A Mechanical Model for Permafrost Freeze-Back Pressure Behavior
Authors: Goodman M.A. , Wood D.B. 
Published: December 2007

Abstract
Arctic oilwell drilling and production may cause extensive thawing of the permafrost which, if allowed to freeze back, may result in collapse loading that should be considered in the casing design. The loading mechanism is associated with the phase-change expansion of Pore water in the permafrost. The mechanical behavior of frozen permafrost. The mechanical behavior of frozen permafrost determines the extent of pressure buildup. permafrost determines the extent of pressure buildup. This paper presents an analytical description of freeze-back pressure behavior in the context of an elastic-Coulomb plastic model. By correlation with field-test data, it is shown that the elastic properties of permafrost govern the maximum pressure on the casing, while The Coulomb plastic properties and the amount of initial thaw influence the time buildup behavior. The model, together with a thermal simulator for predicting initial thaw and freeze-back radii, determines design parameters for Arctic well completions. Results indicate That it is possible to design casing strings to withstand the collapse pressures generated by freeze back, even for large pressures generated by freeze back, even for large thaws.

Introduction
Drilling and production of oil in the Arctic regions causes permafrost to thaw. If thawed permafrost is allowed to freeze back, then external permafrost is allowed to freeze back, then external pressure on the casing is generated by the pressure on the casing is generated by the phase-change expansion of pore water. The magnitude phase-change expansion of pore water. The magnitude of pressure buildup on the casing depends on the mechanical behavior of the frozen permafrost outside the thawed region. If the frozen permafrost does not readily deform to relieve the phase-change expansion, then pressures in excess of collapse pressure could result from the freeze-back process. pressure could result from the freeze-back process. In this paper, an analytical model of the mechanical behavior of permafrost during freeze back is presented. This model is motivated by results from two freeze-back field tests, as well as by results from laboratory tests on simulated permafrost. The following physically motivated permafrost. The following physically motivated assumptions form the basis for the analytical model. 1. Permafrost in the thawed state is porous and permeable. The concept of effective stress is permeable. The concept of effective stress is applicable to thawed permafrost. 2. Permafrost with excess ice is defined as a soil-ice mixture that, upon thaw in an undrained condition, is less than 9 percent undersaturated (0.09 is the coefficient of phase-change expansion). Permafrost with excess ice is considered to be Permafrost with excess ice is considered to be fluid-like. Permafrost without excess ice is considered to be a homogeneous, impermeable, isotropic solid. 3. The loading mechanism associated with freeze back is entirely caused by the phase-change expansion of water in the confined, thawed zone. At the beginning of freeze back, the thawed permafrost is assumed to be saturated, except for permafrost is assumed to be saturated, except for possibly a small gas fraction. Although ice possibly a small gas fraction. Although ice decreases in volume upon thaw, the thawed permafrost is assumed to be resaturated by vertical permafrost is assumed to be resaturated by vertical drainage, by influx of water from drilling muds, or by compaction of the matrix structure caused by the thaw. During freeze back, there is no pressure relief by bleed-off of fluids in the thawed zone or by thermal contraction of permafrost as temperatures are lowered during freeze back. 4. Stresses in frozen permafrost may be considered rate independent for loading rates associated with freeze back. According to laboratory results and the analysis of Appendix B, permafrost is generally viscoelastic, but the viscous or rate-dependent pressure corresponding to the freeze-back strain pressure corresponding to the freeze-back strain rate is negligible compared with the total freeze-back pressure. The field results (Fig. 1) support this pressure. The field results (Fig. 1) support this conclusion since pressure decline after freeze back was no more than 50 to 100 psi. 5. Permafrost subject to freeze-back loading does not fail in tension and does not fracture, but yields in shear according to a Mohr-Coulomb yield criterion and deforms plastically. The Coulomb yield behavior is motivated by the maximum pressure gradient plot of Fig. 2, which shows a straight-line dependence with a slope greater than the lateral overburden gradient.
SPEJ
P. 287