Summary
This work presents a new coupled transient wellbore/reservoir thermal analytical model, consisting of a combined reservoir/casing/tubing system. The analytical model considers flow of a slightly compressible, single–phase fluid in a homogeneous infinite–acting reservoir system and provides temperature–transient data for drawdown and buildup tests at any gauge location along the wellbore. The model accounts for Joule–Thomson (J–T), adiabatic–fluid–expansion, conduction, and convection effects. The wellbore–fluid mass density is modeled as a function of temperature, and the analytical solution makes use of the Laplace transformation to solve the transient heat–flow differential equation, accounting for a transient wellbore–temperature gradient ∂T/∂z. The solutions presented assume moderate– to high–permeability reservoirs and do not consider skin effects in the formation. Results of the analytical model are compared with those of a commercial thermal simulator and with those of available models in the literature. Our model provides more accurate transient–temperature–flow profiles along the wellbore in comparison with previous analytical models in the literature. Furthermore, a generalization of a well–known parameter–estimation method from transient–temperature data is provided.
A single-phase elastic hyperbolic metamaterial with anisotropic mass density
