CN102436537B - Size distribution-based dropped-coal gas discharge volume prediction method - Google Patents

Abstract

The invention discloses a size distribution-based dropped-coal gas discharge volume prediction method, which comprises the steps of: screening and leaking coal samples by using screens with different pore diameters, weighing mass of coal particles with various grain sizes, figuring out a ratio of the mass of the coal particles with various grain sizes to the total mass of the samples and distribution function numerical values corresponding to various grain sizes, and solving parameters of a distribution function by using a bisection method so as to construct a distribution function and a distribution density function of coal particle diameters; for the coal samples with the same grain size, testing corresponding residual gas contents by taking two different kinds of exposure time, determining one parameter in a gas desorption strength relation expression, taking different kinds of exposure time for coal samples with two kinds of grain sizes, determining the other parameter of the gas desorption strength relation expression so as to construct a relation expression of gas residual volume and the gas desorption strength in the coal samples; and finally, calculating the gas desorption volume caused by coal drop by using a double integral expression of unit time coal drop mass, coal particle diameter distribution density function and gas desorption strength to time and diameter, and using the gas desorption volume as the predicted gas discharge volume.

Description

A kind of coal breakage Forecast of Gas Emission method based on domain size distribution

Technical field

The invention belongs to technical field of mine safety, relate to a kind of Forecasting Methodology of gas emission, particularly a kind of Forecasting Methodology of the gas emission caused due to coal breakage.

Background technology

In coal mining process, being caving of coal cinder makes the gas of ADSORPTION STATE become free state, and this process is called desorb.The gas emission caused due to coal breakage accounts for the major part of the total outburst amount of gas, along with the increase of mining depth and mining rate, the coal breakage amount of unit interval and gas emission constantly increase, the gas emission that accurately predicting coal breakage causes, has important function for the design of ventilating system and Safety of Coal Mine Production.

At present, the Forecast of Gas Emission of the coal-face gas density that mainly relies on ventilating system to provide and air quantity are predicted.Such as, mine statistic law (statistical predicted method of mine gas) is that a kind of basis is to this mine or the statistical analysis being close to the actual Gas data of mine, draw the rule that mine gas emission rate changes with mining depth, predict the method for new well or new height gas emission; Point source predicted method (predicted method by different gas source) is divided into several gas source gushed out to mine according to the difference of when and where, on the basis of respectively these Gas sources being predicted, draw the method for mine gas emission rate.

These methods above, can not specify the ratio shared by each point of source gas emission on the one hand, can not determine the instantaneous value of gas emission on the other hand, do not have stronger specific aim simultaneously.

Summary of the invention

The object of this invention is to provide a kind of coal breakage Forecast of Gas Emission method based on domain size distribution, for mining area Design of Ventilation System and Gas Disaster control provide the foundation of science.

Coal breakage Forecast of Gas Emission method of the present invention utilizes the data of three aspects to predict coal breakage gas emission, one is distribution (density) function of particle diameter in coal breakage, two is relations of desorption of mash gas intensity and coal grain diameter, and three is coal breakage quality of unit interval; The coal breakage desorption of mash gas amount computing formula proposed is based on coal breakage domain size distribution, and in distribution function sample, the ratio of coal grain quality and sample gross mass that diameter is less than x is portrayed.

The process of the concrete Forecasting Methodology of the present invention is as follows.

1, coal grain diameter distribution density function is built

The first step: sampling

Take the coal sample of mass M=about 50kg in down-hole, notice that the distribution of particles of various particle diameter in sample conforms to actual as far as possible;

Second step: sieve and weigh

Utilize aperture to be respectively the sieve sieving coal sample of 25mm, 20mm, 15mm, 10mm, 8mm, 6mm, 5mm, 4mm, 3mm, 2mm, 1mm, 0.5mm and 0.2mm, and weigh up the quality of coal grain in each particle size interval;

3rd step: calculate particle size distribution function value

The measurement result of second step is filled up in table 1,

The various particle diameter quality of table 1 and account for the ratio of sample gross mass

Then particle size distribution function is calculated at x _ithe value of (i=0,14)={ 0,0.2,0.5,1,2,3,4,5,6,8,10,15,20,25 ,+∞ } each point, particle size distribution function it has following character:

$F\left(0\right)=0,F\left(x_i\right)=F\left(x_{i-1}\right)+\frac{\mathrm{\Δ}{M}_i}{M},F(+\∞)=1$

Result of calculation is inserted in table 2,

Table 2 particle size distribution function value

4th step: utilize dichotomy determination distributed constant λ

Think that coal particle size obeys χ ²(x, λ) distributes, and its distribution function F (x) is defined as particle diameter and is less than the coal grain quality of x and the ratio of sample gross mass, and namely particle size distribution function and distribution density function are respectively:

$\mathrm{\η}=F\left(x\right)=\frac{1}{2^{\frac{\mathrm{\λ}}{2}}\mathrm{\Γ}\left(\frac{\mathrm{\λ}}{2}\right)}\underset{0}{\overset{x}{\∫}}{\mathrm{\ξ}}^{\frac{\mathrm{\λ}}{2}-1}{e}^{-\frac{\mathrm{\ξ}}{2}}\mathrm{d\ξ}---\left(1\right)$

With

$f\left(x\right)=\frac{1}{2^{\frac{\mathrm{\λ}}{2}}\mathrm{\Γ}\left(\frac{\mathrm{\λ}}{2}\right)}{x}^{\frac{\mathrm{\λ}}{2}-1}{e}^{-\frac{x}{2}},(\mathrm{\λ}\≥1)---\left(2\right)$

Utilize dichotomy determination distributed constant λ, specific practice is as follows:

According to actual measurement, determine the interval [λ of coal grain average diameter X _left, λ _right] be [2,10], calculate functional:

$\mathrm{\Π}=\underset{i=0}{\overset{N}{\mathrm{\Σ}}}{[{\mathrm{\η}}_i-\frac{1}{2^{\frac{\mathrm{\λ}}{2}}\mathrm{\Γ}\left(\frac{\mathrm{\λ}}{2}\right)}\underset{0}{\overset{x_i}{\∫}}{\mathrm{\ξ}}^{\frac{\mathrm{\λ}}{2}-1}{e}^{-\frac{\mathrm{\ξ}}{2}}\mathrm{d\ξ}]}^2---\left(3\right)$

Correspond respectively to λ=λ _leftwith λ=λ _rightvalue:

${\mathrm{\Π}}_{\mathrm{left}}=\underset{i=0}{\overset{N}{\mathrm{\Σ}}}{[{\mathrm{\η}}_i-\frac{1}{2^{\frac{{\mathrm{\λ}}_{\mathrm{left}}}{2}}\mathrm{\Γ}\left(\frac{\mathrm{\λ}}{2}\right)}\underset{0}{\overset{x}{\∫}}{\mathrm{\ξ}}^{\frac{{\mathrm{\λ}}_{\mathrm{left}}}{2}-1}{e}^{-\frac{\mathrm{\ξ}}{2}}\mathrm{d\ξ}]}^2$

${\mathrm{\Π}}_{\mathrm{right}}=\underset{i=0}{\overset{N}{\mathrm{\Σ}}}{[{\mathrm{\η}}_i-\frac{1}{2^{\frac{{\mathrm{\λ}}_2}{2}}\mathrm{\Γ}\left(\frac{\mathrm{\λ}}{2}\right)}\underset{0}{\overset{x}{\∫}}{\mathrm{\ξ}}^{\frac{{\mathrm{\λ}}_{\mathrm{right}}}{2}-1}{e}^{-\frac{\mathrm{\ξ}}{2}}\mathrm{d\ξ}]}^2$

Get calculate functional Π and correspond to λ=λ ₁value Π ₁if, Π _right< Π _left, then λ is got _left=λ ₁, Π _left=Π ₁; If Π _left< Π _right, then λ is got _right=λ ₁, Π _right=Π ₁;

Get again calculate functional Π and correspond to λ=λ ₂value Π ₂if, Π _right< Π _left, then λ is got _left=λ ₂, Π _left=Π ₁; If Π _left< Π _right, then λ is got _right=λ ₂, Π _right=Π ₁;

Repeat above-mentioned steps, obtain an ordered series of numbers λ ₁, λ ₂..., λ _nif, then can think λ=λ _ncorresponding functional Π gets minimum of a value, by λ _nas the estimate of λ, so just obtain coal grain diameter distribution function F (x) and distribution density function f (x).

2, coal breakage desorption of mash gas intensity is measured

Average grain diameter is the residual gas content in the coal of x unit mass:

$W\left(t\right)=\frac{{\mathrm{\&alpha;x}}^{1/4}{W}_0}{{(t_0+t)}^{\mathrm{\&beta;}}}---\left(4\right)$

Wherein, W ₀for the original gas bearing capacity that average grain diameter is the coal of the unit mass of x; X is the diameter of coal cinder; T is coal breakage open-assembly time; α, β are the constant relevant with coal breakage geometry, Coal Characteristics parameter, t ₀being the constant with time dimension arranged to eliminate singularity, getting t ₀=1 (min), therefore, to be the desorption of mash gas intensity of the coal of the unit mass of x be average grain diameter:

$q^{*}(t,x)=-\frac{\&PartialD;W}{\&PartialD;t}=\frac{{\mathrm{\&alpha;\&beta;x}}^{1/4}{W}_0}{{(t_0+t)}^{1+\mathrm{\&beta;}}}---\left(5\right)$

Consider that coal is caving continuously, namely τ=0 has coal to be caving to τ=t, and the particle diameter be caving at moment τ is the desorption of mash gas amount of the coal of x unit, can construct, that is: based on formula (5)

$q(\mathrm{\&tau;},t,x)=\frac{\mathrm{\&alpha;\&beta;}{x}^{1/4}{W}_0}{{[t_0+(t-\mathrm{\&tau;})]}^{1+\mathrm{\&beta;}}}---\left(6\right)$

The first step: determine factor beta

For same particle size x ₀coal sample, get two different coal breakage open-assembly time t ₁and t ₂, measure gas remainder quantity W respectively ₁and W ₂, applying equation (4), has:

$W_1=\frac{\mathrm{\&alpha;}{x}_0^{1/4}{W}_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}---\left(7\right)$

With

$W_2=\frac{\mathrm{\&alpha;}{x}_0^{1/4}{W}_0}{{(t_0+t_2)}^{\mathrm{\&beta;}}}---\left(8\right)$

By formula (7) and formula (8), obtain:

$\mathrm{\&beta;}=\frac{\ln \frac{W_1}{W_2}}{\ln \frac{t_0+t_2}{t_0+t_1}}---\left(9\right)$

Second step: determine parameter alpha

X is respectively for particle diameter ₁and x ₂coal sample, measure coal breakage open-assembly time be t ₁gas remainder quantity with applying equation (4), has:

$W_1^{*}=\frac{{\mathrm{\&alpha;x}}_1^{1/4}{W}_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}---\left(10\right)$

With

$W_2^{*}=\frac{{\mathrm{\&alpha;x}}_2^{1/4}{W}_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}---\left(11\right)$

By formula (10) and formula (11), obtain:

$W_1^{*}-W_2^{*}=\mathrm{\&alpha;}\frac{W_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}(x_1^{1/4}-x_2^{1/4})---\left(12\right)$

Under the prerequisite determining parameter beta, parameter alpha can be determined by formula (12), that is:

$\mathrm{\&alpha;}=\frac{{(t_0+t_1)}^{\mathrm{\&beta;}}}{x_1^{1/4}-x_2^{1/4}}\frac{W_1^{*}-W_2^{*}}{W_0}---\left(13\right)$

3, the gas emission that coal breakage causes calculates and prediction

If the coal breakage quality of unit interval is M (t), desorption of mash gas total amount can be calculated:

$\begin{array}{c}Q=\underset{\mathrm{\&tau;}=0}{\overset{t}{\&Integral;}}\underset{r=0}{\overset{+\&infin;}{\&Integral;}}M\left(\mathrm{\&tau;}\right)q(\mathrm{\&tau;},t,x)f\left(x\right)\mathrm{dxd\&tau;}\\ =\underset{\mathrm{\&xi;}=0}{\overset{t}{\&Integral;}}\underset{r=0}{\overset{+\&infin;}{\&Integral;}}M\left(\mathrm{\&tau;}\right)\frac{1}{2^{\frac{\mathrm{\&lambda;}}{2}}\mathrm{\&Gamma;}\left(\frac{\mathrm{\&lambda;}}{2}\right)}{x}^{\frac{\mathrm{\&lambda;}}{2}-1}{e}^{-\frac{x}{2}}\frac{{\mathrm{\&alpha;\&beta;x}}^{1/4}{W}_0}{{[t_0+(t-\mathrm{\&tau;})]}^{1+\mathrm{\&beta;}}}\mathrm{dxd\&tau;}\end{array}---\left(14\right)$

The desorption of mash gas amount calculated using formula (14) is as the prediction of coal breakage gas emission.

In above-mentioned Forecasting Methodology, be to predict gas emission by the convolution of the desorption strength of the change curve of unit interval coal breakage amount, coal breakage domain size distribution and different-diameter particle.

Particularly, in above-mentioned Forecasting Methodology, utilize the parameter in dichotomy determination diameter distribution function, utilize the parameter of gas remainder quantity determination desorption strength.

Detailed description of the invention

Taking the coal sample of about 50kg in down-hole, is the sieve sieving coal sample of 25mm, 20mm, 15mm, 10mm, 8mm, 6mm, 5mm, 4mm, 3mm, 2mm, 1mm, 0.5mm and 0.2mm respectively with aperture, and weighs up the coal grain quality Δ M of various particle diameter respectively _i.

Calculate the coal grain quality of each particle diameter and the ratios delta η of sample gross mass _i(i=1,2 ..., 14), and result of calculation is inserted in table 3.

The various particle diameter quality of table 3 and account for the ratio of sample gross mass

Calculate particle size distribution function at x _ithe value η of (i=0,14)={ 0,0.2,0.5,1,2,3,4,5,6,8,10,15,20,25 ,+∞ } each point _i(0=1,2 ..., 14), η _i=η _i-1+ Δ η _i, result of calculation is filled out as in table 4.

Table 4 particle size distribution function value

Rule of thumb, the interval of distributed constant λ and coal grain average diameter is [2,10], that is, calculate functional:

$\mathrm{\&Pi;}=\underset{i=0}{\overset{N}{\mathrm{\&Sigma;}}}{[{\mathrm{\&eta;}}_i-\frac{1}{2^{\frac{\mathrm{\&lambda;}}{2}}\mathrm{\&Gamma;}\left(\frac{n}{2}\right)}\underset{0}{\overset{x_i}{\&Integral;}}{\mathrm{\&xi;}}^{\frac{\mathrm{\&lambda;}}{2}-1}{e}^{-\frac{\mathrm{\&xi;}}{2}}\mathrm{d\&xi;}]}^2$

Corresponding to λ _left=2, λ _rightthe value of=10, then utilize dichotomy to obtain and make functional Π get the distributed constant λ value of minimum of a value, computational process is in table 5.

Table 5 dichotomy solves the functional Π value of distributed constant λ and correspondence thereof

Because λ=7.329 are identical in computational accuracy with the functional Π value of λ=7.334 correspondence, and therefore both mean value desirable, namely 7.333 as the estimate of distributed constant λ.So distribution function is:

$F\left(x\right)=\frac{1}{2^{\frac{7.333}{2}}\mathrm{\&Gamma;}\left(\frac{7.333}{2}\right)}\underset{0}{\overset{x}{\&Integral;}}{\mathrm{\&xi;}}^{\frac{7.333}{2}-1}{e}^{-\frac{\mathrm{\&xi;}}{2}}\mathrm{d\&xi;}$

And distribution density function is:

$f\left(x\right)=\frac{1}{2^{\frac{7.333}{2}}\mathrm{\&Gamma;}\left(\frac{7.333}{2}\right)}{x}^{\frac{7.333}{2}-1}{e}^{-\frac{x}{2}}$

Be x for average grain diameter ₀the coal sample of=2mm, tests out coal breakage open-assembly time t ₁=20 (min) and t ₂the gas remainder quantity of=(min) is respectively W ₁=8.11 (t/m ³) and W ₂=3.94 (t/m ³), can factor beta be obtained, that is:

$\mathrm{\&beta;}=\frac{\ln \frac{W_1}{W_2}}{\ln \frac{t_0+t_2}{t_0+t_1}}=0.412$

Exposing gas bearing capacity in front coal seam is W ₀=15.2 (m ³/ t), x is respectively for particle diameter ₁=10 (mm) and x ₂the coal sample of=6 (mm), determining coal breakage open-assembly time is t ₁the gas remainder quantity of=60 (min) is respectively with under the prerequisite determining parameter beta, parameter alpha can be determined, that is:

$\mathrm{\&alpha;}=\frac{{(t_0+t_1)}^{\mathrm{\&beta;}}}{x_1^{1/4}-x_2^{1/4}}\frac{W_1^{*}-W_2^{*}}{W_0}=0.626$

The β value determined and α value are substituted into the relational expression of residual gas content and desorption of mash gas intensity, obtain respectively:

$W\left(t\right)=\frac{0.626x^{1/4}{W}_0}{{(t_0+t)}^{0.412}}$

With

$q(\mathrm{\&tau;},t,x)=\frac{{\mathrm{\&alpha;\&beta;x}}^{1/4}{W}_0}{{[t_0+(t-\mathrm{\&tau;})]}^{1+\mathrm{\&beta;}}}=\frac{0.258x^{1/4}{W}_0}{{[t_0+(t-\mathrm{\&tau;})]}^{1.412}}=\frac{3.925x^{1/4}}{{[t_0+(t-\mathrm{\&tau;})]}^{1.412}}$

The computing formula of the gas emission that coal breakage causes:

$Q=\underset{\mathrm{\&tau;}=0}{\overset{t}{\&Integral;}}\underset{r=0}{\overset{+\&infin;}{\&Integral;}}M\left(\mathrm{\&tau;}\right)q(\mathrm{\&tau;},t,x)f\left(x\right)\mathrm{dxd\&tau;}$

If the coal breakage quality of certain fully-mechanized mining working unit interval is:

$\begin{array}{c}M\left(t\right)=0.4(1+0.3\sin \frac{\mathrm{\&pi;t}}{3000})\\ =\underset{\mathrm{\&xi;}=0}{\overset{t}{\&Integral;}}\underset{x=0}{\overset{+\&infin;}{\&Integral;}}0.4(1+0.3\sin \frac{\mathrm{\&pi;\&tau;}}{3000})\frac{1}{2^{\frac{7.333}{2}}\mathrm{\&Gamma;}\left(\frac{7.333}{2}\right)}{x}^{\frac{7.333}{2}-1}{e}^{-\frac{x}{2}}\frac{3.925x^{1/4}}{{[t_0+(t-\mathrm{\&tau;})]}^{1.412}}\mathrm{dxd\&tau;}\end{array}$

Result of calculation is in table 6.

Table 6 gas emission

Claims (1)

1., based on a coal breakage Forecast of Gas Emission method for domain size distribution, predicted by following steps:

1) coal grain diameter distribution density function is built

Get the coal sample M of some, be the sieve sieving coal sample of 25mm, 20mm, 15mm, 10mm, 8mm, 6mm, 5mm, 4mm, 3mm, 2mm, 1mm, 0.5mm and 0.2mm respectively with aperture, and weigh up the quality Δ M of coal grain in each particle size interval _i;

Calculate the quality Δ M of coal grain in each particle size interval _iwith sample gross mass M than Δ η _i, and calculate particle size distribution function value η;

Think that coal particle size obeys χ ²(x, λ) distributes, and its distribution function F (x) is defined as particle diameter and is less than the coal grain quality of x and the ratio of sample gross mass, and namely particle size distribution function and distribution density function f (x) are respectively:

$\mathrm{\&eta;}=F\left(x\right)=\frac{1}{2^{\frac{\mathrm{\&lambda;}}{2}}\mathrm{\&Gamma;}\left(\frac{\mathrm{\&lambda;}}{2}\right)}\underset{0}{\overset{x}{\&Integral;}}{\mathrm{\&xi;}}^{\frac{\mathrm{\&lambda;}}{2}-1}{e}^{-\frac{\mathrm{\&xi;}}{2}}\mathrm{d\&xi;}---\left(1\right)$

With

$f\left(x\right)=\frac{1}{2^{\frac{\mathrm{\&lambda;}}{2}}\mathrm{\&Gamma;}\left(\frac{\mathrm{\&lambda;}}{2}\right)}{x}^{\frac{\mathrm{\&lambda;}}{2}-1}{e}^{-\frac{x}{2}},(\mathrm{\&lambda;}\&GreaterEqual;1)---\left(2\right)$

According to actual measurement, determine the interval [λ of coal grain average diameter X _left, λ _right] be [2,10], calculate functional:

$\mathrm{\&Pi;}=\underset{i=0}{\overset{N}{\mathrm{\&Sigma;}}}{[{\mathrm{\&eta;}}_i-\frac{1}{2^{\frac{\mathrm{\&lambda;}}{2}}\mathrm{\&Gamma;}\left(\frac{\mathrm{\&lambda;}}{2}\right)}\underset{0}{\overset{x_i}{\&Integral;}}{\mathrm{\&xi;}}^{\frac{\mathrm{\&lambda;}}{2}-1}{e}^{-\frac{\mathrm{\&xi;}}{2}}\mathrm{d\&xi;}]}^2---\left(3\right)$

Correspond respectively to λ=λ _leftwith λ=λ _rightvalue:

${\mathrm{\&Pi;}}_{\mathrm{left}}=\underset{i=0}{\overset{N}{\mathrm{\&Sigma;}}}{[{\mathrm{\&eta;}}_i-\frac{1}{2^{\frac{{\mathrm{\&lambda;}}_{\mathrm{left}}}{2}}\mathrm{\&Gamma;}\left(\frac{{\mathrm{\&lambda;}}_{\mathrm{left}}}{2}\right)}\underset{0}{\overset{x}{\&Integral;}}{\mathrm{\&xi;}}^{\frac{{\mathrm{\&lambda;}}_{\mathrm{left}}}{2}-1}{e}^{-\frac{\mathrm{\&xi;}}{2}}\mathrm{d\&xi;}]}^2---\left(4\right)$

${\mathrm{\&Pi;}}_{\mathrm{right}}=\underset{i=0}{\overset{N}{\mathrm{\&Sigma;}}}{[{\mathrm{\&eta;}}_i-\frac{1}{2^{\frac{{\mathrm{\&lambda;}}_2}{2}}\mathrm{\&Gamma;}\left(\frac{{\mathrm{\&lambda;}}_{\mathrm{right}}}{2}\right)}\underset{0}{\overset{x}{\&Integral;}}{\mathrm{\&xi;}}^{\frac{{\mathrm{\&lambda;}}_{\mathrm{right}}}{2}-1}{e}^{-\frac{\mathrm{\&xi;}}{2}}\mathrm{d\&xi;}]}^2---\left(5\right)$

Get calculate functional Π and correspond to λ=λ ₁value Π ₁if, Π _right< Π _left, then λ is got _left=λ ₁, Π _left=Π ₁; If Π _left< Π _right, then λ is got _right=λ ₁, Π _right=Π ₁;

Get again calculate functional Π and correspond to λ=λ ₂value Π ₂if, Π _right< Π _left, then λ is got _left=λ ₂, Π _left=Π ₁; If Π _left< Π _right, then λ is got _right=λ ₂, Π _right=Π ₁;

Repeat above-mentioned steps, obtain an ordered series of numbers λ ₁, λ ₂..., λ _nif, then can think λ=λ _ncorresponding functional Π gets minimum of a value, by λ _nas the estimate of λ, so just obtain coal grain diameter distribution function F (x) and distribution density function f (x);

2) coal breakage desorption of mash gas intensity is measured

Average grain diameter is the residual gas content in the coal of x unit mass:

$W\left(t\right)=\frac{{\mathrm{\&alpha;x}}^{1/4}{W}_0}{{(t_0+t)}^{\mathrm{\&beta;}}}---\left(6\right)$

Wherein, W ₀for the original gas bearing capacity that average grain diameter is the coal of the unit mass of x; X is the diameter of coal cinder; T is coal breakage open-assembly time; α, β are the constant relevant with coal breakage geometry, Coal Characteristics parameter, t ₀being the constant with time dimension arranged to eliminate singularity, getting t ₀=1 (min), therefore, to be the desorption of mash gas intensity of the coal of the unit mass of x be average grain diameter:

$q^{*}(t,x)=-\frac{\&PartialD;W}{\&PartialD;t}=\frac{{\mathrm{\&alpha;\&beta;x}}^{1/4}{W}_0}{{(t_0+t)}^{1+\mathrm{\&beta;}}}---\left(7\right)$

Consider that coal is caving continuously, namely τ=0 has coal to be caving to τ=t, and the particle diameter be caving at moment τ is the desorption of mash gas amount of the coal of x unit, can construct, that is: based on formula (7)

$q(\mathrm{\&tau;},t,x)=\frac{\mathrm{\&alpha;\&beta;}{x}^{1/4}{W}_0}{{[t_0+(t-\mathrm{\&tau;})]}^{1+\mathrm{\&beta;}}}---\left(8\right)$

The first step: determine factor beta

For same particle size x ₀coal sample, get two different coal breakage open-assembly time t ₁and t ₂, measure gas remainder quantity W respectively ₁and W ₂, applying equation (6), has:

$W_1=\frac{\mathrm{\&alpha;}{x}_0^{1/4}{W}_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}---\left(9\right)$

With

$W_2=\frac{\mathrm{\&alpha;}{x}_0^{1/4}{W}_0}{{(t_0+t_2)}^{\mathrm{\&beta;}}}---\left(10\right)$

By formula (9) and formula (10), obtain

$\mathrm{\&beta;}=\frac{\ln \frac{W_1}{W_2}}{\ln \frac{t_0+t_2}{t_0+t_1}}---\left(11\right)$

Second step: determine parameter alpha

X is respectively for particle diameter ₁and x ₂coal sample, measure coal breakage open-assembly time be t ₁gas remainder quantity with applying equation (6), has:

$W_1^{*}=\frac{{\mathrm{\&alpha;x}}_1^{1/4}{W}_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}---\left(12\right)$

With

$W_2^{*}=\frac{{\mathrm{\&alpha;x}}_2^{1/4}{W}_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}---\left(13\right)$

By formula (12) and formula (13), obtain:

$W_1^{*}-W_2^{*}=\mathrm{\&alpha;}\frac{W_0}{{(t_0+t_1)}^{\mathrm{\&beta;}}}(x_1^{1/4}-x_2^{1/4})---\left(14\right)$

Under the prerequisite determining parameter beta, parameter alpha can be determined by formula (14), namely

$\mathrm{\&alpha;}=\frac{{(t_0+t_1)}^{\mathrm{\&beta;}}}{x_1^{1/4}-x_2^{1/4}}\frac{W_1^{*}-W_2^{*}}{W_0}---\left(15\right)$

3) gas emission that coal breakage causes calculates and prediction

If the coal breakage quality of unit interval is M (t), desorption of mash gas total amount can be calculated:

$\begin{array}{c}Q=\underset{\mathrm{\&tau;}=0}{\overset{t}{\&Integral;}}\underset{r=0}{\overset{+\&infin;}{\&Integral;}}M\left(\mathrm{\&tau;}\right)q(\mathrm{\&tau;},t,x)f\left(x\right)\mathrm{dxd\&tau;}\\ =\underset{\mathrm{\&xi;}=0}{\overset{t}{\&Integral;}}\underset{r=0}{\overset{+\&infin;}{\&Integral;}}M\left(\mathrm{\&tau;}\right)\frac{1}{2^{\frac{\mathrm{\&lambda;}}{2}}\mathrm{\&Gamma;}\left(\frac{\mathrm{\&lambda;}}{2}\right)}{x}^{\frac{\mathrm{\&lambda;}}{2}-1}{e}^{-\frac{x}{2}}\frac{{\mathrm{\&alpha;\&beta;x}}^{1/4}{W}_0}{{[t_0+(t-\mathrm{\&tau;})]}^{1+\mathrm{\&beta;}}}\mathrm{dxd\&tau;}\end{array}---\left(16\right)$

The desorption of mash gas amount calculated using formula (16) is as the prediction of coal breakage gas emission.