Thermal Effect on Fracture Width for Wellbore Strengthening Applications

Abstract

Abstract Most wellbore strengthening (WBS) techniques require an understanding of the width on an induced fracture to design the size and concentration of appropriate mud additives to mitigate the fracture growth. Current methods to estimate fracture width primarily consider stress and rock properties but neglect the effect of the thermal contrast between the drilling fluid and the formation. This paper reports the results of the modeling of the thermal effect on fracture width and proposes a practical method to integrate the thermal effect into current WBS design workflows. The proposed process uses both analytical and numerical methods to investigate the thermal effect. A finite element analysis (FEA) model simulates the coupled stress and temperature field around the borehole, which allows the width of the fracture to be derived at any point along the length. The Abaqus FEA model uses 2-D plane strain elements to allow either steady-state or transient thermal-mechanical analysis. The results of FEA modeling are compared to the semi-analytical solution which only addresses the mechanical effect. Both models use field data to verify and validate results. An equivalent tensile stress is used to derive an analytical solution for fracture width for the case of ‘long-term’ cooling. The results provide a good match to the steady-state thermal elastic FEA results. In the case of transient heat transfer, an approximate analytical solution is derived to describe temperature distribution around the borehole as function of time. Then the analytical solution for thermal stresses is derived based on intact circular borehole. The analytical results are compared and verified with the FEA. Currently, the fracture width in response to a transient thermal event can only be calculated using the FEA model. The change in fracture width due to the temperature disturbance can be superimposed over the elastic fracture width to provide a more accurate estimate of width due to both mechanical and thermal influences for planning WBS formulations. The model demonstrates that the cooling of the borehole with drilling mud results in a wider fracture than that which is predicted by the purely elastic models. If drilling mud temperature is not considered or managed effectively, the failure of the WBS application could result, leading to a lost circulation event. A field case where wellbore cooling occurs and leads to lost circulation is presented.