Most wellbore strengthening (WBS) techniques require an understanding of the width on an induced fractureto design the size and concentration of appropriate mud additives to mitigate the fracture growth. Currentmethods to estimate fracture width primarily consider stress and rock properties but neglect the effect of thethermal contrast between the drilling fluid and the formation. This paper reports the results of the modelingof the thermal effect on fracture width and proposes a practical method to integrate the thermal effect intocurrent WBS design workflows. The proposed process uses both analytical and numerical methods to investigate the thermal effect. Afinite 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 modeluses 2-D plane strain elements to allow either steady-state or transient thermal-mechanical analysis. Theresults of FEA modeling are compared to the semi-analytical solution which only addresses the mechanicaleffect. 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. Inthe case of transient heat transfer, an approximate analytical solution is derived to describe temperaturedistribution around the borehole as function of time. Then the analytical solution for thermal stresses isderived 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 FEAmodel. The change in fracture width due to the temperature disturbance can be superimposed over theelastic fracture width to provide a more accurate estimate of width due to both mechanical and thermalinfluences for planning WBS formulations. The model demonstrates that the cooling of the borehole withdrilling mud results in a wider fracture than that which is predicted by the purely elastic models. If drillingmud 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 circulationis presented.
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