Quilghini变换法在求解密度跃变的水合物热分解Stefan模型精确解中的应用  

Application of Quilghini transformation method to exact solutions of Stefans models for thermal dissociation hydrate with density jump

作　　者：李明川[1,2] 樊栓狮 徐赋海[4] 卢惠东[4] 李晓军[4] LI Mingchuan;FAN Shuanshi;XU Fuhai;LU Huidong;LI Xiaojun(School of Petroleum Engineering,China University of Petroleum,Qingdao 266580,Shandong,China;Key Laboratory of Unconventional Oil&Gas Development(China University of Petroleum),Ministry of Education,Qingdao 266580,Shandong,China;School of Chemistry and Chemical Engineering,South China University of Technology,Guangzhou 510641,Guangdong,China;Dongxin Production Plant,Shengli Oil Field,SINOPEC,Dongying 257094,Shandong,China)

机构地区：[1]中国石油大学(华东)石油工程学院,山东青岛266580 [2]非常规油气开发教育部重点实验室(中国石油大学(华东)),山东青岛266580 [3]华南理工大学化学与化工学院,广东广州510641 [4]中国石化胜利油田分公司东辛采油厂,山东东营257094

出　　处：《化工学报》2024年第10期3763-3774,共12页CIESC Journal

基　　金：中国科学院知识创新工程基金项目(KGCX2-SW-309)。

摘　　要：利用质量守恒原理建立了考虑密度跃变的天然气水合物热分解Stefan模型,通过对有弱解的均匀散度方程分部积分详细推导一般形式的Rankine-Hugoniot跳跃关系,获得了关于界面速度项三次方形式的Stefan耦合条件,但在工程需要误差范围内三次方可以忽略。在Stefan模型中引入速度项使得模型的精确解难以得到。Quilghini变换将质量转化为空间变量,Stefan模型的速度项消失,成为经典的类Stefan模型,再经Quilghini逆变换得到了密度跃变Stefan模型的精确解析解。通过Matlab编程,结合实例研究了超越方程解、温度分布和分解界面的规律性,探索注入温度和密度跃变对超越方程解、穿透深度、穿透时间和水合物位移的影响,密度跃变引起的误差在工程允许范围内。Stefans models for thermal decomposition of natural gas hydrate with density jump is established by using the principle of mass conservation.The general form of Rankine-Hugoniot jump relation was derive in detail,and the Stefan coupling condition in cubic form with respect to the velocity of interface was obtained,but the cubic term could be ignored within the errors of engineering requirements.It is the introduction of velocity terms in the Stefan model that makes it difficult to obtain an exact solution to the model.The mass as a space variable was introduced by the Quilghini transformation,the velocity term was vanished,and become the classical Stefan-likes models.Followed by the inverse Quilghini transformation,the accurate analytical solutions of the Stefans models with density jump could be successfully gained.Through Matlab programming,a concrete example was taken,laws on the solutions of transcendental equation,temperature distribution and dissociation interface were studied,the influences of injection temperature and density jump on solutions of transcendental equation,penetration depth,penetration time and hydrate displacement were probed.The errors caused by density jump were within the permissible ranges of engineering.

关 键 词：Quilghini变换 密度跃变 Stefan模型 Rankine-Hugoniot跳跃关系 天然气水合物 

分 类 号：TQ511.1[化学工程]