Early-time asymptotic, analytical temperature solution for linear non-adiabatic flow of a slightly compressible fluid in a porous layer

This article will present a set of analytical equations for the calculation of early time temperature at the edge of a porous, finite layer experiencing linear flow of a slightly compressible fluid. The equations provide the full, transient temperature solution for the flow of slightly compressible fluids (i.e., liquids and, sometimes, gasses) into horizontal wells. The solution is essential for temperature transient analysis in smart wells—a monitoring approach of great potential, but in early development stage. The early time, analytical model solution provided in the paper will be tested against a rigorous numerical simulation model. The methods proposed here can be applied to a wide variety of well-completion types, flow conditions and system properties. This article will first discuss the problem of transient temperature analysis, the flow conditions and the assumptions required to sufficiently simplify the thermal model so that an analytical solution can be derived. The solution is derived for the temperature change generated by the Joule–Thomson fluid heating under the condition of 2D heat losses to the surrounding formation.