2006高教社杯全国大学生数学建模竞赛题目

5/62006高教社杯全国大学生数学建模竞赛题目（请先阅读

“对论文格式的统一要求”）D题:煤矿瓦斯和煤尘的监测与控制煤矿安全生产是我国目前亟待解决的问题之一，做好井下瓦斯和煤尘的监测与控制是实现安全生产的关键环节（见附件1）。b5E2RGbCAP瓦斯是一种无毒、无色、无味的可燃气体，其主要成分是甲烷，在矿井中它通常从煤岩裂缝中涌出。瓦斯爆炸需要三个条件：空气中瓦斯达到一定的浓度；足够的氧气；一定温度的引火源。p1EanqFDPw煤尘是在煤炭开采过程中产生的可燃性粉尘。煤尘爆炸必须具备三个条件:煤尘本身具有爆炸性；煤尘悬浮于空气中并达到一定的浓度；存在引爆的高温热源。试验表明，一般情况下煤尘的爆炸浓度是30～2000g/m3，而当矿井空气中瓦斯浓度增加时，会使煤尘爆炸下限降低，结果如附表1所示。DXDiTa9E3d国家《煤矿安全规程》给出了煤矿预防瓦斯爆炸的措施和操作规程，以及相应的专业标准(见附件2)。规程要求煤矿必须安装完善的通风系统和瓦斯自动监控系统，所有的采煤工作面、掘进面和回风巷都要安装甲烷传感器，每个传感器都与地面控制中心相连，当井下瓦斯浓度超标时，控制中心将自动切断电源，停止采煤作业，人员撤离采煤现场。具体内容见附件2的第二章和第三章。RTCrpUDGiT附图1是有两个采煤工作面和一个掘进工作面的矿井通风系统示意图，请你结合附表2的监测数据，按照煤矿开采的实际情况研究下列问题：5PCzVD7HxA（1）根据《煤矿安全规程》第一百三十三条的分类标准(见附件2)，鉴别该矿是属于“低瓦斯矿井”还是“高瓦斯矿井”。jLBHrnAILg（2）根据《煤矿安全规程》第一百六十八条的规定，并参照附表1，判断该煤矿不安全的程度（即发生爆炸事故的可能性）有多大？xHAQX74J0X（3）为了保障安全生产，利用两个可控风门调节各采煤工作面的风量，通过一个局部通风机和风筒实现掘进巷的通风（见下面的注）。根据附图1所示各井巷风量的分流情况、对各井巷中风速的要求（见《煤矿安全规程》第一百零一条），以及瓦斯和煤尘等因素的影响，确定该煤矿所需要的最佳（总）通风量，以及两个采煤工作面所需要的风量和局部通风机的额定风量（实际中，井巷可能会出现漏风现象）。LDAYtRyKfE注掘进巷需要安装局部通风机，其额定风量一般为150~400m3/min。局部通风机所在的巷道中至少需要有15%的余裕风量（新鲜风）才能保证风在巷道中的正常流动，否则可能会出现负压导致乏风逆流，即局部通风机将乏风吸入并送至掘进工作面。Zzz6ZB2Ltk名词解释（1）采煤工作面：矿井中进行开采的煤壁(采煤现场)。（2）掘进巷：用爆破或机械等方法开凿出的地下巷道，用以准备新的采煤区和采煤工作面。（3）掘进工作面：掘进巷尽头的开掘现场。（4）新鲜风：不含瓦斯和煤尘等有害物质的风流。（5）乏风：含有一定浓度的瓦斯和煤尘等有害物质的风流。附表1:瓦斯浓度与煤尘爆炸下限浓度关系空气中瓦斯浓度(%)00.51.01.52.02.53.03.54煤尘爆炸下限浓度(g/m3)30~5022.5~37.515~2510.5~17.56.5~12.54.5~7.53~52.5~3.51.5~2.5附表2:各监测点的风速,瓦斯和煤尘的监测数据表监测日期点与班次工作面Ⅰ工作面Ⅱ掘进工作面回风巷Ⅰ回风巷Ⅱ总回风巷日产量（t/d）风速瓦斯煤尘风速瓦斯煤尘风速瓦斯煤尘风速瓦斯煤尘风速瓦斯煤尘风速瓦斯煤尘1早班2.40.7182.070.947.672.220.267.442.130.767.522.090.987.235.150.677.05597中班2.560.628.42.080.857.512.290.267.452.270.667.932.10.897.275.360.67.28晚班2.240.667.612.090.827.512.40.297.622.090.737.142.110.97.075.310.636.82早班2.270.627.692.080.857.72.210.237.312.080.677.332.110.97.255.140.67.06602中班2.410.637.992.130.927.742.290.267.472.230.687.732.160.987.355.390.647.22晚班2.40.667.872.10.897.852.290.227.562.210.717.312.120.937.415.320.627.033早班2.270.787.752.10.897.672.290.277.422.040.837.362.110.957.325.190.687.03639中班2.220.717.712.090.927.562.310.267.482.110.767.252.110.977.265.260.656.93晚班2.290.667.682.090.947.512.150.167.182.020.717.172.121.017.155.050.636.944早班2.310.677.672.090.967.552.210.317.282.110.717.32.1217.25.170.686.95616中班2.370.717.892.080.727.582.110.197.022.170.767.422.120.757.095.140.586.95晚班2.40.627.992.10.877.612.440.187.712.110.687.392.120.97.255.360.586.995早班2.340.617.832.110.847.772.270.287.462.080.667.42.140.897.315.210.617610中班2.430.648.12.140.87.672.360.247.552.170.697.722.160.827.285.370.587.1晚班2.270.697.642.080.997.652.210.217.341.960.757.232.111.037.15.030.656.966早班2.290.727.812.10.977.752.270.27.481.930.777.442.121.027.285.080.667.02588中班2.390.647.962.110.987.542.10.237.242.020.717.642.131.017.135.010.687.06晚班2.310.697.732.1217.462.180.227.1720.757.312.131.077.15.070.686.947早班2.360.77.812.130.777.662.210.237.352.090.747.472.160.827.415.190.67.07582中班2.40.697.952.090.847.632.290.237.542.020.747.472.120.887.245.180.627.12晚班2.520.658.232.070.947.82.240.217.552.270.717.952.070.997.395.290.647.438早班2.490.648.192.140.787.782.270.287.452.210.687.92.160.827.395.340.597.38605中班2.210.737.592.090.87.72.220.267.211.910.777.152.10.847.395.010.626.94晚班2.270.667.672.070.947.682.220.197.372.080.717.212.0917.455.130.637.019早班2.390.597.822.061.017.662.240.167.22.130.647.482.081.057.325.170.617.19585中班2.370.688.082.10.917.572.290.177.472.150.757.282.120.957.315.280.637.03晚班2.270.737.652.080.697.512.290.197.342.060.777.342.120.757.245.190.586.9410早班2.360.657.952.120.877.542.270.327.462.040.737.482.130.97.155.180.656.99620中班2.360.677.852.130.857.852.230.237.392.130.727.172.140.927.335.230.627.07晚班2.360.677.862.110.847.572.240.167.512.10.727.482.140.97.225.210.67.1611早班2.290.77.882.070.847.512.140.227.262.110.747.442.090.897.125.10.626.9616中班2.310.657.742.090.817.852.180.247.242.140.687.222.110.867.55.170.617晚班2.370.698.12.090.837.612.090.276.992.110.757.722.110.887.065.080.647.1127早班2.310.77.992.10.87.782.220.247.152.040.757.452.120.857.315.120.617.06617中班2.360.687.92.120.987.562.250.187.242.150.747.472.151.037.215.260.647.04晚班2.310.727.92.10.857.592.140.287.222.040.777.512.110.97.355.060.667.1228早班2.410.77.982.120.897.752.090.27.132.140.737.512.140.947.465.110.637.18605中班2.250.77.822.090.917.722.340.147.6120.767.572.120.957.265.190.67晚班2.220.687.582.110.827.692.220.197.1320.757.192.140.877.375.110.616.9529早班2.40.688.172.0717.572.140.297.142.130.737.52.11.067.235.10.716.94586中班2.60.618.422.120.687.742.170.217.082.350.658.142.150.747.255.360.547.34晚班2.340.737.882.110.767.592.270.37.2620.787.242.130.827.065.140.636.9230早班2.310.627.912.10.987.642.230.27.212.170.687.492.131.037.235.230.656.97620中班2.370.638.052.110.827.542.240.247.332.130.687.542.130.8675.230.66.98晚班2.40.727.92.110.857.542.110.267.262.150.787.652.130.887.185.110.667.29[注]瓦斯的浓度：%，即体积百分比；煤尘的单位：g/m3；风速的单位：m/s；日产量的单位：t/d。采煤工作面Ⅱ掘进工作面局部通风机风筒待采煤层总回风巷回风巷II主巷道进风巷II采煤工作面Ⅱ掘进工作面局部通风机风筒待采煤层总回风巷回风巷II主巷道进风巷II掘进巷道放大示意图待采煤层待采煤层回风巷I图例局部通风机风量调节风门新鲜风流（进风）乏风流（回风）掘进工作面