MetE13 Sampling 1

October 16, 2017 | Author: Christian Arranz | Category: Standard Deviation, Sampling (Statistics), Errors And Residuals, Mean, Experiment
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Sampling Methods C.G. Arranz, J. Escuro, C.A.V. Magbag, A. Fernandez Department of Mining, Metallurgical and Materials Engineering University of the Philippines, Diliman [email protected], [email protected]

Abstract Sampling is a process mainly concerned on obtaining a representative sample from the bulk it was removed from. This experiment makes use of four common sampling methods, namely increment sampling, grab sampling, coning and quartering, rolling and quartering and Jones Riffles sampling. These processes were used on a 300g population of light and dark-colored pebbles. The goal was to obtain one-eighths of the population. Though resulting to a fairly accurate final sample, each of these methods however, is not without its own limitations and applications. Regardless of how each method is limited, the representativeness of the sample is always of the utmost concern. Proper statistical analysis will show variance between the sample frequencies of the white and black pebbles and its relation to the sample mass. Also, population mean and standard deviation will help to gain insight of the relationship between the bulk population and different samples obtained from different sampling methods. Relationship between the population and samples is the scope of the experiment.

1. Introduction Manual sampling is one method to obtain representative samples, however, it should only be used when mechanical sampling seems to be impractical. In manual sampling, personal biases come into account and the choice of sampling point is of utmost importance. It is also considered to be more expensive because of the slow batch processing of the samples which results to labor wasting in continuous streams sampling. Grab sampling, coning and quartering, shovel sampling, trench sampling, pipe and auger sampling are examples of manual sampling. One of the sampling methods used in this experiment was Grab sampling, which uses a scoop. This method is considered to be inexpensive because of the lowered equipment costs and the ability to measure samples from any accessible place in process stream. However, disadvantages lie on the direct labor which may cause alterations in the sample during collection and testing. This is also used when machine sampling is difficult to operate and the material to be analyzed does not suit the equipment. The sample is usually crushed and pulverized. The top was flattened and was divided into ten equal where the sample is scooped

at each of the parts from the heap placed on a sampling mat. Another method used in the experiment was Coning and Quartering (Figure 1). This method is usually used in sampling large quantities and which can conveniently done using shovels. First, the ore is piled into a cone and then a shovelful of the ore is then heaped over the vertex of the cone. This is to ensure equal distribution of the scooped sample on the cone than compared to normal dumping of sample into a pile (Figure 2). After this step, the operator then spreads the cone into a circular layer of uniform thickness by working around the mound or by removing small shovelfuls from the top then spreading it near the edge. When this step is done, it is then divided into four equal quarters and the two opposite quarters are taken as the sample. This portion may also be coned and quartered and this process could continue until the right size has been achieved. Rolling and Quartering is similar to Coning and Quartering, only differing in the first step. Instead of pouring into a conical pile, the samples are placed on the center of a mat, then the corners of the mat are folded or rolled toward the opposite corner, causing the particles to be mixed and remain at the center. The next step of flattening

the pile into a circular layer of uniform thickness and the quartering procedure remains the same.

2. Methodology Figure 2. Coning and quartering

Approximately three hundred grams of a mixture of light and dark pebbles was obtained. Five sampling techniques were performed in the process of obtaining a representative sample of the 300-gram population. Each sampling technique was done in three trials. After every trial the remaining pebbles - approximately one-eighths (1/8) of the population were weighed and separated based on color, i.e. dark and light. The number of pebbles was counted for the light and dark piles of pebbles. The piles were again weighed. The number of pebbles as well as the weights was recorded.

Figure 3. Chute-type Sample Splitter. The flow indicates how the material will flow when poured over the opening

In increment sampling the whole population was divided into four equal portions. The pebbles were poured onto a mat into a rectangular pile, this was then flattened and divided into four sections. Alternating sections were discarded. The process was repeated twice on the remaining pebbles until one eighths (⅛) of the population was gathered. The light and dark pebbles were segregated from each other, weighed and counted individually.

Another method used was mechanical sampling using a sample splitter, specifically the Jones Riffles Splitter. A typical splitter or riffle is shown in Figure 3. It is composed by a series of shafts that run in alternating directions for when the material is poured into the feed chute, it would flow

alternately over the shafts and would be randomly divided into two equal-sized parts. The sample must be fed using a special pan which have the same width as the top of the chutes, otherwise material obtained will be incorrect as some material will not be caught. If the material is repeatedly divided into smaller parts using this riffle, the errors from each step will be added together giving an increased variance between the samples.

In grab sampling, a certain amount, approximately one eighths of the population was scooped and from these the light and dark pebbles were separated, weighed and counted. In coning and quartering, the 300g sample was poured into a single conical pile, forming a rightconical heap. Then, the heap was flattened and was divided into even quarters. Two opposite quarters were combined and placed in a tray. This was done thrice to get the one eighths (⅛) of the population. Jones Riffles sampling was also done on the 300g sample. After halving using the Jones Riffles, equal amounts of sample were obtained from the population. Half was discarded and the other half is then put again into the Jones Riffle. The aforementioned process was repeated twice until one eighths (⅛) of the original 300g population was obtained. The entire process was also repeated for three trials.

3. Results and Discussion Particle-size distribution methods require compositions from sample that is representative from the bulk where it was taken from. The degree of complexity of the method for the sampling

method would depend on the experiment itself. The goal of this stage is to not only obtain a representative sample but also to remove large deviations for the particle sizes.

Table 3: Increment Sampling Method Mean and Standard Deviation Values

Table 1: Rolling and Quartering Mean and Standard Deviations

Table 4: Grab Sampling Method Mean and Standard Deviation Values

For rolling and quartering, the data indicate that the standard deviations of the number of black pebbles and the total number of pebbles indicate close values between the black pebbles and the total number of pebbles. Also, the standard deviation value of the white pebble weight indicates that the measurement error would be due to the approximation of the weighing scale. The weighing scale itself ‘approximates’ the measurement of the weight.

Grab sampling method all have standard deviation values thereby inferring that the values in the replicates are not precisely close. This indicates more errors in the sampling method aforementioned.

For increment sampling method, the data also indicate zero deviation from the weight of the white and black pebbles.

Table 5: Coning and Quartering Sampling Method Mean and Standard Deviation Values

Table 2: Jones Rifle Sampling Method Mean and Standard Deviation Values For Jones Riffle Sampling Method, the data indicate zero standard deviations of all weight values indicate close values of the replicates. Also, the standard deviation values of the white pebble frequency, black pebble weight, and the total number of pebbles. The source of error may come from the sampling process itself. It may come

The coning and quartering sampling method may have errors in the pebble count due to breakage of some pebbles forming 2 or more segmented pebbles, thereby increasing the count of the white, black and therefore the total number of pebbles. However, there may be minimal errors in the weight determination due to negligible dust assimilation.

Table 6: Population data of pebble samples

4. Conclusion Sampling is accurate if the chosen subsamples of the bulk are truly the representative of said bulk material which can be verified by checking within the limits of analytical error. The sampling methods used successively on one sample in this experiment, namely Increment sampling, Grab sampling, Coning and Quartering, Rolling and Quartering and the Jone Riffles Splitter have produced fairly accurate subsamples. Each method however, is not without its own limitations and applications. Grab sampling is an inexpensive method which is operable at most settings, but is prone to alterations due to manual labor. The Coning and Quartering, Increment Sampling and Rolling and Quartering method are applicable to all types or classes of ores at a larger amount range, but they can be quite laborious at very high amounts and prone to alterations as well. The Jones Riffles Splitter on the other hand can easily be operated and can quickly cut down samples to assay weight, but is only limited to certain particle sizes as it is prone to losing fine particles.

References [1] Newton, Joseph (1947). “An Introduction to Metallurgy”, John Wiley & Sons, Inc., USA, pp.303-305 [2] Merks, JW. “Sampling in Mineral Processing”. Retrieved February 28, 2015. [3]

Faculty of Department of Chemical Engineering, College of Engineering, Michigan Technological University(2009).

[4] Sampling. faculty/kawatra/CM3820_2009_Sampling.pdf. Retrieved November 28, 2011. [5]

US Environmental Protection Agency (2011). Procedures For Laboratory Analysis Of Surface/Bulk Dust Loading Samples. endix/app-c2.pdf. Retrieved November 28, 2011

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