Temperature transient analysis of slightly compressible, single-phase reservoirs

This paper presents new semilog-straight line and temperature-derivative methods (similar to pressure-derivative method commonly used in pressure transient analysis) for interpreting and analyzing temperature transient data from constant-rate drawdown and buildup tests conducted in infinite-acting reservoirs containing slightly compressible fluid of constant compressibility and viscosity. The procedures are based on the analytical solutions accounting for Joule-Thomson (J-T) heating/cooling, adiabatic fluid expansion, conduction and convection effects. The development of the analytical solutions is based on the fact that the effects of temperature changes on pressure transient data can be neglected so that the pressure diffusivity and thermal energy balance equations can be decoupled. The analytical solutions are verified by and are found in excellent agreement with the solutions of a commercial non-isothermal reservoir simulator. It is shown that drawdown and buildup sandface temperature data may exhibit three infinite-acting radial flow (IARF) periods (represented by semilog equations); one at early times reflecting the adiabatic expansion/compression effects, second at intermediate times reflecting the J-T expansion in the skin zone if skin exists, and the third one at late times reflecting J-T expansion effects in the nonskin zone. Performing semilog analyses based on these IARF regimes gives estimates of permeability of skin and nonskin zones as well as radius of the skin zone assuming that the J-T coefficient of the fluid and viscosity is known. Parameters such as skin zone permeability and radius are not readily accessible from conventional pressure transient analysis from which only the skin factor and non-skin zone permeability can be obtained. The applicability of the proposed analysis procedure is demonstrated by considering synthetic and field test data. The results indicate that the analysis procedure provides reliable estimates of skin zone and non-skin zone permeabilities and skin zone radius from drawdown or buildup temperature data jointly with pressure data.