• Author / Uploaded
• joseph kafumbila

• Categories
• Kilogramo
• Masa
• Solución
• Gravedad
• Minerales

Citation preview

DESIGN OF COUNTER CURRENT DECANTATION IN COPPER METALLURGY Joseph Kafumbila

Design of counter current decantation in copper metallurgy © 2016 Joseph Kafumbila [email protected]

Necessity to use filblast technology for cobalt III leaching performed in agitated open leach tanks With the current market value of cobalt, it is time to revisit the technology used for cobalt III leaching in the new hydrometallurgical plants in the Democratic Republic of Congo. Dispersion of SO2 in the leach pulp containing 1 g/L of iron gives slow cobalt leaching kinetic in agitated open leach tanks. The adoption of filblast technology will improve the kinetic of cobalt III leaching, resulting an improvement of cobalt leaching recovery and decreasing in the capex of the leach section. Filblast advice will increase the solubility of SO2 in the leach pulp. The increase in SO2 solubility in the leach pulp will give a rapid cobalt III dissolution reaction. The main advantageous of filblast is that the recycle pump takes big particles of cobalt III minerals residing in the bottom of the leach tank, which will be processing in the filblast advice. In this condition the increase in the cobalt dissolution kinetic will be more significant because the kinetic leaching model of cobalt III dissolution is shrinking core model. The current leaching conditions in the new hydrometallurgical plants require us to test this technology. This technology does not require a major modification of the leach section installation. https://www.researchgate.net/publication/322385532_Necessity_to_use_filblast_technolog y_for_cobalt_III_leaching_performed_in_agitated_open_leach_tanks

Joseph Kafumbila

Page 1

Content 1. GENERAL

5

1.1. PULP WASHING METHOD 1.2. CHARACTERIZATION OF PULP 1.2.1. SOLID 1.2.2. LIQUID 1.2.3. PULP

5 5 6 8 10

2. COUNTER CURRENT DECANTATION

12

2.1. DESCRIPTION OF COUNTER CURRENT DECANTATION 2.2. EQUATIONS OF MASS BALANCE IN CCD 2.2.1. DESIGNATION OF PULP 2.2.2. EQUATIONS OF MASS BALANCE

12 12 12 13

3. DESIGN OF COUNTER CURRENT DECANTATION

16

3.1. PRELIMINARY DATA 3.1.1. CHARACTERISTICS OF FEED PULP 3.1.2. MIXING EFFICIENCY 3.1.3. FLOCCULANT CONSUMPTION 3.1.4. WASH RATIO 3.1.5. SET VALUE OF CONTROL PARAMETER OF UNDERFLOWS 3.2. NUMBER OF THICKENER IN THE CCD

16 16 16 17 17 18 21

4. SETTLING TEST

22

4.1. TYPES OF SETTLING TEST 4.1.1. RULE THUMB SIZING 4.1.2. CYLINDER SETTLING TESTS 4.1.3. DYNAMIC THICKENER TEST WORK 4.2. CYLINDER SETTLING TESTS 4.2.1. EQUIPMENT 4.2.2. CHARACTERIZATION OF PULP 4.2.3. FLOCCULANT PREPARATION 4.2.4. SETTLING TEST 4.2.5. SETTLING CURVE 4.2.6. SIZE OF THICKENER

22 22 22 22 22 22 23 23 23 24 25

5. OPTIMUM NUMBER OF THICKENER IN THE CCD CIRCUIT

27

5.1. OLD METHODS

27

Joseph Kafumbila

Page 2

5.1.1. FIRST METHOD 5.1.2. SECOND METHOD 5.2. NEW METHOD 5.2.1. CONSTRAINTS 5.2.2. FIRST EXAMPLE 5.2.3. SECOND EXAMPLE 5.2.4. OBSERVATIONS

27 27 28 28 28 32 36

6. PROCEDURE OF CCD CIRCUIT SIMULATION

37

6.1. 6.2. 6.3. 6.4. 6.5.

37 37 37 37 39

GENERAL PLANT DESCRIPTION PRELIMINARY DATA OF CCD CIRCUIT SIMULATION TABLE PROCEDURE OF CCD CIRCUIT SIMULATION

7. REFERENCE

Joseph Kafumbila

50

Page 3

Foreword The counter current decantation had been used since 90 years ago in the hydrometallurgical plant. It is currently adopted by all new hydrometallurgical plants located in the Katanga Province of the Democratic Republic of Congo (Ruashi Mining, Mumi Mining etc.) since it is applicable to all products; but its malfunction can limit the production of the plant. This publication is an upgrade of the publication called “Initiation à la simulation des flowsheet” and gives the procedure of CCD circuit design in the simplest way. In the first chapter, the pulp is characterized using three parameters (mass, volume and specific gravity). This publication gives the mathematical expressions that link the three parameters for the two constituents of the pulp (solid and liquid) and for the pulp. Specially, this publication gives the simplest method to determine the specific gravity of solid when the mineralogical composition of solid is available and the specific gravity of liquid when chemical composition liquid is available. In the second chapter, this publication gives the description of CCD circuit and the mass balance equations of thickener and CCD in the steady state condition. The difference with the first publication “Initiation à la simulation des flowsheet”, the flocculant is considered a solid. In the third chapter, this publication gives the preliminary data to have before the design of the CCD circuit and the method for obtaining the value of these preliminary data (the mixing efficiency, the flocculant consumption, the wash ratio and the set value of the control parameter of underflows). In the fourth chapter, this publication gives the procedure of the cylinder free settling test. The purpose of this chapter is to give the simplest method for obtaining the flocculant consumption and sizing the thickener. In the fifth chapter, this publication gives the old and new methods for obtaining the optimum number of thickeners in the CCD circuit. In the new method, the determination of optimum number of thickener is illustrated through two examples using the conventional thickener and the High Rate Thickener. The last chapter gives the procedure of simulation of CCD circuit with the new method on an Excel spreadsheet through the example.

Joseph Kafumbila

Page 4

1.

General

1.1.

Pulp washing method

Pulp washing in the CCD is part of the pulp wash process. The pulp wash process is a special operation that performs both the extraction and the solid - liquid separation. Thus the pulp wash process falls within the category of mass transfer operations for chemical and metallurgical engineering [1]. There are two main kinds of pulp wash techniques:  Wash by dilution: the thickened pulps are, at the entrance of various stages, diluted with corresponding wash solutions to achieve such a perfect mixture as possible. The subsequent solid - liquid separation is generally done by decantation. Such washes technique is suitable for the muddy pulp formed of very fine particles.  Wash by displacement: the impregnation solution of pulp to be washed is generally removed by the wash solution, which is substituted directly to it more or less complete. This kind of wash technique is suitable for the permeable grainy pulp. The solid - liquid separation is usually achieved by filtration or draining. By dilution or by displacement, the pulp wash technique can be done in two main ways:  Split wash or cross flow  Methodical wash or counter current In what follows, it will be treated the pulp wash in the CCD since it is more effective and widely used in the metallurgical industry of Copper.

1.2.

Characterization of pulp

Generally, the suspension of particles in a solution is called pulp. The suspended particles will be called solid and form the solid phase while the impregnation solution is the liquid phase. Therefore, the pulp will always consist of two components: solid and liquid. It will be discussed first the characterization of the two components of pulp before the characterization of pulp. The characterization means, in this publication, the designation of important parameters of a phase and the development of equations linking these parameters.

Joseph Kafumbila

Page 5

1.2.1.

Solid

The solid is characterized by a mass (Ms ) expressed in (kg) and a volume (Vs ) expressed in (m3). The specific gravity (SGs ) expressed in (kg/m3) is the ratio of the mass onto the volume of solid. Equation (1) gives the mathematical expression that links the mass, the volume and the specific gravity of solid. SGs =

(

Ms

(1)

Vs

The solid is considered insoluble in the CCD circuit and the specific gravity of solid is constant. There are two methods for obtaining the specific gravity of solid: the laboratory method and the mineralogical composition method. A.

Laboratory method

When it is possible to have physically the solid, the laboratory method for obtaining the specific gravity of solid consisting of mineral rock finely crushed is as follows:       

Dry the crushed solid in an oven at 80 ° C for 24 hours, Weigh the solid (kg) (weight between 0.100 and 0.300 kg), Put the solid in a test tube of one liter, Add the water in the test tube up to 500 ml, Mix the solid and the water until complete homogenization, Add more water in the test tube to the mark of a liter and, Weigh the volume of one liter of pulp. After the practical operations, the other data is determined as follows:

   

The weight of water is the difference between the weight of pulp and the weight of solid. The volume of water is the ratio of weight onto the specific gravity of water (1,000 kg/m3). The volume of solid is the difference between the volume of pulp and the volume of water. Finally, the specific gravity of solid is the ratio of the weight onto the volume of solid.

Table (1) shows an example for obtaining the specific gravity of solid by the laboratory method. This method seems simple, but it requires great accuracy during the weighing and the measuring of values. Table 1: Specific gravity of solid from the laboratory method Description Weight of solid Weight of pulp Volume of pulp Weight of water Volume of water Volume of solid SG of solid

Joseph Kafumbila

Units kg kg l kg l l kg/m3

Equations

Weight of pulp – Weight of solid Weight of water/specific gravity of water Volume of pulp – volume of water Weight of solid/volume of solid*1000

values 0.141 1.089 1.000 0.948 0.948 0.052 2,711.54

Page 6

B.

Mineralogical composition method

When the solid is not provided in order to obtain its specific gravity by the laboratory method, the determination of specific gravity of solid is taken place by using the mineralogical composition method. This method is based on the principle that rock is a juxtaposition of minerals. Therefore, the mass of rock is the sum of masses of minerals and the volume of rock is the sum of volumes of minerals. Based on these assumptions, the method for obtaining the rock specific gravity consists of:      

Knowing the weight percentage of minerals in the solid. Calculating the weight of minerals in a unit mass of solid. Knowing the respective specific gravity of minerals. Calculating the volumes of minerals. Determining the volume of solid by the addition of volumes of minerals. Calculating the specific gravity of solid by using the equation (1)

The weakness of this method is that it ignores porosities or structural defects of solid. Table (2) shows an example for obtaining the specific gravity of solid by using the mineralogical composition method. The result from Table (2) shows that for a total weight of 1,000 t of solid and a total volume of 359.77 m3 of solid which is the sum of volumes of minerals, the value of specific gravity of solid is 2,779.55 kg/m3. Table 2: Specific gravity of solid from the mineralogical composition Minerals Cu2(OH)2(CO3) Cu3(PO4)2.Cu2(OH)4 2CuO.2SiO2.3H2O CuO CuS Cu2S CuFeS2 CoOOH FeO(OH) Ni(OH)2 CaCO3.MgCO3 MnO2 ZnS SiO2 UO3 Mg2SiO4 Ca2SiO4 CaCl2 Al2SiO5 Cr2O3 CdO Total

Joseph Kafumbila

Grade

weight

% 1.584 0.146 0.199 0.503 0.005 0.005 0.005 0.507 1.954 0.001 0.900 0.127 0.007 77.139 0.004 5.381 0.011 0.025 11.471 0.026 0.001

t 15.836 1.456 1.989 5.029 0.055 0.055 0.055 5.070 19.543 0.010 9.000 1.266 0.067 771.393 0.040 53.805 0.110 0.250 114.710 0.256 0.006 1000

Specific gravity of mineral t/m3 4.00 4.20 2.20 6.40 4.68 5.65 4.20 4.00 3.65 4.10 2.85 4.85 4.00 2.65 10.97 3.15 2.71 2.15 3.25 5.22 8.15

Volume of mineral m3 3.959 0.347 0.904 0.786 0.012 0.010 0.013 1.268 5.354 0.002 3.158 0.261 0.017 291.092 0.004 17.081 0.041 0.116 35.295 0.049 0.001 359.77

Specific gravity of solid kg/m3

2,779.55

Page 7

1.2.2.

Liquid

The liquid is characterized by a mass (ML ) expressed in (kg) and a volume (VL ) expressed in (m3). The specific gravity (SGL ) expressed in (kg/m3) is the ratio of the mass onto the volume of liquid. Equation (2) gives the mathematical expression that links the mass, the volume and the specific gravity of liquid. SGL =

ML

(2)

VL

(

There are two methods for obtaining the specific gravity of liquid: the laboratory method and the chemical composition method. A.

Laboratory method

When it is possible to have physically the liquid, the laboratory method for obtaining the specific gravity of liquid is as follows:  Put the liquid in a test tube of one liter to the mark of a liter,  Weigh the volume of one liter of liquid (g),  And the ratio of weight onto the one liter volume of liquid gives the specific gravity. The specific gravity obtained in this condition is the approximated value at ambient temperature. B.

Chemical composition method

A liquid is homogeneous mixture of solvent and solutes. In this publication, the solvent is water and solutes are the elements appearing in the metallurgy of Copper and dissolved in water as sulphate. These elements appearing in the metallurgy of Copper are listed in the Table (3). The Sodium is on the list since it may come from sodium metabisulfite used as a reducing agent during leaching of trivalent Cobalt. The phosphoric acid comes from pseudo malachite. The index “k” is an identification number of the chemical element in this publication. At this level, it is defined two other parameters; the mass of element of index “k” (Mk ) expressed in (kg) in the liquid and the concentration of element of index “k” (Ck ) expressed in (kg/m3) in the liquid. Equation (3) gives the mathematical expression that links the mass of element of index “k”, the concentration of element of index “k” and the volume of liquid. Mk = VL x Ck

(3)

It has been observed for a liquid containing copper sulphate and sulphuric acid that [2]:  The specific gravity of copper sulphate or sulphuric acid liquid is approximately a linear function of concentration expressed in (%).  The specific gravity of liquids of equal concentration expressed in (%) of copper sulphate and of sulphuric acid is nearly identical.

Joseph Kafumbila

Page 8

(

 The specific gravity of liquid containing appreciable amounts of copper sulphate and sulphuric acid is dependent principally upon the total concentration (%) and is almost independent of their proportion. These observations have been extended to the elements appearing in the Copper metallurgy and the simplest method that allows having the approximated value of specific gravity of liquid from the chemical composition is given. The method consists of finding a total concentration (Cts ) expressed in (kg/m3) of elements as salt in the liquid. In this case, the salt is in form of sulphate except the phosphoric acid. After, the total concentration must be applied in the equation (4) which gives the relation between the liquid specific gravity and the total concentration of elements. The equation (4) comes from data which give the specific gravity of liquid as a function of concentration of element as salt in binary system [3]. Table 3: Elements appearing in metallurgy of copper Element H2SO4 Cu Co Fe Zn Ni Mn Mg Al Ca Na Cr Cd H3PO4

Index (k) 1 2 3 4 5 6 7 8 9 10 11 12 13 14

SGL = -6.139 x 10−4 x [Cts ]2 + 0.9742 x Cts + 1000 (kg/m3)

( (4)

Therefore, it is defined a constant αk of element of index “k”. The constant αk is the value to multiply to the concentration of element index “k” to have the concentration as sulfate salt “Cks ”. The values of constant 𝛼𝑘 are given in Table (4). The value of concentration “Cks ” of element of index “k” is given by equation (5). Cks = αk x Ck

(5) Table 4: value of constant 𝛼𝑘

Elément H2SO4 Cu Co Fe Zn Ni Mn Mg Al Ca Na Cr Cd H3PO4

Joseph Kafumbila

Index (k) 1 2 3 4 5 6 7 8 9 10 11 12 13 14

αk 1.000 2.511 2.629 2.719 2.468 2.635 2.747 4.949 6.337 3.395 3.088 3.769 1.854 1.000

Page 9

(

Thus, the value of total concentration “Cts ” of elements in the liquid will be calculated according to equation (6). Cts = ∑k1 Cks = ∑k1 αk x Ck

(6)

(

Table (5) gives an example for obtaining the specific gravity from the chemical composition of given liquid. The result of Table (5) shows that the value of total concentration “Cts ” of elements in the liquid is 97.251 kg/m3. This value is the sum of concentrations as sulphate salt of elements. By applying the value of total concentration of elements in the equation (4), the value of specific gravity of liquid “SGL ” is 1088.94 kg/m3. It is important to have ten major elements so that the calculated specific gravity of liquid will be closed to the true specific gravity. Table 5: Specific gravity from chemical composition of liquid

1.2.3.

Element

Index (k)

H2SO4 Cu Co Fe Zn Ni Mn Mg Al Ca Na Cr Cd H3PO4 Cts

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Concentration kg/m3 4.956 4.670 11.233 2.925 0.099 0.000 2.812 4.440 1.474 0.455 0.000 0.108 0.001 1.849

αk 1.000 2.511 2.629 2.719 2.468 2.635 2.747 4.949 6.337 3.395 3.088 3.769 1.854 1.000

Cks kg/m3 4.956 11.725 29.532 7.954 0.244 0.000 7.724 21.974 9.341 1.543 0.000 0.407 0.002 1.849 97.251

Pulp

The pulp is a mixture of solid and liquid. The pulp will be characterized by a mass “MP ” expressed in (kg), a volume “VP ” expressed in (m3) and a specific gravity “SGP ” expressed in (kg/m3). Equation (7) gives the mathematical expression that links the mass, the volume and the specific gravity of pulp. SGP =

MP VP

(7)

(

The mass of pulp is the sum of masses of solid and liquid. The mathematical expression of this principle is given by equation (8). MP = M S + ML

(8)

(

The volume of pulp is the sum of volumes of solid and liquid. The mathematical expression of this principle is given by equation (9). VP = VS + VL Joseph Kafumbila

(9) Page 10

(

The mass of solid can also be calculated from the volume of pulp and the specific gravities of pulp, solid and liquid. Equation (10) gives the mathematical expression. (SG −SG )

Ms = (SGP−SGL) x SGs x Vp S

L

(10)

(

The volume percentage of solid in the pulp expressed in (%) is given by equation (11). V

Cvs = V s x 100 (%) p

(11)

(

The weight percentage of solid in the pulp expressed in (%) is given by equation (12). (

M

s Cw = MS x 100 P

Joseph Kafumbila

(12)

Page 11

2.

Counter current decantation

2.1.

Description of counter current decantation

The wash of pulp in the CCD is done according to two principles. The mixture of pulp is done in a particular device (tank, agitated tank or mixer-distributor) and the solid - liquid separation is taken place in the thickener. The scheme of thickener of rank “p” in the CCD containing “n” thickeners is illustrated in Figure p−1 (1). The thickener of rank “p” (T p ) is received the underflow from the thickener of rank “p-1” (Tu ) and p+1 the overflow of thickener of rank “p+1” (To ). Sometimes a solution of flocculant is also added to the p thickener of rank “p” (Tf ) allowing faster settling of solid by flock formation. The thickener of rank “p” is p p produced the underflow (Tu ) and the overflow (To ). The initial pulp (Tu0 ) is fed in the first thickener. The overflow of the first thickener (To1 ) is the recovered solution (rich solution). The wash solution (Ton+1) is fed in the last thickener. The underflow of the last thickener (Tun ) is the final pulp (also called washed pulp).

Figure 1: Scheme of thickener of rank “p” in the CCD containing “n” thickeners

2.2.

Equations of mass balance in CCD

2.2.1.

Designation of pulp

The characterization of pulp gives the basic equations of pulp. Now, the basic equations of CCD will be given. The inlet and outlet flows of thickener of rank “p” are pulps which are characterized by the parameters defined above. For a proper understanding, the parameters of pulp leaving a thickener of rank Joseph Kafumbila

Page 12

p

p

“p” will be preceded by a prefix "Tu " and "To " designating respectively the underflow and overflow of p thickener. The flocculant solution entering the thickener of rank “p” will have a prefix "Tf ".

2.2.2.

Equations of mass balance

The equations of mass balance of CCD are the mathematical expressions given the principles of conservation of mass and volume in a thickener of rank “p” and in the CCD. A. 

Thickener

When a thickener operates in a steady state, the sum of masses of solid entering a thickener is equal to the mass of solid exiting through the underflow. This principle is called the conservation of mass of solid in a thickener. For a thickener of rank “p”, the equation (13) gives the mathematical expression of this principle. p−1

Tu 

p−1

p+1

(

p

Vs + TfP Vs = Tu Vs

(14)

p−1

ML + Tu

p

p

p

ML + Tf ML = To ML + Tu ML

(15)

(

When a thickener operates in a steady state, the sum of volumes of liquid entering a thickener is equal to the sum of volumes of liquid exiting through the overflow and the underflow. This principle is called the conservation of volume of liquid in a thickener. For a thickener of rank “p”, the equation (16) gives the mathematical expression of this principle. p+1

To 

(

When a thickener operates in a steady state, the sum of masses of liquid entering a thickener is equal to the sum of masses of liquid exiting through the overflow and the underflow. This principle is called the conservation of mass of liquid in a thickener. For a thickener of rank “p”, the equation (15) gives the mathematical expression of this principle. To



(13)

When a thickener operates in a steady state, the sum of volumes of solid entering a thickener is equal to the volume of solid exiting through the underflow. This principle is called the conservation of volume of solid in a thickener. For a thickener of rank “p”, the equation (14) gives the mathematical expression of this principle. Tu



p

Ms + TfP Ms = Tu Ms

p−1

VL + Tu

p

p

p

VL + Tf VL = To VL + Tu VL

(16)

(

When a thickener is operated in a steady state, the sum of masses of element entering a thickener is equal to the sum of masses of element exiting through the overflow and underflow. This principle is called the principle of conservation of mass of element in a thickener. For a thickener of rank “p” and an element of index “k”, the equations (17) and (18) give the mathematical expressions of this principle. p+1

To

p+1

VL x To

Joseph Kafumbila

p−1

Ck + Tu

p−1

VL x Tu

p

p

p

p

Ck = To VL x To Ck + Tu VL xTu Ck

( (17) Page 13

p+1

To 

p

p

Mk = To Mk + Tu Mk

p

p+1 Ck ) p p+1 (Tu Ck −To Ck )

(To Ck −To

x 100

p

p

p

T Ms u

(20)

s

p



p

T Ms

(21)

When a CCD operates in a steady state, the sum of masses of solid entering a CCD containing “n” thickeners is equal to the mass of solid exiting through the underflow of thickener of rank “n”. This principle is called the conservation of mass of solid in a CCD circuit. The equation (22) gives the mathematical expression of this principle. ( (22)

When a CCD operates in a steady state, the sum of volumes of solid entering a CCD circuit is equal to the volume of solid exiting through the underflow of thickener of rank “n”. This principle is called the conservation of volume of solid in a CCD circuit. The equation (23) gives the mathematical expression of this principle. (

Tu0 Vs + ∑n1 TfP Vs = Tun Vs 

(

CCD

Tu0 Ms + ∑n1 TfP Ms = Tun Ms 

(

Equation (21) gives the volume of flocculant fed into a thickener of rank “p”. Where 2.650 (kg/m3) is the specific gravity of the flocculant f Tf Vs = 2.650

B.

( (19)

The flocculant consumption Tf Q expressed in (g/t) is the ratio of mass of flocculant fed into a thickener of rank “p” onto the mass of solid fed in the CCD circuit. Equation (20) gives the mathematical expression of flocculant consumption for the thickener of rank “p”. Tf Q = Tf0 M x 106



(18)

(

As mentioned above, in each thickener in the CCD circuit, the wash is done in two steps: the homogenization of feed and the solid-liquid separation in the thickener. The performance of the homogenization is given by mixing efficiency “ME p ” expressed in “%” of thickener of rank “p”. When the homogenization of thickener feed is not complete, the concentration of an element in the overflow is lower than the concentration in the underflow. Equation (19) gives the mathematical expression of mixing efficiency for the thickener of rank “p” and for the element of index “k”. ME p =



p−1

Mk + Tu

(23)

When a CCD operates in a steady state, the sum of masses of liquid entering a CCD circuit is equal to the sum of volumes of liquid exiting through the overflow of thickener of rank “1” and the underflow of thickener of rank “n”. This principle is called the conservation of mass of liquid in a CCD circuit. The equation (24) gives the mathematical expression of this principle. p

Ton+1 ML + Tu0 ML + ∑n1 Tf ML = To1 ML + Tun ML Joseph Kafumbila

( Page 14

(24) 

When a CCD operates in a steady state, the sum of volumes of liquid entering a CCD circuit is equal to the sum of volumes of liquid exiting through the overflow of thickener of rank “n” and the underflow of thickener of rank “n”. This principle is called the conservation of volume in a CCD circuit. The equation (25) gives the mathematical expression of this principle. p

Ton+1 VL + Tu0 VL + ∑n1 Tf VL = To1 VL + Tun VL 



When a CCD is operated in a steady state, the sum of masses of element entering a CCD circuit is equal to the sum of masses of element exiting through the overflow of thickener of rank “1” and the underflow of thickener of rank “n”. This principle is called the principle of conservation of mass of element in a CCD circuit. For an element of index “k”, the equations (26) and (27) give the mathematical expressions of this principle. Ton+1 VL x Ton+1 Ck + Tu0 VL x Tu0 Ck = To1 VL x To1 Ck + Tun VL xTun Ck

(26)

Ton+1 Mk + Tu0 Mk = To1 Mk + Tun Mk

(27)

(Tn+1 o VL ) (T0u MS )

(

x 1.000

(28)

(

p

Equation (29) gives the mathematical expression of wash efficiency “Tu WEk expressed in “%” after the thickener of rank “p” and for element of index “k” in the CCD circuit. p

Tu WEk = 

(

The wash ratio “WR” expressed in (m3/t) is the ratio of the volume of wash solution “Ton+1 VL ” onto the mass of solid to be washed “Tu0 MS ”. Equation (28) gives the mathematical expression of wash ratio for a CCD. WR=



(25)

(

p+1

(T1o VL x(T1o Ck −To

Ck )) p+1 0 0 (Tu VL x(Tu Ck −To Ck ))

x 100

(29)

(

Equation (30) gives the mathematical expression of total flocculant consumption expressed in (g/t) in the CCD circuit containing “n” thickener. Qt =

p

∑n 1 Tf Ms

Joseph Kafumbila

T0u Ms

x 106

(30)

Page 15

(

3.

Design of counter current decantation

3.1.

Preliminary data

The preliminary data is data that you must have before the design of CCD circuit. These data are the following:     

The characteristics of feed pulp The mixing efficiency The flocculant consumption in each thickener The wash ratio The set value of control parameter of underflows

3.1.1.

Characteristics of feed pulp The essential characteristics of feed pulp to be known before the design of CCD circuit are:

    

The solid mass flow MS (kg/h), The specific gravity of solid SGS (kg/m3), The specific gravity of liquid SGL (kg/m3), The chemical composition of feed liquid (Tu0 Ck ), and s The weight percentage of solid in the pulp Cw (%) or the volume percentage of solid in the pulp Cvs (%).

These characteristics come from the characterization of underflow pulp of primary thickener for existing plant. In the case of a new plant, the settling tests must be done on the pulp from the leach tests. The procedure of settling tests will be explained in a separated paragraph.

3.1.2.

Mixing efficiency The Mixing efficiency depends on the method used for the homogenization of thickener feeds.

  

For the agitated tank with a mechanical agitator, the value of mixing efficiency is more than 98% For the no agitated tank but fed tangentially to the internal walls of tank and in counter current, the mixing efficiency is between 95 and 98% For the mixer – distributor advice, the mixing efficiency is between 80 and 95%.

In an existing plant, the mixing efficiency is the average of mixing efficiencies of thickeners in the CCD circuit.

Joseph Kafumbila

Page 16

3.1.3.

Flocculant consumption

The flocculant consumption in each thickener comes from the settling tests done on the outlet pulp of leach circuit. The type of underflow pump (volumetric or centrifugal) must be taken into account for adding the flocculant in the CCD circuit. 

For a plant using volumetric pumps, the flocculant is added only in the primary thickener. A volumetric pump maintains the stability of flocks.



For a plant using the centrifugal pumps, the flocculant is added at 60% of primary thickener consumption level in the first thickener of CCD circuit and at 40% of primary thickener consumption level in the others thickeners of CCD circuit. If “Q” is the flocculant consumption from the settling test done on the outlet pulp of leach circuit, the mathematical expression (31) gives the flocculant consumption for the thickener of rank “p”. p

(

Q

Tf Q= fp x100

(31)

where “ fp “ expressed in (%) is the proportion of flocculant consumption to be added to the thickener of rank “p” comparatively to the flocculant consumption of primary thickener.

3.1.4.

Wash ratio

There are two types of configuration of Copper hydrometallurgy plant – conventional circuit and the split circuit. A.

Conventional circuit

The flow diagram of the conventional circuit is given by Figure (2). The wash ratio depends on the loss of sulphuric acid in the bleed solution of Copper circuit. The loss of sulphuric acid in the bleed of Copper circuit is taken account the free acid and the acid linked to Copper in the solution. In the case of Copper and Cobalt production plant, the concentration of Cobalt in the bleed solution of Copper circuit is also the important parameter. It is better to have a higher concentration of Cobalt to 5 g/l in the bleed solution for reducing the loss of Cobalt in the effluents of Cobalt circuit.

Figure 2: Conventional circuit Joseph Kafumbila

Page 17

B.

Split circuit

The flow diagram of the split circuit is given by the Figure (3). In this case, the free acid and the acid linked to the Copper which are in the solution of underflow pulp of primary thickener are already lost. The wash ratio is limited by the flowrate of the first thickener overflow in the CCD circuit. Generally, the flowrate of overflow of first thickener is limited by the size of secondary Copper solvent extraction circuit. In the case of Copper and Cobalt production plant, the concentration of Cobalt in the bleed solution of Copper circuit is also the important parameter. It is better to have a higher concentration of Cobalt to 5 g/l in the bleed solution for reducing the loss of Cobalt in the effluents of Cobalt circuit.

Figure 3: split circuit

3.1.5.

Set value of control parameter of underflows

A.

Settling test

In the old configuration of CCD circuit, the control parameter of underflow was the volume percentage of solid in the pulp. The value of volume percentage of solid in the pulp came from the characteristics of underflow obtained from the settling test done on the outlet pulp leach circuit. The characteristics of underflow have been obtained after 24 hours of free settling time. At the beginning, the volume percentage of solid in the CCD underflows pulp was the same as the volume percentage of solid in the CCD feed pulp. Later, the values of volume percentage of solid in the CCD underflow pulps were different from the volume percentage of solid in the CCD feed pulp. The volumetric pump with a constant speed has been used for the CCD thickener underflows. The operability of these configurations was very bad because the control of the bed level of solid in the thickeners was difficult. Since 80 years, for the improving of CCD operability, the control parameter of CCD underflows became the specific gravity of underflow pulp and the underflow pump became the centrifugal pump with variable speed. The value of specific gravity of underflow pulp of primary thickener came from the underflow Joseph Kafumbila

Page 18

characteristic obtained from the settling test done on the outlet pulp of leach circuit. The settling time to have the underflow characteristic remains 24 hours. The value of specific gravity of CCD underflow pulp taken as the set value of the control parameter of CCD underflows was the value of specific gravity of underflow pulp of thickener of rank “n” in the CCD circuit having the value of volume percentage of solid of the underflow pulp of primary thickener. The type of thickener used for the primary and the CCD was the conventional thickener. Actually, it has been observed that: 

The weight percentage of solid in the underflow pulp increases with the decreasing of weight percentage of solid in the feed pulp of thickener for the same dosage of flocculant. This correction is obtained from the settling tests done in the Outokumpu laboratory in Finland Figure (4).



The settling rate increases with the decreasing of weight percentage of solid in the feed pulp of thickener. Figure (5) shows an example of the variation of the settling rate with the initial concentration of solid in the pulp [4].



The value of weight percentage of solid in the pulp taken as the set value of the control parameter of the underflows shows directly the pumping characteristic of underflow pulp than the value of specific gravity of pulp.

61

Underflow (% solids)

59 57 55 53 15% solids 25% solids 42% solids

51 49 0

5

10

15

20

25

Flocculent dosage (g/t of solids)

Figure 4: Correlation between the solid pulp concentrations of thickener feed and thickener underflow From these observations, the design of thickener changes from conventional to High Rate Thickener which is capable to make an auto dilution of feed pulp of thickener with the overflow to reach 10% weight percentage of solid in the thickener feed cylinder. The control parameter of underflow becomes the weight percentage of solid in the underflow pulp. The value of weight percentage of solid in the underflow pulp of primary thickener is the value of weight percentage of solid in the underflow pulp obtained from the settling test done on the outlet pulp of leach circuit. The settling time to have the underflow characteristic remains 24 hours. The value of weight percentage of solid in the CCD underflow pulp taken as the control parameter of underflow is the value of weight percentage of solid in underflow pulp of the primary thickener. Joseph Kafumbila

Page 19

In case of simulation of CCD circuit, the important parameter which characterizes the underflow pulp of primary thickener is the volume percentage of solid in the underflow pulp for the conventional or the High Rate Thickener. The volume percentage of solid in the underflow pulp, the specific gravity of liquid and the specific gravity of solid will provide the value of weight percentage of solid in the underflow pulp. The underflow pump will be design according to the rheology test done on the underflow of the primary thickener.

1,40 Settling rate (m/h)

1,20 1,00 0,80 0,60 0,40 0,20 0,00 0

20 40 60 80 100 120 140 160 Solid concentration in thickener feed pulp (kg/m3)

Figure 5: Settling rate versus solid concentration in the thickener feed pulp B.

Rheology test

Actually, the thickener manufactories derive the thickener having the underflow pump with certain characteristics. Depending on the type of thickener, the High Rate Thickener is designed to consistently discharge underflow pulp having a yield stress of less than 25 Pa and the High Density Thickener is designed to consistently discharge underflow pulp having a yield stress of less than 100 Pa. Therefore, the rheology test will provide the maximum value of volume percentage of solid in the underflow pulp. The set value of control parameter of underflows in the CCD circuit is fixed by the type of thickener (High Rate Thickener or High Density Thickener) and the rheology curve. The set value of the control parameter of the underflows (weight percentage of solid in the pulp) is obtained at 20 Pa of yield stress for the High rate Thickener and at 60 Pa of yield stress for the High Density Thickener. The settling time to reach the set value of the control parameter of the underflows must be less than 4 hours for the High Rate Thickener and less than 6 hours for the High density Thickener in the continuous fill test with rake. The rheology tests must be carried out on the underflow pulp of primary thickener to determine the limit of elasticity or "yield stress". The yield stress for the underflow pulp is the pressure required to be applied to the underflow pulp to flow from a stationery bed. The yield stress is a function of the physical properties of pulp (the chemical composition of solid, the particle size distribution, and the solid percentage of pulp), the type of flocculant used, the dosage of flocculant and temperature. Figure 6 shows the example of yield stress variation according to the solid percentage of underflow pulp of Ruashi Mining plants. For the High Rate Thickener, the solid percentage of underflow pulp should not exceed 56.0% and for the High Density Thickener, the solid percentage of underflow pulp should not exceed 60.4% [5]. Joseph Kafumbila

Page 20

200 175

Yield stress (Pa)

150 125 100 75 50 25 0 54

56

58

60

62

64

Underflow pulp solids percentage (%)

Figure 6: Yield stress values versus the underflow pulp percentage of solid of Ruashi Mining plants

3.2.

Number of thickener in the CCD

It has been defined above how to fix the set value of the control parameter of underflows, the mixing efficiency, the flocculant consumption and the wash ratio. It only remains to find the number “n” of thickener to align in a CCD to reach the set value of the wash efficiency or the concentration of recoverable element in the underflow of thickener of rank “n”. It should be noted that the wash efficiency increases with increasing the volume percentage of solid in the underflow pulp, the wash ratio, the mixing efficiency, and the number of thickener in series. The determination of the optimum number of thickener in the CCD circuit will be in another paragraph. The method is to vary the number of thickeners in the CCD circuit until the value of washing efficiency or the value of the concentration of a valuable component in the underflow liquid of the last thickener reach the target value.

Joseph Kafumbila

Page 21

4.

Settling test

4.1.

Types of settling test

There are 3 types of settling test: the rule of thumb sizing, the cylinder settling tests, and the dynamic thickener test work.

4.1.1.

Rule thumb sizing

This type of settling test is used when the indicative feed samples are not available. The performance of the nearly plant with similar feed characteristics can be taken into account.

4.1.2.

Cylinder settling tests

These settling tests are the traditional method for thickener sizing. This method can be conducted with a relatively small amount of feed sample.

4.1.3.

Dynamic thickener test work

The dynamic thickener test work method has been developed by the thickener suppliers until the 1990s. This method is the new version to scale the commercial thickeners. This method requires the larger amount of sample.

4.2.

Cylinder settling tests

4.2.1.

Equipment Settling tests are conducted in one liter graduated cylinder whose dimensions are the following:

     

Height: 463 mm, A graduated height of 10 ml into 10 ml to a liter: Up to a liter equal to 348 mm, An internal diameter: 60 mm, The agitation of the pulp in the test is done manually by upward and downward movements with the aid of a 500 mm long rod equipped at its end with a perforated 50 mm diameter disc, The perforated disc have 6 holes of 12 mm in diameter, The clarity of the solution is estimated using a turbidity meter.

Joseph Kafumbila

Page 22

4.2.2.

Characterization of pulp It is necessary to determine the following characteristics of pulp before starting the settling tests:

     

The temperature of pulp, The pH of pulp, The specific gravity of solid, The specific gravity of liquid, The specific gravity of pulp, The weight percentage of solid in the pulp.

It should be noted that if pH adjustment is necessary, the determination of weight percentage of solid in the pulp comes after the pH adjustment. In the case of High Rate Thickener, the pulp must be diluted with the leach solution to the desired weight percentage of solid in the pulp (10 % of solid).

4.2.3.

Flocculant preparation

The flocculant is prepared into concentrated solution of 5% (stock solution) which is diluted 20 times in use. The flocculant stock solution can be stored for one week. However the retention period of diluted solution can’t exceed 24 hours. The preparation method of flocculant stock solution is:     

Weigh 2.5 g of flocculant, Disperse the flocculant slowly (for 30 minutes) in a one liter beaker containing 500 ml of water with stirring. The mixer will run at a speed sufficient to create a vortex, Leave stirring for 2 hours, Transfer to a polyethylene bottle, taking care to close after filling This stock solution will be diluted 20 times before use. The weight percentage of flocculant in the dilute solution will be 0.25 %.

The dosage of flocculant in the settling test cylinder is done according to the assay gram of flocculant per ton of solid.

4.2.4.

Settling test The settling test is done according to the following procedure:

      

Mix well the diluted pulp in a 5 liters bucket, Fill the settling test cylinder with pulp to a liter, Stir the pulp using the rod ten times with a frequency of one pulse per second, Add the calculated volume of diluted flocculant solution, Continue to stir the pulp approximately 3 times, Start the timer when the settling front of pulp passes by the 1.000 ml graduation of the cylinder, Note the height of the settling front of pulp versus time as prescribed on the running sheet (Table 6 shows the running sheet of settling test), Joseph Kafumbila

Page 23



Determine the clarity of solution after settling test. The Settling tests are repeated several times for different dosages and flocculant types. Table 6: Settling test running sheet Sample Date Type of pulp Temperature pH Times min

white

Test conditions Temperature Type of flocculant pH Solid % Solid specific gravity Liquid specific gravity height (mL) Flocculant dosage (g/t)

0.5 1 1.5 2 2.5 3 4 5 6 8 10 12 14 16 20 25 30 35 40 50 60 24h

4.2.5.

Settling curve During the settling test, it will be observed the following behavior:

 

At the beginning, the large grains are settled quickly and are deposited on the bottom of the cylinder. The height of this zone is increased quickly and stabilized after the settling of grains greater than 0.1 mm. Then, it is quickly appeared, and sometimes immediately, an interface between a clear liquid and a sludge phase.

By plotting the variation of height (h) of interface between the clear liquid and the slurry phase according to the time (t) since the beginning of settling test, the settling curve is obtained (Figure 6). It appears on the settling curve the following four areas: 

Domain I - it corresponds to the original time of flocculation and is often non-existent if the flocculation is fast,



Domain II - this is the area where the flocks begin to gather in flakes and settling rate is constant, Joseph Kafumbila

Page 24



Domain III - from this point, the disruptive action occurs between the flakes and particles. This point is often poorly defined on the curve,



Domain IV - from this point, the isolated solids are in contact and form semi-rigid pseudo-networks. The liquid is discharged through the mass of sediment following the voids created by the pseudonetworks and after sliding the mud layers. This domain is called compression zone.

1000

a Interface Height (mL)

900

I

800 700

II

b

600 500

III IV

400 0

10

20 30 Times (min)

40

50

60

Figure 6: general appearance of the settling curve

4.2.6.

Size of thickener

The classic work on the capacity of a continuously operating thickener was provided by Coe and Clevenger [6]. The choice of flocculant is performed by comparing the settling rate in the Domain (II). The settling rate expressed in (m/h) in this domain II is obtained by equation (32). The settling test giving high settling rate with low flocculent consumption is taken. Vd =

(ha −hb ) (tb −ta )

348

60

x 1.000 x 1.000

(32)

(

Where ha is the height (ml) in the point “a”, hb is the height (ml) in point “b”, t b is the time (min) in the point “b”, t a is the time (min) in the point “a” and 348 is the height (mm) of the settling test cylinder at 1.000 ml. The solid flux “G” expressed in (kg/m2.h) that a thickener can process per unit area and per unit time is given by the equation (33). G=

Vd 1 1 ( i − u) Cs Cs

( (33)

where Csi is the initial solid concentration (kg/m3) of pulp and Csu is the concentration of solid (kg/m3) in the underflow pulp.

Joseph Kafumbila

Page 25

The thickener area is obtained using the equation (34).

S=

Ms G

x 1.2

(34)

where Ms is the solid mass flow (kg/h) and G is solid flux (kg/m2.h).

Joseph Kafumbila

Page 26

(

5.

Optimum number of thickener in the CCD circuit

5.1.

Old methods

There are two old methods for determining the number of thickener in the CCD circuit. These two old methods require knowledge of the values of volume percentage of solid in the pulp fed in the CCD circuit and in the underflows of thickeners.

5.1.1.

First method

When the volume percentage of solid in the pulp fed to the CCD circuit is the same as those of underflows of CCD circuit, the mixing efficiency is 100 % and the flocculant is added only to the primary thickener, the mathematical expression (35) gives the equation for calculating the concentration of an element of index "k" in the liquid of underflow of thickener of rank "p". p+1 Ck p p+1 Tu Ck −Tu Ck

T0u Ck −Tu

= Ωp

(35)

(

The value of Ω𝑝 is given by the mathematical expression (36). (

Ωp = 1+ β1 + β2 + …….. + βp

(36)

The value of β is given by the mathematical expression (37) β=

5.1.2.

Tn+1 o VL

(37)

Tn u VL

(

Second method

When the volume percentage of solid in the pulp fed to the CCD circuit is different from those of underflows CCD circuit, the mixing efficiency is 100 % and the flocculant is added only to the primary thickener, the mathematical expression (38) gives the equation for calculating the concentration of an element of index "k" in the liquid of underflow of thickener of rank "n". The CCD circuit contains "n" thickeners. Tun Ck = γ

γ(n+1) −1 1 xγ2 xγ3 x….xγ(n+1) −1

xTu0 Ck + [1- γ

γ(n+1) −1

]x Ton+1 Ck

1 xγ2 xγ3 x….xγ(n+1) −1

(38)

The value of variable γp is given by the mathematical expression (39).

Joseph Kafumbila

Page 27

(

γp =

p

To VL

p−1 Tu VL

( (39)

The value of γ(n+1) is given by the mathematical expression (40). γ(n+1) =

5.2.

New method

5.2.1.

Constraints

Tn+1 o VL Tn u VL

( (40)

The old methods to calculate the number of thickener to upload the CCD circuit are no longer used today because of: 

When the control parameter of underflows in the CCD circuit becomes the specific gravity of pulp or the weight percentage of solid in the pulp, the value of volume percentage of solid in the pulp becomes a function of specific gravity of solid and specific gravity of liquid. It should also be noted that the specific gravity of liquid is a function of the chemical composition.



In modern CCD circuits, the centrifugal pumps with variable speed are used for the underflow pulp to improve the operability of the circuit. Under these conditions, the flocculant is also added in the CCD circuit



The mixing efficiency must be taken account in the CCD circuit.

Two examples of simulation of a CCD circuit will be made to illustrate the new method of simulation

5.2.2.

First example

A.

CCD circuit description

The CCD circuit is part of Copper and Cobalt production plant from flotation concentrates. The configuration of Copper circuit is the conventional circuit. Accordingly, the overflow of the first thickener in the CCD circuit is mixed with the overflow from the primary thickener and the mixture is the feed of Copper tankhouse. The solution leaving the Copper tankhouse is pumped to the leach section after bleeding excess water. This bleed solution is the feed of Cobalt circuit. B.

Preliminary data of CCD circuit Preliminary data of CCD circuit are the following:

Joseph Kafumbila

Page 28



The pulp to be washed from the primary thickener has the following characteristics: the mass flow (MS ) of 26.250 kg/h, specific gravity of solid (dS ) 2,700 kg/m3, the volume percentage of solid in the pulp after the settling test of 25%.



The concentrations of elements in the liquid are shown in the table (7) Tableau 7: Concentrations of elements in the liquid of feed pulp Elements (kg/m3)

Cu 60.00

Co 29.03

Fe 3.41

Zn 0.28

Ca 0.50

Mn 1.38

Mg 14.22

Al 2.85

H2SO4 16.82



The consumption of flocculant in the primary thickener is 30 g/t. The value of "f1 " is 60% and the value of "f2 " to "fn " is 40%. Note that centrifugal pumps are used for the underflows. The value of weight percentage of flocculant in the solution fed to the thickener is 0.25 %.

  

The value of wash ratio is 1.8 m3/t. The value of mixing efficiency is 95 %. The type of thickener is the conventional.

C.

Simulation results

 First simulation The control parameter of underflows is the specific gravity of pulp. The set value of the specific gravity of underflow pulp is the value of specific gravity of underflow of thickener of rank “n” in the CCD circuit having the volume percentage of solid of the underflow of primary thickener. Table 8 shows the simulation results of the CCD circuit having the number of thickener ranging from 1 to 5. The results of the simulation show that: Wash efficiency increases with increasing the number of thickener in the CCD circuit. Figure 7 shows the wash efficiency of the thickener of rank “n” in the CCD circuit as a function of number “n” of thickener. 100,00

Wash efficiency (%)



90,00 80,00 70,00 60,00 50,00 0

1

2 3 4 5 Number of thickener in the CCD circuit

6

Figure 7: Wash efficiency of CCD circuit versus number of Thickener for the first simulation Joseph Kafumbila

Page 29



The set value of specific gravity of underflows in the CCD circuit decreases with the increasing of number “n” of thickener in the CCD circuit. This is due to the decreasing of specific gravity of underflow liquid of the thickener of rank “n”.



For thickener of rank "p" in the CCD circuit containing "n" thickener, the weight and volume percentages of solid in the underflow pulp decrease with the increasing the number of thickener "n". This is due to the increasing of specific gravity of underflow liquid of thickener of rank “p”. This increasing of specific gravity of underflow liquid of thickener of rank “p” is a consequence of liquid enrichment.



For a CCD circuit containing "n" thickener, the values of weight and volume percentages of underflow pulp increases from the thickener of rank “1” to the thickener of rank “n”. In our case, the increase in the value of volume percentage from the first to the last thickener is 43.41 % for a CCD circuit containing 5 thickeners. Table 8: Simulation results of CCD circuit for the first example (specific gravity – control parameter) Number of Thickener

1

2

3

4

5

Parameters SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2

Joseph Kafumbila

kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % Kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t %

Tu0

Tu1

1623.38 1516.22 41.58 44.52 25.00 25.00 1264.50 1121.63 60.00 23.57 18.00 60.71 1623.38 1478.20 41.58 38.79 25.00 21.23 1264.50 1148.81 60.00 29.55 30 55.52 1623.38 1458.32 41.58 35.73 25.00 19.30 1264.50 1161.44 60.00 32.44 42.00 52.55 1623.38 1446.42 41.58 33.88 25.00 18.15 1264.50 1168.45 60.00 34.08 54.00 50.70 1623.38 1438.86 41.58 32.71 25.00 17.43 1264.50 1172.61 60.00 35.07 66.00 49.52

Tu2

Tu3

Tu4

Tu5

1478.20 45.66 25 1070.93 13.20 78.00 1458.32 1458.32 41.52 46.29 22.43 25.00 1099.38 1044.43 18.91 8.11 75.13 86.48 1446.42 1446.42 1446.42 39.07 43.40 46.67 20.93 23.25 25.00 1114.56 1066.65 1028.56 22.07 12.37 5.16 73.29 84.96 91.41 1438.86 1438.86 1438.86 1438.86 37.55 41.61 44.71 46.91 20.01 22.17 23.83 25.00 1123.42 1079.59 1044.40 1018.49 23.96 14.91 8.10 3.32 72.09

83.94

90.60

94.47

Page 30

 Second simulation Compared to the first simulation, the control parameter of underflows is the weight percentage of solid in the pulp. The set value of the weight percentage of solid in the underflows is the value of the weight percentage of solid in the underflow of primary thickener. Table 9 shows the simulation results of CCD circuit having the number of thickener ranging from 1 to 5. The results of the simulation show that: 

The wash efficiency increases with the increasing the number “n” of thickener in the CCD circuit. Figure 8 shows the wash efficiency after the thickener of rank “n” in the CCD circuit as a function of number “n” of thickeners Table 9: Simulation results of CCD circuit for the first example (Weight percentage of solid – control parameter) Number of Thickener

1

2

3

4

5



Parameters SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2

kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % Kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t %

Tu0

Tu1

1623.38 1481.53 41.58 41.58 25.00 22.82 1264.50 1121.35 60 23.52 18 55.80 1623.38 1518.77 41.58 41.58 25.00 23.39 1264.50 1158.14 60 31.68 30.00 55.68 1623.38 1536.49 41.58 41.58 25.00 23.66 1264.50 1175.84 60 35.84 42.00 55.58 1623.38 1546.49 41.58 41.58 25.00 23.82 1264.50 1185.88 60 38.28 54.00 55.51 1623.38 1552.63 41.58 41.58 25.00 23.91 1264.50 1192.09 60 39.82 66.00 55.48

Tu2

Tu3

Tu4

Tu5

1429.06 41.58 22.01 1070.44 13.10 74.20 1462.53 1403.18 41.58 41.58 22.52 21.61 1102.79 1045.71 19.61 8.35 74.12 83.17 1481.46 1429.27 1388.17 41.58 41.58 41.58 22.81 22.01 21.38 1121.29 1070.64 1031.48 23.50 13.15 5.69 74.06 83.11 88.36 1493.17 1445.51 1407.99 1378.60 41.58 41.58 41.58 41.58 22.99 22.26 21.68 21.23 1132.81 1086.29 1050.28 1022.46 25.99 16.25 9.22 4.04 74.03

83.09

88.33

91.68

For a Thickener of rank "p" in the CCD circuit containing "n" thickener, the volume percentage of solid in the pulp of underflow increases with the increasing the number "n” of thickeners. This is due Joseph Kafumbila

Page 31

to the increasing of specific gravity of underflow liquid of thickener of rank "p". This increasing of specific gravity of underflow liquid is a consequence of enrichment of liquid. 

For a CCD circuit containing "n" thickeners, the values of volume percentages of solid in the underflow decrease from the thickener of rank “1” to the thickener of rank “n”. In this case, the decrease in the value of volume percentage is 11.21 % for a CCD circuit containing "5" thickener. 100,00

Wash efficiency (%)

90,00 80,00 70,00 60,00 50,00 0

1

2 3 4 5 Number of thickener in the CCD circuit

6

Figure 8: Wash efficiency of CCD circuit versus number of Thickener for the second simulation

5.2.3.

Second example

A.

CCD circuit description

The CCD circuit is part of Copper and Cobalt production plant from oxide ores. The configuration of Copper circuit is the conventional circuit. So, the overflow of the first thickener in the CCD circuit is mixed with the overflow from the primary thickener and the mixture is the PLS of Copper solvent extraction. The raffinate from the Copper solvent extraction is pumped to the leach section of ores after bleeding excess water. This bleed is the feed of Cobalt circuit. B.

Preliminary data of CCD circuit Preliminary data from the CCD circuit are as follows:



The Pulp to be washed from the primary thickener has the following characteristics: the mass flow (MS ) of 260,000 kg/h, the specific gravity of solid (dS ) of 2,600 kg/m3, the volume percentage of solid in the pulp after the settling tests of 36.92 %.



The concentrations of elements in the liquid are shown in the table (10) Tableau 10: Concentration of elements in the liquid of CCD feed pulp Elements (kg/m3)

Cu 8.04

Co 10.14

Joseph Kafumbila

Fe 0.80

Zn 0,10

Ca 0,50

Mn 2.75

Mg 3.80

Al 1.17

H3PO4 1.82

H2SO4 1.99 Page 32

    C.

The flocculant consumption in the primary thickener is 40 g/t. The value of "f1 " is 60% and the value of "f2 " to "fn " is 40%. Note that centrifugal pumps are used to pump underflows. The value of weight percentage of flocculant in the solution fed to the thickener is 0.25 %. The value of wash ratio is 1.8 m3/t. The value of mixing efficiency is 95 %. The type of thickeners is the High Grade Thickener. Simulation results

 First simulation The control parameter of underflows is the specific gravity of pulp. The set value of the specific gravity of underflows is the value of specific gravity of underflow of thickener of rank “n” having the volume percentage of solid in the pulp of the underflow of primary thickener. Table 11 gives the simulation results of CCD circuit with the number of thickeners ranging from 1 to 5. The results of simulation show that: 

The Wash efficiency increases with the increasing the number of thickener in the CCD circuit. Figure 9 shows the wash efficiency of the thickener of rank “n” in the CCD circuit as a function of number “n” of thickener. 100,00

Wash efficiency (%)

95,00 90,00 85,00 80,00 75,00 70,00 0

1

2 3 4 Number of thickener in the CCD

5

6

Figure 9: Wash efficiency of CCD circuit versus number of Thickener for the first simulation 

The set value of specific gravity of underflows decreases with the increasing of number “n” of thickener in the CCD circuit. This is due to the decreasing of specific gravity of underflow liquid of thickener of rank “n”.



For thickener of rank "p" in the CCD circuit containing "n" thickener, the weight and volume percentages of solid in the underflow pulp decrease with the increasing the number “n” of thickener in CCD circuit. This is due to the increasing of specific gravity of underflow liquid. This increasing of specific gravity of underflow liquid is a consequence of enrichment of liquid. Joseph Kafumbila

Page 33



For a CCD circuit containing "n" thickener, the values of weight and volume percentages of solid in the underflow pulp increase from the thickener of rank “1” to the thickener of rank “n”. In this case, the increase of value of volume percentage from the first to the last thickener is 3.45 % for a CCD circuit containing 5 thickeners. Table 11: Simulation results of CCD circuit for the second example (specific gravity – control parameter) Number of Thickener

1

2

3

4

5

Parameters SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2

kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % Kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t %

Tu0

Tu1

1642.18 1605.61 58.46 59.79 36.93 36.93 1081.46 1023.49 8.04 2.22 24.00 72.35 1642.18 1596.02 58.46 58.82 36.93 36.10 1081.46 1028.72 8.04 2.73 40.00 71.60 1642.18 1592.72 58.46 58.48 36.93 35.83 1081.46 1030.41 8.04 2.89 56.00 71.39 1642.18 1591.51 58.46 58.36 36.93 35.73 1081.46 1030.95 8.04 2.95 72.00 71.36 1642.18 1591.06 58.46 58.33 36.93 35.69 1081.46 1031.09 8.04 2.96 88.00 71.39

Tu2

Tu3

Tu4

Tu5

1596.02 60.12 36.93 1008.27 0.76 90.36 1592.72 1592.72 59.77 60.28 36.62 36.93 1010.83 1003.04 1.02 0.28 90.18 96.47 1591.51 1591.51 1591.51 59.64 60.13 60.32 36.51 36.81 36.93 1011.70 1004.05 1001.13 1.10 0.38 0.11 90.15 1591.06 59.59 36.47 1011.97 1.12 90.17

96.43 98.69 1591.06 1591.06 60.08 60.27 36.77 36.88 1004.4 1001.51 0.41 0.14 96.43

98.68

15191.06 60.34 36.93 1000.42 0.04 99.52

 Second simulation Compared to the first simulation, the control parameter of underflows is the weight percentage of solid in the pulp. The set value of weight percentage of solid in the underflows is the value of weight percentage of solid in the underflow pulp of primary thickener. Table 12 shows the simulation results of the CCD circuit having the number of thickener ranging from 1 to 5. The results of simulation show that: Joseph Kafumbila

Page 34



The Wash efficiency increases with the increasing of number of thickener in the CCD circuit. Figure 10 shows the wash efficiency of thickener of rank “n” in the CCD circuit as a function of the number “n” of thickeners.

Table 12: Simulation results of CCD circuit for the second example (Weight percentage of solid – control parameter) Number of Thickener

1

2

3

4

5

Parameters SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2 SGP Cw Cv SGL C2 Qt p WE2

kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % Kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t % kg/m3 % % kg/m3 kg/m3 g/t %

Tu0

Tu1

1642.18 1585.52 58.46 58.46 36.93 35.65 1081.46 1023.47 8.04 2.22 24 70.81 1642.18 1591.18 58.46 58.46 36.93 35.78 1081.46 1029.16 8.04 2.77 40.00 70.77 1642.18 1593.08 58.46 58.46 36.93 35.82 1081.46 1031.08 8.04 2.96 56.00 70.79 1642.18 1593.74 58.46 58.46 36.93 35.84 1081.46 1031.74 8.04 3.02 72.00 70.85 1642.18 1593.93 58.46 58.46 36.93 35.84 1081.46 1031.93 8.04 3.04 88.00 70.91

Tu2

Tu3

Tu4

Tu5

1570.48 58.46 35.31 1008.48 0.80 89.40 1573.25 1565.23 58.46 58.46 35.38 35.19 1011.22 1003.28 1.05 0.31 89.38 95.90 1574.25 1566.40 1563.23 58.46 58.46 58.46 35.40 35.22 35.15 1012.21 1004.42 1001.29 1.15 0.41 0.12 89.41 95.89 98.38 1574.58 1566.83 1563.70 1562.45 58.46 58.46 58.46 58.46 35.41 35.23 35.16 35.13 1012.54 1004.84 1001.76 1000.51 1.18 0.45 0.16 0.05 89.45

95.91

98.38

99.35



For the thickener of rank "p" in the CCD circuit containing "n" thickener, the volume percentage of solid in the underflow pulp increases with the increasing the number “n” of Thickener in the CCD circuit. This is due to the increasing of specific gravity of underflow liquid of thickener of rank “p”. This increasing of specific gravity of underflow liquid is a consequence of the enrichment of liquid.



In a CCD circuit containing "n" thickener, the values of volume percentages of solid in the underflow decrease from the thickener of rank “n” to the thickener of rank “n”. In this case, the decrease in the value of volume percentage is 1.98 % for a CCD circuit containing "5" thickeners.

Joseph Kafumbila

Page 35

100,00

Wash efficiency (%)

90,00 80,00 70,00 60,00 50,00 0

1

2 3 4 5 Number of thickener in the CCD circuit

6

Figure 10: Wash efficiency of CCD circuit versus number of Thickener for the second simulation

5.2.4.

Observations

The results of the four simulations of the two CCD circuits show that the use of pulp specific gravity as control parameter of underflows gives high wash efficiency than the use of weight percentage of solid in the underflows. This is true in the case of using a conventional or High Rate Thickener. On the other hand, the value of pulp specific gravity does not give directly to the operator an accurate indication of underflow pumping characteristics (the volume percentage of solid in the pulp). The operability of the CCD circuit using the weight percentage as the control parameter of underflow is high because the volume percentage of solid decreases from the first to the last thickener in the CCD circuit. The decreasing of volume percentage of solid goes in the direction as the degradation of flock in the underflow pulp. The decreasing in the value of volume percentage of solid in the underflow pulp from the first to the last thickener is important when the value of specific gravity of underflow liquid of the feed pulp is big.

Joseph Kafumbila

Page 36

6.

Procedure of CCD circuit simulation

6.1.

General

The simulation of a CCD circuit will be done on an Excel spreadsheet (Microsoft). Excel spreadsheet gives numbers and formulas in the form of a table (rows and columns). The Excel spreadsheet is made of lines (numbered with numbers) and of columns (numbered with letters). The intersection of a row and a column is called "cell." A cell is identified by a letter and a number. The Excel spreadsheet can contain up to 65,536 rows and 256 columns, more than 17 million cells. Each of the cells of the spreadsheet can contain data (numbers, text, date,..) which are entered directly or automatically calculated.

6.2.

Plant description

The CCD circuit is part of Copper and Cobalt production plant from flotation concentrates. The configuration of Copper circuit is the conventional circuit. Consequently, the overflow of first thickener in the CCD circuit is mixed with the overflow from the primary thickener and the mixture is the feed of Copper tankhouse. The solution leaving the Copper tankhouse is pumped to the leach section of Copper concentrates after bleeding excess water. This bleed solution is the feed of Cobalt circuit.

6.3.

Preliminary data of CCD circuit

The Preliminary data of the CCD circuit are the as the first example of CCD circuit simulation. The only differences are:  

The number of thickener in the CCD circuit is 2. The set value of control parameter of underflow is: -

The weight percentage of solid in the pulp. The set value of weight percentage of solid in the underflows is the value of weight percentage of solid of the underflow of primary thickener.

-

The specific gravity of the pulp. The set value of specific gravity of underflows is the value of the underflow specific gravity of last thickener having the volume percentage of solid of underflow of primary thickener.

6.4.

Simulation table

The simulation table of CCD circuit is given by Table 13 as it appears on the Excel spreadsheet. Table 13 is divided into four small tables. The first small table is the simulation table. The columns of this first small show the names of the inlet and outlet pulps of thickeners in the CCD circuit. The lines show the pulp parameters. On this first simulation table, the preliminary data attached to the pulp parameters of CCD circuit are also included. The second small table shows preliminary data that are not the pulp parameters. The third table shows the wash efficiency after each thickener in the CCD circuit. The fourth table shows data of the "Solver" program of Excel. Joseph Kafumbila

Page 37

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

To2

To3

0.00

0.00

L

Table 13: Simulation table for CCD circuit with two thickeners Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv kg/m3 Cts H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu0

Tf1

Tu1

To1

Tf2

0.00

2,650.00 1,000.00 0.25

Tu2

26,250.00

2,700.00

2,650.00 1,000.00 0.25

25.00 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Mg

Al

Data g/t m3/t

f1 ME

Results WE %

T1

T2

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV

Tu2 CV

H2SO4

Cu

Q WR

30.00 1.80

Joseph Kafumbila

60 95

% %

f2

40

%

Co

Fe

Zn

Ca

Mn

Page 38

6.5.

Procedure of CCD circuit simulation The simulation procedure of CCD circuit having two thickeners is as follow:

1.

Calculation of missing parameters of pulp 𝑻𝟎𝒖

-

In the Cell « D9 », type “=D6/D12” In the cell “D8”, type “ =D9/D15*100” In the cell “D10”, type “=D8-D9” In the cell “D16”, type “=$L17*D17+$L18*D18+$L19*D19 +$L20*D20+$L21*D21+$L22*D22+$L23*D23+$L24*D24+$L25*D25 In the cell “D13”, type “=-6.139*10^-4*D16^2+0.9742*D16+1,000” In the cell “D7”, type “=D13*D6” In the cell “D5”, type “=D6+D7” In the cell “D11”, type “=D5/D8” In the cell “D14”, type “=D6/D5*100” In the cell “D26”, type “=D$10*D17” Copy the formula of cell “D26” into the cells of column “D” from “D27” to “D34”

-

2. Calculation of missing parameters of pulp 𝑻𝟑𝒐 -

In the cell “K10”, type “=D6*C38/1.000” In the cell “K16”, copy the formula of cell “D16” In the cell “K13”, copy the formula of cell “D13” In the cell “K7”, type “=K10*K13” In the cell “K5”, type “=K7/(100-K14)*100” In the cell “K6”, type “=K5-K7” In the cell “K9”, type “=K6” because the value of To3 Ms is zero In the cell “K8”, type “=K9+K10” In the cell “K11”, type “=K5/K8” Copy the formula of cell “D26” into the cells of column “K” from “K26” to “K34”

3. Calculation of missing parameters of pulp 𝑻𝟏𝒇 -

In the cell “E6”, type “=D6*C37*F37/100/1000/1000” In the cell “E5”, type “=E6/E14*100” In the cell “E7”, type “=E5-E6” In the cell “E9”, type “=E6/E12” In the cell “E10”, type “=E7/E13” In the cell “E8”, type “=E9+E10” In the cell “E11”, type “=E5/E8”

4. Calculation of missing parameters of pulp 𝑻𝟐𝒇 -

In the cell “H6”, type “=D6*C37*I37/100/1000/1000” In the cell “H5”, type “=H6/H14*100” In the cell “H7”, type “=H5-H6” In the cell “H9”, type “=H6/H12” In the cell “H10”, type “=H7/H13” In the cell “H8”, type “=H9+H10” Joseph Kafumbila

Page 39

-

In the cell “H11”, type “=H5/H8”

5. Calculation of mass and volume flows of pulp 𝑻𝟏𝒖 -

In the cell “F6”, type “=D6+E6” In the cell “F9”, type “=D9+E9”

The control parameter of underflows is the weight percentage of solid in the pulp. The set value of weight percentage of solid in the underflows is the value of weight percentage of solid of the underflow of primary thickener. -

In the cell “D44”, type the number “25.00”. this value is the started value of Tu1 CV for solver 1 variables

The control parameter of underflows is the specific gravity of pulp. The set value of specific gravity of underflows is the value of specific gravity of underflow of last thickener having with the volume percentage of solid of the underflow of primary thickener. -

In the cell “D44”, type the number “25.00”. this value is the started value of Tu1 CV for solver 1 variables

-

In the cell “F15”, type “=D44” In the cell “F8”, type “=F9/F15*100” In the cell “F10”, type “=F8-F9” In the cell “F16”, copy the formula of cell “D16” In the cell “F13”, copy the formula of cell “D13” In the cell “F7”, type “=F10*F13” In the cell “F5”, type “=F6+F7” In the cell “F12”, type “=F6/F9” In the cell “F11”, type “F5/F8”

6. Calculation of mass and volume flows of pulp 𝑻𝟐𝒖 -

In the cell “I6”, type “=F6+H6” In the cell “I9”, type “=F9+H9”

The control parameter of underflows is the weight percentage of solid in the pulp. The set value of weight percentage of solid in the underflows is the value of weight percentage of solid of the underflow of primary thickener. -

In the cell “E44”, type the number “25.00”. this value is the started value of Tu2 CV for solver 1 variables

The control parameter of underflows is the specific gravity of pulp. The set value of specific gravity of underflows is the value of specific gravity of underflow of last thickener having with the volume percentage of solid of the underflow of primary thickener (because Tu2 is the underflow of the last Thickener). -

In the cell “E44”, type “=D15”

-

In the cell “I15”, type “=E44” In the cell “I8”, type “=I9/I15*100” In the cell “I10”, type “=I8-I9” In the cell “I16”, copy the formula of cell “D16” In the cell “I13”, copy the formula of cell “D13” In the cell “I7”, type “=I10*I13” In the cell “I5”, type “=I6+I7” In the cell “I12”, type “=I6/I9” Joseph Kafumbila

Page 40

-

In the cell “I11”, type “=I5/I8”

7. Calculation of mass and volume flows of the pulp 𝑻𝟐𝟎 (start with the overflow of the lost thickener) -

In the cell “J7”, type “=F7+H7+K7-I7” In the cell “J10”, type “=F10+H10+K10-I10” In the cell “J5”, type “=J7/(100-J14)*100” In the cell “J6”, type “=J5-J7” In the cell “J9”, type “=J6” because the value of To2 Ms is zero In the cell “J8”, type “=J9-J10” In the cell “J13”, type “=J7/J10” In the cell “J11”, type “=J5/J8”

8. Calculation of mass and volume flows of pulp 𝑻𝟏𝟎 -

In the cell “G7”, type “=D7+E7+J7-F7” In the cell “G10”, type “=D10+E10+J10-F10” In the cell “G5”, type “=G7/(100-G14)*100” In the cell “G6”, type “=G5-G7” In the cell “G9”, type “=G6” because the value of To1 Ms is zero In the cell “G8”, type “=G9-G10” In the cell “G13”, type “=G7/G10” In the cell “G11”, type “=G5/G8”

At this level, it appears table 14 giving the simulation table when the control parameter of underflows is the weight percentage of solid and Table 15 gives the simulation table when the control parameter of underflows is the specific gravity of pulp.

9. Calculation of concentrations and mass flows of elements in liquid -

In the cell “D47”, type the number “1.00”. This value is the started value of Tu2 C1 for solver 2 variables In the cell “E47”, type the number “1.00”. This value is the started value of Tu2 C2 for solver 2 variables In the cell “F47”, type the number “1.00”. This value is the started value of Tu2 C3 for solver 2 variables In the cell “G47”, type the number “1.00”. This value is the started value of Tu2 C4 for solver 2 variables In the cell “H47”, type the number “1.00”. This value is the started value of Tu2 C5 for solver 2 variables In the cell “I47”, type the number “1.00”. This value is the started value of Tu2 C10 for solver 2 variables In the cell “J47”, type the number “1.00”. This value is the started value of Tu2 C7 for solver 2 variables In the cell “K47”, type the number “1.00”. This value is the started value of Tu2 C8 for solver 2 variables In the cell “L47”, type the number “1.00”. This value is the started value of Tu2 C9 for solver 2 variables

-

In the cell “I17”, type “=D47” In the cell “I18”, type “=E47” In the cell “I19”, type “=F47” In the cell “I20”, type “=G47” In the cell “I21”, type “=H47” In the cell “I22”, type “=I47” In the cell “I23”, type “=J47” In the cell “I24”, type “=K47” In the cell “I25”, type “=L47”

Joseph Kafumbila

Page 41

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

L

To2 47,375.3 0.00 47,375.33 47.38 0.00 47.38 1,000.00

To3 47,250.0 0.00 47,250.0 47.25 0.00 47.25 1,000.00

1,000.00 0.00

1.000.00 0.00

Table 14: Simulation table for CCD circuit with two thickeners Tu0 63,131.4 26,250.00 36,881.4 38,89 9,72 29,17 1,623,38 2,700.00 1,264.50 41,58 25.00 347,69 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85 490.58 1,750.00 846.71 99.46 8.17 14.58 40.25 414.75 83.13

Tf1 189.00 0.47 188.53 0.19 0.00 0.19 1001.56 2,650.00 1,000.00 0.25

g/t m3/t

f1 ME

Results WE %

T1

T2

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV 25.00

Tu2 CV 25.00

H2SO4

Cu

Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv kg/m3 Cts H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu1 55,417.7 26,250.47 29,167.2 38.89 9.72 29.17 1,425.00 2,700.00 1,000.00

To1 55,278.0 0.00 55,278.0 47.56 0.00 47.56 1,162.20 1,162.20 0.00

Tf2 126.00 0.32 125.69 0.13 0.00 0.13 1,001.56 2,650.00 1,000.00 0.25

25.00 0.00

Tu2 55,418.3 26,250.79 29,167.6 38.89 9.72 29.17 1,425.00 2,700.00 1,000.00 25.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Data Q WR

30.00 1.80

Joseph Kafumbila

60 95

% %

f2

40

%

Co

Fe

Zn

Ca

Mn

Mg

Al

Page 42

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

To2 47,375.3 0.00 47,375.3 47.38 0.00 47.38 1,000.00

To3 47,250.0 0.00 47,250.0 47.25 0.00 47.25 1,000.00

1.000.00 0.00

1.000.00 0.00

L

Table 15: Simulation table for CCD circuit with two thickeners Tu0 63,131.4 26,250.0 36,881.4 38,89 9,72 29,17 1,623,38 2,700.00 1,264.50 41,58 25.00 347,69 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85 490.58 1,750.00 846.71 99.46 8.17 14.58 40.25 414.75 83.13

Tf1 189.00 0.47 188.53 0.19 0.00 0.19 1001.56 2,650.00 1,000.00 0.25

g/t m3/t

f1 ME

Results WE %

T1

T2

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV 25.00

Tu2 CV 25.00

H2SO4

Cu

Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv kg/m3 Cts H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu1 55,417.7 26,250.5 29,167.2 38.89 9.72 29.17 1,425.0 2,700.0 1,000.0

To1 55,278.0 0.00 55,278.0 47.56 0.00 47.56 1.162.20 1,162.20 0.00

Tf2 126.00 0.32 125.69 0.13 0.00 0.13 1,001.56 2,650.00 1,000.00 0.25

25.00 0.00

Tu2 55,418.4 26,250.8 29,167.6 38.89 9.72 29.17 1,425.00 2,700.00 1,000.00 25.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Data Q WR

30.00 1.80

Joseph Kafumbila

60 95

% %

f2

40

%

Co

Fe

Zn

Ca

Mn

Mg

Al

Page 43

-

In the cell “I26”, type “=I$10*I17” In the cells of column “I” started from I27 to I34, copy the formula of cell “I26”

-

In the cell “J17”, type “=K17+F$38/100*(I17-K17)” In the cells of column “J” started from J18 to J25, copy the formula of cell “J17” In the cells of column “J” started from J26 to J34, copy the formula of cell “I26”

-

In the cell “F26”, type “=I26+J26-K26” In the cells of column “F” started from F27 to F34, copy the formula of cell “F26” In the cell “F17”, type “=F26/F$10” In the cells of column “F” started from F18 to F25, copy the formula of cell “F17”

-

In the cell “G17”, type “=J17+F$38/100*(F17-J17)” In the cells of column “G” started from G18 to G25, copy the formula of cell “G17” In the cells of column “G” started from G26 to G34, copy the formula of cell “I26”

10. “constraints” of solver 1 The control parameter of underflows is the weight percentage of solid in the pulp. The set value of weight percentage of solid in the underflows is the value of weight percentage of solid of the underflow of primary thickener. -

In the cell “D45”, type “=D14-F14” In the Cell “E45”, type “=D14-I14”

The control parameter of underflows is the specific gravity of pulp. The set value of specific gravity of underflows is the value of specific gravity of underflow of last thickener having with the volume percentage of solid of the underflow of primary thickener. -

In the cell “D45”, type “=F11-I11”

11. “Constraints” of solver 2 -

In the Cell “D48”, type “=D26+K26-G26-I26” In the Cell “E48”, type “=D27+K27-G27-I27” In the Cell “F48”, type “=D28+K28-G28-I28” In the Cell “G48”, type “=D29+K29-G29-I29” In the Cell “H48”, type “=D30+K30-G30-I30” In the Cell “I48”, type “=D31+K31-G31-I31” In the Cell “J48”, type “=D32+K32-G32-I32” In the Cell “K48”, type “=D33+K33-G33-I33” In the Cell “L48”, type “=D34+K34-G34-I34”

At this level, it appears table 16 giving the simulation table when the control parameter of underflows is the weight percentage of solid and Table 17 gives the simulation table when the control parameter of underflows is the specific gravity of pulp.

Joseph Kafumbila

Page 44

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

Tu2 56,220.6 26,250.8 29,969.8 38.89 9.72 29.17 1,445.63 2,700.00 1,027.51 46.69 25.00 28.76 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 29.17 29.17 29.17 29.17 29.17 29.17 29.17 29.17 29.17

To2 48,555.2 0.00 48,555.2 47.38 0.00 47.38 1,024.90

To3 47,250.0 0.00 47,250.0 47.25 0.00 47.25 1,000.00

1,024.90 0.00

1.000.00 0.00

0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 45.01 45.01 45.01 45.01 45.01 45.01 45.01 45.01 45.01

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

L

Table 16: Simulation table for CCD circuit with two thickeners Tu0 63,131.4 26,250.0 36,881.4 38,89 9,72 29,17 1,623,38 2,700.00 1,264.50 41,58 25.00 347,69 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85 490.58 1,750.00 846.71 99.46 8.17 14.58 40.25 414.75 83.13

Tf1 189.00 0.47 188.53 0.19 0.00 0.19 1001.56 2,650.00 1,000.00 0.25

g/t m3/t

f1 ME

Results WE %

T1

T2

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV 25.00 -4.153 H2SO4 1.000 344.2

Tu2 CV 25.00 -5.112 Cu 1.000 1,603

Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv kg/m3 Cts H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu1 57,399.8 26,250.5 31,149.3 38.89 9.72 29.17 1,475.97 2,700.00 1,067.96 45.73 25.00 73.13 2.543 2.543 2.543 2.543 2.543 2.543 2.543 2.543 2.543 74.17 74.17 74.17 74.17 74.17 74.17 74.17 74.17 74.17

To1 54,475.8 0.00 54,475.8 47.56 0.00 47.56 1,145.33

60 95

% %

f2

40

%

Co 1.0000 700.3

Fe 1.000 -46.89

Zn 1.000 -138.2

Ca 1.000 -131.8

Mn 1.000 -106.1

1,145.33 0.00

Tf2 126.00 0.32 125.69 0.13 0.00 0.13 1,001.56 2,650.00 1,000.00 0.25

2.463 2.463 2.463 2.463 2.463 2.463 2.463 2.463 2.463 117.17 117.17 117.17 117.17 117.17 117.17 117.17 117.17 117.17

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Data Q WR

30.00 1.80

Joseph Kafumbila

Mg 1.000 268.4

Al 1.000 -63.2

Page 45

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

Tu2 56,220.6 26,250,8 29,969.8 38.89 9.72 29.17 1,445.63 2,700.00 1,027.51 46.69 25.00 28.76 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 29.17 29.17 29.17 29.17 29.17 29.17 29.17 29.17 29.17

To2 48,555.2 0.00 48,555.2 47.38 0.00 47.38 1,024.90

To3 47,250.0 0.00 47,250.0 47.25 0.00 47.25 1,000.00

1,024.90 0.00

1.000.00 0.00

0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 0.950 45.01 45.01 45.01 45.01 45.01 45.01 45.01 45.01 45.01

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

L

Table 17: Simulation table for CCD circuit with two thickeners Tu0 63,131.4 26,250.0 36,881.4 38,89 9,72 29,17 1,623,38 2,700.00 1,264.50 41,58 25.00 347,69 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85 490.58 1,750.00 846.71 99.46 8.17 14.58 40.25 414.75 83.13

Tf1 189.00 0.47 188.53 0.19 0.00 0.19 1001.56 2,650.00 1,000.00 0.25

g/t m3/t

f1 ME

Results WE %

T1

T2

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV 25.00 30.338 H2SO4 1.000 344.3

Tu2 CV 25.00

Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv s kg/m3 Ct H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu1 57,399.8 26,250.5 31,149.3 38.89 9.72 29.17 1,475.97 2,700.00 1,067.96 45.73 25.00 73.13 2.543 2.543 2.543 2.543 2.543 2.543 2.543 2.543 2.543 74.17 74.17 74.17 74.17 74.17 74.17 74.17 74.17 74.17

To1 54,475.8 0.00 54,475.8 47.56 0.00 47.56 1,145.33

60 95

% %

f2

40

%

Co 1.000 700.4

Fe 1.000 -46.88

Zn 1.000 -138.2

Ca 1.000 -131.8

Mn 1.000 -106.1

1,145.33 0.00

Tf2 126.00 0.32 125.69 0.13 0.00 0.13 1,001.56 2,650.00 1,000.00 0.25

2.463 2.463 2.463 2.463 2.463 2.463 2.463 2.463 2.463 117.17 117.17 117.17 117.17 117.17 117.17 117.17 117.17 117.17

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Data Q WR

30.00 1.80

Joseph Kafumbila

Cu 1.000 1603.7

Mg 1.000 258.4

Al 1.000 -63.2

Page 46

12. Solver 1 and 2 operations Excel solver program execution is as follows: 1) On the ‘Data’, in the ‘Analysis group’ click solver (if the solver command is not available, you must activate the solver add-in). 2) In the ‘Set objective’ box, enter the cell reference “D45” of Table 16 or Table 17 (first constraint of solver 1). 3) Click “Value of” and then type the number “0” in the box. 4) In the “By Changing Variable Cells” box, enter the reference for each variable of solver 1 and 2 (blue color in Table 16 or Table 17). Separate the references with commas (English version). 5) In the ‘Subject to the constraints’ box, enter solver constraints by doing the following: a) In the ‘Solver Parameters’ dialog box, click ‘Add’. b) In the ‘Cell Reference’ box, enter the cell reference of constraints of solver 1 and 2 (green color in Table 16 or Table 17)(do not take the first constraint of solver 1). c) Click the ‘relationship’ ‘=‘, in the ‘Constraint’ box, type the number ‘0’. Click ‘Add’ for the second solver constraint. When the last solver constraint is added (cell ‘L48’), click ‘OK’ 6) Click ‘Solve’. To keep the solution values on the worksheet, in the ‘Solver Results’ dialog box, click ‘Keep solver solution’.

13. Calculation of wash efficiency For both simulation having the control parameter of the underflow pulp the weight percentage of solid in the pulp or the specific gravity of the underflow pulps. -

In the cell “D41”, type “=G10*(G18-J18)/(D10*(D18-J18))*100 In the cell “E41”, type “=G10*(G18-K18)/(D10*(D18-K18))*100

At this level, it appears table 18 giving the table of optimized simulation when the control parameter of underflows is the weight percentage of solid and Table 19 gives the table of optimized simulation when the control parameter of underflows is the specific gravity of pulp.

Joseph Kafumbila

Page 47

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

Tu2 63,132.5 26,250.8 36,881.7 44.18 9.72 34.45 1,429.07 2,700.00 1,070.43 41.58 22.01 75.93 3.67 13.10 6.34 0.75 0.06 0.11 0.30 3.11 0.62 126.57 451.49 218.45 25.66 2.11 3.76 10.38 107.00 21.45

To2 47,376.1 0.00 47,376.1 44.77 0.00 44.77 1,058.29

To3 47,250.0 0.00 47,250.0 47.25 0.00 47.25 1,000.00

1,058.29 0.00

1.000.00 0.00

3.49 12.45 6.02 0.71 0.06 0.10 0.29 2.95 0.59 156.22 557.28 269.63 31.67 2.60 4.64 12.82 132.08 26.47

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

L

Table 18: Simulation table for CCD circuit with two thickeners Tu0 63,131.4 26,250.0 36,881.4 38,89 9,72 29,17 1,623,38 2,700.00 1,264.50 41,58 25.00 347,69 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85 490.58 1,750.00 846.71 99.46 8.17 14.58 40.25 414.75 83.13

Tf1 189.00 0.47 188.53 0.19 0.00 0.19 1001.56 2,650.00 1,000.00 0.25

g/t m3/t

f1 ME

Results WE %

T1 55.68

T2 74.20

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV 23.39 0.000 H2SO4 3.673 0.000

Tu2 CV 22.01 0.000 Cu 13.104 0.000

Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv s kg/m3 Ct H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu1 63,132.6 26,250.5 36,882.1 41.57 9.72 31.85 1,518.76 2,700.00 1,158.14 41.58 23.39 183.56 8.88 31.68 15.33 1.80 0.15 0.26 0.73 7.51 1.51 282.79 1008.77 488.08 57.33 4.71 8.41 23.20 239.08 47.92

To1 47,563.9 0.00 47,563.9 42.28 0.00 42.28 1,125.08

60 95

% %

f2

40

%

Co 6.340 0.000

Fe 0.745 0.000

Zn 0.061 0.000

Ca 0.109 0.000

Mn 0.301 0.000

1,125.08 0.00

Tf2 126.00 0.32 125.69 0.13 0.00 0.13 1,001.56 2,650.00 1,000.00 0.25

8.61 30.72 14.86 1.75 0.14 0.26 0.71 7.28 1.46 364.02 1,298.51 628.26 73.80 6.06 10.82 29.87 307.75 61.68

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Data Q WR

30.00 1.80

Joseph Kafumbila

Mg 3.106 0.000

Al 0.622 0.000

Page 48

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

B

C

D

E

F

G

H

I

J

K

Tu2 57,487.2 26,250.8 31,236.4 38.89 9.72 29.17 1,478.20 2,700.00 1,070.93 45.66 25.00

To2 57,569.6 0.00 57,569.6 54.27 0.00 54.27 1,060.76

To3 47,250.0 0.00 47,250.0 47.25 0.00 47.25 1,000.00

1,060.76 0.00

1.000.00 0.00

3.70 13.20 6.39 0.75 0.06 0.11 0.30 3.13 0.63 107.94 385.03 186.29 21.88 1.80 3.21 8.86 91.25 18.29

3.52 12.54 6.07 0.71 0.06 0.11 0.29 2.97 0.60 190.79 680.60 329.29 38.68 3.18 5.67 15.65 161.30 32.33

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

L

Table 19: Simulation table for CCD circuit with two thickeners Tu0 63,131.4 26,250.0 36,881.4 38,89 9,72 29,17 1,623,38 2,700.00 1,264.50 41,58 25.00 347,69 16.82 60.00 29.03 3.41 0.28 0.50 1.38 14.22 2.85 490.58 1,750.00 846.71 99.46 8.17 14.58 40.25 414.75 83.13

Tf1 189.00 0.47 188.53 0.19 0.00 0.19 1001.56 2,650.00 1,000.00 0.25

g/t m3/t

f1 ME

Results WE %

T1 55.52

T2 78.00

Solver 1 Variables Constraints Solver 2 Variables Constraints

Tu1 CV 21.23 0.000 H2SO4 3.701 0.000

Tu2 CV 25.00

Parameter kg/h Mp kg/h Ms kg/h ML m3/h Vp m3/h Vs m3/h VL kg/m3 SGp kg/m3 SGs kg/m3 SGL % Cw % Cv kg/m3 Cts H2SO4 kg/m3 Cu kg/m3 Co kg/m3 Fe kg/m3 Zn kg/m3 Ca kg/m3 Mn kg/m3 Mg kg/m3 Al kg/m3 H2SO4 kg/h Cu kg/h Co kg/h Fe kg/h Zn kg/h Ca kg/h Mn kg/h Mg kg/h Al kg/h

Tu1 67,680.7 26,250.5 41,430.3 45.79 9.72 36.06 1,478.20 2,700.00 1,148.81 38.79 21.23 171.23 8.28 29.55 14.30 1.68 0.14 0.25 0.68 7.00 1.40 298.73 1,065.62 515.58 60.56 4.97 8.88 24.51 252.55 50.62

To1 53,209.2 0.00 53,209.2 47.56 0.00 47.56 1,118.70

60 95

% %

f2

40

%

Co 6.387 0.000

Fe 0.750 0.000

Zn 0.062 0.000

Ca 0.110 0.000

Mn 0.304 0.000

1,118.70 0.00

Tf2 126.00 0.32 125.69 0.13 0.00 0.13 1,001.56 2,650.00 1,000.00 0.25

8.05 28.70 13.89 1.63 0.13 0.24 0.66 6.80 1.36 382.65 1,364.97 660.42 77.58 6.37 11.37 31.39 323.50 64.84

αk 1.000 2.511 2.629 2.719 2.468 3.395 2.747 4.949 6.337

Data Q WR

30.00 1.80

Joseph Kafumbila

Cu 13.201 0.000

Mg 3.129 0.000

Al 0.627 0.000

Page 49

7. 1) 2) 3) 4) 5) 6)

Reference ANONYME, Lavage des pulpes (théorie algébrique), Industrie Minérale – Les techniques, octobre 1981, p. 565590. HOLLER h.d., Peffer E.L., Relation between composition and density of aqueous solutions of copper sulphate and sulphuric acid, Bulletin of the bureau of standards, Vol. 13. David R. Lide, CRC Handbook of chemistry and physics, Internet version 2005. Joel B. Christian, Improve clarifier and thickener Design and operation, Chemical Engineering Progress, July 1994. M.C. MULLIGAN, Soluble metal recovery improvement using high density thickeners in a CCD circuit: Ruashi II case study, the journal of southern African institute of mining and metallurgy, Vol. 109, Johannesburg, November 2009. Kourosh Behrouzi, Majid Vafaei Fard, Anabito Raeiszadeh, Aida Faeghi nia, Water recycling at processing plants in water scarce regions – a case study of thickener design for the Mansour Abad Processing plant, Proceeding tailings and mine waste, Vancouver, 2011.

Pre-feasibility studies of copper hydro-metallurgical plants Pre-feasibility study is conducted first to sort out applicable scenarios. It is desirable to do some pre-feasibility studies of your own or with help of consultant before evaluation feasibility study done by engineering offices. If you find out early that the proposed plant design project idea is not feasible, it will save your money. The paper is the metallurgical engineering paper that gives the opportunity to do pre-feasibility study of copper hydrometallurgical plants of your own. The paper gives the update of the design criteria and metallurgical constraints of copper solvent extraction and the models of preliminary flow diagram mass balance of heap leaching, conventional, split circuits. The models of preliminary flow diagram mass balance are executable on Microsoft Excel spreadsheet. https://fr.scribd.com/document/358056400/Pre-feasibility-Studies-of-CopperHydrometallurgical-Plants

Joseph Kafumbila

Page 50