Summary Lost circulation, a major complication of drilling operations, is commonly treated by adding materials of various types, shapes, and particle-size distributions to the drilling mud. Generally known as wellbore strengthening, this technique often helps the operator to drill with higher mud gradients compared with that suggested by the conventional fracture-gradient or borehole-fracture-limit analysis. The underlying mechanisms through which a wellbore is strengthened, however, are not yet fully understood. This study explores these wellbore-strengthening mechanisms through an analytical solution to the related solid-mechanics model of the wellbore and its adjacent fractures. The provided solution is generic in that it takes into account the mechanical interaction of multiple fractures between one another and the wellbore under an arbitrary state of in-situ stress anisotropy. An additional generality in this solution arises from its unification and quantification of some solid-mechanics aspects of the previous hypotheses that have been published on the subject—i.e., stress cage, as well as the tip isolation and its effect on the fracture-propagation resistance. In relation to the stress-cage theory, the study investigates the wellbore-hoop-stress enhancement upon fracturing. The findings indicate that the induced hoop stress is significant at some regions near the wellbore, especially in the general vicinity of the fracture(s). However, given the strong dependency of wellbore stress on the mechanical and geometrical parameters of the problem, generalizing these results to the entire region around the wellbore may not always be trivial. The study also examines tip isolation, a common feature of fracture-closure and propagation-resistance hypotheses, through the analysis of partially reduced fracture pressures and a breakdown criterion, defined by the critical stress-intensity factor of the formation rock.

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A new indirect method to measure fraction solid in molten metals is presented. The method is based on the phenomena that when a metal sample (solid or liquid) rotates in a magnetic field (or the magnetic field rotates around a stationary sample), circulating eddy currents are induced in the sample, which generate an opposing torque related to amount of solid phase in a solidifying melt between the liquidus and solidus temperatures. This new technique is applied for measuring fraction solid on commercial A319 aluminum alloy. The solidification curves obtained by the proposed method at different cooling rates are in good agreement with predictions made by the Scheil model.

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