Adaptive Thermal Operator Learning for Near-Wellbore Recovery and Early Drill Stem Test Flow Inference after Drilling Circulation

Abstract

Background temperature disequilibrium created during drilling circulation can remain around the wellbore for a substantial period after pumping stops. In petroleum, gas, and geothermal wells, this persistence complicates the interpretation of post-circulation flow behavior because the fluid entering the wellbore during early cleanup or testing may sample a thermally disturbed region rather than the undisturbed formation. The difficulty becomes more pronounced when a well experiences multiple operational transitions, including circulation, shut-in recovery, perforation, early inflow, and multirate test periods, before thermal stabilization is achieved. This paper develops a distinct operator-learning framework for estimating near-wellbore thermal recovery and using that estimate for early drill stem test flow inference. The proposed model combines radial heat diffusion, axial wellbore energy transport, multientry inflow mixing, and sequential state updating in a regime-aware reduced-order structure. A physics-constrained memory mechanism is introduced so that information learned during circulation and shut-in is preserved when the well transitions into flow, thereby reducing the loss of thermal history that commonly biases early-time interpretation. The framework treats the disturbed temperature field as a latent state, infers its evolution from pressure, temperature, and rate data, and links that state directly to entering fluid temperature and transient flow estimation. The paper derives the governing equations, constructs the reduced dynamical representation, develops an online estimation strategy, analyzes stability and identifiability, and proposes a field-oriented validation protocol. The resulting formulation is intended to improve early-time test interpretation in wells where near-wellbore thermal recovery remains incomplete and where fixed-regime inference is vulnerable to systematic error.