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Multiplicity of the chemical, biological, electrochemical and operational variables and nonlinear behavior of metal extraction in bioleaching environments complicate the mathematical modeling of these systems. This research was done to predict copper and iron recovery from a copper flotation concentrate in a stirred tank bioreactor using a fuzzy logic model. Experiments were carried out in the presence of a mixed culture of mesophilic bacteria at 35° C, and a mixed culture of moderately thermophilic bacteria at 50° C. Input variables were method of operation (bioleaching or electrobioleaching), the type of bacteria and time (day), while the recoveries of copper and iron were the outputs. A relationship was developed between stated inputs and the outputs by means of “if-then” rules. The resulting fuzzy model showed a satisfactory prediction of the copper and iron extraction and had a good correlation of experimental data with R-squared more than 0.97. The results of this study suggested that fuzzy logic provided a powerful and reliable tool for predicting the nonlinear and time variant bioleaching processes.

Conventional or electrochemical bioleaching of copper from concentrates in stirred tank reactors is one of the most complex and difficult processes in hydrometallurgy. It not only is nonlinear and time variant, but also is hardly defined. The bioleaching process has been constituted of two interacting subsystems: an abiotic system, which is a mineral suspension in a solution of chemical and electrochemical compounds and gases as well as a biological system, composed of a singular or mixed culture of microorganisms. For mathematical modeling of this process, mass transfer between three different phases that is too complicated, must be taken into account [

The use of fuzzy logic, which reflects the qualitative and inaccurate nature of human reasoning, can enable expert systems to be more flexible [

Considering, the multiplicity of various chemical, biological, electrochemical and operational parameters, nonlinear behavior of metal extraction in bioleaching processes, and the high ability of knowledge based systems in such complex media, in this research, a multi input-multi output fuzzy logic model was defined to predict copper and iron recovery from a flotation copper concentrate in a stirred electro-bioreactor. The proposed model predicts the nonlinear behavior of conventional and electrochemical bioleaching processes successfully.

Data used in this fuzzy logic modeling was obtained from an experimental work performed previously by the author and his coworkers [_{2}) as the major mineral and pyrite (FeS_{2}) as the minor one. Experiments were carried out in a three compartment electro-bioreactor at 10% (w/v) solid content. A mixed culture of mesophilic bacteria and a mixed culture of moderately thermophilic bacteria were used at 35˚C and 50˚C, respectively. Experiments were conducted in nutrient medium, 9 K; stirring rate, 450 rpm; applied potential, 420 mV (in electrobioleaching tests); initial pH, 1.8; and aeration rate, 1.3 L∙min^{−1}. The potential of the working electrode was controlled with respect to the reference electrode using a Solartron Sl 1287 potentiostat. The details of apparatus and techniques used have been previously described [

A fuzzy logic system is a nonlinear mapping of an input data (feature) vector into a scalar output [

Fuzzification is the process of finding the membership degrees. A membership function (MF) is a curve that

defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1 (Fuzzy Logic Toolbox). The value 0 represents a complete non-membership, the value 1 represents a complete membership function and values in between are used to represent partial membership. The input and output variables have been fuzzified according to the linguistic sets shown in

Ordinary (crisp) sets are a special case of fuzzy sets, in which the membership function only takes two values: 0 (non-membership) and 1 (membership) [

Fuzzy rules could be derived from both expert’s reasoning and linguistic expressions and from the relationships between the system variables. To model the process, a fuzzy rule-based system was constructed with the 34 fuzzy if-then rules (

Symbol | N | EL | VVL | VL | mlL | L | LM | mlM |
---|---|---|---|---|---|---|---|---|

Meaning | Negligible | Extremely low | Very very low | Very low | More or less low | Low | Low medium | More or less medium |

Symbol | M | MH | mlH | H | VH | VVH | EH | |

Meaning | Medium | Medium high | Moe or less high | High | Very high | Very very high | Extremely high |

IF | THEN | ||||
---|---|---|---|---|---|

And | And | And | |||

Run | Method | TOB | Time | Cu recovery | Fe recovery |

1 | BL | MES | EL | EL | mlL |

2 | BL | MES | VL | VVL | VVL |

3 | BL | MES | L | VL | L |

4 | BL | MES | LM | mlL | L |

5 | BL | MES | M | L | LM |

6 | BL | MES | MH | ML | M |

7 | BL | MES | H | ML | M |

8 | BL | MES | VH | mlM | M |

9 | BL | MES | EH | M | M |

10 | BL | MT | EL | VVL | L |

11 | BL | MT | VL | VVL | L |

12 | BL | MT | L | VL | LM |

13 | BL | MT | LM | ML | MH |

14 | BL | MT | M | ML | MH |

15 | BL | MT | MH | mlH | MH |

16 | BL | MT | H | mlH | H |

17 | BL | MT | VH | VH | H |

18 | BL | MT | EH | VH | H |

19 | ELB | MES | EL | VL | M |

20 | ELB | MES | VL | mlL | MH |

21 | ELB | MES | L | L | MH |

22 | ELB | MES | LM | M | MH |

23 | ELB | MES | M | MH | H |

24 | ELB | MES | H | mlH | H |

25 | ELB | MES | EH | VH | H |

26 | ELB | MT | EL | mlH | M |

27 | ELB | MT | VL | L | MH |

28 | ELB | MT | L | MH | MH |

29 | ELB | MT | LM | mlH | H |

30 | ELB | MT | M | mlH | MH |

31 | ELB | MT | MH | VVH | VH |

32 | ELB | MT | H | VVH | VH |

33 | ELB | MT | VH | VVH | VH |

34 | ELB | MT | EH | EH | EH |

Interpreting fuzzy AND as the minimum, one can rewrite rules as the form that is more concise:

where

Each rule corresponds to a fuzzy relation given by Equation (6):

The fuzzy inference engine is the core of a fuzzy system. It is used to simulate the thinking and decision-making modes of human beings to solve problems [

Having translated each rule

The process of reducing final obtained fuzzy set is termed defuzzification that converts the output fuzzy set that is inferred from the fuzzy inference engine to an ordinary value in

where

Modeling of complex and nonlinear copper bioleaching behavior (conventional and electrochemical) was done by a fuzzy logic model. A knowledge base containing if-then rules was developed in a natural language to store a human expert’s experience.

Variation of copper and iron recovery during electrobioleaching and bioleaching processes using both mixed mesophilic bacteria and mixed moderately thermophilic bacteria have been shown in

From

A fuzzy logic model was obtained to predict the recoveries of copper and iron from a chalcopyrite copper

concentrate by conventional and electrochemical bioleaching processes. The recoveries of these metals are targeted functions for hydrometallurgical extraction of copper from copper flotation concentrates. The input variables were the method of process (bioleaching or electrobioleaching), the type of bacteria (mesophilic and moderately thermophilic bacteria) and time (day). A fuzzy relationship was developed between stated inputs and the outputs by means of “if-then” rules. The comparison of the experimental data and predicted values of the model showed a good match between them, in which the R-squared of the model was more than 0.97 in each series of data. The results showed the capability of the fuzzy model to flexibly predict complex and nonlinear bioleaching processes and it is a powerful tool for metal extraction in such a complicated system.

The authors would like to thank the National Iranian Copper Industry Company (NICICO) that allowed them to use experimental data for conducting this research.