Abstract
In this paper, we provide new analytical and semi-analytical solutions based on a coupled wellbore/reservoir thermal model to investigate the information content of transient temperature measurement made within the vertical wellbore across from the producing horizon or at a gauge depth above it during drawdown and buildup tests. Our investigation leads to new interpretation/analysis methodologies of sandface and wellbore transient temperature data based on temperature-derivative and straight line methods for estimating near wellbore and far field formation parameters. Slightly compressible, single-phase, and homogeneous infinite-acting reservoir system with skin effect is considered. The analytical solutions accounts for Joule-Thomson heating/cooling, adiabatic fluid expansion, conduction and convection effects both in the wellbore and reservoir. The development of the analytical and semi-analytical solutions is based on the fact that the effects of temperature changes on wellbore and reservoir pressure transient data can be neglected so that the wellbore mass and momentum and reservoir pressure diffusivity equations and thermal energy balance equations in the wellbore and reservoir can be decoupled. The semi-analytical solution for predicting sandface temperatures is verified by use of a general purpose thermal simulator. Wellbore temperatures at a certain gauge depth are evaluated through analytical steady-state and transient wellbore temperature equations which couple the semi-analytical reservoir temperature model based on the conventional wellbore storage model or the more general model accounting for momentum effects in the wellbore. Results show that drawdown sandface temperatures are totally dominated by advection, whereas buildup sandface temperature data are dominated by conduction. Drawdown and buildup sandface temperature data exhibit two semilog straight lines; one at early-times reflecting the effects of adiabatic fluid expansion in the in the skin zone near the wellbore, whereas the late-time semilog straight line reflecting the Joule-Thomson effects and exhibiting the non-skin zone properties. For temperature measurements made at locations above the producing horizon, the wellbore temperature is strongle dependent upon distance above the producing horizon, geothermal gradient, and radial heat losses from the wellbore fluid to the formation on the way to gauge. Our results indicate that skin-zone properties seems very difficult to estimate from the drawdown and buildup wellbore temperatures unless the gauge location is not far from the producing zone. Buildup wellbore temperature seems mostly dominated by wellbore heat losses as compared to drawdown wellbore temperature data and hence cannot reflect the formation properties.