This paper presents a semi-analytical wellbore/reservoir model1 that can describe general wellbore effects, especially the thermal effect, on high-temperature gas well pressure-buildup tests. A numerical simulator has been developed from the model. Using different combinations of wellbore and reservoir parameters, the simulator generated curve shapes that differed with wellbore thermal effects. Many of the curve shapes have been observed in the field.2,3 Using the results from this paper, engineers can distinguish between 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 gas well pressure-buildup tests by running the simulator to determine the minimum 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 flow regimes (laminar, transitional, and turbulent) inside the wellbore are modeled for calculating the friction factor. As one boundary condition, a simple analytical reservoir model was connected to the wellbore model at the bottomhole using Duhamel's principle. Heat-loss effects account for forced-convectional heat transfer inside the tubing, heat conduction between tubing and formation, natural convection and radiation heat transfer of annular fluid, and transient heat flow in the formation. Pressure, temperature, velocity, and gas properties inside the wellbore can be predicted at any depth during an entire pressure-buildup test. Variable wellbore storage, momentum, and thermal effects can be simulated.