Abstract
Drilling instability is always one of the major challenges to drilling engineers. The temperature differential and pressure differential affect the borehole instability by altering the stress concentration at near wellbore region through poro-elastic and thermal elastic stresses. The temperature gradient and pressure gradient between the drilling fluid and formation change not only from conduction and convection, but also from interacting to each other. In low mobility formation such as shale, the thermo-induced pore pressure is important while in high mobility formation, the pressure effect on the temperature is not negligible.
Furthermore, the imbalance in chemical potentials between the formation pore fluid and wellbore drilling fluid will cause the solvent and solutes to diffuse and transport. This will alter the fluid pressure due to chemical osmosis pressure. In this paper, a fully coupled borehole stability model is proposed including thermal, pore, chemical effect. In the model, not only pressure, heat conduction and convection are included, but also the interaction of pressure and heat are incorporated. The model is solved by superimposing method and finite difference method which otherwise is impossible to be obtained from analytical solution.
Introduction
Investigations to determine the factors impacting borehole instability have increased over the past decade as drilling engineers are faced with increasing challenges to drill through complex lithologies demanding equally complex solutions to minimize potential borehole stability issues. Various factors have been studied, including the impacts of thermal and mechanical properties on the stress field maintaining borehole stability [1, 2, 3, 4, and 5]. This paper couples the effects of these factors, as well as those generated by chemical potential driven osmotic equilibration forces, into a single model. The process required inserting, or superimposing, certain analytical solutions within the structure of a finite difference method solution. The model considers fluid and heat diffusion, including both heat conduction and convection, and also the impact of these forces on the osmotic potential between the formation and drilling fluids [6, 7, 8, 9, and 10]. While the magnitude of impact of each of these interactive parameters on the solution to stress/strain focused model will vary from case to case, a small effect may still be significant in considerations involving a narrow window of potential control.
Theoretical Models
The fully coupled chemical- thermal- poro-mechanical borehole stability model field equations include:
• Fluid diffusion equation.
• Heat diffusion and convection equation
• Chemical solute diffusion equation
• Geo-mechanical Equilibrium Equation
• Thermo Poro-elastic stress-strain and strain-displacement relationship
• Failure Criteria
The solute concentration, temperature and pressure distribution are obtained from the coupled diffusion equations. By solving the general equilibrium equation, stress-strain, strain displacement equations, the stresses around borehole are obtained.
