Coal particle gas emission amount prediction system and method based on real gas state

文档序号：1844419 发布日期：2021-11-16 浏览：26次中文

阅读说明：本技术 一种基于真实气体状态的煤粒瓦斯放散量预测系统及方法 (Coal particle gas emission amount prediction system and method based on real gas state ) 是由徐浩刘伟秦跃平张凤杰毋凡褚翔宇闫林晓郭铭彦韩东阳赵政舵刘晓薇于 2021-10-20 设计创作，主要内容包括：本申请属于借助于测定材料的化学或物理性质来测试或分析材料技术领域,提供了一种基于真实气体状态的煤粒瓦斯放散量预测系统及方法,该方法以压缩因子校正理想气体状态方程,得到真实游离瓦斯气体状态方程；以游离瓦斯密度为自变量,对常规的以压力为自变量的朗格缪尔单分子层吸附等温方程进行修正,计算吸附态的瓦斯含量；将其与游离态的瓦斯含量结合得到简化的煤粒总瓦斯含量朗格缪尔型方程；对该简化方程进行微分,得到煤粒游离态瓦斯密度梯度驱动的解吸放散模型；并基于有限差分数值方法和高斯-赛德尔迭代法,对所述煤粒态瓦斯密度梯度驱动的解吸放散模型进行求解,得到煤粒累计瓦斯解吸量预测曲线,以对煤粒瓦斯放散量进行预测。(The application belongs to the technical field of testing or analyzing materials by means of determining chemical or physical properties of the materials, and provides a system and a method for predicting coal particle gas emission quantity based on a real gas state, wherein the method corrects an ideal gas state equation by a compression factor to obtain a real free gas state equation; correcting a conventional Langmuir monolayer adsorption isothermal equation with pressure as an independent variable by taking the density of free gas as the independent variable, and calculating the gas content in an adsorption state; combining the coal particles with the free gas content to obtain a simplified Langmuir equation of the total gas content of the coal particles; differentiating the simplified equation to obtain a desorption and diffusion model driven by the density gradient of the free gas of the coal particles; and solving the desorption and diffusion model driven by the coal particle state gas density gradient based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulated gas desorption amount prediction curve so as to predict the coal particle gas diffusion amount.)

1. A coal particle gas diffusion quantity prediction method based on a real gas state is characterized by comprising the following steps:

step S100, differentiating the simplified Langmuir equation of the total gas content of the coal particles according to the desorption time of gas in the coal particles and the distance from the center of the coal particles to any position in a sphere of the coal particles to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particles;

the desorption and diffusion model driven by the density gradient of the coal particle free gas is as follows:

the density of the gas in a real free state; the real free gas density is calculated based on a real free gas state equation according to the gas pressure and the gas temperature; the real free gas state equation is as follows:

in the formula:is the gas pressure;the molar mass of the gas;is the universal gas constant;Tis the gas temperature;

Zis a gas compression factor; the gas compression factor is obtained by calculation according to a linear variation relation between the gas compression factor and the gas pressure, and the linear variation relation between the gas compression factor and the gas pressure is as follows:

the initial conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

the boundary conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

in the formula (I), the compound is shown in the specification,the initial gas pressure inside the coal particles;the gas pressure on the outer surface of the coal particles;is the radius of the coal particles;is a first fitting constant, having a value of-0.012561,the fitting constant is a second fitting constant and takes the value of 1;

and S200, solving the desorption and diffusion model driven by the density gradient of the free gas of the coal particles based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a prediction curve of the accumulated gas desorption amount of the coal particles so as to predict the gas diffusion amount of the coal particles.

2. The method according to claim 1, wherein in step S100, the simplified langmuir-type equation of the total gas content of the coal grains is obtained by fitting the sum of the free gas content and the gas content in an adsorbed state according to the langmuir equation;

the simplified Langmuir-type equation of the total gas content of the coal particles is as follows:

in the formula (I), the compound is shown in the specification,the total gas content of the coal particles is unit mass;is the gas content in the adsorbed state;is the gas content in the free state;、respectively, constants related to the total gas content of the coal particles;the density of the gas in the true free state.

3. The method of claim 2, wherein, according to the formula:

calculating to obtain the content of the free gas；

In the formula (I), the compound is shown in the specification,is a coefficient related to the free gas content;represents the porosity of the coal particles;the density of the gas in a real free state;is a standard molar volume;apparent density of coal particles;is the molar mass of the gas.

4. The method according to claim 2, wherein the adsorbed gas content is obtained by modifying a conventional langmuir monolayer adsorption isotherm equation with pressure as an independent variable based on a gas dynamics theory with the true free gas density as an independent variable; the content of the adsorbed gas is as follows:

in the formula (I), the compound is shown in the specification,is the gas content in the adsorbed state;is a constant related to the saturated adsorption amount;is a process constant related to the rate of adsorption and desorption;and the density of the real free gas is obtained.

5. The method according to claim 1, wherein step S200 comprises:

step S201, dividing the distance from the center of the coal particle to any position in a sphere of the coal particle and the desorption time of gas in the coal particle to obtain a spherical shell node and a desorption time node of the coal particle;

s202, differentiating the desorption and diffusion model driven by the density gradient of the coal particle free gas based on a finite difference numerical method according to the spherical shell node and the desorption time node to obtain a difference equation of gas flow;

step S203, solving a difference equation of the gas flow based on a Gauss-Seidel iteration method to obtain a predicted value of the accumulated gas desorption amount of the coal particles;

and S204, drawing a prediction curve of the accumulated gas desorption amount of the coal particles according to the predicted value of the accumulated gas desorption amount of the coal particles so as to predict the gas diffusion amount of the coal particles.

6. The method of claim 5, wherein the differential equation for the gas flow is:

in the formula (I), the compound is shown in the specification,the numbers of the spherical shell nodes are shown,；is the number of the desorption time node,；N、Lrespectively are the numerical values corresponding to the boundary conditions of the spherical shell node and the desorption time node,N、Lare rational numbers.

7. The method of claim 6,

in step S203, the solving the difference equation of the gas flow based on the gaussian-seidel iteration method to obtain a predicted value of the accumulated gas desorption amount of the coal particles includes:

solving the density of the free gas obtained by the differential equation of the gas flow according to a formula:

calculating to obtain a predicted value of the accumulated gas desorption amount of the coal particles;

in the formula (I), the compound is shown in the specification,is shown asThe coal particle accumulated gas desorption amount predicted value of each desorption time node;；Lis a numerical value corresponding to the boundary condition of the desorption time node,Lis a rational number;is as followsnThe desorption time node is opposite ton-a time difference of 1 desorption time node,。

8. the method according to claim 1, wherein step S200 is followed by:

and verifying the desorption and diffusion model driven by the density gradient of the free gas of the coal particles according to the matching degree of the experimental data of the constant-pressure adsorption and desorption experiment of the gas of the coal particles under the isothermal condition and the prediction curve of the accumulated gas desorption amount of the coal particles.

9. The method of claim 8, wherein the constant-pressure adsorption and desorption experiment of coal gas particles at the constant temperature comprises: the method comprises a coal particle sample preparation stage, a test preparation stage, a gas adsorption stage and a constant pressure gas desorption stage.

10. A system for predicting gas emissions from coal particles based on true gas conditions, comprising:

a model building unit configured to: differentiating the simplified Langmuir equation of the total gas content of the coal particles according to the desorption time of the gas in the coal particles and the distance from the center of the coal particles to any position in a sphere of the coal particles to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particles;

the desorption and diffusion model driven by the density gradient of the coal particle free gas is as follows:

in the formula:is the gas pressure;the molar mass of the gas;is the universal gas constant;Tis the gas temperature;

the initial conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

the boundary conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

in the formula (I), the compound is shown in the specification,the gas pressure on the outer surface of the coal particles;is the radius of the coal particles;is a first fitting constant, having a value of-0.012561,the fitting constant is a second fitting constant and takes the value of 1;

a gas prediction unit configured to: and solving the desorption and diffusion model driven by the free gas density gradient of the coal particles based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulated gas desorption amount prediction curve so as to predict the gas diffusion amount of the coal particles.

Technical Field

The application relates to the technical field of testing or analyzing materials by means of measuring chemical or physical properties of the materials, in particular to a coal particle gas emission prediction system and method based on a real gas state.

Background

In the coal mining process, gas disasters are huge disasters, and the safety production of a coal mine is seriously threatened. Meanwhile, gas in the coal bed is extracted and utilized as a coal bed gas resource, so that the gas disaster danger can be reduced, and unconventional clean resources can be reasonably utilized. As is known, the coal bed gas content is an indispensable basic parameter for coal mine gas danger degree evaluation, gas disaster control and coal bed gas resource exploration and development in China. The gas content testing method comprises a direct method and an indirect method.

When the gas content of the coal bed is directly measured by underground on-site sampling, the gas is easy to lose in the process of collecting the coal sample. Thus the direct method requires the calculation of several parts including the amount of gas lost during sampling, the amount of desorption on site and the amount of residual laboratory. It is generally customary to employThe method is used for calculating the loss amount of the gas,the method is derived from the Barre formula method. The barrel formula rule is that coal particles are assumed to be isotropic homogeneous spherical particles, gas diffusion is caused by content/concentration gradient, the diffusion coefficient is a fixed value, an analytical solution formula of diffusion is obtained based on a Fick diffusion formula, and the barrel formula rule also belongs to an empirical formula for predicting gas desorption in a short time in principle. However, currently, according to the fick model of the constant diffusion coefficient, whether the numerical solution or the analytic solution is greatly deviated from the experimental data on the whole time scale, so the fick law may not be applicable to describing the coal particle gas diffusion process any more. Thus, based on Fick's law as a theoretical basisThere are many challenges to law. It is necessary to fundamentally set out that a more rational diffusion model than fick's law (concentration gradient driven) is proposed.

In addition, the indirect method needs to measure basic parameters such as original gas pressure, porosity and adsorption constant of the coal seam. The gas content mainly comprises two parts: firstly, calculating the gas adsorption quantity of the coal according to a Langmuir equation; and the second is the amount of free gas obtained by conversion according to a gas state equation. However, there is a problem in that the amount of free gas is calculated by approximately considering the free gas as an ideal gas, and the compression factor is regarded as 1, and the deviation of the actual real gas from the ideal gas is not considered. This treatment is not reasonable because the ideal gas is used under conditions of high temperature and low pressure. With the increase of the mining depth of the coal bed, the pressure is already beyond the low-pressure range, and the temperature of the coal bed is generally between 15 and 30 ℃, and the coal bed does not belong to the high-temperature range. Therefore, the problem obviously exists in that the ideal gas state equation is still adopted for the gas under the conditions of high pressure and normal temperature. It is necessary to calculate the free gas content using the real gas state equation, which is more rigorous.

Therefore, there is a need to provide an improved solution to the above-mentioned deficiencies of the prior art.

Disclosure of Invention

The present application is directed to a system and a method for predicting a coal gas emission amount based on a real gas state, so as to solve or alleviate the above problems in the prior art.

In order to achieve the above purpose, the present application provides the following technical solutions:

the application provides a coal particle gas diffusion quantity prediction method based on a real gas state, which comprises the following steps:

the desorption and diffusion model driven by the density gradient of the coal particle free gas is as follows:

in the formula:is the gas pressure;the molar mass of the gas;is the universal gas constant;Tis the gas temperature;

Zis a gas compression factor; the gas compression factor is obtained by calculation according to the linear variation relation between the gas compression factor and the gas pressureThe linear variation relationship between the gas compression factor and the gas pressure is as follows:

the initial conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

the boundary conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

Preferably, in step S100, the simplified langmuir-type equation of the total gas content of the coal grain is obtained by fitting the sum of the free gas content and the gas content in the adsorption state according to the langmuir equation;

the simplified Langmuir-type equation of the total gas content of the coal particles is as follows:

Preferably, according to the formula:

calculating to obtain the content of the free gas；

Preferably, the adsorbed gas content is obtained by correcting a langmuir monolayer adsorption isothermal equation based on a gas dynamics theory according to the real free gas density; the content of the adsorbed gas is as follows:

Preferably, step S200 includes:

step S203, solving a difference equation of the gas flow based on a Gauss-Seidel iteration method to obtain a predicted value of the accumulated gas desorption amount of the coal particles;

Preferably, the differential equation of the gas flow is:

Preferably, in step S203, the solving the difference equation of the gas flow based on the gaussian-seidel iteration method to obtain the predicted value of the accumulated gas desorption amount of the coal particles includes:

solving the density of the free gas obtained by the differential equation of the gas flow according to a formula:

calculating to obtain a predicted value of the accumulated gas desorption amount of the coal particles;

preferably, after step S200, the method further includes:

Preferably, the isothermal coal particle gas constant pressure adsorption and desorption experiment comprises: the method comprises a coal particle sample preparation stage, a test preparation stage, a gas adsorption stage and a constant pressure gas desorption stage.

The embodiment of the present application further provides a coal gas diffusion amount prediction system based on the real gas state, including:

the desorption and diffusion model driven by the density gradient of the coal particle free gas is as follows:

in the formula:is the gas pressure;the molar mass of the gas;is the universal gas constant;Tis the gas temperature;

the initial conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

the boundary conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

Compared with the closest prior art, the technical scheme of the embodiment of the application has the following beneficial effects:

in the application, the ideal gas state equation is corrected by a compression factor to obtain a real free gas state equation; correcting a conventional Langmuir monolayer adsorption isothermal equation with pressure as an independent variable by taking the density of free gas as the independent variable, and calculating the gas content in an adsorption state; combining the coal particles with the free gas content to obtain a simplified Langmuir equation of the total gas content of the coal particles; differentiating the simplified equation to obtain a desorption and diffusion model driven by the density gradient of the free gas of the coal particles; and solving the desorption and diffusion model driven by the coal particle state gas density gradient based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulated gas desorption quantity prediction curve so as to predict the coal particle gas diffusion quantity, and finally verifying the constructed desorption and diffusion model driven by the coal particle free state gas density gradient based on the matching degree of the experimental data of the coal particle gas accumulated desorption quantity and the simulation prediction curve of the coal particle accumulated gas desorption quantity.

The method is based on a real free gas state equation, and the free gas density is calculated; the method has the advantages that the density of free gas is used as an independent variable, the conventional Langmuir monolayer adsorption isothermal equation with pressure as the independent variable is corrected, the gas content in an adsorption state is calculated, and then a desorption and diffusion model driven by the density gradient of the free gas of the coal particles is constructed.

The method provided by the application fully considers the difference of the application conditions between the real gas and the ideal gas, better conforms to the migration process of the actual gas of the underground coal bed, overcomes the defect of predicting the gas dispersion amount based on the ideal gas state equation, can greatly improve the accuracy of predicting the gas dispersion amount, provides a basis for calculating and predicting the gas content of the coal bed, and provides a basis for modeling and predicting the underground gas extraction and the coal bed gas extraction production amount.

The prediction method provided by the application also has the characteristics of quickness and convenience in calculation, and the result can be output only within a few seconds by inputting the parameters.

In a traditional gas desorption and diffusion experiment in a laboratory, the gas desorption and diffusion limit is generally reached after more than ten hours, and even if the experiment is continued, the desorption and diffusion amount is not obviously changed. Some empirical/semi-empirical formulas and theoretical models can only guarantee the prediction accuracy of the gas desorption and dispersion amount in a short time, and the error in the whole longer time scale range is larger. The prediction method provided by the application can accurately predict the dynamic change of the gas desorption amount in the coal in a longer time period by setting the time step length and the iteration times, and is not limited by the experiment duration.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application. Wherein:

fig. 1 is a schematic flow chart of a method for predicting gas emissions of coal particles based on real gas conditions according to some embodiments of the present application;

FIG. 2 is a schematic illustration of gas compression factors at different temperatures and different pressure scales provided according to some embodiments of the present application;

FIG. 3 is a graph of temperatures provided according to some embodiments of the present applicationTAnd a first fitting constantαA relationship graph;

FIG. 4 is a schematic diagram of a spherical coal particle mesh and node partitioning provided in accordance with some embodiments of the present application;

FIG. 5 is a flow diagram providing a differential equation solution for gas flow according to some embodiments of the present application;

FIG. 6 is a schematic diagram of a process flow of isothermal coal bed gas pressure swing adsorption desorption experiments provided in accordance with some embodiments of the present application;

fig. 8 is a schematic structural diagram of a coal gas emission prediction system based on a real gas state according to some embodiments of the present application.

Detailed Description

The present application will be described in detail below with reference to the embodiments with reference to the attached drawings. The various examples are provided by way of explanation of the application and are not limiting of the application. In fact, it will be apparent to those skilled in the art that modifications and variations can be made in the present application without departing from the scope or spirit of the application. For instance, features illustrated or described as part of one embodiment, can be used with another embodiment to yield a still further embodiment. It is therefore intended that the present application cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

Exemplary method

In the coal bed gas exploitation process, gas in an adsorption state in a coal matrix/coal particles is continuously desorbed and converted into free gas, then the free gas is diffused and flows into cracks, and finally the free gas seeps into a drill hole. Therefore, the gas flow in the coal seam is a very complicated diffusion seepage process, which also causes difficulty in predicting the desorption amount and the total yield of the coal seam gas.

Currently, when modeling and predicting the desorption amount and yield of the coal bed gas, the scholars still follow Fick's law on the gas flow in the coal matrix/coal particles, which is inherently problematic. In the modeling process, the calculation of the content of the free gas is treated as an ideal gas, and the compression factor is treated as 1, but the real gas in the coal does not follow an ideal gas state equation, and the treatment method can definitely cause the error prediction of the desorption amount and the yield of the coal bed gas.

The method comprises the steps of taking the difference of applicable conditions between real gas and ideal gas into full consideration, and providing a coal particle gas diffusion quantity prediction method based on a real gas state, wherein the free gas density of the real gas is calculated based on a real free gas state equation; according to the free gas density of the real gas, correcting the Langmuir monolayer adsorption isothermal equation based on the gas dynamics theory to obtain the content of the adsorbed gas; fitting the sum of the free gas content and the adsorbed gas content according to the Langmuir equation to obtain a simplified Langmuir type equation of the total gas content of the coal particles; according to the desorption time of gas in the coal particles and the distance from the center of the coal particles to any position in the sphere of the coal particles, differentiating the simplified Langmuir equation of the total gas content of the coal particles to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particles; solving the desorption and diffusion model driven by the free gas density gradient of the coal particles based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulated gas desorption amount prediction curve so as to predict the gas diffusion amount of the coal particles; and finally, verifying the constructed desorption and diffusion model driven by the density gradient of the free gas of the coal particles based on the matching degree of the experimental data of the gas accumulative desorption amount of the coal particles and the simulation and prediction curve of the gas accumulative desorption amount of the coal particles.

The method provided by the embodiment of the application considers the difference of the application conditions between the real gas and the ideal gas, more conforms to the migration process of the actual gas of the underground coal bed, overcomes the defect of predicting the gas diffusion amount based on the ideal gas state equation, overcomes the defect of large deviation between the desorption diffusion amount and the experimental data obtained based on the Fick diffusion model in the prior art, and greatly improves the matching degree between the theoretical prediction value of the coal particle free gas desorption diffusion amount and the experimental measurement data.

Fig. 1 is a schematic flow chart of a method for predicting gas emissions of coal particles based on real gas conditions according to some embodiments of the present application; as shown in fig. 1, the method includes steps S100 to S200, specifically:

and S100, differentiating the simplified Langmuir equation of the total gas content of the coal particles according to the desorption time of the gas in the coal particles and the distance from the center of the coal particles to any position in a sphere of the coal particles to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particles.

The desorption and diffusion model driven by the density gradient of the coal particle free gas is as follows:

the initial conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

the boundary conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

in the formula (I), the compound is shown in the specification,is a first constant related to the total gas content of the coal particles,Is a second constant related to the total gas content of the coal particles;is the apparent density of coal particles, t/m³；Is gas standard density, t/m³；The desorption time of the gas in the coal particles is s;micro-channel diffusion coefficient in cm for free gas²/s；The distance m from the center of the coal particle to any position in the sphere of the coal particle;the initial gas pressure inside the coal particles is MPa;the molar mass of the gas is g/mol;is a universal gas constant, 8.314J/(mol. K);is the gas temperature, K;the gas pressure on the outer surface of the coal particles;is the radius of the coal particles;is a first constant of the fit, and,is a second fitting constant;the density of the gas in the true free state.

According to the gas pressure and the gas temperature, calculating to obtain the real free gas density based on the real free gas state equation. The real free gas state equation is obtained by correcting an ideal gas state equation through a gas compression factor.

Real gas at any given temperature and pressureThe deviation of the product (gas pressure and volume) from the ideal gas varies from substance to substance. Some researchers have chosen to approximate the true gas equation of state with an ideal gas equation of state for the sake of simplifying the calculation, i.e. consider the gas compressibility factor in the pores of the coal seam as 1. This is somewhat imprecise and ideally the gas is used at high temperature and low pressure. And the pressure of the coal bed is already beyond the low-pressure range along with the increase of the mining depth, the temperature of the coal bed is generally 15-30 ℃, and the coal bed does not belong to the high-temperature range, so that the real gas equation and the ideal gas equation always have deviation, and the ideal gas equation is selected to approximately represent the real gas equation, which may cause errors. The compression factors under different pore gas pressures are different, and for the situation, the gas compression factor is more direct and accurate to correct the ideal gas state equation to describe the property of the real gas.

The real free gas state equation obtained by correcting the ideal gas state equation through the gas compression factor is as follows:

in the formula:pis the gas pressure, MPa;Zis the gas compression factor.

In the prior art, the gas compression factor is calculated by a gas state equation and some iteration methods according to the pressure, the temperature and the measured gas density obtained by experiments.

In the embodiment of the application, according to the corresponding free-state gas densities at different pressures and temperatures obtained by experimental data, the experimental data with the gas pressure scale of 0.01-5MPa and the temperature scale of 290K-360K are selected, and the gas compression factors at different gas temperatures and different pressure scales are obtained through calculation. The relationship between the gas compression factors at different gas temperatures and different pressure scales is shown in fig. 2.

As can be seen from FIG. 2, the gas compression factorZAs a function of gas pressurepThe linear change is shown in the following table, and the corresponding relationship between specific values is as follows:

in the context of table 1, the following,in order to fit the correlation coefficient linearly,the larger the fitting accuracy. From the above table, the different temperatures can be obtainedT) Gas pressure below (p) And gas compression factor: (Z)The linear equation of (a):

in the formula (I), the compound is shown in the specification,is a first constant of the fit, and,is a constant of the second fit to the first fit,、as a function of temperature.

As shown in Table 1, for the linear relationship fit, the second fitting constantβThe variation is not large.

In the embodiment of the application, the second fitting constant is ，Selecting at different temperaturesThe value is 1. When the pressure is 0, the compression factor is 1. Namely, it is consistent with the case that when the gas is not subjected to the pressure, it can be approximately regarded as the ideal gas, and the compression factor can be regarded as 1.

FIG. 3 is a graph of temperatures provided according to some embodiments of the present applicationTAnd a first fitting constantThe relationship, as shown in FIG. 3, is temperatureTAndcan be expressed by a polynomial equation:

wherein E represents the base of the power of 10 in scientific notation, e.g. 。

The expression between the gas compression factor and the temperature and gas pressure is summarized as:

in the examples of the present application, the experiments were carried out at a constant temperature of 35 ℃ (308.15K), with T =308.15K andsubstituting the equation of the gas compression factor and the gas pressure under the experimental pressure humidity by the equation of the =1, namely, the linear change relation between the gas compression factor and the gas pressure can be obtained.

The linear variation relationship between the gas compression factor and the gas pressure is expressed as:

the traditional gas compression factor is a function of gas pressure and temperature, when an ideal gas state equation is corrected based on the function to calculate the content of free gas, a nonlinear equation occurs, and the calculation expression of the content of free gas becomes more complex and is inconvenient to calculate.

In the examples of the present application, the temperature is varied according to the experimental data: (T) Gas pressure below (p) And gas compression factor: (Z)The linear relation of the gas compression factors is obtained by fitting, so that the calculation process of the gas compression factors is simplified, the calculation efficiency is improved, and the calculation difficulty of the gas compression factors is reduced.

In some embodiments of the present application, the simplified langmuir-type equation for the total gas content of the coal particle is fit to the sum of the free gas content and the adsorbed gas content in accordance with the langmuir equation in step S100. The simplified Langmuir-type equation for the total gas content of the coal particles is as follows:

in the formula (I), the compound is shown in the specification,is the total gas content of coal particles per unit mass, cm³/g；Gas content in adsorbed state, cm³/g；Gas content in free form, cm³/g。

The calculation process of the gas content in the adsorption state and the gas content in the free state is as follows:

calculating the gas content in the adsorption stateThe process specifically comprises the following steps: for the convenience of solution, and in accordance with the desorption and diffusion model driven by the coal particle free gas density gradient provided by the present application, in the embodiment of the present application, the langmuir equation is corrected by replacing the gas pressure with the true free gas density with reference to the derivation process of the langmuir monolayer isothermal adsorption equation, that is, the conventional langmuir equation with the gas pressure as an independent variable is corrected to an equation with the true free gas density as an independent variable, and the gas content in the adsorption state is calculated.

Specifically, according to the real free gas density, based on the gas dynamics theory, the Langmuir monolayer adsorption isothermal equation is corrected according to the formula:

calculating to obtain the gas content in the adsorption state；

In the formula (I), the compound is shown in the specification,is a constant related to the amount of saturated adsorption, cm³/g，The adsorption capacity is in direct proportion to the total adsorption number of the coal particle sample of unit mass and is greatly influenced by the pore structure of the coal particle sample;is a process constant related to the rate of adsorption and desorption,mainly affected by temperature and the forces acting between the adsorbate and the gas molecules.

It should be noted that, in the following description,、different from the conventional adsorption constant (i.e. Langmuir equation adsorption constant before correction), but、The method is basically consistent with the conventional method and the flow for acquiring the adsorption constant, namely:

firstly, converting a pressure balance point on an adsorption isotherm into a free gas density balance point through a real gas state equation, and then obtaining a constant by fitting the free gas density and the accumulated adsorption quantity through the above formula、。

Calculating the gas content in the free stateThe process specifically comprises the following steps:

according to the formula:

calculating to obtain the content of free gas；

In the formula (I), the compound is shown in the specification,in cm as a coefficient related to the free gas content³/(g·MPa)；Represents the porosity of the coal particles;is the density of free gas;is the standard molar volume, L/mol.

The total content expression of the free gas and the adsorbed gas in the coal particles is obtained as follows:

it is considered herein that the free gas content and the adsorbed gas content are added together and fitted in the form of langmuir equation, which is essentially a form that does not change. Therefore, the mathematical expression form of the total gas content of the coal particles can be simplified as much as possible, and the simplified langmuir-type equation of the total gas content of the coal particles is specifically as follows:

in the formula (I), the compound is shown in the specification,is a first constant related to the total gas content of the coal particles,And fitting by referring to a method for calculating the adsorption constant of the coal particles according to the isothermal adsorption line of the coal particles as a second constant related to the total gas content of the coal particles.

In step S100, according to the desorption time of the gas in the coal particle and the distance from the center of the coal particle to any position in the sphere of the coal particle, differentiating the simplified langmuir type equation of the total gas content of the coal particle to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particle, specifically:

first, the following assumptions are made: the coal particles are regarded as isotropic and homogeneous spherical particles; neglecting the tiny deformation caused by the adsorption and expansion of the coal particle gas; the gas desorption and diffusion flow process in the coal particles is driven by the density gradient of free gas; surface diffusion of the pore surfaces of the coal particles is not considered; the gas flow in the coal particles is an isothermal process; the gas diffusion and circulation quality in the coal particles is in direct proportion to the density gradient of the free gas, namely the gas diffusion is driven by the density gradient of the free gas.

The thickness of the coal particles isThe spherical shell node as a research object has the following components according to the mass conservation law:

combining the above formula with a simplified langmuir type equation of total gas content of the coal particles, and differentiating the simplified langmuir type equation of total gas content of the coal particles to obtain a desorption and diffusion model (a continuous differential equation of coal particle gas desorption unsteady state diffusion flow) driven by a coal particle free state gas density gradient, wherein the model is as follows:

step S200, solving the desorption and diffusion model driven by the coal particle free state gas density gradient based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulative gas desorption amount prediction curve so as to predict the coal particle gas diffusion amount, wherein the method comprises the following steps of S201-S204:

step S201, dividing the distance from the center of the coal particle to any position in the sphere of the coal particle and the desorption time of gas in the coal particle to obtain a spherical shell node and a desorption time node of the coal particle.

Fig. 4 is a schematic diagram of mesh and node division of spherical coal particles provided according to some embodiments of the present application, and as shown in fig. 4, the mesh and node division is performed on spherical coal particles, specifically:

the coal particles are regarded as isotropic and homogeneous spherical particles, and the radius line of the sphere is divided into two parts from the sphere center position of the coal particlesNA spherical shell node. Since the gas pressure and the gas content change more drastically the closer to the surface of the coal particles, the pitch of the nodes from the center of the sphere to the surface of the sphere is set to a tendency to become smaller in an equal ratio. The middle points of two adjacent nodes are taken as concentric spherical surfaces, and the spherical coal particles are divided into 3 parts:N-1each including a spherical shell nodeiThe middle spherical shell, the solid sphere taking the spherical shell node 0 as the center and the spherical shell nodeNThe outer surface of the spherical coal particles. The node number of the coal grain spherical shell isi=0、1、2……N；

According to the desorption time length, dividing desorption time nodes which are numbered asj=0、1、2……L。

N、LAre respectively asThe boundary conditions of the spherical shell node and the desorption time node correspond to numerical values,N、Lare rational numbers.

And S202, differentiating the desorption and diffusion model driven by the density gradient of the coal particle free gas based on a finite difference numerical method according to the divided spherical shell nodes and desorption time nodes to obtain a difference equation of gas flow.

According to the mass conservation law, namely the net gas amount flowing in and out of each spherical shell node control unit body is equal to the gas variable quantity of the unit body, the first step is establishedjAt the moment of desorptionNAnd obtaining a complete nonlinear difference equation system with the density of the free gas of each spherical shell node as an unknown quantity to obtain a gas flow difference equation.

For the interior of coal particles (i.e. 1 st to 1 st)N-1Individual spherical shell node), coal particle center (i.e., 0 th spherical shell node), coal particle outer surface (i.e., 0 th spherical shell node)NSpherical shell node), respectively obtaining a differential equation of gas flow corresponding to each condition, which is as follows:

for the internal 1 st to 1 st of coal particlesN-1The differential equation of the gas flow of each spherical shell node is as follows:

for a solid pellet centered on the 0 th spherical shell node, only gas flows out but not in during desorption, so the differential equation of the gas flow is:

for the outer surface of the coal particles, i.e. secondNThe gas pressure at each spherical shell node is:

based on the three cases, the difference equation for the gas flow is obtained as follows:

And S203, solving a difference equation of the gas flow based on a Gauss-Seidel iteration method to obtain a predicted value of the accumulated gas desorption amount of the coal particles.

Fig. 5 is a flow chart of a solution flow of a differential equation for gas flow provided according to some embodiments of the present application, as shown in fig. 5, the solution flow specifically includes:

program initialization operations, including: defining variables, constants and arrays, and inputting values and arrays corresponding to the variables to initialize;

specifically, in the embodiment of the present application, taking a coal sample of a certain coal mine as a case, the following simulation parameters are input during program initialization: apparent density of coalρ _aIs 1200 kg/m³(ii) a Constant related to total gas content of coal particlesaIs 29.06 cm³(ii)/g; langmuir constantbIs 38.92 cm³(ii)/g; average radius of coal particlesR0.26 mm; gas diffusion coefficient of micro-channelK _mIs 2.86X 10^- ⁸cm²S; porosity of coal matrixn _mIs 0.036; the mass of the coal sample is 50 g; sample tank free space body100.19 ml; the initial desorption pressure in the coal particles is 2MPa, and the constant pressure on the outer surface is 0.1 MPa; the temperature was kept constant at 35 ℃.

Calculating desorption time step length according to the division of the desorption time nodes;

setting an initial value of the density of the free gas, and assigning a constant column vector and a coefficient matrix;

solving the density of the free gas based on a Gauss-Seidel iterative method; and judging whether the relative error between the solved free gas density and the initial value of the free gas density is smaller than a set threshold value (0.0001). If the relative error between the solved free gas density and the initial value of the free gas density is smaller than a set threshold value, outputting the solved free gas density; and if the relative error between the solved free gas density and the initial value of the free gas density is larger than or equal to the set threshold value, resetting the initial value of the free gas density, solving the free gas density based on the Gauss-Seidel iterative method again, calculating the relative error between the new free gas density and the reset initial value of the free gas density, and determining whether the relative error is smaller than the set threshold value. The density of the free gas is repeatedly solved; until the relative error between the solved free gas density and the initial value of the free gas density is smaller than a set threshold value;

according to the density of the free gas obtained by solving, according to the formula:

calculating a coal particle accumulated gas desorption amount predicted value corresponding to the current desorption time node;

in the formula, representsjA desorption time node (i.e. thejTime) of the coal particles accumulated gas desorption amount predicted value, cm³/g；Is as followsnThe desorption time node is opposite ton-1The time difference of each desorption time node,。

and repeating the steps according to the divided desorption time nodes until the coal particle accumulative gas desorption amount predicted value corresponding to all the desorption time nodes is obtained through calculation.

And S204, drawing a prediction curve of the accumulated gas desorption amount of the coal particles according to the predicted value of the accumulated gas desorption amount of the coal particles so as to predict the gas diffusion amount of the coal particles.

Drawing desorption time according to the predicted value of the accumulated gas desorption amount of the coal particles obtained in the step S203The predicted value of the accumulated gas desorption amount of the coal particles is the abscissaThe cumulative gas desorption amount of the coal particles is a prediction curve on the ordinate.

In some embodiments of the present application, step S200 is followed by:

FIG. 6 is a schematic diagram of a process flow of isothermal coal bed gas pressure swing adsorption desorption experiments provided in accordance with some embodiments of the present application; as shown in fig. 6, the constant pressure adsorption and desorption experiment of coal particle gas at the equal temperature includes: the method comprises a coal particle sample preparation stage, a test preparation stage, a gas adsorption stage and a constant pressure gas desorption stage. The method comprises the following specific steps:

and (3) carrying out isothermal coal particle gas constant-pressure adsorption and desorption experiments by adopting a high-temperature high-pressure adsorption instrument.

A coal particle sample preparation stage: firstly, selecting a fresh large coal sample under a coal mine, sealing, preserving and transporting the coal sample back to a laboratory. The coal blocks are crushed into coal particles with the particle size of 0.18mm to 0.25mm, and the coal particles are put into a sample tank after being dried.

A test preparation stage: and (3) carrying out air tightness detection and free space volume calibration on the coal particle gas constant-pressure adsorption and desorption experimental device at the equal temperature. And then carrying out vacuum-pumping treatment on the whole experiment system, wherein the experiment system comprises: a sample tank, a reference tank, and control valves between the sample tank and the reference tank.

And (3) gas adsorption stage: and filling gas into the reference tank, opening the control valve between the sample tank and the reference tank after the gas pressure in the reference tank is stable, filling the gas into the sample tank through the reference tank, and closing the control valve between the sample tank and the reference tank when the gas pressures of the sample tank and the reference tank are balanced. And (3) the coal particles begin to adsorb gas, when the pressure of the sample tank is kept stable, the gas in the coal particles reaches an adsorption and desorption balance state, and the balance gas pressure value at the moment is recorded to obtain an initial desorption pressure value.

And (3) a constant-pressure gas desorption stage: after the gas in the coal particles is adsorbed and desorbed to reach an equilibrium state, the reference tank and the sample tank are pumped to atmospheric pressure, and a control valve between the sample tank and the reference tank is closed to desorb the gas in the coal particles. Because the pressure on the outer surface of the coal particles is continuously increased in the desorption process, in order to achieve the gas desorption state of the coal particles under the condition of constant pressure, when the sample tank is increased by about 0.01MPa, the control valve is opened to communicate the reference tank and the sample tank, so that the pressure in the sample tank is reduced to atmospheric pressure again, the control valve is closed, and then the reference tank is pumped to the atmospheric pressure. This process is repeated continuously to ensure that the coal particles are always subjected to constant pressure gas desorption at one atmosphere.

And observing and recording the gas pressure value at each moment in the isothermal coal particle gas constant-pressure adsorption and desorption experiment process, and finishing the isothermal coal particle gas constant-pressure adsorption and desorption experiment when the gas pressure of the sample tank is kept stable.

And calculating the gas desorption amount of the coal particles in unit mass in unit time according to the gas pressure values of two adjacent moments obtained in the isothermal coal particle gas constant-pressure adsorption and desorption experiment, and adding the gas desorption amounts to obtain the experiment accumulated coal particle gas desorption volume.

According to the formula:

calculating to obtain an experimental value of the accumulated gas desorption amount of the coal particles;

in the formula (I), the compound is shown in the specification,the experimental desorption and diffusion time h is shown;is composed ofAccumulating the gas desorption volume of the coal particles in the experiment in the time period, wherein the gas desorption volume is cm 3/g;and-1 each representsAnd-gas pressure in sample tank, MPa, at time 1;represents the volume of free space of the sample tank, mL;the standard gas molar volume at the experimental temperature, mL/mol, is indicated.

FIG. 7 is a graph comparing a coal particle cumulative gas desorption amount prediction curve to a coal particle cumulative gas desorption amount experimental value, provided in accordance with some embodiments of the present application; comparing the coal particle accumulated gas desorption amount prediction curve with a coal particle accumulated gas desorption amount experimental value obtained by a coal particle gas constant pressure adsorption and desorption experiment under the isothermal condition, as shown in fig. 7, the coal particle accumulated gas desorption amount prediction curve obtained by the coal particle gas diffusion amount prediction method based on the real gas state is better than the coal particle accumulated gas desorption amount experimental value data obtained by the coal particle gas constant pressure adsorption and desorption experiment under the isothermal condition, which shows that the coal particle gas diffusion amount prediction method based on the real gas state provided by the application has good accuracy and reasonable prediction result, can provide a basis for gas extraction treatment and design and gas output amount prediction work of a coal mine, and provides a certain reference for underground gas extraction design and coal bed gas output prediction work.

In the method, the free gas density of the real gas is calculated based on the real free gas state equation; according to the free gas density of the real gas, correcting the Langmuir monolayer adsorption isothermal equation based on the gas dynamics theory to obtain the content of the adsorbed gas; fitting the sum of the free gas content and the adsorbed gas content according to the Langmuir equation to obtain a simplified Langmuir type equation of the total gas content of the coal particles; according to the desorption time of gas in the coal particles and the distance from the center of the coal particles to any position in the sphere of the coal particles, differentiating the simplified Langmuir equation of the total gas content of the coal particles to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particles; solving the desorption and diffusion model driven by the free gas density gradient of the coal particles based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulated gas desorption amount prediction curve so as to predict the gas diffusion amount of the coal particles; and finally, verifying the constructed desorption and diffusion model driven by the density gradient of the free gas of the coal particles based on the matching degree of the experimental data of the gas accumulative desorption amount of the coal particles and the simulation and prediction curve of the gas accumulative desorption amount of the coal particles.

The desorption and diffusion model of the coal particle free gas density gradient drive constructed in the application overcomes the defect that the traditional desorption and diffusion quantity obtained based on the Fick diffusion model and the experimental data have large deviation, and greatly improves the matching degree of the theoretical prediction value of the desorption and diffusion quantity of the coal particle free gas and the experimental measurement data.

The prediction method provided by the application also has the characteristics of quick and convenient calculation, and the result can be output only by inputting parameters.

In a traditional gas desorption and diffusion experiment in a laboratory, the gas desorption and diffusion limit is generally reached after more than ten hours, and even if the experiment is continued, the desorption and diffusion amount is not obviously changed. According to the prediction method provided by the application, the dynamic change of the desorption amount of the gas in the coal in a longer time period can be accurately predicted by setting the time step length and the iteration times, and the method is not limited by the experiment duration.

Exemplary System

FIG. 8 is a schematic diagram of a system for predicting gas emissions from coal particles based on true gas conditions according to some embodiments of the present disclosure; as shown in fig. 8, the system includes: the model building unit 700 and the gas prediction unit 800 are specifically:

a model building unit 700 configured to: differentiating the simplified Langmuir equation of the total gas content of the coal particles according to the desorption time of the gas in the coal particles and the distance from the center of the coal particles to any position in a sphere of the coal particles to obtain a desorption and diffusion model driven by the free gas density gradient of the coal particles;

the desorption and diffusion model driven by the density gradient of the coal particle free gas is as follows:

in the formula:is the gas pressure;is the mole of gasQuality;is the universal gas constant;Tis the gas temperature;

the initial conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

the boundary conditions of the desorption and diffusion model driven by the density gradient of the coal particle free gas are as follows:

a gas prediction unit 800 configured to: and solving the desorption and diffusion model driven by the free gas density gradient of the coal particles based on a finite difference numerical method and a Gauss-Seidel iteration method to obtain a coal particle accumulated gas desorption amount prediction curve so as to predict the gas diffusion amount of the coal particles.

In some optional embodiments of the present application, the model construction unit 700 comprises an equation simplification subunit configured to: the simplified Langmuir-type equation of the total gas content of the coal particles is obtained by fitting the sum of the free gas content and the adsorbed gas content according to the Langmuir equation;

the simplified Langmuir-type equation of the total gas content of the coal particles is as follows:

In some alternative embodiments of the present application, the equation reduction subunit includes: a free gas content calculation module configured to: according to the formula:

calculating to obtain the content of the free gas；

In some optional embodiments of the present application, the equation reduction subunit further comprises: an adsorbed gas content calculation module configured to: the adsorbed gas content is obtained by correcting a Langmuir monolayer adsorption isothermal equation based on a gas dynamics theory according to the real free gas density; the content of the adsorbed gas is as follows:

In some optional embodiments of the present application, the gas prediction unit 800 includes: the device comprises a coal particle dividing subunit, a difference subunit, a resolving subunit and an analog curve generating subunit;

the coal particle molecular dividing unit is configured as follows: dividing the distance from the center of the coal particle to any position in a sphere of the coal particle and the desorption time of gas in the coal particle to obtain a spherical shell node and a desorption time node of the coal particle;

the difference subunit is configured to: according to the spherical shell node and the desorption time node, based on a finite difference numerical method, differentiating the desorption and diffusion model driven by the density gradient of the coal particle free gas to obtain a difference equation of gas flow;

the solution operator unit is configured to: solving a difference equation of the gas flow based on a Gauss-Seidel iteration method to obtain a predicted value of the accumulated gas desorption amount of the coal particles;

an analog curve generation subunit configured to: and drawing a prediction curve of the accumulated gas desorption amount of the coal particles according to the predicted value of the accumulated gas desorption amount of the coal particles so as to predict the gas diffusion amount of the coal particles.

In some optional embodiments of the present application, in the differential sub-unit, the differential equation of the gas flow is:

In some optional embodiments of the present application, in the calculating subunit, the calculating a difference equation of the gas flow based on the gaussian-seidel iteration method to obtain a predicted value of the cumulative gas desorption amount of the coal particles includes:

solving the density of the free gas obtained by the differential equation of the gas flow according to a formula:

calculating to obtain a predicted value of the accumulated gas desorption amount of the coal particles;

in some optional embodiments of the present application, the system for constructing a coal particle permeability evolution model under the adsorption condition further includes:

a model verification unit configured to: and verifying the desorption and diffusion model driven by the density gradient of the free gas of the coal particles according to the matching degree of the experimental data of the constant-pressure adsorption and desorption experiment of the gas of the coal particles under the isothermal condition and the prediction curve of the accumulated gas desorption amount of the coal particles.

In some optional embodiments of the present application, in the model verification unit, the isothermal coal particle gas constant pressure adsorption and desorption experiment includes: the method comprises a coal particle sample preparation stage, a test preparation stage, a gas adsorption stage and a constant pressure gas desorption stage.

The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

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