Simulation of flotation circuits in Zarand coal washing plant

Transcription

1 Applied mathematics in Engineering, Management and Technology () 5: Simulation of flotation circuits in Zarand coal washing plant Mehdi Nahvi Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Sirjan, Iran, Abbas Sam Department of Mining Engineering, Shahid Bahonar University of Kerman, Iran, Seyed Morteza Moosavirad Department of Mining Engineering, Zarand Collage, Shahid Bahonar University of Kerman, Iran, Abstract Flotation sector in mineral processing plants is one of the important parts that include the highest energy consumption and production costs. One of the computational aspects related to the sector is the mass balance of the flotation cells. Hence, in this paper, software has been developed to perform the mass balance and optimization processes with less time and error. The major advantage of this software is the ease of use that the user does not need to have programming sills and it also provides an optimum solution for different flotation cells. In this article, first, we discussed how to perform the mass balance for flotation cells and the corresponding formulas, then an example of flotation cells of a coal washing plant, in Zarand, is resolved manually and at the end by simulating and optimizing the example manually solved in the software, both results were compared. This indicates the validity of the operation performed by the software. The amounts of the initial waste discharge that is one of the input parameters were 89, 6 and 5.5, for each cell, respectively, the adjusted amounts of waste discharge for each cell were 7.5, and.45 respectively, after simulation and optimization in software. Keywords: Optimization, Simulation, Flotation, Mass balance, Processing, Coal washing.introduction The flotation sector in mineral processing plants has the highest level of energy consumption and production costs, following crushing sector. It is one of the complex parts of the processing plants, and is coupled with time-consuming computations with enormous errors. Over time, excessive extractions have led to reduce the mineral carat in mines. This has led to many problems in the mineral processing sector. Much research has been done on optimizing the flotation performance, including optimization of flotation circuit performance using genetic algorithms [], manual circuit modeling and circuit optimization using mathematical equations [], and modeling flotation circuit design of minerals []. One of the important factors in the flotation sector is the mass balancing of flotation cells. In each flotation cell, given the nown parameters such as mineral species, the load or feed, carat in concentrate and feed, hydraulic follower inetic constant of particles, cell retention time and so on, many unnown parameters such as solid and carat percentage of concentrates, waste discharge of concentrate, the final carat, final recovery and more can be obtained, and this is called mass balance of flotation cells.. Software Specifications Since the calculations of the flotation sector are time consuming and fraught with errors,software has been developed to do all mass balancing calculations of flotation cells, the specialized software is designed for any number of cells and in any specified path, it calculates metallurgical and mass parameters of all flotation cells individually and puts them for comparison as well, and at the end the cumulative carat and recovery are calculated. The high accuracy and the ease of use justify the need for using the software; the importance of the features is evident in large numbers of flotation cells. In the software environment one can: 459

2 Applied mathematics in Engineering, Management and Technology () 5: Draw flotation operation schema easily, by selecting the number of flotation cells, feed and output of processing plants Use flows automatic drawing feature by clicing on each flotation cell and the cells are easily connected Be aware of potential errors in the flowchart during any time of operation schema drawing with the help of diagnostic system Using the software simple system of data entry one can: Access to all features of the cells and edit them by double-clicing on each cell in a complex window. Observe a summary of the characteristics of the flow and enter the rate of output mass flow by clic once on each flow Enter any type of data easily (carat, solid rate, pulp rate, solid percentage and class carat) Tae advantage of the strong diagnostic system of the software, that warn the user of entering wrong data According to the drawn schema and entered data, software: Creates mass conservation equations automatically and calculates the flow rates Calculates the solid percentage Calculates the carat of each cell and the final carat Calculates the waste output and concentrate of each mineral group Calculates the water recovery to concentrate separately for each cell Corrects waste mass flow rate and calculates the final mass flow rate for each cell. Calculates the recovery of each cell and the final recovery.. Material and Methods. Mass balancing of flotation cells For mass balancing of each flotation cell, the specified following parameters must be provided: Informationabout following Cell-based modelselection The number of mineralgroups Each cell specifications (solid content of feed and concentrates, cell waste discharge, mixing patterns, water recovery to the concentrate per cell) The feed rate of each mineral group Physical characteristics of each mineralgroup Initial retention time Given the above information, flotation cell mass balance is obtained using the following parameters : Final optimized waste discharge parameters of each cell Solid waste discharge for each cell Concentrate discharge ofeach cell Water recovery to concentrate for each cell Water content of concentrate, waste and feed Carat and recovery of each cell Final carat and recovery Improved retention time Given the parameters of the first part and by using the mass balance equations the output parameters mentioned above can be calculated. The equations used in the mass balance are as follows []: Hydraulic recovery can be obtained from equation (). 46

3 Applied mathematics in Engineering, Management and Technology () 5: R i = z i R w +R w (z i ) () Where, R i : Hydraulic recovery R w : Water recovery to concentrate z i : mineral classification coefficient of interest of size i As the recovery is a function of time and inetic constant, particle recovery of any type, and the rate of concentrate can be calculated based on one of three equations () and () and (4). R = τ +τ PM () R = e τ pf (τ +) n ( τ ) سلول PM n + PF () R = e τ pf (τ s +) (τ s +) Wellermodel (4) Where, R: Recovery (%) : Kinetic constant ( / min) (τ pf,τ s,τ): retention time (min) of the pup in the cell Water discharge to waste (T w ) and different particles discharge to waste (T i ) is determined by equation (5). Q t= Q f Q c = Q f n C i i= (5) D i C w Where, C i : Concentrate rate for species i (t / h) C w : Water content of concentrate (t / h) D i : Density of species i (g / m ) If there is a significant difference between Q t calculated and Q t obtained at previous round based on a given error, the computation will be stopped, otherwise, process will be started all over again. For example, if the parameters, τ pf,τ and τ s, are measured in the waste discharge Q t, the values of these parameters for Q t are as equation (6) [4]. τ pf, τ s, τ = (τ pf, τ s, τ ) Q t Q (6) t. Results and discussion.. Simulation of flotation circuit combinations The simulation of flotation circuit combinations aims at determining metallurgical parameters of the circuit. The main part of the optimization process implementation offlotation circuit combinations, is metallurgical circuit efficiency modeling. Several models have been proposed to do metallurgical calculations in the steadystate, that the inetic model (usually first-order inetic) is the most common. In Figure, all possible combinations for cells are shown regardless of the physics of flotation process. In this figure, F is circuit feed input, f i is circuit feed portion of celli,c ij andt ij are concentrate mass component and 46

4 Applied mathematics in Engineering, Management and Technology () 5: waste output of cell j to celli, respectively. It is worth noting that in these flows, subscript zero means outside the circuit. For example, C j is concentrate portion output of cell j which leaves the circuit as product [5]. Figure : All possible combinations for three-cell circuit If the feed input to the flotation circuit based on the flotation rate coefficient () divided into X species and the circuit contains N rows of cells, then the mass balance of the th species, (=,,,X) in the i th row of cells (i=,,,n) will be as equation (7). F i = F N i + C N j C ij + T j C ij = C i + T i j =I j =I (7) Where, F i : total feed input from the th species to the i th row of cells F i : the amount of th species in the fresh feed input to the i th row of cells C i : total concentrate output from the j th row of cells of the th species T i : total waste output from the j th row of cells of the th species Note that C ij and t ij values are between zero and one. Enriching agent g i for the th species of the i th row of cells is defined as equation (8). g i = C i T i (8) By replacing equation (8) in equation (7) we have: F i = t ij + g i g i C ii T N i j =I( t ij + g j C ij )T j j i (9) Generally: G ij = t jj + g i g i C jj : i = j t ij + g j C ij i j () In order to solve mass balance equations for circuits with a large number of cell rows more easily, equation (9) can be written in matrix form and calculations can be done using matrices equations. Thus, for three rows of cells, equation (9) can be written as equation (). 46

5 F F F = Applied mathematics in Engineering, Management and Technology () 5: t + g g C t + g C t + g C t + g C t + g g C t + g C t + g C t + g C t + g g C T T T ().. Problem Solving Zarand coal washing plant flotation circuit mass balance consisting of three rows of cells (Figure ) for five species of non-ash and fast floating ash, non-ash and slow floating ash and non-floating substances, based on the given information, was calculated as follows: (amount of feed input to the circuit is (t / h)) Figure : A circuit combination consisting of three rows of flotation cells Table : Feed specifications Kineticconstant (min ) Density(g/m ) Per coal Per feed(%) Species

6 Applied mathematics in Engineering, Management and Technology () 5: Table : Specifications of three rows of flotation cell waste Mixing model Per solid discharge (m h) z τ (min) τ pf (min) cons feed cell Cell Cell Cell According to Figure, circuit structural variables are obtained as table () Table : circuit structural variables F F F C C C C C C C C C C C C T T T T T T T T T T T T According to Figure, the calculations of circuit modeling in equilibrium state are done for each species separately. Where, t, f, c, are the carats of the valuable substance in concentrate, feed and waste, respectively. Amount of fresh feed entering each row of cells was calculated for three species according to the fraction of feed that transfers to the rows one, two and three and the feed portion of each species: F t =.5 = 4.6 F t =.4 = 4.5 F t =. =. F t 4 =.6 =.9 F t 5 =. =.46 F i = 4.6 F i = 4.5 F i =. F i 4 =.9 F i 5 =.46 Then, considering the retention time equivalent to the calculated retention time, g i was calculated from equation (8) for all species. (First, second and third rows of the matrices correspond to the first, second and third rows of cells, respectively). g i = g i =.8.. g i = g i 4 = g i 5 = According to equation (), the correlation matrix G was calculated for each species. 464

7 Applied mathematics in Engineering, Management and Technology () 5: G = G =.8... G = G 4 = G 5 = According to equation (), by multiplying the inverted correlation matrix by the matrix of fresh feed input to each row, the waste output of each cell was calculated for all five species.. T i =. T i = T i =.46 T 4 i =.8.46 T 5 i =.46 After determining the amount of waste output from each row of cells, the amount of concentrate output from each row of cells was calculated, using equation (7): 4. C i =..7 C i =.9. C i =. C 4 i =.4.7 C 5 i = The recovery amount of water to concentrate and waste discharge and other metallurgical parameters are calculated using the results of the first stage of modeling (Table 4). Table 4: the results of the first iteration of the test step cell F(t/h) C(t/h) T(t/h) W f (t/h) W c (t/h) W t (t/h) R w (%) Q t ( m h ). Simulation and optimization through software 465

8 Applied mathematics in Engineering, Management and Technology () 5: Considering the circuit path in Figure, the circuit was simulated in software and the optimization process was performed by owing the input parameters required by the software. Software would continue until the difference between the waste discharge of the last step and that of previous step is equal to considered error (.). In Figure () and (4) the input and output screen of the optimization in the software can be seen [6]. Figure : software input screen Figure 4: software output screen 466

9 Applied mathematics in Engineering, Management and Technology () 5: As the optimization process performed by the software, the results of the iterations steps can be seen in tables (5) and (6). Table 5: Results of steps to, by the software step cell F(t/h) C(t/h) T(t/h) W f (t/h) W c (t/h) W t (t/h) Q t ( m h ) 5 Table 6: Results of steps 4 and 5, by the software 4 step cell.5.5 F(t/h) C(t/h) T(t/h) W f (t/h) W c (t/h) W t (t/h) Q t ( m h ) After optimization process, the results of the last (fifth column of Table 6) and the first (Table 4) stages were compared. 467

10 Applied mathematics in Engineering, Management and Technology () 5: Conclusion Comparing the results of the first and the last stages revealed that the optimization process has been continued by the software to achieve optimal and efficient results. The results indicate the accuracy of the software. Accordingly, maing use of the software in every flotation cell of coal and other minerals helps achieve a better and optimal performance. When using this software, the error rate is lowered and also, because the software calculates the mass balance of all cells in the circuit simultaneously, and provides the user with the solution, deciding to control the operation will be easier, faster and with fewer errors. References [] Ghobadi p. Yahyaei m. Banisi s." Optimization of the performance of flotation circuits using a genetic algorithm oriented by process-based rules", International Journal of Mineral Processing. Vol. 98, pp. 74-8,. [] David A. Méndez Edelmira D. Galvez Luis A. Cisternas." Modeling of grinding and classification circuits as applied to the design of flotation processes", Computers and Chemical Engineering. Vol., pp. 97-, 9. [] Luis A. CisternasEdelmira D. Ga lvez Maria F. Zavala, Julio Magna."A MILP model for the design of mineral flotation circuits",international Journal of Mineral Processing. Vol. 79, pp. 5-6, 6. [4] Abu-Ali, M.H. Abdel Sabour S.A. "Optimizing the design of flotation circuits: an economic approach". Miner. Eng. Vol. 6, pp ,. [5] Ferreira, J.P. Loveday, B.K. "An improved model for simulation of flotation circuits".minerals Engineering Vol., pp ,. 468