1、BRITISH STANDARD BS 5551-2.7: 1988 Fertilizers Part 2: Sampling Section 2.7 Recommendations for minimum mass of increment of a solid fertilizer to be taken to be representative of the total sampling unit UDC 631.8:543.05:620.113:531.422:06.052.6BS5551-2.7:1988 This British Standard, having been prep
2、ared under the directionof the Chemicals Standards Committee, was published under the authority ofthe Board of BSI and comes into effect on 30 September 1988 BSI 11-1999 The following BSI references relate to the work on this standard: Committee reference CIC/37 Draft for comment 87/53554 DC ISBN 0
3、580 16785 2 Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Chemicals Standards Committee (CIC/-) to Technical Committee CIC/37, upon which the following bodies were represented: Association of Public Analysts Department of Trade and Ind
4、ustry (Laboratory of the Government Chemist) Fertiliser Manufacturers Association Ltd. Institute of Trading Standards Administration Ministry of Agriculture, Fisheries and Food Amendments issued since publication Amd. No. Date of issue CommentsBS5551-2.7:1988 BSI 11-1999 i Contents Page Committees r
5、esponsible Inside front cover Foreword ii 1 Scope and field of application 1 2 Basic theory 1 3 Fertilizers composed of particles of the same nature 1 4 Fertilizers composed of particles of different nature 2 5 General comment on the reduction of samples 3 6 Selection of the mass of the smallest inc
6、rement in the case of grouping of the increments 3 Annex Calculation of m 4 Table 1 Value of C in relation to number of dividing operations 2 Table 2 Examples of limit values of m 2 Table 3 Values of minimum mass for similar size distributions 2 Table 4 Values of minimum mass for size distribution w
7、hich vary greatly 3 Table 5 Values of minimum mass for two constituents with very different densities 3BS5551-2.7:1988 ii BSI 11-1999 Foreword This Section of BS5551 has been prepared under the direction of the Chemicals Standards Committee in order to provide recommendations for the minimum mass of
8、 increment to be taken to be representative of the total sampling unit when sampling a solid fertilizer. For some years the United Kingdom has participated in the standardization of methods of sampling fertilizers through Subcommittee2, Sampling, of Technical Committee134, Fertilizers and soil condi
9、tioners, of the International Organization for Standardization (ISO). As international agreement is reached on the methods, it is proposed to publish them as Sections of BS5551. The standard is published in four Parts, each Part being subdivided into Sections and, where appropriate, Subsections. The
10、 four Parts are: Part 1: Terminology and labelling; Part 2: Sampling; Part 3: Physical properties; Part 4: Chemical analysis. This Section of Part2is identical with ISO/TR7553:1987 “Fertilizers Sampling Minimum mass of increment to be taken to be representative of the total sampling unit”. This docu
11、ment has been published by ISO as a type3technical report, which is a document containing information in a form different from that usually published in International Standards. In this case the document contains some of the theoretical background to the derivation of formulae for calculating the mi
12、nimum mass of an increment and gives examples of values in tables. This document complements other standards for sampling fertilizers, both published and in course of preparation. For ease of production the text of the international technical report has been used for this British Standard. Some term
13、inology and certain conventions are not identical with those used in British Standards; attention is drawn especially to the following. The comma has been used as a decimal marker. In British Standards it is current practice to use a full point on the baseline as the decimal marker. The symbol “ml”
14、has been used to denote millilitre. In British Standards it is current practice to use the symbol “mL”. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Stand
15、ard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages1 to 5 and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indic
16、ated in the amendment table on the inside front cover.BS5551-2.7:1988 BSI 11-1999 1 1 Scope and field of application When sampling is carried out on a batch of fertilizer, an increment is taken from N units. Each of these increments may be taken either by means of partial sampling devices, if their
17、validity (absence of any particular bias) is assured, or by treating the complete item with a suitable reduction device (absence of bias). This British Standard specifies, for the latter case, the extent of mass reduction beyond which the error in the representativity of the increment can no longer
18、be ignored. It may also be used to establish the minimum mass of any intermediate increment during the treatment of the sample, up to analysis. Where partial sampling devices are used, this limiting mass can be much more important. 2 Basic theory Taking into account the granular nature of solid fert
19、ilizers, the sampled mass cannot be reduced indefinitely without losing all representativity. However, it is possible to relate the mass of the sample to a minimum error of representativity, as a function of the variability in composition of the product sampled and of its particle size distribution.
20、 Emphasis should, however, be placed on the nature of the minimum limit value of this error to which can, in practice, be added large errors due to the variability of the increments, often associated with defective sampling devices (spears in particular). It should also be noted that this error occu
21、rs at each reduction operation on the sample after its constitution. Particular attention is drawn to the fact that, in preparing the test portion from the laboratory sample, representativity can easily be lost if the masses sampled at a given point are insufficient with respect to particle size dis
22、tribution and variability in composition or if they do not follow the rule of equiprobability of choice. This concept is, in fact, empirically admissible because, in the case of determinations where grinding is allowed, such an operation is generally carried out before the test portion is taken. Sta
23、tistical studies now make it possible to calculate accurately a relation between these magnitudes. In cases where grinding is not possible (for example determination of particle size distribution), they also enable a relationship to be obtained between the mass of the test portion and the error of r
24、epresentativity. Two types of fertilizer may be encountered: a) Fertilizer in which all the particles are essentially of the same nature Once the variability in analysis from one particle to another is known, it is possible to calculate statistically, on the basis of a normal distribution, the numbe
25、r of particles, and thus the minimum mass, required so as not to exceed a given uncertainty. b) Fertilizer in which the particles are of a different nature (bulk blends) Once the percentage of the least abundant constituent to be analysed is known, it is possible to calculate statistically, on the b
26、asis of a binomial distribution, the number of particles, and thus the minimum mass, required so as not to exceed a given uncertainty. 3 Fertilizers composed of particles of the same nature The analyses vary continuously from particle to particle following a normal or an approximately normal distrib
27、ution with a coefficient of variation generally between10% and40% (40% in extreme cases with fertilizers obtained via an almost dry mixing stage). Calculation on the basis of the theory of normal distributions indicates that, if the standard deviation for variations in particle analysis is called an
28、d the desired precision at95% bilateral probability2 E , the mass of this increment is given, approximately, by the formula where mis the mean diameter of the particles as defined in the Annex; is the density of the particles; 2 Ecorresponds to the overall error of judgement desired and is expressed
29、 in the same way as , for example as an absolute value; C is a coefficient which renders the error connected with the limitation of the increment mass negligible compared with E . It will be chosen as equal to at least5, as random errors are added to the square. Hence, approximating ;/6 to 0,5, The
30、value of C will depend on the number of operations or divisions carried out on the initial increment(s), up to taking the test portion. The relationship is given in Table 1.BS5551-2.7:1988 2 BSI 11-1999 Table 1 Value of C in relation to number of dividing operations Table 2 gives limit values of m,
31、for typical values of , C, and m . Table 2 Examples of limit values of m = 2 g/ml, C = 5 4 Fertilizers composed of particles of different nature The second group of fertilizers includes dry mixtures (bulk blends or others) without any notable agglomeration of the constituents. In these products, the
32、 variation in composition of the constituents is low compared with the heterogeneity of the constituents and it is ultimately the latter factor which dictates the mass of the increment. Since the density of each of the constituents is approximately the same, to within 20%, calculation on the basis o
33、f the binomial law leads to the equation if the size distributions of the constituents are similar. Eis expressed as a function of unity and not as a percentage, in the same way as y; y corresponds to the amount of the least abundant constituent, expressed as a fraction of unity. Table 3 gives the v
34、alues of this minimum mass for m=1,2and4mm and y =0,05,0,15 and0,50assuming that =2g/ml and C=5. If the size distributions vary greatly (segregation during transport causes problems, so that the manufacture of this type of fertilizer should be avoided) the equation becomes The index1is attached to t
35、he component corresponding to the amount y. Table 4 gives the values of this minimum mass for 1=1mm and 2=2mm; 1 =2mm and 2 =1mm and y =0,05,0,15 and0,50, assuming that =2g/ml and C =5. Table 3 Values of minimum mass for similar size distributions Number of dividing operations 0 1 2 3 4 C 5 10 15 20
36、 25 / E m 1 mm 2,5 mm 4 mm 10 mm 5 0,12 g 2 g 8 g 125 g 10 0,5 g 8 g 32 g 500 g 20 2 g 32 g 130 g 2 000 g 40 8 g 125 g 510 g 8 000 g E - y m 1 mm 2 mm 4 mm E /y 0,01 0,02 0,05 0,01 0,02 0,05 0,01 0,02 0,05 0,05 950 g 240 g 40 g 7 600 g 1 900 g 300 g 60 800 g 15 200 g 2 450 g 0,15 285 g 70 g 12 g 2 2
37、60 g 570 g 90 g 18 100 g 4 530 g 720 g 0,50 50 g 12 g 2 g 400 g 100 g 16 g 3 200 g 800 g 130 gBS5551-2.7:1988 BSI 11-1999 3 Table 4 Values of minimum mass for size distributions which vary greatly The case in which the densities of the two constituents are very different is even more hazardous with
38、regard to precision of sampling, segregation giving rise to even greater errors. In this case, the equation is again modified and becomes For 1=1,5g/ml, 2=2,5g/ml and C = 5 the following sample table (Table 5) is obtained: Table 5 Values of minimum mass for two constituents with very different densi
39、ties It can be seen that a mean can be taken without great error if the minor constituent is not that with the larger mean diameter. 5 General comment on the reduction of samples It can be seen that, according to the type of product for sampling, the precautions which have to be taken can vary great
40、ly. These conditions of the mass/particle size ratio must also be respected at all stages in the preparation of reduced or final samples up to and including the stage at which the test portion is taken for analysis. It follows that any reduction in the sample quantity should, in general, be accompan
41、ied by crushing. If the fertilizer is to be kept in its original state, then a large quantity of sample must be retained, or a loss in representativity must be accepted. For example, for a mixed granular fertilizer with y =0,15, if the starting value of mis4mm, the initial increment is approximately
42、4500g for a2% precision. If this is reduced to200g while retaining the same representativity, it must be crushed until a value of mof about1,4mm is obtained, and for a test portion for analysis of2g, it must be ground so that m. 0,3mm. If the sample is reduced to500g without crushing, an additional
43、error of representativity is introduced which will more than quadruple the standard deviation of the overall uncertainty, which will go from2% to8% relative. 6 Selection of the mass of the smallest increment in the case of grouping of the increments (k by k before analysis) In this case, the minimum
44、 masses defined above shall be respected throughout all the dividing operations up until testing, but at the start it is sufficient that each grouping of k increments attain this minimum mass. It would then be possible to select a mass for the initial increment k times smaller. It is important to be
45、 aware of the need for particular care with regard to the validity of the sampling apparatus, which must provide an absolute guarantee of the equiprobability of the particles comprising the increments. E /y 1= 1 mm 2= 2 mm 2= 1 mm 1= 2 mm 0,01 0,05 0,01 0,05 y 0,05 1 285 g 52 g 7 250 g 290 g 0,15 58
46、0 g 24 g 2 000 g 80 g 0,50 225 g 9 g 225 g 9 g E /y 1= 1 mm 2= 2 mm 2= 1 mm 1= 2 mm 0,01 0,05 0,01 0.05 y 0,05 1 150 g 46 g 5 450 g 218 gBS5551-2.7:1988 4 BSI 11-1999 Annex Calculation of m If the particle size distribution of the fertilizer is relatively broad, the mean diameter mmay be calculated
47、from a size distribution analysis. By definition, mcorresponds to the mean diameter of a hypothetical size distribution having a single particle size classification which, with an increment of mass would enable the same precision to be obtained as that obtained with the actual distribution. The incr
48、ement of mass of the actual distribution corresponds to and the precision is derived as follows: Thus, and Also and Substituting for 1/ from equation (2), equation (1) becomes Substituting for ifrom equation (3), this becomes Substituting from equation (4), gives hence . (1) hence . (2) hence . (3)
49、C m i= M . (4)BS5551-2.7:1988 BSI 11-1999 5 Therefore where is the number of particles in the increment; i is the number of particles in each size classification; is the density of the particles; i is the mean diameter of each size classification; m i is the mass of each class; x i is the content of each class; x m is the mean content of the increment; is the standard deviation of the content on the scale of the particle; (x
