Abstract
Thermal disequilibrium around a wellbore can persist for a substantial time after drilling circulation ends, especially in deep or high-temperature settings where the contrast between circulating fluid and native formation temperature is pronounced. This persistence is operationally important because perforation, cleanup, and drill stem testing are often performed before the disturbed rock has fully recovered. Under those circumstances, the earliest fluids entering the wellbore do not represent the undisturbed reservoir alone. Instead, they carry the thermal signature of a near-wellbore region whose temperature has been altered by prior circulation and whose recovery remains incomplete. The result is that early pressure and temperature measurements reflect a coupled transient involving radial heat recovery, inflow redistribution, and wellbore transport rather than a stabilized reservoir response. This paper develops a multiscale reconstruction framework for that problem. The proposed model describes circulation-induced thermal memory in the formation through a reduced radial field, links that field to interval-scale entering fluid temperature by means of an inflow-weighted thermal functional, and embeds the resulting entry conditions into a multirate drill stem test response model. A regularized inverse procedure is then introduced to estimate the hidden thermal state, interval contributions, and uncertain transport parameters from pressure, temperature, and rate data. The analysis emphasizes early-time and late-time asymptotics, identifiability of the disturbed radial profile, and the practical conditions under which thermal memory materially alters inflow interpretation. The resulting formulation is intended to improve early drill stem test diagnostics in recently circulated wells where conventional equilibrium assumptions are not yet valid.