A description of rheological model for gelled crude oil using fractional order derivatives

Key words:  fractional order derivatives  gelled crude oil  viscoelasticity  rheological model  creep model

Abstract:

A new rheological model with fractional order derivatives was proposed to describe the creep characteristics and dynamic viscoelasticity of gelled crude oil. The quasi-Burgers rheological model wa$ established by combining the Maxwell model and the quasi-Kelvin model with fractional order derivatives, from which the creep compliance expression of Burgers model with fractional order derivatives was derived. Experimental results show that this model is capable of describing the creeping process of the gelled crude oil precisely, while the classic models for viscoelastic solids and for viscoelastic fluids can not fit the experimental creep curve well. Experimental results also show that both the quasi-Kelvin model with fractional order derivative and the quasi-standard linear model can describe the dynamic viscoelasticity exactly，while the classic models for viscoelastic solids cannot fit the experimental creep curve well.