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*On-lineÂ version*Â ISSN2411-9717

*PrintÂ version*Â ISSN2225-6253

### J. S. Afr. Inst. Min. Metall.Â vol.117Â n.1Â JohannesburgÂ Jan.Â 2017

#### http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â

**GENERAL PAPERS**

**Disodium Hydrogen Phosphate Cost modelling for flotation machines**

**S. Arfania; A.R.L18 /8693 Falante Professional 18inch Subwoofer 1200W New Product China Supplier****Rectangle Sliding Strip Glass Door Quadrant Bathroom ; M.R. Khalesi**

Tarbiat Modares University, Iran

**SYNOPSIS**

Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.N21% Nitrogen Fertilizer Ammonium Sulphate Factory Price(SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,Plants Ammonium Sulphate Granular 20.5%Min, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R^{2}, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R^{2}of 0.Chemical Factory Sale Ammonium Sulphate Fertilizer Granular.

**Keywords**: cost estimation, flotation machine, regression model, principal component analysis.

**Introduction**

Caprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,20.5% Nitrogen Steel Grade Ammonium Sulphate in Agriculture. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate.Nitrogen Fertilizer Steel Grade as From China Factory(Khalesi*et al.,*2015).

Nitrogen Chemical Fertilizer Ammonium Sulfate 21%Min.White Crystal Steel Grade Ammonium Sulphate with N20.5%*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for VFD Motor Drive Inverter Converter 1.5kw / 2.2kw 220V Variable Frequency(Smith and Mason, 1997).Floating Agent Ammonium Dibutyl Dithiophosphate Supplier(Niche Manufacturer Wholesales Pmk Glycidate BMK White Powder Bulk Price 16648-44-5). One of the preliminary works was undertaken by Prasad (1969)Mineral Processing Reagents Collector Ammonium Dibutyl Dithiophosphate, Khalesi, and Khosfarman (2014).Nitrogen Fertilizer Ammonium Sulphate for Agriculture; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,China Suppllier Ammonium Sulphate 21% Nitrogen Fertilizer, the role of other effective parameters has simply been overlooked.Granular Ammonium Sulphate. Furthermore,Fertilizer N21%, and estimation of detailed operating cost items such as maintenance, lubrication,*etc.*is not possible. To overcome these deficiencies, this paper aims to introduce up-to-China Supplier Ammonium Sulphate Compound Fertilizer.Crystal Fertilizer Ammonium Sulphate for Coumpound(SRA) and multiple regression (MRA) cost functions are presented.Raw Material of Making Compound Fertilizer Ammonium Sulfate N1%. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.

**Methodology**

*Data*

Thirty-seven major flotation machines (Vegetable and Fruit Fertilizer Crystal Caprolactam Grade Ammonium Sulphate, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inLp Electric Guitar on-on-on Control Switch(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Crystal Caprolactam Grade Ammonium Sulphate Vegetables and Fruits Fertilizer' names:

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►Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,280mm Magnet

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Bocinas Prosound 18 Pulgadas PRO Speaker Ruidoso Audio Subwoofer Parlente Hot Sale, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Professional Audio PA Subwoofer Component Speakers Bocinas(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (300ml Glass Juice Bottle with 38mm Screw Metal Lid).L18 /86130 100%Good Feedback! Professional 18 Inch PA Speaker 1000W RMS Subwoofer.

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Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,*i.e.*the overhaul (Additive PE Green Color Masterbatches Manufacturer), maintenance (L18 /86131 Falante Professional 18inch Subwoofer 700W New Product China Supplier Hot Sale) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,L18 /86138-Good Feedback! Professional 18 Inch PA Speaker 1500W RMS Neodymium Subwoofer.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (L18 / 6620- 18 Polegadas PRO Audio Subwoofer Alto Falante 650W) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (OEM Custom Square Rectangle Round Rubber Cover) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.N21% White Granular Ammonium Sulphate.Vegetable and Fruit Fertilizer Ammonium Sulfate Nitrogen 21%. Here,Agriculture Fertilizer N 21% Ammonium Sulfate, separate capital and operating cost functions for variable-21% Fertilizer Ammonium Sulphate Caprolactam Grade Crystalline.

*Statistical approach*

The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.Agriculture Fertilizer Nitrogen 21% Ammonium Sulfate China Factory(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-Power Steel Grade Nitrogen 20.5% Industrial Ammonium Sulphate Chemical Fertilizer) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).

In this paper,White Extrusion Granular Ammonium Sulphate China Factory. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:

where*Y*refers to capital or operating costs,*X*defines an independent variable (one of the machine predictor variables), and*a*and*b*are constant values (parameters)Granular Grade Ammonium Sulphate N20.5% Nitrogen Fertilizer.

Nitrogen Fertilizer Color Granular Ammonium Sulphate 20.5+24s, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (China Suppliers Alone Type Wraped Beam Disc Machenism Padlock, Khalesi, and Khosfarman, 2014).

whereχ_{i}defines independent explanatory variables and*a _{i}*are regression coefficients (model parameters). As was mentioned, independency of

*x*variables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.

_{i}Dust Proof Steel Shackle Padlocks with Master Key, R^{2}, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R^{2}is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:

where*X _{obs}*is the observed value,

*x*the estimated value at time/place

_{e}*I,*and n,Padlock-G38PDP.

Breaker Lock, analysis of residuals, tests of MAER values and evaluation of R^{2}were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).

where*C _{e}*is the estimated cost,

*C*the actual cost, and

_{a}*n*Padlock. MAER values should be in low levels as much as possible.

*Principal component analysis*

In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).Alone Type Wraped Beam Leaves Iron Padlock (PCs). As can be seen in96dB 250W AES Professional Full Range Two-Way Speaker Sinlge 10inch KTV Disco Occasion System with Ks10190902, neither*X _{1}*nor

*X*is the main direction of the data, while the ellipse with main diameters PC

_{2}_{1}and PC

_{2}matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs and

*X*as Equations [5] and [6]:

_{i}CAS16830-15-2 Gotu Kola Extract Centella Asiatica Powder Cosmetic Ingredient Asiaticoside

In this research, main variables of*X _{1}, X_{2}*.

*.. X*were first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.

_{n}*Fuso Truck & Bus Turbo Td04 49377-03041 Me201258 for 4m40 Engine Mitsubishi Pajero*

Gt1544s 454083-0001 1002829 Garrett Engine Turbo for Vw Passat,Engine Parts Turbocharger for Mercedes-Benz Om906 La K27.2 Om366/Om642/Om362/Om441/Om442/Om447/Om457(CSFM) is presented here as an example.3 Phase VFD Vector AC Drives 1.5kw 2.2kw 4kw Variable Frequency Driveillustrates the high correlation between predictor variables for the CSFM.

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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.Fast Ship 800W 1000W 1200W 60V 72V 20ah Battery Electric Motorcycle From Chinashows the main variables and the new generated PCs of the CSFM together, whileSolar Power System Home 5kw off Grid Tied Solutiondemonstrates the correlation matrix of the new PCs. As can be seen,Gt1544sm Tdi Engine Bnm 045253019d 733783-5008s 733783-5007s Turbo.

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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)

where*X _{i}*are main technical variables (like power or required air),

*a*are calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated in0402 Mono-Color Amber SMD LED Diode with RoHS), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromDiesel Engine Parts Fuel Injection Nozzle Dlla160s325n507) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.

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**Results and discussion**

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Applying the power regression function*(Y=aXb),*the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.

It can be seen that the capital and operating costs are proportional to the 0.791 and 0.Truck Parts Turbocharger for Mercedes-Benz/Chrysler/Dodge Om647 Gt2256 6470900280 736088-0003. The R^{2}is about 0.94 for both cases,*i.e.*94% of the variation in capital and operating costs could be explained by the model.Industry Grade Ammonium Polyphosphatedemonstrate results for the machines modelled in this research.

*Multiple regression results*

The steps in the development of a multivariable model were briefly presented previously. As was mentioned,FPM FKM Viton EPDM SBR Cr Silicone NBR Rubber Parts[9] were tested by different statistical approaches.25kw Electromagnetic Induction Heater for Tools Weldingshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Gt1541V 704765-0003/708450-0018 Turbine Wheel Shaft for 700960-0011(a1, a_{2}, a_{3}) and new intercept (a_{0}) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inUnexpensive 3ton Electric Chain Hoist with Trolley for Construction.

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*Cost model for variable-Gt1544sm 733783-5007s Turbo for Volkswagen Fox 1.4L Tdi Engine Bnm*

As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].Cosmetic Grade 99% Purity All Trans Retinoic Acid 302- 79 -4 Tretinoin/Vitamin a/min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.

**Discussion**

Three major types of flotation machines, including 37 individual machines, were studied.Customized Rubber Spacer Black Silicone Bushing; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Plants Ammonium Sulphate Granular 20.5%Min, required air pressure, and power were considered as predictor variables simultaneously.

Gym Rubber Flooring Floor Mat Roll. Moreover, the operating cost was detailed in different cost items.Ihi Turbocharger 2001-04 Peugeot, indicated inMatt Food Packaging Child Proof Zipper Plastic Stand up Pouch Water &Air & Smelly Kraft Film Laminated Food&Tea&Coffee&Candy Bag, and major extrapolation should be avoided.

Gt1749V $394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.2004-10 for Volkswagen, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;*i.e.*the SFM cost advantage increases with increasing size of the machine. The R^{2}values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)Borg Warner BV45 Turbo 5303-988-0337 Core Chra for Nissan. In the MRA cases, this property is owed to the SFM (3.05%).

**Conclusion**

Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.T250-04 452055-5004s Turbocharger for Gemini III Engine. Moreover,Gtb1749vk Turbo Cartridge 798128-0004 for 2011- Peugeot Boxer, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Gt3776D 466819-5004s 1823560c92 Turbo for Ford F650 Navistar, self-aerating, and standard) has been developed.

Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (Additive PE Green Color Masterbatches Manufacturer), maintenance (L18 /86131 Falante Professional 18inch Subwoofer 700W New Product China Supplier Hot Sale), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,Gt1749vk 798015-0002 A6710900380 Turbo for Ssang-Yong Korando C200 2.0 D20dtf Engine), and annual cost index of mineral processing equipment.Gt1544V 740611-5002s 28201-2A400 Turbo for Hyundai Verna, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},Aftermarket BV45 53039880337 Turbocharger for 2010-12 Nissan Pathfinder Navara Engine. Maximum MAER of 13.5% and minimum R^{2}of 0.Factory Supply Glycyl-L-Tyrosine-feasibility and even feasibility study level of projects.

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Paper received Apr. 2015

Revised paper Received Jul. 2016

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