煤粒瓦斯扩散的理论模型及其解析解

建立了第三类边界条件下的煤粒瓦斯扩散的物理数学模型,用数学物理方法求出了其解析解,并测算了煤粒瓦斯扩散参数,分析结果表明,传质毕欧准数反映了煤粒瓦斯扩散场的特点,传质傅立叶准数则反遇了扩散场随时间的动态特征。该模型包含以往的第一类边界条件下的扩散模型,所以更具广泛性。     

瓦斯球向流动的数学模拟

本文把瓦斯在煤粒中的流动过程看作是气体在多孔介质中的扩散运动。通过模拟和对一些矿井煤样的实际测定,验证了Fick扩散模型的适用性;运用相似理论探讨了煤粒内部的瓦斯流动状态、浓度分布规律以及球向流动场的特点。经模拟和实测结果对比,初步肯定了用扩散模型描述低破坏类型煤的瓦斯放散过程是比较理想的。     

第二类和第三类边界条件下非均匀内热源导热微分方程中的热流分流和叠加

本应用热流的分流和叠加原理，得出第二类和第三类边界条件下，带非均匀内热源物体导热微分方程的解。     

基于两种数学模型的煤粒瓦斯放散数值解算

设计了煤粒瓦斯解吸实验,得到4种粒径煤样在4组不同初始压力条件下累积解吸量随时间变化的实测曲线.根据菲克扩散定律与达西渗流定律分别建立了瓦斯在球形煤粒中放散的数学模型,通过有限差分的方法并利用VB编程进行解算,得到煤粒在不同初始压力下的累积解吸量.通过与实验结果对比,表明达西模拟结果与实验结果匹配度较高,而菲克模拟结果与之偏离较大.验证了煤粒中的瓦斯放散更符合达西定律.     

基于达西定律的煤粒瓦斯放散数值模拟研究

为了证明煤粒瓦斯解吸放散与视煤粒为球体无关,将煤粒简化为圆柱体进行研究。基于达西定律,建立柱坐标系下的瓦斯放散方程,运用有限体积法进行离散并无因次化,编制Visual Basic程序进行解算。通过对比分析模拟结果和实验结果,发现两者拟合程度很高,再一次证实了瓦斯在煤粒内部微孔隙中的流动符合达西定律,且进一步说明煤粒瓦斯放散规律与所选用煤粒形状无直接关系。     

土壤中溶质运移的数学模型及其解析解

首先给出了非均匀土壤中考虑水动力弥散尺度效应的一维溶质运移两区模型,然后在初始浓度为零,半无限一维空间内第一类边界条件下,推导出了可动区和不动区溶质浓度分布Cm(x,t）,Cim(x,t）的解析表达式。     

非线性随机振动体系首次越界时间的统计特性

在随机平均法的基础上，对受平稳激励影响的非线性振动体系振幅响应过程的首次越界时间进行了研究，通过对Ｐｏｎｔｒｙａｇｉｎ方程边界条件的确定，给出了首次越界时间的各阶统计矩，并利用摄动法，给出了可靠度的解析形式的近似解。     

非线性随机振动体系首次越界时间的统计特性

在随机平均法的基础上，对受平稳激励影响的非线性振动体系振幅响应过程的首次越界时间进行了研究．通过对Ｐｏｎｔｒｙａｇｉｎ方程边界条件的确定，给出了首次越界时间的各阶统计矩，并利用摄动法，给出了可靠度的解析形式的近似解     

半扩散边界下污染土中污染物一维扩散解析解

针对以往大多关于污染物扩散研究假设的理想边界,在单层污染土层介质中考虑了更贴近实际情况的半扩散边界,并建立了该边界条件下污染物向周围土层扩散的模型。基于分离变量法得到了污染土中浓度随深度及时间变化的解析解。利用Matlab编制了相应计算程序并与COMSOL TDS模块数值仿真和已有解析解的结果进行对比,验证了解析解的可靠性。分析了复杂边界条件对污染物扩散及污染物通量的影响及其敏感性。结果表明:浓度随S di值增大而减小;S di值相差越大对土层内上下浓度分布影响越大;通量随S di值增大而增大,但增速降低。     

W(x,t)普遍结果的推导

用分离变量法求解数理方程定解问题时，要求其第一、二、三类边界条件必须是齐次的。若为非齐次的，必须寻求恰当的辅助函数W(x，t)，进行变换，将其化为齐次的。从稳定条件下的线性非齐次边界条件出发，给出了W(x，t)的统一形式，进而将其推广到非稳定条件下的非齐次边界条件，得到W(x，t)的一般的结果。     

多孔介质质扩散系数线性模型中的参数估计方法

本文提出一种在第三类边界条件下,通过理论计算蒸发规律与实测蒸发规律之间的最佳逼近,瞬态测定计算变物性质扩散系数的参数估计方法。设计并制造了真空蒸发实验装置。在假设质扩散系数为舍湿量线性函数的情况下,对石膏板和水泥板的质扩散系数进行了测量计算。实验和计算结果表明,测试及计算方法简单可行,容易进行控制,测定时间较稳态方法大大缩短,因此比较实用可靠。     

A rapid and accurate direct measurement method of underground coal seam gas content based on dynamic diffusion theory

Coal seam gas content is frequently measured in quantity during underground coal mining operation and coalbed methane (CBM) exploration as a significant basic parameter. Due to the calculation error of lost gas and residual gas in the direct method, the efficiency and accuracy of the current methods are not inadequate to the large area multi-point measurement of coal seam gas content. This paper firstly deduces a simplified theoretical dynamic model for calculating lost gas based on gas dynamic diffusion theory. Secondly, the effects of various factors on gas dynamic diffusion from coal particle are experimentally studied. And sampling procedure of representative coal particle is improved. Thirdly, a new estimation method of residual gas content based on excess adsorption and competitive adsorption theory is proposed. The results showed that the maximum error of calculating the losing gas content by using the new simplified model is only 4%. Considering the influence of particle size on gas diffusion law, the particle size of the collected coal sample is below 0.25 mm, which improves the measurement speed and reflects the safety representativeness of the sample. The determination time of gas content reduced from 36 to 3 h/piece. Moreover, the absolute error is 0.15–0.50 m³/t, and the relative error is within 5%. A new engineering method for determining the coal seam gas content is developed according to the above research.     

松散煤体中氧气扩散系数的实验研究

根据松散介质中气体扩散的理论分析。得出了松散煤体中氧气等效扩散系数的理论计算公式。在静态扩散双容积法的基础上，建立了松散煤体中气体扩散系数的实验测定装置，通过测定氧气在不同空隙率松散煤体中的等效扩散系数，确定了它的理论计算公式中修正系灵敏的取值范围，从而得出其与空隙率的函数关系。最后根据热力学原理，推算出松散煤自燃过程中不同温度和压力时氧气等效扩散系数的近似计算公式。     

Time-varying diffusion characteristics of different gases in coal particles

Based on the analytical solution of gas diffusion in spherical coal particles with a constant diffusion coefficient, a calculation method of time-varying diffusion coefficient is proposed by constructing objective function. The time-varying diffusion behavior of methane, nitrogen and carbon dioxide in the coal particles was studied. The results show that with the increase of diffusion time, the diffusion coefficients of methane, nitrogen and carbon dioxide gas in the coal particles exhibit an attenuation characteristic, eventually approaching a limit value individually. The diffusion coefficient of carbon dioxide is larger than methane, and the diffusion coefficient of nitrogen is smallest. Significant phenomenon of limited diffusion was observed for coal of strong adsorption capability. Through the analysis of the diffusion coefficient of gases at different diffusion time, a mathematical model describing the time-varying diffusion characteristic of gases is obtained. The implementation of mixed gases to replace coal bed methane has a very important practical significance.     

混凝土水分扩散表面因子理论模型与验证

针对混凝土湿度场对混凝土结构耐久性、混凝土表面干缩应力以及干缩裂缝等的影响,研究混凝土湿度场中水分扩散表面因子这一关键因素.引入混凝土表面孔隙面积和孔隙中的水分扩散系数2个参数,推导混凝土湿度场的第3类边界条件.将混凝土表面水分对流扩散简化为不可压缩流体一维平板壁面对流传质问题,根据质量守恒和平板壁面对流传质理论,建立混凝土干燥过程水分扩散表面因子的理论模型以及模型的近似解.结果表明,理论模型和试验检测结果之间具有良好的相关性.     

变扩散系数离子渗氮模型的建立与验证

在离子渗氮过程中，扩散系数D是随氮质量分数而变化的。结合这一情况，利用Crank-Nicolsion差分方程，并假定工件的硬度值与其含氮量是成正比关系，建立基于变扩散系数的离子渗氮的新模型，并利用Matlab工具对其进行计算机模拟及实验验证。结果表明，20CrMnTi渗氮8和10h后，实测的横截面显微硬度曲线与通过本模型计算而得的硬度曲线较好地相符；本模型成功地模拟了离子渗氮过程的氮质量分数变化。同时，随着时间的延长，迭代法对误差进一步放大。本模型只需通过简单易行的硬度测量，即可对离子渗氮过程的氮质量分数分布进行定量地预测，获得较为满意的结果，对指导生产具有很大的意义。     

Experiment of gas diffusion and its diffusion mechanism in coal

In coal, the gas mainly exists in a free or an adsorption state. When the coal containing gas is damaged, gas desorption and diffusion will occur which can result in gas disaster. This research on gas desorption and diffusion provides a theoretical basis for gas disaster mechanism and prevention. The influence of pressure and temperature on gas diffusion is studied by the experiment. And the mechanism of pressure and temperature on gas diffusion is also analysed. The research results indicate that gas diffusion capacity increases with increasing temperature under the same pressure for the same coal sample. This is mainly because the temperature increases, gas molecular hot motion is severer, kinetic energy of gas molecular increases, and gas desorption quickens, therefore gas diffusion capacity changes stronger. Under other unchanged conditions, the greater gas adsorption balance pressure, the more gas adsorption content, and the higher the initial gas concentration. When gas diffusion begins, the greater the gas concentration gradient, the faster the gas diffusion speeds.     

A general solution and approximation for the diffusion of gas in a spherical coal sample

The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the diffusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken. The results indicate that the square root relationship of gas release is the first term of the approximation, and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a spherical coal sample.     

计算混凝土中氯离子扩散系数的实用方法

在海洋环境中,含有大量的氯离子,而氯离子是引起钢筋锈蚀的一个重要因素,因此预测混凝土中氯离子的浓度是计算海洋环境中钢筋初始锈蚀时间的前提,而氯离子扩散系数又是预测氯离子浓度的要素。但传统的计算氯离子扩散系数的方法比较繁琐而且误差较大,本文将传统的计算模型进行了转化,给出一种简单且更加合理的计算方法。