HANDOUT 2: METALLURGICAL ACCOUNTING

Transcription

1 HANDOUT 2: METALLURGICAL ACCOUNTING This handout was developed primarily from Chap 2 of Wills book (Wills, BA, 1979, Mineral Processing Technology, Pergamon Press,1 st Ed.) Metallurgical accounting is simply the accounting of minerals entering and leaving a process. It is an important aspect of mineral processing since otherwise, without it, important parameters such as recovery or efficiency would not be known. Plant operations also depend on metallurgical accounting to ensure that operations are efficient and not resulting in too many losses. Sampling and assaying are the two components of metallurgical accounting. It is believed that if theoretical and actual recoveries of a process differ by over 1%, sampling and assaying are to blame. Sampling and Weighing To determine true plant recovery/losses, one needs to sample the ore before primary crushing (typically the entry point into the plant). However, due to the reasons below, this is not done unless ores of different type need to be accounted for separately: - rom ore particles are of vastly different sizes and quality - Segregation occurs on the belt based on particle sizes. Therefore, fine and coarse particles can be expected to be of different quality and moisture content. Unless very large 1 samples are taken, it may not be possible to get a truly representative value. Sampling is best done when there is some homogeneity in material, especially with regards to particle sizes. Therefore, it is common to sample following crushing/grinding. Moisture Sampling Surface moisture impacts the weight and quality of samples. However, unless it is measured at sampling, there is no way to know the moisture content since most assaying is done on dry samples (samples are dried before lab analysis). However, due to the often intricate procedures needed to collect assay samples, analyzing assay samples for moisture content gives wrong numbers since there is moisture loss in the time-consuming sampling process. Therefore, moisture measurement is often done on samples collected separately from assay samples. Grab sampling is often done for moisture. This is a quick method where approximately equal amounts are randomly taken from material stream/pile. Samples are weighed immediately, dried as needed, and then weighed again (after the surface moisture is all gone). Therefore: % surface moisture = (wet weight dry weight) X 100 / wet weight While drying the sample, one must be careful not to dry the sample at too high a temperature. Otherwise, minerals may break down changing their physical/chemical nature. For example, sulfur dioxide is often lost in sulfide minerals when overheated. Typically, temperatures under 105 o C are preferred, though with samples containing mercury, drying temperatures can be as low as 80 o C. 1 5% of total weight, eg. 25 tons for material flowing at 500 tph, assuming samples are collected hourly

2 Assay Sampling Since samples need to be representative of the entire material pool/stream, they should be taken at locations that naturally minimize variability. One such location is where the material is at a free fall. Sample cuts need to be made perpendicular to the stream, across the entire width of the stream. Many times, a device takes sample cuts at regular intervals. In such cases, the cumulative sample is more representative than the individual samples. The more the cuts that go into a sample, the better it represents the material. Additionally, particle sizes play a role. Gy s formula is used to obtain an idea of the sample size required to obtain a given accuracy: ML Cd = 2 L M s 3 (1) Where M = minimum weight of required sample (gms) L = weight of the entire lot (gms) C = sampling constant for the material = f.g.β.c d or d 0.95 = particle size at the 95 th percentile (in cm) s = relative sampling error f = shape factor g = factor dependent on particle size distribution β = liberation factor c = composition factor The factors impacting C can be estimated as follows 2 : The shape factor is selected based on the size of the majority of the particles. It is 0.5 for most particles (see f below). d d d d f= 1 f= 0,524 f= 0,5 f= 0,1 2 Pentti Minkkinen, Lappeenranta Univ. of Technology, Powerpoint presentation, Applications of Sampling Theory Yu, S., Calibration of Online Analyzers, MS (Mining) Thesis, UAF, 2003

3 The liberation factor, β, depends on the degree of liberation (see below), i.e. is the mineral liberated (separate mineral and gangue particles) or embedded. Note that if we were sampling for ash in coal, the mineral would be ash. d L = d L β =1 β is computed as follows: β = L d β max =1 where L and d are the lengths of the material and mineral particle respectively. The size distribution factor, g, is typically 0.25, and is based on the ratio of the large to small particles (d 0.95 /d 0.05 ). It is selected as below: Wide range in size (d 0.95 /d 0.05 >4), g = 0.25 Medium range in size (2< d 0.95 /d 0.05 <4), g= 0.50 Small range in size (1< d 0.95 /d 0.05 <2), g=0.75 No range, all the same (d 0.95 /d 0.05 =1), g=1.0 The composition factor is estimated from: 1 a c = [(1 a) r + at] a where a is the fractional mineral content, r is the mineral density (g/cc) and t is the density of the material (g/cc) being sampled. Note that the obtained error is the relative sampling error and is related to the absolute error as follows: s 2 A = s 2. μ mineral where, μ mineral is the average quality value of the mineral. Therefore, any sample obtained from such a program would have a quality range of ±2*s A

4 Example: Assume that samples of coal weighing 60 lbs are taken from a coal stream flowing at 6600 lbs per minute to measure the ash content, which is typically around 11%. Particles are rarely outside the 1-4 inch range. The liberation factor for ash was previously determined at 0.4. The density of coal and ash are 94 lbs/cft (1.5 g/cc) and 156 lbs/cft (2.5 g/cc). Compute the sampling error for this campaign. Answer: a = 0.11, r = 2.5 and t=1.5 (1 0.11) c = [(1 0.11) * *1.5] 0.11 = 19.3 From the problem, it appears that d 0.05 and d 0.95 are 1 in and 4 in, respectively. Therefore, g = 0.25 For coal, a shape factor, f, of 0.5 seems most appropriate. β has been given to be 0.4 Therefore, C = f.g.β.c = 0.5*0.25*0.4*19.3 = 0.97 From (1), s 3 Cd ( L M ) = ML 2 Where C = 0.97 d 0.95 = 4 in = 10 cm L = 6600 lbs = 6600*453 = gms M = 60 lbs =60*453 = Therefore, ( ) s = = * s =.19, i.e. 19% Therefore, for an expected ash value of 11%, the absolute standard deviation will be sqrt(0.035*11%) or 0.62% ash. Thus, if we obtain a sample that has a value of 9.8% ash, the above problem implies that its true ash value is 9.8 ± 2*0.62 What happens if we double the sample size? For 120 lb sample, s absolute drops to 0.44% from 0.62%. Tripling the sample size reduces the same to 0.35%. However, as you keep increasing the sample weight, the impact on accuracy reduces significantly. Therefore, the difference between a giant sample and a somewhat large sample may not be that much. In other words, no need to go into the trouble of taking giant samples.

5 Sample Collection Automatic samplers are typically used in any systematic program. These typically involve a cutter that goes across the material stream to obtain a slice of the flow. The following is required of these samplers: - the sampling device needs to intersect the stream perpendicular to the flow - entire width of the stream needs to be sampled - the cutter should be wide enough for the sample and should travel at constant speed. Typically, cutter opening width should be over 3 times the top size. A common falling ore sampling device is the Vezin sampler. As shown in the pictures below, it essentially consists of a rotating cutter that intersects the material stream periodically. The collected material is diverted to a separate volume reduction process. Vezin Sample Cutter: sepor.com consep.com.au - Vezin Sampler

6 Sampling devices called poppet valves are used for pulp sampling in pipes. These are typically used in pipes where the flow is upward. They are similar to a syringe inserted into the pipe. When the valve is open, the pulp stream enters the sampling tube. The opening and closing of the poppet value is typically automatically controlled based on sampling requirements. Sample Preparation The collected sample often needs to be prepared before analysis. This is because, for quality control purposes, assaying can only be done on samples that meet certain criteria. A major criteria is sample size. Chemical or other analysis techniques can only applied to small quantities of finely ground material. Therefore, large samples have to be properly reduced, so that the reduced sample is representative of the collected sample. Indeed, one could think of this as sampling within sampling. The two major steps in reduction are: Homogenization: This is done so that the next step, splitting, is more accurate. This typically involves crushing and/or grinding. At the very least, the sample should be thoroughly mixed before proceeding to the next step. Splitting: Reducing the large sample to required smaller amounts. This is done by various techniques such as coning and quartering, table sampling and riffling, to split the sample into two identical halves. Note that splits are never truly identical, with coning and quartering being the least accurate. In all cases, particle sizes play a big role. Splitting is repeated as many times as necessary to obtain the right quantity of material. Many times, homogenization and splitting are done in a loop, if necessary. See below the various steps in the ALS Chemex (Fairbanks) procedures for preparing samples. Sample In Weigh and label Drying if Primary needed crusher Rejected but stored for reference 250 gms Sample Split Jaw Crusher Rejected but stored for reference Pulverized Sample Split Screened and sent off to next stage Coning and quartering consists of three steps. The first step involves piling the sample into a conical mound. In the next step, the cone is flattened into a circle. In the third step, the circular pile is split into four conic quarters, by means of two perpendicular diameters. Two opposite quarters are kept, while the other two are discarded. To remove bias, when C&Q is repeated (if necessary), the same two quarters are kept.

7 Table sampler is used for larger samples (>5 kg). It involves an inclined table that contains a series of holes and prisms. As the dropped sample goes down the incline, it meets rows of prisms that split and guide the sample. The material that falls through the holes gets discarded. The material that reaches the end of the end of the table is the required subset. Jones riffle splitter is a popular device. It consists of alternating rectangular slots that splits the sample and feeds them to two trays. The content of one of the trays is the sample. For eliminating bias, the same tray should be designated as keep when riffling is repeated. Elements of Modern Metallurgical Accounting In a modern prep plant, many aspects of the sampling and assaying are combined and automated, and conducted in real time. Some form of accounting is often done in real time, though real-time sampling and analysis is also used for process control as well. Online Analysis In many situations, online analysis (OLA) has combined and automated the various steps involved in sampling and analysis. OLA systems typically consist of a sampling system, designed to sample a fixed quantity at fixed periods, and an analysis system, that prepares the sample (crushing) and conducts real time analysis/assays using a variety of radiation based techniques. OLA systems have increased in popularity over the years due to increased accuracies. Benefits include quick assaying combined with savings in labor, though many times, considerable effort is required to keep these systems constantly calibrated. Automatic process control based on these systems are sometimes seen, though due to accuracy concerns, their application is mostly restricted to informational rather control uses. Factors that impact their performance include particle size, radiation penetration depths, heterogeneity in material, presence of materials that hurt measurement accuracies and representativeness of sampled areas/quantities. It is, therefore, not surprising that these systems are mostly seen in those processes where material is mostly consistent (i.e. in processes that are deep in the process flow sheet, after several levels of liberation/separation), rather than in the early stages, such as with rom ore.

8 Tonnage Measurement Real time weighing of ore typically involves the belt since weighing is mostly done while the ore is moving. This way, material flow is not interrupted. Modern belt scales combine strain gauge load cells (in conveyor frames), belt speed sensors and modular construction for accuracies such as ±0.5%. Often, material, especially the product, is weighed on its way to the customer. Such weighing takes place while the material is loaded in trucks or trains. Typically weighing is combined with product sampling. However, since sampling from train cars is not conducive to obtaining thermo.com representative samples, one must be careful to use a probe so that the sample is obtained from the entire depth of the material bed and not just the surface. Solid flow rate in slurry/pulp streams is commonly obtained by determining the flow rate (voluminous). Flow rate is obtained by different practical methods. A common method is to redirect the main flow into a container for a fixed amount of time. By measuring the volume of slurry, one can determine the flow rate. While the container is being filled a small sample is taken from the stream. This sample is dried to obtain the proportion of dry solids in the stream. Density cans, containers of known volume, can also be used to determine the solid flow rate. Here, the filled density cans are weighed to obtain the slurry density. The amount of time taken to fill the density can gives the flow rate. The mass flow rate, M, is obtained from: FDx M = 100 kg/sec Where F is the flow rate in litres/sec, D is the slurry/pulp density in kg/liter and x is the % solids by weight in the pulp. If the specific gravity of the solid material, d, is known then, for 1 liter of pulp: xd (100 x) D Total volume = + 100d d( D 1) x = D( d 1) A problem with the above method, of course, is that the solid/ore density is rarely a known constant. Note that modern flow meters for slurries/pulp use a variety of techniques to obtain real time flow rates. Radioactive density gauges also exist that combine with the flow meter readings to continuously output dry solids flow rate.

9 The two main accounting systems are: Accounting Systems i. Retrospective system. It is assumed that the theoretical recovery is the true recovery. Plant feed is back-calculated from the concentrate production using material balance equations. Assumes there are no losses. ii. The check in/check out system: Plant feed is measured accurately. Actual plant recovery is calculated from actual concentrate production. This is a better method since it allows comparison between real achievements vs. theoretical targets. Retrospective Method: Assays are taken of the feed, concentrate and tailings. Typically, the only weight that is obtained is that of the concentrate. This is demonstrated below for a single product example. Assume that a plant produces a concentrate of assay c at a rate of C tons per day (tpd). Let the feed rate and assay be F and f respectively, while the tailing rate and assay be T and t. Weight balance, input weight = output weight Similarly, mineral weight balance F = T + C Ff = Tt + Cc Combining, Ratio of Concentration, F/C = (c-t)/(f-t) Recovery (Cc/Ff)X100 = 100 X c(f-t)/[(c-t)f] As an example, suppose a plant produces tons of concentrate per hour at 42% metal, with head grade (feed) of 3.5% and tailings grade of 0.79%. What is the feed rate? F/C from above = ( )/( ) = F = x = tons per hour. Recovery: ( ) X 42 /[( )x3.5] = 78.9% Note that in this method of accounting, errors made while sampling the low grade tailings and feed have a large impact on computed recovery. Check-In/Check-Out system: Really, the major difference between this and the other accounting system that losses are accounted for in this system. The previous system assumed no losses (F=T+C). In this method of accounting, every major aspect of the plant is measured (weights and assays) accurately. Then, a material balance is done periodically (such as weekly or monthly). Attempts, such as re-directing spills to sumps, are made to minimize losses. The table below shows an example of such accounting. The actual recovery for the table below is 93% though the theoretical recovery is (the losses) = 94.28%.

10 While conducting metal balances, one must not forget to keep track of metal contained within the processes, such as in thickeners, agitators, transportation etc. It is easy to assume that the metal trapped in these processes ( inventory ) is constant over the period. As the example in the table below shows, the inventory (in-plant and other) changed by +54 tons of concentrate and -4.3 tons of metal at the end of the month.