Numerical modeling of the thermal front during steam-cyclic treatment of the well’s near-bottom-hole zone, taking into account the variable thermophysical properties of a saturated reservoir

Problem Statement. Traditional methods for numerically describing paracyclic effects on the near-wellbore region are based on the hypothesis that the thermal conductivity and heat capacity of rocks are constant. This simplification fails to adequately reproduce the heat transfer pattern in a situation where both the temperature field and the ratio of liquid, vapor, and oil phases continuously evolve over time.

Objective. To develop a mathematical framework and a computational procedure for determining the evolution of the temperature field during a wellbore treatment, in which the effective thermal conductivity and volumetric heat capacity are explicitly parameterrized by the current values of temperature and saturation of formation fluids.

Results. An implicit finite-difference scheme was implemented on an adaptive grid with node condensation in the vicinity of the wellbore. A detailed numerical simulation of the full processing cycle, including three stages: coolant injection, soaking (imbibition), and product extraction, was performed. Using the Marx–Langenheim relationship, thermal energy losses in the roof and base of the productive interval were quantified. Curves were constructed for the time evolution of the heated zone radius, and specific steam consumption per ton of additional oil produced was determined. It was found that switching from a constant-coefficient model to thermodynamically dependent characteristics shifts the estimated duration of the imbibition stage by 12–18%. A software product written in Python was developed.

Practical Relevance. The proposed model and software code enable more accurate prediction of the required imbibition duration, provide a scientifically sound basis for selecting steam injection modes, and contribute to a reduction in specific steam consumption. This directly improves the effectiveness of cyclic thermal stimulation of oil wells.