Analytical Models for Interpretation and Analysis of Transient Sandface and Wellbore Temperature Data

The objectives of this study are to (i) provide analytical transient coupled wellbore/reservoir model to interpret/analyze transient temperature drawdown/buildup data acquired at both the producing horizon (sandface) and a gauge depth above the producing horizon (wellbore) and (ii) delineate the information content of both transient sandface and wellbore temperature measurements. The analytical models consider flow of a slightly compressible, single-phase fluid in a homogeneous infinite-acting reservoir system and provide temperature-transient data for drawdown and buildup tests produced at constant rate at any gauge location along the wellbore including the sandface. The production in the wellbore is assumed to be from inside the production casing. The models account for Joule-Thomson (J-T), adiabatic fluid-expansion, conduction and convection effects as well as nearby wellbore damage effects. The well/reservoir system considered is a fully penetrating vertical well in a two-zone radial composite reservoir system. The inner zone may represent a damaged (skin) zone, and the outer (non-skin) zone represents an infinitely extended reservoir. The analytical solutions for the sandface transient temperatures are obtained by solving the decoupled isothermal (pressure) diffusivity and temperature differential equations for the inner and outer zones with the Boltzmann transformation, and the coupled wellbore differential equation is solved by Laplace transformation. The developed solution compares well with the results of a rigorous thermal numerical simulator and determines the information content of the sandface and wellbore temperature data including skin zone effects. The analytical models can be used as forward models for estimating the parameters of interest by nonlinear regression built on any gradient-based estimation method such as the maximum likelihood estimation (MLE).