A Geomodel for Pore Pressure Prediction Based on A Viscoelastic Compaction Law

Abstract

It is important to develop a model that simulates in situ pore pressure profile especially in an overpressured interval mainly because of wellbore instability, hydraulic fracturing treatment, lost circulation, kick, and blowout. The current methodology for predicting pore pressure depends on the Terzaghi's total stress but requires the accurate determination of the effective stress in the rock. The sedimentary processes occurring in a basin put the rock under compaction, which can be viscoelastic. The normal-compaction methods of predicting pore pressure consider only mechanical compaction, but viscous compaction is important to consider, especially beyond 2000 meters of the subsurface. In this study, a model for predicting pore pressure was developed by applying an effective stress law that considers viscoelastic compaction into the Terzaghi's stress equation. From the relationship defining effective stress and the rate of deformation, the author posed an expression for the total effective stress in terms of time. The applicable boundary condition was with respect to the transit time through the rock. Using transit time data for a Gulf Coast wellbore at 10,000 ft yielded a pressure gradient of 0.885 psi/ft, which compares to 0.863 psi/ft obtained from the modified Eaton's model and 0.9132 psi/ft obtained from the Zhang model. Another pressure required for a wellbore at 30,000 ft yielded a pressure gradient of 0.535 psi/ft, which compares with 0.52 psi/ft obtained from measured formation pressure. Thus, the results indicate that the viscoelastic compaction accurately defines the pore pressure profile in a rock. Furthermore, simulation results indicate that the most important variable affecting pore pressure is the overburden stress.