Using finite element method, a numerical procedure is developed that is suitable for analysing the time-dependent changes in stress and fluid pressure in reservoirs due to the installation and operation of wellbores. The methodology incorporated allows for the mechanical failure of the formation and the influx of solid panicles which may occur in weakly-cemented materials. The numerical model is verified against closed-form solutions and applied to analyze a field problem involving an extensive damage to the formation accompanied by production of the solids into a well bore installed in a weakly-cemented oil sand formation. The application of the model provides an insight into the complex mechanisms which control formation stability and the physical changes that occur as a result of formation collapse.
In the oil and gas industry, wellbore instability is a continuing problem which adds substantially to drilling and operating costs. Instability in formations composed of loosely-cemented materials, can result in sand inflow or production during the oil recovery phase. Sand production leads to excessive operating cost and in some instances has led to well suspension. Even though these stability problems are widely encountered, the mechanisms and processes controlling the occurrence of instabilities and the transition from stable to plastic and subsequently to tensile failure leading to reservoir damage and associated influx of the solids. The objective of this paper is to provide a credible numerical procedure for understanding the mechanisms of instability in soils or weakly cemented rocks around wellbores and a practical tool for analyzing the response wells in damaged reservoirs.
As a vertical borehole is drilled, the radial stress at the face of the borehole decreases from the in-situ horizontal stress value to the fluid pressure in the hole. Well face failure results from the mechanical inability of the wall material to sustain the loss of radial support and the redistributed stresses. In uncemented formations, the potential for solid particles influx develops once fluid starts flowing towards the wellface; however, in cemented formations solids influx will only occur after the fluid-pressure gradient exceeds a certain critical value. The maximum sustainable fluid-pressure gradient depends on strength properties, and fluid characteristics of the formation. Schematic representation of the possible changes in geometry and material characteristics that can develop around producing wells in loosely-cemented formations is shown in Figure 1.
Risnes et al. (1982) developed theoretical formulations for the stress and pore pressure distributions around a cylindrical cavity in an elastic perfectly-plastic material under conditions of steady-state seepage. The formulations account for the development of plastic shear failure and the solutions are valid until the inception of tensile failure. The tensile stress state results from a combination of shear stress in the formation caused by creating the opening, and seepage pressure caused by the fluid flowing into the opening. Risnes et al. (1982) also provided an expression for the critical flowrate necessary to induce tensile stress throughout the formation.
