Abstract: In reference literature(1)Schechter and Gidley established a mathematical model of the reactant concentration C^P in a single pore to simulate the acidizing process.In order to get the average concentration C^P,they define a parameter "α" in(1).They assume that "α" depends on the pore geometry,the diffusion coefficient and the reaction velocity constant; but is independent to the time and axial position of the pore.Under some coditions,a formula of C^P depending on α is given in(1).It is recognized that the method proposed above must prove that α is independent to the time t and axial position of the pore Z,and α can be determined.However,this is impossible.In this paper,C^P is solved directly from a mathimatical model mentioned above,under some conditions,and thus,an expression of C^P is obtained.According to the result it is proved that even if a single pore is defined,α still depends on Z andt,and the values of α can spread in an infinite interval.As a result,α can not be detemined.Thus,the method used to solve C^P in(1) should be modified before its application.

摘要： Schechter和Gidley模拟酸化过程,给出了孔隙中反应物浓度C^P的数学模型,为了求解平均浓度C^P,模型中定义了一个系数α,并认为α仅依赖孔隙的几何尺寸、扩散系数和反应速度常数,而不依赖于孔隙的轴向位置和时间,并在一定假设条件下,给出了平均浓度C^P的表达式,该式依赖于α.作者认为,上述方法必须证明α与孔隙的轴向位置z、时间t无关,并设法测定α.本文使用特征线法与特征函数法,直接求解反应物浓度C^P的数学模型,得到了C^P的显式解,并由此得到C^P的表达式.这里得到的C^P与C^P的表达式都不依赖于α.利用所得结果,还证明了:即使是给定的单个孔隙,α也是依赖于z、t的,α的取值可以散布在无穷区间,α无法确定,从而Schechter和Gidley所述求解C^P的方法是错误的.

关键词: 表面反应, 定解问题, 数学模型, 平均浓度, 反应物浓度, 表达式, 孔隙, 假设条件, 定解条件, 酸化