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Mineral Processing Flow Sheet Design Through A Group Contribution Method
19th European Symposium on Computer Aided Process Engineering – ESCAPE19 J. Jeżowski and J. Thullie (Editors) © 2009 Elsevier B.V. All rights reserved.
Mineral Processing Flow Sheet Design Through A Group Contribution Method Gonzalo I. Herreraa, Edelmira D. Gálvezb,c, Luis A. Cisternasa,c a
Dept. Chem. Eng., Universidad de Antofagasta, Antofagasta, Chile. Centro de Investigación Científico Tecnológico para la Minería, Antofagasta, Chile c Dept. Metallurgical Eng., Universidad Católica del Norte, Antofagasta, Chile b
Abstract d’Anterroches and Gani [1] have introduced the concept of process-group contributions for process flowsheet property estimation and process flowsheet synthesis and design. This concept has been highlighted through a flowsheet property model for distillation operations. In this work a group contribution model have been development for flowsheet properties for flotation circuit. The model was adjusted based on simulated values for a set of flotation circuits. This model will be the base for the development of a systematic strategy for computer aided mineral flow-sheet design, where modelling, synthesis and design are integrated tasks. Keywords: process group contribution, process synthesis, flotation circuit. 1. Introduction Flotation is a practical method to separate valuable minerals based on differences in surface properties of the particles from milled mineral mixtures. Also new applications as the separation of individual plastics of equal density in waste streams containing a mixture of plastics have appeared. In froth flotation, various types of equipment exist which promote particles-bubbles encounter which contribute to controlling the balance between high recovery of the desired metal, and a high grade value of the metal in the product outflow. Past
213
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G.I. Herrera et al.
experience has shown single step separation is inefficient, and the inclusion of several complementary and supportive steps are required. Taking into account the large volume of material to be treated and its associated costs, choices related to the configuration of the separation system are critical. Modelling and simulation of a mineral process flowsheet usually involve identifying the structure of the flowsheet, deriving model equations to represent each operation, and solving the resulting total model equations according to one of various available simulation strategies. The flowsheet synthesis problem determines the type of operations and their sequence needed to achieve the extraction of valuable components from the raw materials. The flowsheet design problem determines the optimal values for the conditions of operation and related variables for the synthesized flowsheet. It can be noted that the flowsheet modelling, synthesis and design problems are related since for generation and screening of flowsheet alternatives (synthesis/design), some form of flowsheet models are needed. Also, flowsheet models are needed for verification of the synthesis/design problem solution. In mineral process synthesis three types of approaches exist: a) the methods that employ heuristics or are knowledge based [2]; b) the methods that employ mathematical or optimization techniques [3-4], and c) the methods that employ physical insights [5]. A review of methods for conceptual flotation circuit design has been recently published [6]. d’Anterroches and Gani [1] have introduced the concept of process-group contributions for process flowsheet property estimation and process flowsheet synthesis and design, and they presented a property model for distillation operations. The objective of this work is to develop a group contribution model for flowsheet properties applied to flotation circuit. 2. Group Contribution Model Development The generation of the group contribution method was carried out in two steps: 1) data generation of flotation circuit properties and 2) model development and model adjustment. 2.1. Data generation The supposition that the flotation process corresponds to a first order reaction is broadly used. If a group of solid particles transported in a pulp collide with bubbles within certain defined volume, the valuable (hydrophobic) mineral will adhere to upward bubbles, becoming separated from the gangue. This phenomenon can be considered as a simple mechanism where flotation is a pseudoreaction between the solid particles (A) and the bubbles (B) where A+BĺAB. If the concentration of bubbles is constant, then the flotation kinetic can be represented as a first order pseudoreaction. Then, the mineral flotation can be modeled considering that a mineral is formed of different classes or pseudospecies that have the same floatability. It means floatability represents
Mineral Processing Flow Sheet Design through a Group Contribution Method
215
the propensity of the particles to be floated according to its composition and size given certain flotation environment conditions (pH, Eh, reagent type, concentration), in such a way the most valuable particle, i.e., the most completely liberated valuable particle, has the greater floatability value in an intermediate particle size. Then, in figure 1, the following equations can be written:
Ci
Ti Fi
(1)
Wi
(1 Ti ) Fi
(2)
Where Ti is the ratio of flow of concentrate and feed of class specie i. The ratio may be obtained from plant data, values from pilot plants, or theoretical or empirical models. For example, for a bank of N cells,
Ti
1
1 (1 kiW ) N
(3)
Where ki is the first order kinetic constant of class specie i, and W the retention time in one cell. In order to adjust a group contribution model, recovery values for different flotation circuits were generated by the simulation of several flotation circuit. Figure 2 shows a superstructure that represents a total of twenty four flotation circuits: two circuits with two flotation stages, four circuits with three flotation stages and eighteen circuits with four flotation stages. Each flotation stage was simulated using the equation 2, for multiple hypothetical classes of minerals. Each hypothetical mineral was generated with random values for the kinetic constant, cell retention time, and N=1, 3, 5 and 7 in equation 3.
2.2. Model adjustment To generate the group contribution model two types of contribution were considered. First, it was considered each flotation stage can be characterized by the ratio of flow of concentrate and feed, Ti . Then the interconnections among flotation stages were considered, represented by the product of the ratios of concentrate/feed or tail/feed and concentrate/feed or tail/feed as it is the case: Ti Ti , Ti (1 Ti ) , or (1 Ti ) (1 Ti ) . Then the model for recuperation of one pseudospecie has the following form: R D ¦ E i N i Ti ¦¦ J i , j N i , j / i , j i
i
(3)
j
Where D , Ei and J i , j are adjusted parameters, and Ti and / i , j are process-group contributions. The adjusted parameters were fitted to simulated recovery values for mineral class with low recovery (0 to 10%), medium recovery (10 to 60%)
G.I. Herrera et al.
216
and high recovery (60 to 100%). The D values were -3.5542, -5.9192, and 2.5507 for low, medium and high recoveries. The values for Ei are given in table 1 and some J i , j values in table 2. Good results have been obtained in the prediction of recovery (see figure 3).
Figure 1. Flotation Stage
Figure 2. Superstructure of flotation circuit
Table 1. Values for Ei groups. Flotation stage groups
Recovery
TR
TC
TCC
TS
Low
1.8913
1.9870
-3.2947
0.0348
Medium
2.0104
2.3000
-5.1205
-1.0106
High
1.3011
1.2367
-1.0042
-1.3571
3. Example
To explain the use of the equation 3, let us consider the flotation circuit shown in figure 4, where a mineral conformed by two pseudospecies, one with high recovery and another with low recovery, is fed. The equation 3 for this case corresponds to:
R D ETR TR ETC TC J TRTC TRTC 2J TR (1TC )TR (1 TC )
J (1T
R )(1TC
)
(1 TR )(1 TC )
(4)
Mineral Processing Flow Sheet Design through a Group Contribution Method
Table 2. Some values of J i , j Flotation stages groups, / i , j
J i, j
217
values
I
j
low
medium
High
TR 1 TR TC TCC TR 1 TR
TC TS TS TS 1 TC 1 TC
0.4251
2.6465
1.2645
0.7060
1.3288
0.6314
-0.3160
0.8209
2.6079
-0.2917
1.1177
3.4985
1.8040
3.1885
1.1269
3.0154
6.0501
2.5505
1.0 0.9 0.8
Recuperation Group contribution
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Recuperation (Simulation)
Figure 3. Recuperation values: Group contribution versus simulated values
Figure 4. Flotation circuit for the example.
G.I. Herrera et al.
218
For values of T R 0 .9 0 6 and TC 0 .7 1 6 for the high recovery speudospecie, the calculated valor of R, in equation 4, corresponds at 0.867, while the mass balance value of R corresponds at 0.873. On the other hand, for the low recovery speudospecie, with values of T R 0 .0 7 and TC 0 .0 5 , R correspond at 0.009 and 0.007 for equation 4 and mass balance respectively. 4. Conclusion and future work
A group contribution model was presented for the recovery estimates in flotation circuits. For the analyzed circuits the method gives acceptable results for process synthesis purpose. Works to include circuits with more flotation stages, development of an approach for the selection of T values, and an approach for the determination of the maximum number of flotation stages are under way. 5. Acknowledgements
We thank the CONICYT for financing and support of the work reported in this manuscript (FONDECYT 1060342). The authors want to thank to Rafiqul Gani for his valuable contribution to this work. 6. References [1] d’Anterroches L., R. Gani, 2005, Group contribution based process flowsheet synthesis, design and modelling, Fluid Phase Equilibria 228–229 , 141–146 [2] Connolly, A.F., R.G.H. Prince, 2000, Performance improvement in minerals beneficiation circuits by retrofitting ,Separation and Purification Technology 19, 77–83 [3] Guria C, Verma M, Gupta SK, Mehrotra, 2005, Simultaneous Optimization of The Performance of Flotation Circuits And Their Simplification Using The Jumping Gene Adaptations of Genetic Algorithm, International Journal of Mineral Processing, 77 (3): 165-185. [4] Cisternas LA, Mendez DA, Galvez ED, Jorquera R., 2006, A MILP model for design of flotation circuits with bank/column and regrind/no regrind selection, International Journal of Mineral Processing, 79 (4), 253-263. [5] Gálvez E.D., 1998, A shortcut procedure for the design of mineral separation circuits, Minerals Engineering, 11 ( 2), 113-123. [6] Mendez D.A., Gálvez E.D., Cisternas LA, 2008, State of the art in the conceptual design of flotation circuits, Int. J. Miner. Process. In press, doi:10.1016/j.minpro.2008.09.009
Mineral Processing Flow Sheet Design Through A Group Contribution Method Gonzalo I. Herreraa, Edelmira D. Gálvezb,c, Luis A. Cisternasa,c a
Dept. Chem. Eng., Universidad de Antofagasta, Antofagasta, Chile. Centro de Investigación Científico Tecnológico para la Minería, Antofagasta, Chile c Dept. Metallurgical Eng., Universidad Católica del Norte, Antofagasta, Chile b
Abstract d’Anterroches and Gani [1] have introduced the concept of process-group contributions for process flowsheet property estimation and process flowsheet synthesis and design. This concept has been highlighted through a flowsheet property model for distillation operations. In this work a group contribution model have been development for flowsheet properties for flotation circuit. The model was adjusted based on simulated values for a set of flotation circuits. This model will be the base for the development of a systematic strategy for computer aided mineral flow-sheet design, where modelling, synthesis and design are integrated tasks. Keywords: process group contribution, process synthesis, flotation circuit. 1. Introduction Flotation is a practical method to separate valuable minerals based on differences in surface properties of the particles from milled mineral mixtures. Also new applications as the separation of individual plastics of equal density in waste streams containing a mixture of plastics have appeared. In froth flotation, various types of equipment exist which promote particles-bubbles encounter which contribute to controlling the balance between high recovery of the desired metal, and a high grade value of the metal in the product outflow. Past
213
214
G.I. Herrera et al.
experience has shown single step separation is inefficient, and the inclusion of several complementary and supportive steps are required. Taking into account the large volume of material to be treated and its associated costs, choices related to the configuration of the separation system are critical. Modelling and simulation of a mineral process flowsheet usually involve identifying the structure of the flowsheet, deriving model equations to represent each operation, and solving the resulting total model equations according to one of various available simulation strategies. The flowsheet synthesis problem determines the type of operations and their sequence needed to achieve the extraction of valuable components from the raw materials. The flowsheet design problem determines the optimal values for the conditions of operation and related variables for the synthesized flowsheet. It can be noted that the flowsheet modelling, synthesis and design problems are related since for generation and screening of flowsheet alternatives (synthesis/design), some form of flowsheet models are needed. Also, flowsheet models are needed for verification of the synthesis/design problem solution. In mineral process synthesis three types of approaches exist: a) the methods that employ heuristics or are knowledge based [2]; b) the methods that employ mathematical or optimization techniques [3-4], and c) the methods that employ physical insights [5]. A review of methods for conceptual flotation circuit design has been recently published [6]. d’Anterroches and Gani [1] have introduced the concept of process-group contributions for process flowsheet property estimation and process flowsheet synthesis and design, and they presented a property model for distillation operations. The objective of this work is to develop a group contribution model for flowsheet properties applied to flotation circuit. 2. Group Contribution Model Development The generation of the group contribution method was carried out in two steps: 1) data generation of flotation circuit properties and 2) model development and model adjustment. 2.1. Data generation The supposition that the flotation process corresponds to a first order reaction is broadly used. If a group of solid particles transported in a pulp collide with bubbles within certain defined volume, the valuable (hydrophobic) mineral will adhere to upward bubbles, becoming separated from the gangue. This phenomenon can be considered as a simple mechanism where flotation is a pseudoreaction between the solid particles (A) and the bubbles (B) where A+BĺAB. If the concentration of bubbles is constant, then the flotation kinetic can be represented as a first order pseudoreaction. Then, the mineral flotation can be modeled considering that a mineral is formed of different classes or pseudospecies that have the same floatability. It means floatability represents
Mineral Processing Flow Sheet Design through a Group Contribution Method
215
the propensity of the particles to be floated according to its composition and size given certain flotation environment conditions (pH, Eh, reagent type, concentration), in such a way the most valuable particle, i.e., the most completely liberated valuable particle, has the greater floatability value in an intermediate particle size. Then, in figure 1, the following equations can be written:
Ci
Ti Fi
(1)
Wi
(1 Ti ) Fi
(2)
Where Ti is the ratio of flow of concentrate and feed of class specie i. The ratio may be obtained from plant data, values from pilot plants, or theoretical or empirical models. For example, for a bank of N cells,
Ti
1
1 (1 kiW ) N
(3)
Where ki is the first order kinetic constant of class specie i, and W the retention time in one cell. In order to adjust a group contribution model, recovery values for different flotation circuits were generated by the simulation of several flotation circuit. Figure 2 shows a superstructure that represents a total of twenty four flotation circuits: two circuits with two flotation stages, four circuits with three flotation stages and eighteen circuits with four flotation stages. Each flotation stage was simulated using the equation 2, for multiple hypothetical classes of minerals. Each hypothetical mineral was generated with random values for the kinetic constant, cell retention time, and N=1, 3, 5 and 7 in equation 3.
2.2. Model adjustment To generate the group contribution model two types of contribution were considered. First, it was considered each flotation stage can be characterized by the ratio of flow of concentrate and feed, Ti . Then the interconnections among flotation stages were considered, represented by the product of the ratios of concentrate/feed or tail/feed and concentrate/feed or tail/feed as it is the case: Ti Ti , Ti (1 Ti ) , or (1 Ti ) (1 Ti ) . Then the model for recuperation of one pseudospecie has the following form: R D ¦ E i N i Ti ¦¦ J i , j N i , j / i , j i
i
(3)
j
Where D , Ei and J i , j are adjusted parameters, and Ti and / i , j are process-group contributions. The adjusted parameters were fitted to simulated recovery values for mineral class with low recovery (0 to 10%), medium recovery (10 to 60%)
G.I. Herrera et al.
216
and high recovery (60 to 100%). The D values were -3.5542, -5.9192, and 2.5507 for low, medium and high recoveries. The values for Ei are given in table 1 and some J i , j values in table 2. Good results have been obtained in the prediction of recovery (see figure 3).
Figure 1. Flotation Stage
Figure 2. Superstructure of flotation circuit
Table 1. Values for Ei groups. Flotation stage groups
Recovery
TR
TC
TCC
TS
Low
1.8913
1.9870
-3.2947
0.0348
Medium
2.0104
2.3000
-5.1205
-1.0106
High
1.3011
1.2367
-1.0042
-1.3571
3. Example
To explain the use of the equation 3, let us consider the flotation circuit shown in figure 4, where a mineral conformed by two pseudospecies, one with high recovery and another with low recovery, is fed. The equation 3 for this case corresponds to:
R D ETR TR ETC TC J TRTC TRTC 2J TR (1TC )TR (1 TC )
J (1T
R )(1TC
)
(1 TR )(1 TC )
(4)
Mineral Processing Flow Sheet Design through a Group Contribution Method
Table 2. Some values of J i , j Flotation stages groups, / i , j
J i, j
217
values
I
j
low
medium
High
TR 1 TR TC TCC TR 1 TR
TC TS TS TS 1 TC 1 TC
0.4251
2.6465
1.2645
0.7060
1.3288
0.6314
-0.3160
0.8209
2.6079
-0.2917
1.1177
3.4985
1.8040
3.1885
1.1269
3.0154
6.0501
2.5505
1.0 0.9 0.8
Recuperation Group contribution
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Recuperation (Simulation)
Figure 3. Recuperation values: Group contribution versus simulated values
Figure 4. Flotation circuit for the example.
G.I. Herrera et al.
218
For values of T R 0 .9 0 6 and TC 0 .7 1 6 for the high recovery speudospecie, the calculated valor of R, in equation 4, corresponds at 0.867, while the mass balance value of R corresponds at 0.873. On the other hand, for the low recovery speudospecie, with values of T R 0 .0 7 and TC 0 .0 5 , R correspond at 0.009 and 0.007 for equation 4 and mass balance respectively. 4. Conclusion and future work
A group contribution model was presented for the recovery estimates in flotation circuits. For the analyzed circuits the method gives acceptable results for process synthesis purpose. Works to include circuits with more flotation stages, development of an approach for the selection of T values, and an approach for the determination of the maximum number of flotation stages are under way. 5. Acknowledgements
We thank the CONICYT for financing and support of the work reported in this manuscript (FONDECYT 1060342). The authors want to thank to Rafiqul Gani for his valuable contribution to this work. 6. References [1] d’Anterroches L., R. Gani, 2005, Group contribution based process flowsheet synthesis, design and modelling, Fluid Phase Equilibria 228–229 , 141–146 [2] Connolly, A.F., R.G.H. Prince, 2000, Performance improvement in minerals beneficiation circuits by retrofitting ,Separation and Purification Technology 19, 77–83 [3] Guria C, Verma M, Gupta SK, Mehrotra, 2005, Simultaneous Optimization of The Performance of Flotation Circuits And Their Simplification Using The Jumping Gene Adaptations of Genetic Algorithm, International Journal of Mineral Processing, 77 (3): 165-185. [4] Cisternas LA, Mendez DA, Galvez ED, Jorquera R., 2006, A MILP model for design of flotation circuits with bank/column and regrind/no regrind selection, International Journal of Mineral Processing, 79 (4), 253-263. [5] Gálvez E.D., 1998, A shortcut procedure for the design of mineral separation circuits, Minerals Engineering, 11 ( 2), 113-123. [6] Mendez D.A., Gálvez E.D., Cisternas LA, 2008, State of the art in the conceptual design of flotation circuits, Int. J. Miner. Process. In press, doi:10.1016/j.minpro.2008.09.009