Online Inverse Modeling of Transient Near-Wellbore Thermal Recovery for Multirate Drill Stem Test Diagnostics after Circulation

Abstract

Thermal disequilibrium created by drilling circulation can persist in the rock surrounding a well long after pumping has stopped, and the persistence of that disturbed zone complicates the interpretation of early drill stem test measurements. In many wells, the fluid entering the wellbore during cleanup and early flow does not originate from a thermally undisturbed formation state, but instead moves through a near-wellbore region whose temperature has been altered by prior circulation and has only partially recovered during shut-in. Because fluid properties, inflow enthalpy, and wellbore temperature response depend on that evolving thermal environment, early-time pressure and temperature diagnostics may be biased when analyzed with fixed-equilibrium assumptions. This paper develops an online inverse modeling framework for transient near-wellbore thermal recovery in circulated wells undergoing multirate drill stem testing. The framework combines radial heat diffusion in the formation, axial wellbore energy transport, compressible inflow, and temporally varying operational modes within a unified reduced-order state representation. The disturbed thermal field is treated as a latent process inferred sequentially from pressure, temperature, and rate observations, while uncertain transport and inflow parameters are updated in a regularized manner that preserves consistency with prior thermal history. The paper derives the governing equations, introduces a reduced radial-axial thermohydraulic representation, formulates a recursive estimation procedure, analyzes identifiability and stability, and outlines a field-oriented validation strategy. The resulting formulation is intended to improve the interpretation of early multirate drill stem test data in settings where the near-wellbore thermal state remains in transition and where conventional fixed-regime analyses may misrepresent entering fluid temperature and inferred flow behavior.