in PLS PLS A g/l.96 Ratio O/A R e. Saturation ratio SR % 80 Number of extration stage Stage of rank mixer effiieny Mef e % 9 Stage of rank mixer effiieny Mef e % 95 Stripping step Copper onentration in spent eletrolyte SP Cu g/l 35 Aid onentration in spent eletrolyte SP A g/l 80 Copper onentration in advane eletrolyte AD Cu g/l 50 Number of stripping stage Stage of rank mixer effiieny Mef s % 98 Stage of rank mixer effiieny Mef s % 85 Stati simulation program table of option of ExS onfiguration is given in Table 8 as it appears on Exel Mirosoft spreadsheet. Data from Table 7 have red olor. In extration table, designation α n, H n and J n are respetively the values of equilibrium orrelation α and onstants H and J of stage of rank n for alulating the value of opper onentration in aqueous phase from the value of opper onentration in organi phase. Designation A n, C n, D n and E n are the Points A, B, C, and D from extration step MaCabe Thiele diagram of stage of rank n. In stripping table, designation π n, L n and M n are respetively the values of equilibrium orrelation π and onstants L and M of stage of rank n for alulating the value of opper onentration in aqueous phase from the value of opper onentration in organi phase. Designation A n, C n, D n and E n are the Points A, B, C, and D from stripping step MaCabe Thiele diagram of stage of rank n Extration step Data Simulation program design is started with solver variables of data. These solver variables will be data of all mathematial expressions of extration step. 3

34 - In the ell F6 of solver variable of PLS flowrate (PLS flow), enter the number giving the value of PLS flowrate data that is in the ell C6. - In the ell F7 of solver variable of PLS opper onentration (PLS Cu), enter the number giving the value of PLS opper onentration data that is in the ell C7. - In the ell F8 of solver variable of PLS free aid onentration (PLS A), enter the number giving the value of PLS aid onentration data that is in the ell C8. - In the ell F9 of solver variable of saturation ratio (SR), enter the number giving the value of saturation ratio data that is in the ell C9. - In the ell F0 of solver variable of ratio (R e ), enter the number giving the value of ratio (R e ) data that is in the ell C0. - In the ell F of solver variable of mixer effiieny ( Mef e ), enter the number giving the value of mixer effiieny ( Mef e ) that is in the ell C. - In the ell F of solver variable of mixer effiieny (Mef e ), enter the number giving the value of mixer effiieny (Mef e ) that is in the ell C. Solver onstraints of solver variables of extration step data are the following: - In the ell I6, enter formula: =F6-C6. - In the ell I7, enter formula: =F7-C7. - In the ell I8, enter formula: =F8-C8. - In the ell I9, enter formula: =F9-C9. - In the ell I0, enter formula: =F0-C0. - In the ell I, enter formula: =F-C. - In the ell I, enter formula: =F-C. Starting value The starting value of extratant volume perentage of simulation program is random number between and 3%. The starting value of extratant volume perentage is used in all mathematial expression of extration step as extration volume perentage data. The optimum value of extratant volume perentage is known at the end of simulation program by running Exel Solver program. The starting value of extratant volume perentage is the expeted value of extratant volume perentage for those who have experiene. For this ase, hosen starting value is 5%. - In the ell F5, enter the number 5. General The value of organi flowrate is in the ell C8. This value is given by the mathematial expression (47) where the values of ratio (R e ) is in the ell F0 and PLS flowrate is in the ell F6. 33