A Fractional Calculus Model for Viscoelasticity of Tight Sandstone

Viscous deformation of reservoir rocks possesses great significances in predicting long-term response of reservoirs subjected to drilling and hydraulic fracturing activities. Laboratory testing of a tight sandstone reservoir rock reveals time- dependent viscous deformation in response to applied differential stress. Replacing the Newton dashpot in the traditional Maxwell model with the Abel dashpot, the traditional Maxwell model was modified as the fractional Maxwell model. And then the fractional Maxwell model, Merchant model, Burgers model and generalized Kelvin model were utilized to fit the creep curve. The fractional Maxwell model fitted the creep curve with the best accuracy and the least parameters among the four models and especially this was the case at the beginning stage of the creep curve. And the fractional Maxwell model overcomes the shortcoming of incapability of describing the nonlinear creep behavior by the traditional Maxwell model. More fractional derivate models may be expected in describing more complicated rheological scenarios in future studies.