天然气水合物注热开采数学模型

根据热力学第一定律及天然气水合物分解机理，在合理假设基础上，建立了包括物质守恒方程、能量守恒方程、分解动力学方程及辅助方程的天然气水合物注热开采数学模型。对数学模型进行差分处理得到差分方程组，采用隐式求解压力、显式求解饱和度（IMPES）的方法，考虑天然气水合物分解的压力、温度平衡条件，对模型进行求解，据此编制了数值模拟器。数值模拟器很好地拟合了注热开采实验的产气速率和温度分布，验证了数学模型的有效性。数值模拟及注热开采实验分析表明，天然气水合物注热开采可分为自由气释放、水合物分解及边界效应3个阶段，水合物分解存在分解前缘，注入端一侧水合物大部分已经分解，出口端一侧水合物分解较少，饱和度较高。图5表1参11

Mathematical model for natural gas hydrate production by heat injection

According to the first law of thermodynamics and the mechanism of natural gas hydrate decomposition, a mathematical model of thermal recovery comprising mass and energy conservation equations, kinetic equations of decomposition and the auxiliary equations is established on the basis of reasonable assumptions. Difference disposal is implemented for the mathematical model to obtain the difference equation set. Taking the pressure and temperature equilibrium conditions of natural gas hydrate decomposition into account, the model is resolved using the method of IMPES and a numerical simulator is built. The simulator can match well with the gas rate and temperature distribution of thermal recovery experiments and the validity is demonstrated. The thermal recovery process of natural gas hydrate can be divided into three periods: the release of free gas, the decomposition of natural gas hydrate, and the boundary effect. There exists decomposition front in the process of natural gas hydrate decomposition. The hydrate near the injection end is almost decomposed, whereas most of the hydrate near the exit end is not decomposed, exhibiting a high saturation.