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Transient heat convection in a circular microchannel for hydrodynamically fully developed and thermally developing flow conditions is analytically solved by the integral transform and the Laplace transform techniques. A prescribed wall temperature boundary condition is assumed. The effects of velocity slip, temperature jump, and viscous heating are investigated. The results confirm that the viscous heating effects increase the Nusselt number for the specified conditions.

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Subhydrostatic or low bottomhole pressure wells are wells with large hydrostatic overbalance, that is, the hydrostatic pressure of the fluid column inside coiled tubing, drillpipe, or similar well intervention means is greater than the wellbore pressure at the corresponding vertical depth. The number of subhydrostatic wells is growing as more and more fields mature. Consequently, there is an increasing number of interventions required for these wells to improve and/or optimize their production. U-tubing of the fluid column is a very common and uncontrolled phenomenon during interventions in subhydrostatic wells that can cause problems. In this paper the focus will be on coiled tubing interventions; however, the same basic principles apply to other areas as well.A backpressure valve (BPV) is a device that is used in subhydrostatic wells to hold the fluid column inside coiled tubing to prevent U-tubing. The BPV compatibility with other components in the toolstring is a critical operational requirement. Following recent tests conducted with the BPVs readily available in the market, it has been shown that these are not appropriate for a number of applications. One example is an application involving pressure pulse telemetry. For pressure pulse telemetry, conventional BPVs either cannot pass the pressure signals or greatly attenuate the magnitude of them.A backpressure valve that is fully compatible with pressure pulse telemetry has been developed and will be presented in this paper. The root cause of why the conventional BPVs were not able to transmit pressure pulse will be discussed using the results from fundamental physics, computational fluid dynamics analysis, and lab and filed experiments. Finally, a typical set of results from a field trial using the new valve will be presented.