Study on the Construction of a Nonlinear Creep Constitutive Model of Salt-Gypsum Rock in the Bayan Deep and the Critical Value of Wellbore Shrinkage Liquid Column Pressure

Aiming at the problems of borehole shrinkage and pipe sticking caused by creep in salt-gypsum rock formations during deep well drilling, multi-field coupling creep experiments on deep salt-bearing gypsum mudstone were carried out. Furthermore, a nonlinear creep constitutive model was constructed based on the Drucker–Prager criterion, and the critical value of liquid column pressure for borehole shrinkage was determined through numerical simulation. Experiments show that at 140 °C, salt-gypsum rock is mainly subjected to brittle failure with single shear fracture, while at 180 °C, multiple sets of cross-cutting shear bands form, shifting to plastic flow-dominated composite failure. The coupling effect of confining pressure and deviatoric stress is temperature-dependent; the critical deviatoric stress is independent of confining pressure at 140 °C, but decreases significantly with increasing confining pressure at 180 °C, revealing that salt-gypsum rock is more prone to plastic flow under high temperatures and confining pressure. The creep constitutive equation was further determined, and fitting parameters show that the stress exponent m = 2–5 and the time exponent n decrease linearly with the increase in deviatoric stress, and the model can accurately describe the characteristics of three-stage creep. The numerical simulation found that there is a nonlinear relationship between the drilling fluid density and borehole shrinkage; the shrinkage rate exceeds 1.47% when the density is ≤2.0 g/cm3, and the expansion amount is >1.0 mm when ≥2.4 g/cm3. The critical safe density range is 2.1–2.3 g/cm3, which is consistent with the field data in the Bayan area. The research results provide an experimental basis and quantitative method for the dynamic regulation of drilling fluid density in deep gypsum rock formations, and have engineering guiding significance for preventing borehole wall instability.