The slider and the dashpot are in series, regardless whether the dashpot is in series or in parallel with a spring.
The slider and the dashpot are in parallel.
Creep, the time-dependent deformation of rock, has a promising application in petroleum engineering, as it may contribute to establish a physical barrier preventing leakage from the reservoir through the casing annulus. The contact between the rock and the casing is the first step to establish such a barrier. In this study, we simulate how the contact pressure increases after contact. The contact pressure is first evaluated based on two constitutive models built in FLAC. The simulation shows that the long-term contact pressure will increase from the preset wellbore pressure and eventually reach the in situ stress state, regardless of the mechanical property of the rock and the relative size of the casing annulus. This contact pressure is simulated also with a MATLAB code, which models the shale response as a Bingham viscoplastic material. The MATLAB simulation shows that the long-term contact pressure is controlled by the mechanical property of the rock and the relative size of the casing annulus. The feature of the Bingham viscoplastic model is then compared to a hollow cylinder test with external loading increasing step by step. We conclude that the Bingham viscoplastic model shows a more reasonable and conservative evaluation of the contact pressure.