Time-dependent wellbore (in)stability during oil and gas drilling account for a significant amount of lost rig time and substantially increased drilling costs ($700 million annually according to conservative estimates). Coupled time-dependent processes have been previously described in the realm of the poroelasticity theory. This wellbore (in)stability modeling approach allows the drilling engineer to systematically include the stress variation around the wellbore and the associated rock deformation and pore pressure changes. In this paper, in addition to the analyses conducted on the previously derived solutions for thermal and pore fluid diffusion, the time-dependent solution for stresses and pore pressures considering the mud and formation shale activities are presented. These solutions are the basis of the software, PBORE-3D, which utilizes contemporary programming techniques and can perform analyses of stress/pore pressure, formation failure, mud weight, and mud-salinity design for drilling shale formations. The model is especially useful in the prediction and visualization of time-dependent break-outs created due to inadequate mud weights; as well as time-dependent alteration of the near wellbore stress concentration caused by excessive mud weights leading to lost circulation problems. A case study is presented in this work which demonstrates the straightforward application of the model to challenging drilling conditions.


It is well established that time-dependent processes are responsible for instability and failures in wellbore drilling. Time-dependency in wellbore stability analysis is a result of the coupled phenomena of pore fluid diffusion and formation stress variation. This coupled diffusion-deformation phenomenon is explained on the basis of the theory of poroelasticity.1

Cost effective and successful drilling requires that the drilling fluid pressure be maintained within a tight mud-weight window dictated by the stress and pressure analyses around the wellbore. The time-dependent nature of the stress and pore pressure variation around the wellbore results in the mud-weight window varying with time. The gradient of temperature between the drilling mud and the rock formation is also an important issue in wellbore stability analyses. The temperature gradient will significantly affect the time-dependent stresses and pore pressure distributions around the wellbore. In addition, mud salinity and formation exposure time need to be considered while drilling in chemically reactive formations such as shale, using a water based mud (WBM).

Analytical solutions for inclined boreholes in a general three-dimensional in-situ state of stress, accounting for time-dependent fluid diffusion, thermal and chemical effects, have been published and extensively applied in evaluating potential time-dependent effects on wellbore stability.2,3 These solutions are implemented in software, PBORE-3D, developed for industry application. The solutions can perform analyses of stress/pore pressure, formation failure, mud weight and mud salinity design for drilling in shale formations.3,4 The software also treats the thermal and viscous effects.5,6

In this paper, the poromechanics approach used in obtaining solutions for the inclined borehole problem, which form a basis for the models in PBORE-3D, is described. Further, PBORE-3D is used for evaluating time-dependent effects on wellbore stability for a field case study.

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