SPE JOURNAL, cilt.22, sa.4, ss.1156-1177, 2017 (SCI İndekslerine Giren Dergi)
This paper presents new analytical and semianalytical solutions derived from a coupled transient-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. The solutions consider flow of a slightly compressible, single-phase fluid in a homogeneous infinite-acting reservoir system with skin modeled as a composite zone adjacent to the wellbore and account for the Joule-Thomson (J-T) heating/cooling, adiabatic-fluid expansion, conduction and convection effects both in the wellbore and reservoir. They are developed depending on the assumption that the effects of temperature changes on wellbore and reservoir-pressure-transient data can be neglected so that the mass- ,momentum-, and energy-balance equations in the wellbore and reservoir can be decoupled. The semianalytical 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 the analytical steady-state and transient-wellbore-temperature equations coupled with a semianalytical reservoir-temperature model accounting for conservation of momentum in the wellbore. Results show that drawdown-and buildup-sandface-temperature data may exhibit two semilog straight lines: one at early times reflecting the effects of adiabatic-fluid expansion in the skin zone near the wellbore, and the other, the late-time semilog straight line, reflecting the J-T effects and exhibiting the nonskin-zone properties. However, the wellbore-temperature measurements made at locations above the producing horizon may not exhibit these semilog straight lines because they are strongly 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. It is found that the skin-zone properties are very difficult to be estimated from drawdown-and buildup-wellbore temperatures unless the gauge location is not far from the producing zone. Specifically, we found that buildup-wellbore temperature is mostly dominated by wellbore-heat losses compared with drawdown wellbore-temperature data, and hence may not be useful to estimate the formation properties, including skin-zone properties.