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Optimization of gold liberation is a function of hydrocyclone (cyclone) classi-fication efficiency with regard to a given target of 80% passing 75 μm at Josay Goldfields Limited. Key performance parameters that control the classification efficiency are hydrocyclone feed density, hydrocyclone feed pressure and throughput under fairly constant grinding process conditions. The hydrocyclone feed density related linearly to overflow product of percentage passing 75 μm and showed statistical linearity at even 1% critical level of significance. The paper provides a relation between cyclone feed density and cyclone overflow product size fraction as a function of cyclone efficiency. Gradient of the relation establishes the standard unit of performance which depicts the classification efficiency as percentage passing 75 μm per percentage solids of cyclone feed density. This measurement provides a timely corrective action of key performance control parameters. The selected seven days samples space used in the assessment was due to the effect of a daily production deficiency on the overall profit margin of Josay Goldfields as company.

Efficiency is the relationship between the amount of input (energy) into a machine and the output or amount that it produces [_{50} as a convention for cyclone efficiency deduction). The d_{50} measures the 50% probability that, a cut-off point of a given particle size fraction in the feed will report at the underflow (spigot product). Per design description from the [_{50} method at the Josay Goldfields Limited laboratory, is about 24 hours which always come as postmortem result with regards to the uninterrupted nature of the production plant process dynamics. This postmortem result prevents well-timed operational parameter control to gain the required size fraction for the leaching process which is fed with the overflow product from the classification unit process.

Consequently, this investigation provides an efficiency assessment alternative to close the lack of well-timed operating parameter control gap for the hydrocyclones unit at Josay Goldfields Limited. This paper aims at enhancing managerial assessment of classification (hydrocyclone) efficiency. The framework for the assessment covers the use of statistical analysis to measure the level of efficiency of a hydrocyclone classification unit. Primarily, the extent of relationship of the underlining assumptions (i.e. fairly uniform hydrocyclone feed pressure and throughput under constant grinding process conditions) and operating limitations were authenticated.

Conservatively, at Josay Goldfields Limited, hydrocyclone is used as classifying device that makes use of centrifugal force to increase the settling rate of particles. Two clusters of twenty four hydrocyclones are used at the classification unit process. Each hydrocyclone is made up of a cylindrical section (Feed box) connected to a conical shaped vessel with an opening at the apex (Spigot). The cylindrical section is closed off at the top with a pipe protruding into the body of the cyclone. This is called the vortex finder. The feed is introduced under pressure through the feed inlet, tangential to the cylindrical section of the cyclone. This produces a spiral motion, which generates a vortex in the cyclone with a low pressure zone along the vertical axis of the cyclone.

Operationally, particles in the pulp stream are subjected to an outward centrifugal force and inward drag force or centripetal force by the use of high capacity pump. The coarsest or heaviest particles are pulled by centrifugal force to the inner walls of the cyclone displacing the finer (i.e. lighter) particles and excess water towards the center. Thus particles are graded by size and mass from outside to inside of the spinning mixture. The coarsest or heaviest particles spiral down the walls and discharges through the apex as underflow product (spigot product).The finer or lighter particles and excess water report as overflow product. The split of particles is dependent on the balance between the centrifugal and drag forces. Hence the overall performance of a cyclone depends on the relative values of the radial and tangential velocities at all positions. Other factors that contribute to the overall cyclone performance are fluid viscosity, solids densities, fluids densities and effective values of cyclone components diameters [

Essentially, the inadequacy and ambiguity of information on the efficiency of

hydrocyclone operation at the process plant is a recipe for production deficiencies. Therefore, hydrocyclone operation for seven days were collated from twelve months 2016 yearly production report to ascertain their respective efficiencies with regards to least square regression analysis equations. The seven days samples space was selected to reflect the sensitivity of a daily production deficiency of hydrocyclone operation on the profit margin of Josay Goldfields as company. That is each day’s deficiency of hydrocyclone operation has a direct reduction effect on the gold produce which is direct function of profit margin. Quantitative evaluations of the hydrocyclones overflow products were obtained to enhance pragmatic conclusions. [

From the Josay Goldfields Limited 2016 yearly production report, quarterly clusters (three month per quarter) of hydrocyclone sample data were formed. Each quarterly data was evaluated to generate corresponding mean data of seven days for cyclone feed density, overflow density, overflow density of +75 µm, Mill feed rate and cyclone pressure at a sampling frequency of one hour interval. Subsequently, yearly mean data of seven days was obtained out of the quarterly data as shown in

Subjecting each of the day’s feed densities and overflow percentage passing 75 µm variables to statistical linearity analysis, shows a linear relation at even 1% critical level of significance [^{2} of 0.6011, 01013, 0.0612 and 0.0151 for cyclone feed density, overflow density, mill feed rate and cyclone pressure respectively. The R^{2} for regression of percentage passing 75 µm on cyclone feed density, shows a strongest relation with highest dependency as compared to the other parameters [^{2 }relationship factor points

Day No. | Time (hr) | Feed density (% solid) | Overflow density (% solid) | Overflow +75µm density (% solid) | Mill feed rate (t/hr) | Cyclone Pressure (kPa) | Overflow Percentage Passing 75 µm (%) |
---|---|---|---|---|---|---|---|

1 | 800 | 60 | 30 | 12 | 671 | 111 | 54 |

900 | 58 | 28 | 7 | 617 | 111 | 59 | |

1000 | 57 | 23 | 5 | 669 | 110 | 78 | |

1100 | 56 | 25 | 5 | 655 | 112 | 80 | |

1200 | 58 | 28 | 8 | 618 | 110 | 71 | |

1300 | 58 | 29 | 6 | 645 | 110 | 79 | |

1400 | 60 | 28 | 9 | 655 | 115 | 52 | |

1500 | 56 | 30 | 6 | 669 | 110 | 85 | |

1600 | 57 | 25 | 7 | 671 | 111 | 72 | |

1700 | 56 | 26 | 7 | 684 | 113 | 73 | |

1800 | 59 | 28 | 5 | 615 | 110 | 62 | |

1900 | 55 | 27 | 8 | 605 | 114 | 86 | |

2 | 800 | 60 | 30 | 5 | 498 | 118 | 59 |

900 | 59 | 25 | 6 | 645 | 110 | 55 | |

1000 | 59 | 31 | 12 | 603 | 116 | 61 | |

1100 | 60 | 31 | 10 | 687 | 120 | 52 | |

1200 | 58 | 27 | 8 | 620 | 117 | 62 | |

1300 | 58 | 30 | 6 | 479 | 110 | 65 | |

1400 | 57 | 27 | 4 | 510 | 111 | 85 | |

1500 | 57 | 29 | 4 | 447 | 113 | 86 | |

1600 | 51 | 21 | 6 | 505 | 110 | 92 | |

1700 | 58 | 30 | 6 | 479 | 118 | 71 | |

1800 | 58 | 25 | 5 | 480 | 110 | 69 | |

1900 | 57 | 28 | 4 | 495 | 115 | 75 | |

3 | 800 | 54 | 27 | 8 | 587 | 115 | 90 |

900 | 58 | 25 | 6 | 634 | 115 | 76 | |

1000 | 59 | 30 | 9 | 600 | 110 | 70 | |

1100 | 61 | 28 | 9 | 568 | 114 | 52 | |

1200 | 60 | 27 | 8 | 630 | 118 | 51 | |

1300 | 58 | 30 | 8 | 570 | 110 | 69 | |

1400 | 56 | 24 | 6 | 529 | 113 | 75 | |

1500 | 57 | 29 | 7 | 449 | 111 | 76 | |

1600 | 56 | 25 | 6 | 507 | 120 | 80 | |

1700 | 58 | 29 | 8 | 572 | 119 | 72 | |

1800 | 58 | 29 | 9 | 498 | 116 | 69 | |

1900 | 56 | 24 | 6 | 594 | 113 | 75 |

Day No. | Time (hr) | Feed density ( % solid) | Overflow density (% solid) | Overflow +75 µm density (%solid) | Mill Feed Rate (t/hr) | Cyclone Pressure (kPa) | Overflow Percentage Passing 75 µm (%) |
---|---|---|---|---|---|---|---|

4 | 800 | 57 | 23 | 6 | 568 | 117 | 68 |

900 | 59 | 25 | 6 | 643 | 112 | 55 | |

1000 | 58 | 26 | 9 | 602 | 115 | 65 | |

1100 | 56 | 26 | 7 | 597 | 117 | 73 | |

1200 | 58 | 27 | 8 | 595 | 117 | 70 | |

1300 | 58 | 28 | 9 | 496 | 113 | 68 | |

1400 | 57 | 29 | 7 | 573 | 120 | 76 | |

1500 | 56 | 25 | 6 | 498 | 111 | 80 | |

1600 | 53 | 21 | 5 | 572 | 112 | 93 | |

1700 | 56 | 27 | 9 | 490 | 119 | 70 | |

1800 | 57 | 24 | 6 | 585 | 111 | 75 | |

1900 | 58 | 29 | 6 | 590 | 110 | 79 | |

5 | 800 | 55 | 27 | 7 | 469 | 110 | 74 |

900 | 55 | 29 | 6 | 654 | 118 | 79 | |

1000 | 57 | 25 | 6 | 604 | 115 | 76 | |

1100 | 55 | 28 | 7 | 597 | 119 | 75 | |

1200 | 57 | 27 | 6 | 623 | 120 | 78 | |

1300 | 56 | 24 | 7 | 507 | 111 | 71 | |

1400 | 57 | 24 | 6 | 582 | 113 | 75 | |

1500 | 56 | 27 | 6 | 508 | 111 | 78 | |

1600 | 57 | 25 | 7 | 512 | 115 | 72 | |

1700 | 56 | 23 | 5 | 572 | 117 | 78 | |

1800 | 55 | 25 | 5 | 459 | 112 | 80 | |

1900 | 56 | 27 | 7 | 595 | 116 | 74 | |

6 | 800 | 57 | 28 | 9 | 670 | 120 | 68 |

900 | 59 | 25 | 9 | 657 | 110 | 68 | |

1000 | 59 | 26 | 8 | 681 | 118 | 69 | |

1100 | 57 | 30 | 9 | 662 | 117 | 70 | |

1200 | 59 | 27 | 8 | 598 | 115 | 70 | |

1300 | 58 | 29 | 9 | 654 | 112 | 69 | |

1400 | 57 | 30 | 9 | 625 | 114 | 70 | |

1500 | 57 | 25 | 9 | 780 | 113 | 68 | |

1600 | 58 | 25 | 6 | 717 | 110 | 76 | |

1700 | 56 | 28 | 7 | 688 | 112 | 75 | |

1800 | 55 | 23 | 6 | 598 | 114 | 74 | |

1900 | 55 | 27 | 8 | 579 | 112 | 70 |

7 | 800 | 56 | 27 | 7 | 611 | 113 | 74 |
---|---|---|---|---|---|---|---|

900 | 57 | 30 | 8 | 608 | 110 | 73 | |

1000 | 57 | 25 | 7 | 663 | 111 | 72 | |

1100 | 56 | 27 | 8 | 712 | 113 | 70 | |

1200 | 58 | 29 | 9 | 617 | 115 | 69 | |

1300 | 56 | 26 | 8 | 597 | 113 | 83 | |

1400 | 57 | 25 | 9 | 615 | 114 | 68 | |

1500 | 55 | 27 | 8 | 646 | 112 | 70 | |

1600 | 55 | 29 | 8 | 617 | 114 | 72 | |

1700 | 58 | 28 | 9 | 648 | 111 | 65 | |

1800 | 57 | 27 | 8 | 651 | 112 | 68 | |

1900 | 56 | 28 | 7 | 600 | 116 | 85 |

to its regression equation variables as the most reliable parameters for controlling the cyclone efficiency.

Basically, efficiency is given by the ratio of output to input and can be expressed as a percentage [^{2} values, the ^{2} (i.e. r^{2 }= 0.6011), depicts the most dependable relation with regard to key parameter controlling the cyclone efficiency as compared to Figures 3-5. The output product which is the cyclone overflow size fraction, is represented as percentage

passing 75 µm (i.e. Y-axis) and input as cyclone feed density (i.e. X ? axis). This arrangement is in conformity with the operational principles of hydrocyclones which have cyclone feed density as input and cyclone overflow product as output. Pragmatically, the r^{2} of Figures 3-5 point to the fact that, the influence of these related parameters on the output cannot be neglected since r^{2} is not equal to zero. Therefore, these factors (input parameters of Figures 3-5) are to be kept under fairly uniform and constant state, to annul their effect on the overall result. That is, cyclone pressure and mill rate are to be kept under constant or uniform state as input parameters.

The regression analysis equation (Y = a + bx) obtained from the

As the variable of x-axis approaches the higher cyclone feed percentage solids (i.e. x-intercept on the graphs), classification approaches a point of impossibility. That is, the classification process approaches a point of less water or liquid in cyclone feed content which is detrimental to differential settling enhancement within particles of the given slurry in the system. Convexly, as x (input or cyclone feed density) approaches zero (0), the y (output) approaches a point where there is less solid or only water flowing through the cyclone. The zero feed density corresponds to a point on y-axis, where practically only water comes as overflow which shows theoretical optimum percentage passing 75 µm as y-inter- cept on the graphs. Hence, per these deductions, the operational limits for this linear model are cyclone feed densities greater than zero and less than the point where classification is impossible. The linear regression method makes use of all variables of the individual samples under consideration, giving it a higher potential of a lower deviation as compared to conventional estimation of cyclone d_{50} method of forming a composite samples and subsequently dividing them for size analysis. Again, linear regression method gives a quicker and a more convenient method of estimating efficiency by expressing the efficiency as standard unit of the require size fraction of the cyclone feed that appears in the overflow product. Moreover, the linear relation method gives a better account of the end result by evaluating each sample value instead of conventional method which depends on average value with the probability of skewness. Furthermore, the linear representation offers the deduction within the managerial domain by assessing the cause and effect parameters that need attention to ensure high efficiency. Conversely, the conventional method expresses the probability of a particle size fraction appearance in at the underflow product (Spigot product) with ambiguity of assessment within the concepts outside the metallurgical domain.

The expression of linear relationship between hydrocyclone feed density and overflow product size fraction as a function of efficiency, enhances well-timed operational parameter control. This improves the production of required size fraction for the subsequent leaching process to the classification unit. On one hand, the conventional method is associated with errors that may occur in the numerous sequences of test works. It does not give direct relationship for immediate trouble shooting due to the long turnaround time of the test work process. On the other hand, linear relationship between hydrocyclone feed density and overflow product size fraction provides the means of control to achieve expected output target. This is due to short turnaround time of test work involved in the method and the expression of efficiency as percentage of the overflow percentage passing 75 µm (output) size fraction per percentage solid of the cyclone feed density (input). Additionally, statistical analysis of hydrocyclone efficiency has higher accuracy due to evaluation of the individual samples in sequential analysis as compared to conventional method of estimation under composite sampling process. The R^{2} for regression of overflow percentage passing 75 µm on cyclone feed density shows a strongest relation with highest dependency. This affirms the use of the linear relation between the two parameters as a control variable for the classification process. Notably, the assumptions for this linear model are cyclone feed density greater than zero (i.e. eliminating the occurrence of y-intercept situation) and less than the cyclone feed density at the point where classification is impossible (i.e. x-intercept on the graph). Limitation in this research is the existing probability of human error due to the manual wet size analysis for the determination of overflow percentage passing 75 µm. Finally, the linear representation enhances managerial evaluation of the cause and effects parameters that need attention to guarantee high efficiency.

Yeboah, O. and Arthur, S. (2017) Expressing Efficiency as a Function of Key Performance Control Para- meters: A Case Study of Hydrocyclone Unit Process at Josay Goldfields Limited, Tarkwa, Ghana. Open Journal of Business and Management, 5, 476-486. https://doi.org/10.4236/ojbm.2017.53041