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为定量分析煤层瓦斯流动模型简化求解所引起的误差,分别采用朗格缪尔方程与抛物线方程表示瓦斯含量,建立了两种煤层瓦斯单向流动数学模型(朗格缪尔式与抛物线式),并利用克里钦夫斯基近似法得到了抛物线式模型的简化形式(克里钦夫式).通过求解得到了3种数学模型下的煤壁瓦斯压力、含量分布的对比曲线和瓦斯比流量与时间关系的对比曲线,定量分析了抛物线式、克里钦夫式相比朗格缪尔式计算结果的相对误差.结果表明:抛物线式的计算误差较小;克里钦夫式则有较大的误差,在计算的初始时刻,克里钦夫式计算结果比朗格缪尔式大若干倍,并以较大的速率衰减,经较短时间后,克里钦夫式与朗格缪尔式的计算结果有相同的变化趋势,而前式的计算结果明显小于后式.
In order to quantitatively analyze the error caused by the simplified solution of coal seam gas flow model, the gas content was expressed by the Langmuir equation and the parabola equation respectively. Two mathematical models of gas unidirectional flow (Langmuir and Parabola) And the simplified form of the parabola model (Klitschov equation) is obtained by using the Klitschowski approximation method. The gas pressure, the comparison curve of the content distribution and the gas flow ratio Compared with the time curve, the relative error of the parabolic and Klinkin-style Langmuir formulas is quantitatively analyzed.The results show that the parabolic error is small, Large error in the initial moment of calculation, Klitschchef calculation results several times larger than Langmuir-style and decay at a larger rate, after a short period of time, Klitschchev and Langhammer The results of the Er equation have the same trend, while the results of the preceding equation are obviously less than the latter.