GB2116698A - Coal analysis using x-rays - Google Patents

Coal analysis using x-rays Download PDF

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Publication number
GB2116698A
GB2116698A GB8205674A GB8205674A GB2116698A GB 2116698 A GB2116698 A GB 2116698A GB 8205674 A GB8205674 A GB 8205674A GB 8205674 A GB8205674 A GB 8205674A GB 2116698 A GB2116698 A GB 2116698A
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Prior art keywords
ash
intensity
ray
concentration
spectrometer
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GB8205674A
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Lawrence Thorne
Gregory Mccormick
Brian Downing
Brian John Price
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APPLIED RESEARCH LAB Ltd
Coal Industry Patents Ltd
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APPLIED RESEARCH LAB Ltd
Coal Industry Patents Ltd
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Priority to GB8205674A priority Critical patent/GB2116698A/en
Priority to DE19833306464 priority patent/DE3306464A1/en
Priority to FR8303170A priority patent/FR2522412A1/en
Publication of GB2116698A publication Critical patent/GB2116698A/en
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/22Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
    • G01N23/223Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material by irradiating the sample with X-rays or gamma-rays and by measuring X-ray fluorescence
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/20Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
    • G01N23/203Measuring back scattering
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00Investigating materials by wave or particle radiation
    • G01N2223/07Investigating materials by wave or particle radiation secondary emission
    • G01N2223/076X-ray fluorescence

Abstract

Method and apparatus for the determination of ash content (and of individual elements) in coal, comprising irradiating a sample of the coal with X-rays in the 1-40 keV energy range, detecting the intensity of the X-ray fluorescence spectra for at least the elements aluminium, calcium, silicon and iron, detecting the intensity of a portion of the backscattered X-ray radiation in the range 12-14 keV and processing the detected intensities to give a corrected value for the concentration of ash in the sample.

Description

SPECIFICATION Coal analysis using X-rays This invention concerns an apparatus and a method for analysing coal using X-rays.
Coal inevitably contains non-carbonaceous material which remains in the form of an ash residue when the coal is fully pyrolysed. The ash content of coal, as a percentage by weight of the coal, is a very important parameter in establishing the value of the particular coal, and there is the need for expensive coal processing to reduce the ash levels to those acceptable by customers. Certain other components of coal are also of considerable importance, of which we would mention the elements chlorine, sulphur and phosphorus as being those of current greatest interest as pollutants.
The classic method of determining ash in coal is to fully pyrolyse a weighed sample of coal, and then to weigh the ash residue. This is a time-consuming and expensive procedure, and routine testing of many samples from an individual mine can require considerable resources in manpower.
It has been proposed to use X-ray backscatter measurements to determine ash in coal, in U.K. patent specification No. 965 303, and instruments using the backscatter technique are in use in the British coal industry. Patent specification No. 965,303 states that there are three forms of radiation treatment which are relevant to the problem of determining ash content in coal, namely beta particle backscattering, X-ray absorption and X-ray backscattering. The invention of specification No. 965303 is stated to overcome the problem of interference by the iron content in the ash, in an X-ray backscatter method, since X-ray absorption was found to be far too dependent upon the thickness of the sample.This is still true, but although X-ray backscatter instruments are in use and give a quick result, experience has shown that backscatter is not very accurate and, in particular, requires calibration in respect of each set of samples from a different source, for example, even in the case of different seams being mined in the same pit. That is, experience has shown that the relationship between X-ray backscatter measurements and the ash content of a sample is highly dependent upon the source of the coal sample. This is believed to be because not only does the quantity of ash vary within different seams, quite apart from the question of whether the coal is contaminated with rock cut from the roof or floor of the seam, but also the seams were laid down at widely different geological times and the minerals contained in the ash also vary.
A proposal to measure ash in coal by absorption of X-rays is contained in U.K. patent application No.
762,432 but this method has not met with practical success.
It has also been proposed to analyse for sulphur in coal by measurement of X-ray fluoresence of iron and applying a correction from backscatter, in British Patent Specification No. 2,043,876. Another proposal, contained in British Patent Specification 2,056,668 uses radiation of two separate energies to cause fluoresence of iron and measures backscatter and fluorescence.
We have now devised an improved method of analysing coal for ash and for other components by element using X-rays, by means of which accurate results can be obtained without the necessity for recalibration in respect of samples from each different source. That is, excellent results can be achieved in comparison with classic chemical analyses, for any coal from a given geographical area.
Accordingly, the present invention provides a method for analysing solid carbonaceous material, which comprises detecting the intensity of X-ray fluorescence spectra for at least the elements aluminium, calcium, silicon and iron, emitted by the material when bombarded with X-rays of energy in the range 1 to 40 K e V, detecting the intensity of a portion of the backscattered X-ray radiation in the range 12-14 K e V and processing the detected intensities to give a corrected value for the concentration of ash in the material.
The invention also provides an improved X-ray spectrometer which comprises a source of X-rays of energy in the range 1 to 40 K e V, means for irradiating a sample of solid carbonaceous material, means for detecting the intensity of X-ray fluorescence spectra for at least the elements aluminium, calcium, silicon and iron and means for detecting the intensity of a portion of the backscattered X-ray radiation in the range 12-14 K e V from the material sample. Suitably, the spectrometerwill include, or will be connected to, processing means capable of processing the detected intensities to give a corrected value for the concentration of ash in the material. The corrected value may then be stored, displayed or transmitted by the processing means to enable the corrected value to be recorded.Preferably, the backscatter is measured using a non-dispersive detector channel operating in the 12-14 K e V band; it is not believed that this has previously been suggested for use in the field of the invention.
Preferably, the invention includes the analysis of one or more of chlorine, sulphur and phosphorus by the detection of X-ray fluorescence spectra, and suitably the processing means provides results giving concentrations calculated as weight percentages for all of the elements individually detected, together with ash. More preferably, the processing means corrects the concentration of sulphur detected by X-ray fluorescence by the inclusion of a term derived from the detected value of backscattered radiation, and may correct the concentration of all the other elements.
There are commercially available X-ray fluorescence spectrometers which may be simultaneous or sequential spectrometers, and it is preferred to use a spectrometer using an X-ray tube having a rhodium anode. Other anodes may be used, however, although for the analysis of material such as coal, chromium anodes are found to give relatively poor results for backscatter measurement and tungsten gives relatively poor results for the lighter elements such as silicon and aluminium.An especially preferred simultaneous spectrometer is marketed by Applied Research Laboratories of Luton, Bedfordshire, England, a division of Bausch and Lomb Inc., as the "CHEM-X" X-ray Quantometer, which can be easily modified from its standard function of X-ray fluoresence spectrometer by the replacement of one of the detection stations with a special monochromatorto measure the direct radiation emerging from one of the primary collimators. We have found that this modification gives improved counting statistics and a larger signal change per percent ash content change in the material sample, than a monochromator set to the Compton line.
The solid carbonaceous material to be analysed according to the invention is preferably coal or coke, which terms are intended to include low to high rank coals, cokes and chars. The invention may also be used for the analysis of other materials such as lignite or brown coal, peats, oil shales and solid products or by-products of the coal industry.
Processing of the data consisting of the count rates for the various elements detected and the backscatter may be done by micro- or mini-computer connected on line to the spectrometer; the spectometer may include such a computer, suitably connected to a printer or a display screen, built into the casing for the whole instrument, ion the computer may be mounted separately. The processing of the results may be done in a number of different ways each capable of giving a reproducible corrected answer for ash concentration by the inclusion of terms derived from the count rates for, or computed concentration of, the elements calcium, silicon, aluminium and iron.In all cases, what is used is an equation which gives an approximation of ash concentration based on the summation of terms from the above-named elements and a correction from the backscatter, and may take the form, for example, of C(ash) = Ao + log8I(ash)+ Z K, C, 1-n where C(ash) is the computed concentration of ash Ao is a constant, for example 29.6128 Al is a constant, for example -3.1859 I(ash) is the average number of counts for backscatter over the test period K's are constants, for example KAl = 1.31, Ksi = 2.53, KCa = 3.42 and KFe = 1.02, and C's are the concentrations of individual elements Si, Ca, Fe and Al.
The constants are derived from comparison with the results of classic chemical analysis for a test groups of coals and the value of the "K" constants given above were derived from a group of coals from the National Coal Board's East Midlands region and ought to be the same for each spectrometer of the same type, whereas the "A" constant will vary according to the individual instrument used.
An alternative approach is to obtain a linear regression equation by using a program in which the laboratory results by chemical analysis are systematically regressed against variables such as detected counts, cross-products of detected counts and count inverses, adding or removing variables until a high correlation coefficient is achieved (that is, greater than 0.98). Such an approach for any element takes into account the presence of the many other components of the sample, which may absorb or emit fluorescence of the detected wavelength. Higher accuracy may be achieved by including more variables, for example, weight percentages of moisture or volatiles, but these were avoided in the interests of maintaining simplicity. As regards ash, a regression equation was evolved using this technique, in which the term
1 lHkscatter) was highly significant.
These approaches necessitate initially at least the comparison of large numbers of analyses by both X-rays and by conventional chemical methods; and the larger the number of samples used, the better the equations finally derived. It must be realised, however, that this is dependent upon the accuracy of the chemical analyses.
Thus a suitable statistical model is the following "intensity model" E1 A + BijI + IiCij Ii where Ej = concentration of element; Aj, Bij, C are constants li = Intensity of channel j (or in the case of backscatter loge Intensity or
liN/muensity) Preferably, material samples from a given geographical area are used, with the result that a processing program can be derived which gives consistently good results for any material of the same overall type originating within that area. It is also possible to cover a whole country in this way, providing that the number of accurately analysed samples is sufficient, but users may then have to accept a slightly slower overall standard of accuracy.
Another form of correction equation for ash (and for any element which requires correction) is described by Rasberry and Heinrich (Analytical Chemistry, Vol.46 No. 1 Jan 1974). This "concentration model" required linear regressions and also a matrix inversion. It offers the possibility of reduced standard deviations of errors compared to the intensity model, but the equations reached by full matrix inversion are complex, with many terms and they require more complete information on the coal analysis in certain cases.
The matrix inversion may alternatively be performed implicitly by the iterative solution of simultaneous equations. The above intensity model would provide a suitable first approximation to use in this process.
The swiftness and ease of analyses according to the invention is striking in comparison with conventional chemical analysis which take many hours processing time, not all of which involve human intervention, however. After preparation of a sample (also necessary in classic analysis), it is loaded into the instrument of the invention, where it is irradiated for a predetermined time, for example 100 seconds; within two minutes, therefore, the analysis, including the calculated corrected value for ash, is displayed or printed out.
A "CHEM-X" apparatus, modified by the inclusion of a backscatter detector as described above, was used to analyse for the elements Si, Al, Ca, Fe, P, S and Cl and to estimate ash, in ground coal samples from low and high ash coals from seven different collieries within the National Coal Board's East Midlands region.
Each sample was crushed to -72 mesh B.S.S. and compressed into pellets in aluminium sample cups. No grinding was employed, and care was taken to ensure the oversize was less than 1%. The spectrometer used an X-ray tube with rhodium anode operated at 40 K eV, and counts were taken for all the parameters simultaneously over a 100 second count time. A DEC microcomputer processed the results to give an estimated ash content for each sample, as shown in Table I below, using an equation of the form first shown above.
TABLE I ASH % Method of Sample Pyrolysis Invention Difference Error CN1 4.25000 4.16213 -0.08787 2.0676X CN3 4.20000 4.25288 0.05288 1.2589H CN6 4.25000 4.07961 -0.17039 4.0092iS CN7 4.25000 4.22956 -0.02043 0.4808X CN8 4.44000 4.47159 0.03159 0.71143 CN9 4.06000 3.98146 -0.07854 1.93460 CN12 5.29000 5.21593 -0.07407 1.40018 CN14 3.94000 3.70910 -0.23090 5.86030 CN16 4.26000 4.22965 -0.03035 0.71239 CN19 5.31000 5.19410 -0.11590 2.18265 TL1 3.80000 3.80119 0.00119 0.03120 TL2 3.23000 3.13289 -0.09711 3.00663 TL4 3.36000 3.37569 0.01569 0.46690 TL5 2.94000 2.83819 -0.10181 3.46291 TL7 3.55000 3.53677 -0.01323 0.37276 TL13 3.54000 3.70500 0.16500 4.66111 TL14 3.59000 3.66748 0.07748 2.15813 TL15 3.16000 3.08705 -0.07295 2.30847 TL18 3.75000 3.83755 0.08755 2.33463 TL20 4.06000 4.04477 -0.01523 0.37520 ON1 7.79000 7.87797 0.08797 1.12925 ON2 9.33000 9.38669 0.05669 0.60757 ON3 9.71000 9.72490 0.01490 0.15347 ON4 10.54000 10.61010 0.07010 0.66511 ON6 8.94000 8.86647 -0.07353 0.82246 ON7 9.91000 10.09284 0.18284 1.84501 ON8 10.78000 10.81767 0.03767 0.34948 ON9 10.00000 10.12233 0.12233 1.22332 ON10 10.86000 10.97412 0.11411 1.05078 ON11 8.15000 8.12300 -0.02700 0.33133 ON12 8.37000 8.38133 0.01133 0.13536 ON13 8.64000 8.70288 0.06288 0.72775 ON14 8.04000 8.09622 0.05622 0.69929 ON15 8.82000 8.80811 -0.01189 0.13478 ON16 9.85000 9.88717 0.03717 0.37734 ON17 7.36000 7.22220 -0.13780 1.87229 TABLE 1 continued Method of Sample Pyrolysis Invention Difference Error ON18 7.95000 7.97083 '0.02083 -0.26197 ON19 8.31000 8.46190 0.15190 1.82797 ON20 8.91000 8.94666 0.03666 0.41140 WP1 12.66000 12.89166 0.23166 1.82985 WP3 10.97000 11.04523 0.07523 0.68579 WP2 12.10000 12.08719 -0.01281 0.10590 WP4 11.85000 11.93208 0.08208 0.69263 WP5 9.67000 9.83193 0.16193 1.67453 WP6 10.95000 11.06301 0.1130 1.03201 WP7 11.66000 11.71652 0.05652 0.48470 WP8 10.56000 10.68634 0.12634 1.19636 WP9 10.98000 11.09074 0.11074 1.00856 WP10 8.58000 8.60272 0.02272 0.26483 WP11 11.61000 11.66686 0.05686 0.48971 WP12 9.56000 9.45984 -0.10016 1.04768 WP13 9.88000 9.83376 -0.04624 0.46805 WP14 11.33000 11.05131 -0.27869 2.45979 WP15 12.09000 11.92961 -0.16040 1.32668 WP16 12.86000 12.51565 -0.34435 2.67768 WP17 11.21000 11.06559 -0.14441 1.28824 WP18 9.44000 9.50991 0.06991 0.74060 WP19 11.15000 11.08118 -0.06882 0.61724 WP20 11.47000 11.82939 0.35939 3.13327 CV2 18.43000 18.22693 -0.20307 1.10184 CV3 20.12000 20.10522 -0.01478 0.07347 CV4 18.11000 18.13720 0.02720 0.15021 CV5 18.54000 18.27867 -0.26133 1.40954 CV7 17.79000 18.01865 0.22864 1.28524 CV8 18.58000 18.66920 0.08920 0.48010 CV9 20.33000 20.36668 0.03667 0.18039 CV12 17.34000 17.52041 0.18041 1.04042 TY1 16.44000 16.51678 0.07677 0.46699 TY2 16.57000 16.42290 -0.14711 0.88779 TY3 17.56000 17.67002 0.11002 0.62654 TY4 17.15000 16.95983 -0.19017 1.10889 TY5 17.39000 17.30476 -0.08525 0.49020 TY6 17.68000 17.42343 -0.25657 1.45121 TY7 17.88000 16.62100 -0.25900 1.44857 TY8 18.10000 18.27307 0.17307 0.95616 TY9 19.45000 19.58851 0.13851 0.71212 TY10 18.04000 18.00959 -0.03041 0.16858 TY11 15.03000 15.22179 0.19178 1.27601 PL1 14.34000 14.39103 0.05103 0.35583 PL2 16.63000 16.56136 -0.06864 0.41277 PL3 19.37000 19.29269 -0.07732 0.39915 PL4 16.21000 16.15876 -0.05124 0.31613 PL5 19.10000 18.74281 -0.35719 1.87010 PL6 21.25000 20.99755 -0.25245 1.18800 PL7 14.37000 14.34840 -0.02160 0.15034 PL8 17.24000 17.47935 0.23934 1.38829 PL9 15.34000 15.40437 0.06437 0.41961 PL16 18.92000 19.14256 0.22256 1.17632 Standard error of estimate = 0.13997 Low ash and high ash groups of samples.
The same apparatus was used in another series of tests in which correction equations prepared by linear regression based on 122 sample coals were applied to all the elements analysed for as well as ash, and compared to results using the same apparatus but taking direct conversion of count rates to concentrations without any correction. The results are summarised in Table 2 below, from which it can be seen that a statistically significant improvement is achieved for individual elements (silicon and aluminium show the least improvement because of the accuracy of analysis by X-ray fluoresdcence) and the improvement for ash is extremely noteworthy. Ash was calculated in known manner from the backscatter readings alone in the uncorrected results.
TABLE 2 Comparison of CHEM-X Uncorrected and Corrected Values CHEM-X CHEM-X Uncorrected Corrected Analyte Range % C/C S.D. C/C S.D Ash 2.9-21.7 0.87 2.810 0.999 0.306 Sulphur 0.6-2.4 0.87 0.251 0.996 0.045 Chlorine 0.3-0.6 0.96 0.021 0.995 0.018 Phosphorus 0.002-0.034 0.96 0.002 0.990 0.001 Silicon 0.42 - 5.25 0.99 0.277 0.997 0.111 Aluminium 0.39-3.59 0.98 0.167 0.997 0.074 Calcium 0.09 - 0.61 0.87 0.060 0.982 0.023 Iron 0.37-1.75 0.86 0.181 0.994 0.034 C/C = Correlation coefficient, S.D. - error around the coefficient line (percentage) = Standard Deviation

Claims (13)

1. A method for analysing solid carbonaceous material containing ash, which comprises detecting the intensity of X-ray fluorescence spectra for at least the elements aluminium, calcium, silicon and iron, emitted by the material when bombarded with X-rays of energy in the range 1 to 40 KeV, detecting the intensity of a portion of the backscattered X-ray radiation in the range 12-14 KeV and processing the detected intensities to give a corrected value for the concentration of ash in the material.
2. A method according to claim 1, wherein the carbonaceous material is coal or coke.
3. A method according to claim 1 or 2, wherein the intensity of X-ray fluorescence spectra for one or more of chlorine, sulphur and phosphorus are also detected.
4. A method according to claim 1,2 or 3, wherein the detected intensity of any one or more of the elements is processed to give a corrected value for the concentration of that element in the material.
5. A method according to any one of claims 1 to 4, wherein the ash is determined by processing the detected intensities according to the equations.
C(ash) = Ao + Al loge l(ash) + E: Kn Cn 1-n where C(ash) is the computed concentration of ash Ao is a constant Al is a constant l(ash) is the average number of counts for backscatter over the test period K's are constants, and C's are the concentrations of the individual elements Si, Ca, Fe and Al.
6. A method according to any one of claims 1 to 4, wherein the concentration of an individual element, or ash, is determined by processing the detected intensities according to the equation.
Ej = A1 + BijI + IiQ Ii where Ej = computed concentration of the individual element or ash Aj,Bij, Cij are constants Ij = Intensity of channel j or, where the channel measures backscatter, loge Intensity of
1/ < lntensity.
7. A method according to claim 1, substantially as hereinbefore described.
8. An improved X-ray spectrometer for the analysis of solid carbonaceous material containing ash, which comprises a course of energy in the range 1 to 40 KeV, means for irradiating a sample of the material, means for detecting the intensity of X-ray fluorescence spectra for at least the elements aluminium, calcium, silicon and iron and means for detecting the intensity of a portion of the backscattered X-ray radiation in the range 12-14 KeV from the material sample.
9. A spectrometer according to claim 8, including, or connected to, processing means capable of processing the detected intensities to give a corrected value for the concentration of ash in the material.
10. A spectrometer according to claim 8 to 9, wherein the backscatter intensity is measured using a non-dispersive detector channel operating in the 12-14 KeV band.
11. A spectrometer according to any of claims 8 to 10, wherein the X-ray source is an X-ray tube having a rhodium anode.
12. A spectrometer according to any one of claims 8 to 11, which is a simultaneous spectrometer.
13. A spectrometer according to claim 8, substantially as hereinbefore described.
GB8205674A 1982-02-26 1982-02-26 Coal analysis using x-rays Withdrawn GB2116698A (en)

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Application Number Priority Date Filing Date Title
GB8205674A GB2116698A (en) 1982-02-26 1982-02-26 Coal analysis using x-rays
DE19833306464 DE3306464A1 (en) 1982-02-26 1983-02-24 METHOD AND DEVICE FOR ANALYZING SOLID CARBONATED MATERIAL WITH ASH CONTENT, IN PARTICULAR COAL
FR8303170A FR2522412A1 (en) 1982-02-26 1983-02-25 METHOD AND APPARATUS FOR ANALYZING CARBON MATERIALS CONTAINING ASH BY X-RAY SPECTROMETRY

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CN104089967A (en) * 2014-07-15 2014-10-08 南京市产品质量监督检验院 Quick measurement method for aluminum, calcium or silicon content of solid plane material product
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WO1984004594A1 (en) * 1983-05-12 1984-11-22 Broken Hill Pty Co Ltd Characterizing and handling multi-component substances
GB2152713A (en) * 1983-05-12 1985-08-07 Broken Hill Pty Co Ltd Characterizing and handling multi-component substances
GB2223574A (en) * 1988-08-24 1990-04-11 Denver Process Equipment Limit Radiometric analysis
ES2114490A1 (en) * 1996-05-07 1998-05-16 Acerinox Sa Method for the quantitative X-ray microanalysis of metal alloys based on a set of standard samples of the alloy and a mathematical adjustment model.
CN104089967A (en) * 2014-07-15 2014-10-08 南京市产品质量监督检验院 Quick measurement method for aluminum, calcium or silicon content of solid plane material product
CN104089967B (en) * 2014-07-15 2017-04-19 南京市产品质量监督检验院 Quick measurement method for aluminum, calcium or silicon content of solid plane material product
EP3726202A1 (en) * 2019-04-15 2020-10-21 L'air Liquide, Société Anonyme Pour L'Étude Et L'exploitation Des Procédés Georges Claude Method for on-line control of a slag forming gasification process and installation for a gasification process
US11499105B2 (en) 2019-04-15 2022-11-15 L'air Liquide, Societe Anonyme Pour L'etude Et L'exploitation Des Procedes Georges Claude Method of online control of a slag forming gasification process and plant for a gasification process
CN111239172A (en) * 2020-02-24 2020-06-05 河北龙凤山铸业有限公司 Method for determining phosphorus content in coal
CN113960092A (en) * 2021-11-10 2022-01-21 天津海关化矿金属材料检测中心 Method for rapidly detecting ash content of coal

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