天然气水合物注热水分解径向数学模型

Radial Mathematical Model for Hot Water Dissociation Frontal Brim of Natural Gas Hydrates

在一半无限大区域水合物分解过程描述基础上,建立了Stefan移动边界径向拟稳定传热数学模型,利用Paterson指数积分函数求解了分解带和水合物带的温度精确解,结合Deaton方法和Clausius-Clapeyron分解热方程确定水合物分解前缘位置。对一给定物性参数的稳定水合物储层例子进行计算,得出了水合物径向分解规律:随着径向距离增加温度急剧下降到分解温度8.416℃,再降到储层温度5.33℃,分解前缘位置变化趋势变缓;随着时间增加温度从5.33℃缓慢上升到8.416℃后急剧上升,时间足够长接近注入热水温度100℃;随着时间增加径向半径增加趋势减缓,分解时间到150 d时80～100℃温度变化为27.3℃,100～150℃温度变化为49.3℃。

Based on the description of dissociation process of natural gas hydrate in a semi-infinite zone, a radial pseudo-stationary mathematical model of heat transfer was built with Stefan moving boundary, and accurate solution of temperature applied in dissociation zone and natural gas hydrate zone was calculated by using Paterson method of exponential integral function. In addition, the location of dissociation frontal brim of natural gas hydrate was determined by combining Deaton method with Clausius-Clapeyron equation for decomposition heat. Radial dissociation laws of natural gas hydrate were obtained through an example of a steady hydrate reservoir whose physical parameters are known： with the increasing of radial range, temperature of hydrate reservoir drops abruptly to 8.416℃ （dissociation temperature） and further to 5.33℃ （reservoir temperature）, and the location of dissociation frontal brim changes slowly; besides, with the increase of time, the temperature rises sharply after increasing slowly from 5.33 ℃ to 8.416℃, and after adequate days will reach 100℃ （the injected hot water temperature）; furthermore, radius of hydrate dissociation grows slowly, and after 150 days supposed dissociation temperature changes 27.3℃ for 80-100℃ and 49.3℃ for 100-150℃.