CN117589809A - Method for predicting coke cold state strength based on nuclear magnetic structure parameters - Google Patents

Method for predicting coke cold state strength based on nuclear magnetic structure parameters Download PDF

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CN117589809A
CN117589809A CN202311530763.2A CN202311530763A CN117589809A CN 117589809 A CN117589809 A CN 117589809A CN 202311530763 A CN202311530763 A CN 202311530763A CN 117589809 A CN117589809 A CN 117589809A
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coke
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daf
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刘丹丹
申岩峰
王美君
岳伟明
燕慧
王雷雷
邓韶博
杨伯威
周文艳
侯晓瑞
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SHANXI COKING CO Ltd
Taiyuan University of Technology
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SHANXI COKING CO Ltd
Taiyuan University of Technology
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    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N24/00Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
    • G01N24/08Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects by using nuclear magnetic resonance
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Abstract

The invention relates to a method for predicting coke cold state strength based on nuclear magnetic structure parameters, which constructs volatile component V of raw coal daf Predicted value of the ratio of aliphatic carbon to aromatic carbon (f) al /f ar ) Prediction Empirical formula (f) al /f ar ) Prediction =0.0129V daf 0.0683 obtaining the predicted value of the aliphatic carbon/aromatic carbon ratio of the raw material coal, and combining the ash content, sulfur content, bonding index and colloid layer index of the raw material coal according to the formula M 40 =2.67A d +24.38(f al /f ar ) Prediction +16.04S t,d +0.29G‑1.43Y‑0.43X+46.80,M 10 =‑0.56A d +3.20(f al /f ar ) Prediction ‑2.74S t,d -0.36G+0.40Y-0.05X+40.04 calculation of cold strength of coke obtained by predicting coking of raw material coal. Compared with the coking results of a small-scale coke oven and a large-scale coke oven, the prediction method has high accuracy and strong coal applicability, and can not generate larger due to the change of the coal types, the coal blending scheme and the properties of the coke ovensWave motion.

Description

Method for predicting coke cold state strength based on nuclear magnetic structure parameters
Technical Field
The invention belongs to the technical field of coal blending and coking in the coking industry, relates to a method for predicting coke quality in coal blending and coking production, and in particular relates to a method for predicting coke cold strength.
Background
Coke plays a vital role in blast furnace smelting, and the quality of the coke affects various technical and economic indexes of the blast furnace. Although part of the action of coke is replaced with the development of the blast furnace oxygen-enriched coal injection technology, the coke ratio is reduced, but the framework supporting action of the coke is still not replaced.
The residence time of the coke in the blast furnace skeleton area is prolonged, the load is increased, and the time of the coke in the blast furnace, which is corroded by oxidation reaction, alkali metal and slag and molten iron, is longer, so that the development of iron and steel enterprises has more strict requirements on the quality of the coke.
At present, most of coking enterprises rely on expert experience for selecting a coal blending scheme, and the coal blending scheme is determined through a coke oven test, so that the whole process is time-consuming and labor-consuming, the prediction result is often deviated from actual production, and the method has little guiding significance on the actual production.
On the other hand, various models such as linear regression, support vector machines, neural networks and the like for predicting coke quality are also established at present.
For example Cai Chengwang et al (Coke quality prediction model study based on Linear regression [ J]Modern chemical research 2023 (1): 1-4.) dry base ash in coal blend index was selectedContent (A) m,d ) Volatile content of dry ashless base (V) daf ) The bond index (G), the air-dried base fixed carbon content (FC) ad ) Sulfur content of dry radical (S) m,t,d ) The gum layer indices (X and Y) establish a linear regression-based coke quality prediction model. However, the data source of the model is only limited to the data of the same production period of the coking plant, and the model is not suitable for other coal blending schemes due to the complexity of coal types and the huge difference of coking coal resources.
Lijiang et al (Coke quality prediction based on coal quality comprehensive index J]Clean coal technology, 2021, 27 (S02): 175-180.) the dry base volatile content (a) of the blended coal is selected d ) The fineness, the cohesiveness index (G), the Oya expansion degree (b) and the colloid layer index (X and Y) are taken as basic indexes, and the dry base volatile content (A) of the blended coal is selected d ) Fineness, bond index (G), osub-expansion (b), gum layer index (X and Y), vitrinite maximum reflectance (R) max ) The active component and the inert component are comprehensive indexes, and two algorithms of K-nearest neighbor (KNN) and a support vector machine are adopted to predict coke quality. However, the volatile content in the input index of the model is limited to 19.52% -22.40%, and after the volatile content exceeds the range, the prediction accuracy is reduced, and the application range of the model is smaller due to larger input data limitation.
One common problem of the existing coke quality prediction model is that most of input indexes are selected from macro coal quality indexes of coal, however, due to the complexity of coal quality composition, even different batches of coal samples extracted from the same mine point have certain difference in indexes, and the coking coal production uses more coal types, so that the difference is larger, and the limitation of a plurality of models is larger. The reason for this is mainly because the average coal quality index cannot accurately reflect the non-uniformity of the coal sample.
In summary, for the establishment of the coke quality prediction model, the characteristics of the coal blend must be accurately reflected in the selection of the model input index, and the coking process must be fully reflected and described from the nature thereof. The coking process of coal is essentially a series of chemical reactions of coal molecules that occur under the action of temperature, and all macroscopic properties of the coking process depend on the spatial structure of the coal sample. Therefore, from the structure of coal, the structural characteristic parameters influencing the coke quality in the coking process are searched, and the method is important for accurately and reasonably predicting the coke quality and improving the universality of a prediction model.
Disclosure of Invention
The invention aims to solve the defects of the existing coke quality prediction model and provides a method for predicting the cold state strength of coke based on nuclear magnetic structure parameters.
Fat carbon/aromatic carbon ratio f al /f ar Is a conventional nuclear magnetic structure parameter used for characterizing the molecular structure of coal. The invention takes the volatile matters of the raw material coal as a bridge, constructs the empirical relationship between the volatile matters of the raw material coal and the ratio of fatty carbon to aromatic carbon, and obtains the volatile matters V of the raw material coal through easy detection daf Calculating the content of the fat carbon/aromatic carbon ratio predictive value (f) al /f ar ) Prediction And fully considers the influence of other characteristic index factors of raw coal such as ash content, sulfur content, bonding index, colloid layer index and the like on the quality of coke in the coking process, and predicts the cold strength of the coke by using a predicted value of the ratio of aliphatic carbon to aromatic carbon, so that the prediction of the quality of the coke is more accurate, and the method has wide industrial application value.
Specifically, the method for predicting the cold state strength of the coke based on the nuclear magnetic structure parameter of the invention is to measure the parameters of the volatile component, ash content, sulfur content, bonding index, maximum thickness of a colloid layer and final shrinkage of raw material coal, and according to the volatile component V of the raw material coal daf Predicted value of the ratio of aliphatic carbon to aromatic carbon (f) al /f ar ) Prediction Empirical formula between:
(f al /f ar ) prediction =0.0129V daf -0.0683
Obtaining the predicted value (f) of the fat carbon/aromatic carbon ratio of the raw material coal al /f ar ) Prediction
Substitution formula:
M 40 =2.67A d +24.38(f al /f ar ) prediction +16.04S t,d +0.29G -1.43Y -0.43X +46.80
M 10 =-0.56A d +3.20(f al /f ar ) Prediction -2.74S t,d -0.36G +0.40Y -0.05X +40.04
Predicting the crushing strength M of coke obtained by coking with the raw coal 40 And abrasion resistance M 10
Wherein:
(f al /f ar ) prediction -a predicted value of the fat carbon/aromatic carbon ratio of the feed coal;
M 40 predictive value of crushing strength of coke obtained by coking raw coal,%;
M 10 -predicted values of the abrasion resistance of the coke obtained by coking the raw material coal,%;
V daf -drying of raw coal without ash-based volatiles,%;
A d -dry base ash,%;
S t,d dry base sulfur content of feed coal,%
G, the cohesiveness index of raw material coal;
y is the maximum thickness of the colloid layer of the raw material coal, and mm;
x-final shrinkage of raw coal, mm.
Wherein the raw material coal is various raw material coals which can be used for coking or coal blending coking, including various single coals suitable for coking and blended coals suitable for coking.
By adopting the method for predicting the cold strength of the coke based on the nuclear magnetic structure parameter, the cold strength of the coke obtained by coking with various raw material coals suitable for coking can be accurately predicted.
Preferably, however, when the raw coal is dried, there is no ash-based volatile component V daf 20 to 35 percent of dry base ash A d Less than or equal to 12 percent, and drying sulfur S t,d Less than or equal to 2%, the bonding index G is more than or equal to 72, the maximum thickness Y of the colloid layer is 12-25 mm, and when the final shrinkage degree X is 25-45 mm, the prediction result of the cold state strength of the coke is moreAnd (5) adding accuracy.
More preferably, when the raw coal is dry, ashless based volatile V daf 22 to 32 percent of dry base ash A d Less than or equal to 10 percent, and dry sulfur S t,d Less than or equal to 1%, the bonding index G is 72-82, the maximum thickness Y of the colloid layer is 12-16 mm, and when the final shrinkage degree X is 28-40 mm, the error between the predicted value and the actual measured value of the cold state strength of the coke is smaller, and the correlation is higher.
The invention analyzes and determines the volatile content, ash content, sulfur content, bonding index, maximum thickness of colloid layer and final shrinkage of raw material coal for blending coal coking with different coal grades, which are different in volatile content and nuclear magnetic structure parameter fat carbon/aromatic carbon ratio, and coal quality characteristics, and separately cokes each raw material coal to obtain cokes, and determines the crushing strength M of each coke 40 And abrasion resistance M 10 The method comprises the steps of carrying out a first treatment on the surface of the And (3) performing multiple linear regression on the acquired data by utilizing statistical analysis software, constructing an empirical formula of the relationship between the volatile component of the raw coal and the nuclear magnetic structure parameter, and between the nuclear magnetic structure parameter, ash content, sulfur content, bonding index, maximum thickness of a colloid layer, final shrinkage, and the crushing strength and wear resistance of the coke, and establishing a coke cold state strength prediction formula and method.
According to the invention, through introducing the nuclear magnetic structure parameter of the coal with the fat carbon/aromatic carbon ratio, the influence of microstructures of different coal types on the coke quality is considered, and various factors influencing the coke cold state strength in the coal blending coking process are fully considered, so that a formula and a method for predicting the coke cold state strength with high accuracy and strong universality are established, the defect that the microstructure does not consider the influence of the microstructure on the coke quality is perfected by a general prediction empirical formula, various factors influencing the coke quality are more comprehensively and reasonably considered, the prediction on the coke quality and the optimization on a coal blending scheme are accurately and effectively realized, the time cost and the economic cost of coal blending coking are saved, and the cost reduction and synergy of coking enterprises are realized.
The invention combines the coal blending ratio adopted in the actual coking production process of a coking plant to carry out a small-scale coke oven test and a large-scale coke oven test, compares the actual crushing strength and wear resistance of the coke with the actual crushing strength and wear resistance of the coke predicted by using the coal quality analysis data and the nuclear magnetic structure parameters, and proves that the prediction method established by the invention has high prediction precision and strong applicability to coal types, and does not generate larger fluctuation due to the change of the coal types, the coal blending scheme and the coke oven properties.
The coke cold state strength prediction method considers various factors influencing coke quality in the coking process, takes the ratio of aliphatic carbon to aromatic carbon as one of input variables of influencing factors, ensures that a prediction result is more scientific and accurate, saves manpower and material resources of coking production, and reduces the production cost of coking enterprises.
Description of the embodiments
The following describes the present invention in further detail with reference to examples. The following examples are presented only to more clearly illustrate the technical aspects of the present invention so that those skilled in the art can better understand and utilize the present invention without limiting the scope of the present invention.
The production process, the experimental method or the detection method related to the embodiment of the invention are all conventional methods in the prior art unless otherwise specified, and the names and/or the abbreviations thereof are all conventional names in the field, so that the related application fields are very clear and definite, and a person skilled in the art can understand the conventional process steps according to the names and apply corresponding equipment to implement according to conventional conditions or conditions suggested by manufacturers.
The various instruments, equipment, materials or reagents used in the examples of the present invention are not particularly limited in source, and may be conventional products commercially available through regular commercial routes or may be prepared according to conventional methods well known to those skilled in the art.
The coke cold state strength prediction method in the following embodiment of the invention specifically comprises the following steps:
volatile component V of single coal or blended coal is measured according to GB/T30732-2014 Industrial analysis method of coal daf And ash A d The content is as follows;
sulfur content S of single coal or mixed coal is measured according to GB/T31391-2015 "elemental analysis of coal t,d The content is as follows;
the bond index G and the maximum thickness Y of the gum layer and the final shrinkage X of the individual coals or blended coals were measured according to GB/T5447-2014 and GB/T479-2016, respectively.
The measured volatile components V of single coal or blended coal daf The content is brought into an empirical formula:
(f al /f ar ) prediction =0.0129V daf -0.0683
Calculating to obtain the predicted value (f) of the fatty carbon/aromatic carbon ratio of the single coal or the blended coal al /f ar ) Prediction
And then the obtained predicted value and the ash content A of the single coal or the blended coal are measured d Content of sulfur S t,d The content, the bonding index G, the maximum thickness Y of the colloid layer and the final shrinkage X are substituted into the formula:
M 40 =2.67A d +24.38(f al /f ar ) prediction +16.04S t,d +0.29G -1.43Y -0.43X +46.80
M 10 =-0.56A d +3.20(f al /f ar ) Prediction -2.74S t,d -0.36G +0.40Y -0.05X +40.04
Predicting the crushing strength M of the coke obtained by coking with the single coal or the blended coal 40 And abrasion resistance M 10
Examples
Example 1
6 kinds of single coal used in the actual coal blending scheme of the coking plant are selected, wherein the lean coal 1 is from Shanxi province, and the volatile component content (V daf ) 15.64%, bond index 11; coking coal 1 was from the Shandong Zaozhuang area and had volatile content (V daf ) 17.97%, bond index 80; fat coal 1 was obtained from Shanxi Lv Liang Zhou, volatile content (V daf ) 30.37% bond index 99;1/3 coking coal comes from the area of Shanxi Fen, volatile content (V daf ) 33.37%, bond index 85; the gas coal 1 was obtained from the region of mountain-western Xin, volatile content (V daf )33.88, bond index 66; the medium caking coal is from Shanxi area and has volatile content (V daf ) 38.51% and bond index 25.
Using a model Bruker Avance III MHz 600 13 C CP/MAS/TOSS NMR is used for detecting nuclear magnetic resonance carbon spectrograms of various single coals, obtaining carbon skeleton information of the single coals, and calculating fat carbon/aromatic carbon ratio f of different single coals al /f ar
And decomposing the nuclear magnetic spectrum of the single coal into 16 different types of carbon, and performing peak-splitting fitting to obtain parameters of different carbon structures in the coal. Wherein:
fat carbon content (f) al ) The calculation formula of (2) is as follows:
f al =f al 1 +f al a +f al 2 +f al 3 +f al 4 +f al 5 +f al O1 +f al O2
aromatic carbon content (f) ar ) The calculation formula of (2) is as follows:
f ar =f ar O1 +f ar O2 +f ar H +f ar B +f ar S +f ar O3
wherein: f (f) al 1 Is aliphatic methyl carbon content; f (f) al a Is aromatic methyl carbon content; f (f) al 2 Is aliphatic C (2) carbon content; f (f) al 3 Is methylene carbon content; f (f) al 4 Is the methine carbon content; f (f) al 5 Is quaternary carbon content; f (f) al O1 Is the content of oxymethylene carbon; f (f) al O2 Is the content of oxygen methoxy carbon; f (f) ar O1 Is the n-oxo aromatic protonated carbon content; f (f) ar O2 Is the content of normal oxygen aromatic branched carbon; f (f) ar H Is aromatic protonated carbon content; f (f) ar B Is the carbon content of the aromatic bridgehead; f (f) ar S Is the alkylated aromatic carbon content; f (f) ar O3 Is phenol and phenol ether carbon content.
The remaining two parameters f a C1 And f a C2 The hydroxyl carbon content and the carbonyl carbon content, respectively, do not participate in the calculation of the aliphatic carbon content and the aromatic carbon content, and are not described in detail herein.
By passing through 13 The type of primary carbon-containing chemical bonds of each of the above individual coals obtained by peak-fitting of the C NMR spectrum are shown in table 1.
The fat carbon/aromatic carbon ratio f of each individual coal was calculated from the above formula based on the carbon contents of each type obtained in Table 1 al /f ar . The volatile component V of each single coal measured according to GB/T30732-2014 'Industrial analysis method of coal' instrument method daf Is carried into an empirical formula of the invention to calculate the predicted value (f) of the fatty carbon/aromatic carbon ratio of each single coal al /f ar ) Prediction . The specific results are compared in table 2.
As can be seen from the data in Table 2, in the nuclear magnetic resonance measurement-related data of each individual coal, the difference between the predicted value and the measured value of the aliphatic carbon/aromatic carbon ratio was about.+ -. 0.05.
Examples 2 to 6
5 coal blending schemes used in actual production of a coking plant are selected, 40kg small coke oven coking experiments are respectively carried out, and the specific coal blending schemes are listed in table 3.
In addition to the 5 individual coals listed in example 1, lean coal 2 was from shanxi chang zhi region, volatile content (V daf ) 16.78%, bond index 52; coking coal 2 is from shanxi luliang region and has volatile content (V daf ) 20.69%, bond index 82; coking coal 3 is obtained from the mountain-and-western-style in the advanced region, and has volatile component content (V daf ) 22.47%, bond index 79; fat coal 2 is obtained from the mountain and the mountain in the middle of the jin, and the volatile content (V daf ) 32.04%, bond index 91; the gas coal 2 comes from the Shanxi area of the Fenton area, and the volatile content (V daf ) 36.83% and a bond index of 75.
The mass of coal charged into the furnace for each coking test was 44.4kg, the moisture mass ratio was 10%, and the bulk density was 0.75t/m 3 And (3) charging into a furnace for conventional coking, wherein the temperature of the charged coal is 800 ℃, the temperature of the center of a coke cake is 900 ℃, and the coking time is 17.5 hours.
According to GB/T2006-2008 'determination method of mechanical Strength of Coke', the crushing Strength M of Coke obtained by coking of 5 coal blending schemes and coal is tested 40 And abrasion resistance M 10 Actual measurements and specific results are shown in Table 4.
The volatile content, ash content, sulfur content, bonding index, maximum thickness of colloid layer and final shrinkage degree of the blended coal are measured, and the crushing strength M corresponding to each coke is calculated and predicted according to the coke cold state strength prediction model provided by the invention 40 And abrasion resistance M 10 The predicted values of (2) are also shown in Table 4.
Also, by using the above-measured index data of the characteristics of the blended coal according to the present invention, the crushing strength M of the coke is predicted under the condition that the input data is unchanged, referring to a coke quality linear regression prediction model provided by a coke quality prediction method, system, equipment and medium of CN 116228009A, a Hua Hui computing technology (Shanghai Co., ltd 40 And abrasion resistance M 10 The predicted values are also shown in Table 4 for comparison.
As can be seen from Table 4, the coke crushing strength M obtained by the process of the present invention 40 And abrasion resistance M 10 The error values of the predicted value and the measured value of the 40kg coke oven test are about +/-1.5% and +/-0.5%, which are obviously smaller than the error of the literature method, and are probably due to the inventionCompared with the direct use of volatile matters as input variables, the fatty carbon/aromatic carbon ratio predicted value provided by the bright prediction method can reflect the characteristics of the blended coal more accurately.
Examples 7 to 11
5 coal blending schemes used in actual production of a coking plant are selected, 300kg coke oven coking experiments are respectively carried out, and the specific coal blending schemes are listed in table 5.
The coal charge mass for each coking test was 370kg, with a moisture mass ratio of 10% at a bulk density of 0.75t/m 3 And (3) charging into a furnace for conventional coking, wherein the temperature of charging coal is 770 ℃, the temperature of a coke cake center is 1050 ℃, and the coking time is 20h. Testing the crushing strength M of cokes obtained by coking 40 And abrasion resistance M 10 Actual values, specific results are listed in table 6.
The predicted values of crushing strength and abrasion resistance and the predicted values of literature for each coke were obtained in the same manner as in examples 2 to 6, and are shown in Table 6 together for comparison.
The results in Table 6 prove that the coke cold state strength prediction model of the invention also ensures higher accuracy and universality and has smaller prediction error from a 40kg small-scale coke oven test to a 300kg coke oven test.
Examples 12 to 16
In order to further verify the application of the coke cold strength prediction model provided by the invention in industry, the coke quality of 5 coal blending schemes used in the actual production of a 6m coke oven in a coking plant is adopted for prediction. The specific blending schemes are listed in table 7.
Wherein the lean coal is produced in Shanxi chang zhi district, and the volatile content (V daf ) 13.98% and a bond index of 15; the gas coal 3 is from the Yanan region of Shaanxi, and the volatile content (V daf ) 40.74% bond index 86.
Also give the coke crushing strength M 40 And abrasion resistance M 10 The results of the actual measurement of (c), the predicted value of the method of the present invention, and the predicted value of the literature are shown in Table 8.
As can be seen from the comparison data from the small-scale coke oven test to the large-scale coke oven test, the coke cold state intensity prediction model provided by the invention can ensure higher accuracy in the actual application process, has strong universality, and has small difference between the predicted coke cold state intensity and the actual coke cold state intensity. Therefore, the coke cold state strength prediction model provided by the invention can predict the coke quality in coking production, realize the optimization of a coal blending scheme and save the time cost and the economic cost of coal blending and coking.
The above embodiments of the invention are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Various changes, modifications, substitutions and alterations may be made by those skilled in the art without departing from the principles and spirit of the invention, and it is intended that the invention encompass all such changes, modifications and alterations as fall within the scope of the invention.

Claims (4)

1. The method for predicting the cold strength of the coke based on the nuclear magnetic structure parameters is characterized by measuring the parameters of the volatile component, ash content, sulfur content, bonding index, maximum thickness of a colloid layer and final shrinkage of raw material coal, and according to the volatile component V of the raw material coal daf Predicted value of the ratio of aliphatic carbon to aromatic carbon (f) al /f ar ) Prediction Empirical formula between:
(f al /f ar ) prediction =0.0129V daf -0.0683
Obtaining the predicted value (f) of the fat carbon/aromatic carbon ratio of the raw material coal al /f ar ) Prediction
Substitution formula:
M 40 =2.67A d +24.38(f al /f ar ) prediction +16.04S t,d +0.29G -1.43Y -0.43X +46.80
M 10 =-0.56A d +3.20(f al /f ar ) Prediction -2.74S t,d -0.36G +0.40Y -0.05X +40.04
Predicting the crushing strength M of coke obtained by coking with the raw coal 40 And abrasion resistance M 10
Wherein:
(f al /f ar ) prediction -a predicted value of the fat carbon/aromatic carbon ratio of the feed coal;
M 40 predictive value of crushing strength of coke obtained by coking raw coal,%;
M 10 -predicted values of the abrasion resistance of the coke obtained by coking the raw material coal,%;
V daf -drying of raw coal without ash-based volatiles,%;
A d -dry base ash,%;
S t,d dry base sulfur content of feed coal,%
G, the cohesiveness index of raw material coal;
y is the maximum thickness of the colloid layer of the raw material coal, and mm;
x-final shrinkage of raw coal, mm.
2. The method of predicting the cold strength of coke of claim 1, wherein the feed coal is a variety of feed coals useful in coking or coal blending coking.
3. The method for predicting cold strength of coke as claimed in claim 1, wherein the raw coal is dried with no ash-based volatile component V daf 20 to 35 percent of dry base ash A d Less than or equal to 12 percent, and drying sulfur S t,d Less than or equal to 2%, the bonding index G is more than or equal to 72, the maximum thickness Y of the colloid layer is 12-25 mm, and the final shrinkage degreeX is 25-45 mm.
4. The method for predicting cold strength of coke as claimed in claim 1, wherein the raw coal is dried with no ash-based volatile component V daf 22 to 32 percent of dry base ash A d Less than or equal to 10 percent, and dry sulfur S t,d Less than or equal to 1 percent, the bonding index G is 72 to 82, the maximum thickness Y of the colloid layer is 12 to 16mm, and the final shrinkage degree X is 28 to 40mm.
CN202311530763.2A 2023-11-16 2023-11-16 Method for predicting coke cold state strength based on nuclear magnetic structure parameters Pending CN117589809A (en)

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