Julien Marck

A model of planar borehole propagation

Drilling geometrically complex boreholes in the subsurface has been made possible with the development of downhole tools that steer the bit. This paper proposes a model of borehole propagation that can be used not only to predict the bit trajectory, here restricted to a vertical plane, but also to assess the conditions leading to abnormal situations. The model is formulated from considerations involving (a) a bit/rock interaction law that relates the force and moment on the bit to its penetration into the rock, (b) kinematic relationships that describe the local borehole geometry from the bit motion, and (c) a beam model of the bottom-hole assembly (BHA) that expresses the force and moment at the bit as functions of both the loads applied on the BHA and the geometrical constraints imposed by the stabilizers that center the BHA in the borehole. The coupling between the model components leads to the formulation of a delay differential equation that governs the evolution of the borehole inclination, with spa...

Spiraled Boreholes: An Expression of 3D Directional Instability of Drilling Systems

Energy-Water-Environment Sustainability (EWES) is an interdisciplinary program in the Department of Civil & Environmental Engineering that prepares students to tackle various grand challenges in engineering. Abstract: Occurrence of borehole spiraling is predicted by analyzing the delay-differential equations governing the propagation of a borehole. The analytical nature of the propagation equations makes it possible to conduct a systematic stability analysis in terms of a key dimensionless group that controls the directional stability of the drilling system. An application to a field case is discussed, as well as the simulations conducted by integrating the equations of borehole propagation. They illustrate that, for unstable systems, the model predicts spiraled boreholes with a pitch comparable to what is observed in the field. Furthermore, they show that a limit cycle, characterized by bounded magnitude of the oscillations, is attained if a nonlinearity is introduced in the bit response.

Withdrawal of Fluid from a Poroelastic Layer

This paper analyzes the problem of a sink segment extracting fluid from a poroelastic layer bounded by two semi-infinite impermeable elastic strata. This problem can be reduced to one of the classic elasticity theory, with the gradient of the pore pressure field in the reservoir acting as a pseudo-body force, and the jumps of pore pressure at the interfaces between the reservoir and the adjacent layers inducing pseudo-tractions. The solution of this elastic problem is obtained using integral transforms. The asymptotic behaviors are then emphasized and conceptual models are introduced that capture the salient features of the small and large time asymptotes.