Research and Application of the Unsteady Heat Transfer Analytical Model for SAGD

Abstract

The thermal losses to overburden and underburden in Steam-Assisted Gravity Drainage (SAGD) arise from unsteady heat transfer as the steam chamber continuously changes shape. No accurate analytical solution currently exists. Here we enforce energy conservation, redefine the outer boundary, and reformulate the unsteady-conduction model, establishing a relation between heat-penetration depth and cumulative heat transfer per unit area, and propose a new solution pathway. This method first parameterizes heat-penetration depth, then integrates to obtain cumulative heat transfer, and finally differentiates to compute stratal heat loss. This workflow provides a quantitative route to overburden and underburden thermal losses in SAGD. Coupling the framework with Butler’s oil-rate formula yields closed-form expressions for key SAGD indicators—water production, steam-heat utilization, and oil–steam ratio—derived from unsteady heat conduction. Through axial discretization, the approach accommodates heterogeneity along the horizontal section in a typical SAGD well pattern. We also implement a production-grade program that ingests geological, thermodynamic, and operational inputs and rapidly evaluates multiple outputs, including stratal heat loss, steam-heat utilization, and oil–steam ratio. Against CMG thermal simulation, the overburden heat-loss deviation remains within 5%, substantially improving index-prediction efficiency. Using the Qigu Formation reservoir in the Liu-1 well area of the Karamay Oilfield, Xinjiang, as a case study, we apply the analytical model to optimize planar well spacing to 70 m. For a representative well pair (Well Group A), predictions show that thermal losses to both strata increase and then decline, peaking when the steam chamber reaches the boundary. Sensitivity analysis indicates negative correlations between heat loss and oil saturation, permeability, porosity, and oil-zone thickness, whereas overburden/underburden thermal diffusivity correlates positively with oil–steam ratio. The ranked sensitivity, from strong to weak, is: overburden/underburden thermal diffusivity, oil-zone thickness, oil saturation, permeability, and porosity. The results support index prediction, layout planning, parameter optimization, and measure selection in SAGD-developed heavy-oil reservoirs. The numerical implementation supports batch evaluation and scenario screening, enabling rapid sensitivity sweeps and uncertainty assessment without sacrificing interpretability. We validate the workflow by reproducing time histories of overburden heat loss and by checking consistency of derived indicators with field trends and CMG-STARS benchmarks under identical controls, grids, and rock–fluid properties. The discretized representation preserves mass and energy balances within each segment and allows segment-level attribution of heat sinks and production response. In addition, the program exposes intermediate variables, such as penetration depth and apparent heat capacity, which facilitate diagnostic checks and calibration when early measurements become available. These features make the approach suitable for pre-FEED studies and for operational surveillance and optimization.