Semi-analytical model for thermal effect on gas well pressure-buildup tests

This paper presents a semi-analytical wellbore/reservoir model(1) that can describe general wellbore effects, especially the thermal effect, on high-t emperature gas well pressure-buildup tests. A numerical simulator has been developed from the model. Using different combinations of wellbore and rese rvoir parameters, the simulator generated curve shapes that differed with w ellbore thermal effects. Many of the curve shapes have been observed in the field.(2,3) Using the results from this paper, engineers can distinguish b etween general wellbore effects and reservoir behavior in the pressure data , which will make the interpretation more accurate. Also, with the help of the simulator developed from the model, engineers can effectively design ga s well pressure-buildup tests by running the simulator to determine the min imum time required to obtain the data not distorted by the wellbore effects .(4) The governing equations of the wellbore model are based on mass, momentum, and energy balances for single-phase gas in one-dimensional space. The gas pressure/volume/temperature correlation was also used. Different how regime s (laminar, transitional, and turbulent) inside the wellbore are modeled fo r calculating the friction factor. As one boundary condition, a simple anal ytical reservoir model was connected to the wellbore model at the bottomhol e using Duhamel's principle. Heat-loss effects account for forced-convectio nal heat transfer inside the tubing, heat conduction between tubing and for mation, natural convection and radiation heat transfer of annular fluid, an d transient heat flow in the formation. Pressure, temperature, velocity, an d gas properties inside the wellbore can be predicted at any depth during a n entire pressure-buildup test. Variable wellbore storage, momentum, and th ermal effects can be simulated.