基于分数阶导数的盐岩流变本构模型

盐岩流变特性的研究对诸多地下工程如战略能源储备、CO2封存、高放废物处置等具有十分重要的意义.本文从分数阶导数出发,在常黏性系数Abel黏壶基础上,提出了一种新的变黏性系数的Abel黏壶元件.通过将分数阶Abel黏壶代替经典西原模型中Newton黏壶的方法,构建了基于分数阶导数的盐岩流变本构模型,并给出了流变本构模型的解析解.论文进一步应用程控流变仪进行了湖北江汉油田王储1井盐岩试件的单轴流变实验,基于盐岩流变实验数据,对分阶导数流变本构模型的参数进行了拟合分析,确定了模型中的参数.论文还进行了分数阶流变模型中的参数敏感性分析,揭示了应力水平、分数阶导数阶数、黏性系数对流变应变的影响规律,并验证了分数阶流变本构模型在特殊条件下可退化为经典西原模型.研究发现,本文提出的分数阶流变本构模型可以更好反映盐岩流变的三阶段尤其是加速流变阶段.

Time-based fractional derivative approach to creep constitutive model of salt rock

A modeling approach to the creep behavior of natural rock salt is of special interest for many underground engineering such as underground storage of natural gas and crude oil, and a permanent repository of CO2 and radioactive and toxic wastes. Based on the definition of fractional derivative, the Abel dashpot with a constant viscosity coefficient is generalized to an Abel dashpot with a variable viscosity coefficient, referred to as a new time-dependent element. By replacing a Newtonian dashpot in the classical Nishihara model with the fractional derivative Abel dashpot of a variable viscosity coefficient, a new creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional derivative creep constitutive model is given theoretically. Moreover, a computer-controlled creep set-up is employed to measure creep strain of a salt rock sample under the condition of uniaxial compression, taking from the Chuwang Well No.l, Jianghan Oilfield, Hubei Province. The parameters of the fractional derivative creep model are determined by fitting to the experimental results of time-dependent deformation of salt rock. In addition, a sensitivity study for the analytic solution of the time-based fractional derivative model is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient on a creep strain of salt rock. Furthermore, it is shown that the time-based fractional derivative model in the paper can be simplified to the classical Nishihara model in the special case. It is indicated that the fractional derivative creep model proposed in the paper gives a precise description of the three stages of creep especially the tertiary stage, i.e., an unsteady state period.