Temperature measured from a permanent downhole gauge in a well after the well shut-in provides a unique perspective for surveillance and production management purposes. For example, in deepwater environment, production engineers need to know the temperature status of a shut-in well before it is being restarted since different temperature profiles along the wellbore may need very different restarting strategies for flowing assurance purposes. A number of "rule-of-thumb" or complicated numerical simulations are either not reliable or impractical.
This paper presents a semi-analytical model to estimate the temperature transient behavior after the well shut-in. The model is solved numerically through inverse Laplace transform and integration. This solution gives temperature distribution profile and history in any location along the radial direction for a given production time and shut-in duration. To make it more general for other wells, an empirical correlation is provided through regression on the calculated type curves. The difference between this semi-analytical solution with other previous efforts will be discussed.
The applications of the solution to this model are multiple folders. For example, we can use the solution to predict the temperature behavior after the well shut-in, which can be used for flow assurance purposes. Furthermore, matching the calculated temperature with the measured temperature at the same location will yield the well local heat transmissibility coefficient. Some field examples are provided to demonstrate these applications.