A critical review of analytical oil flow rate models for vapour extraction and its non-condensable gas-based hybrids

Analytical models are the preliminary reservoir engineering processes performance prediction tools that are quick and less costly compared with experiments and simulations when sufficiently modelled which motivates evaluation of oil drainage rate modelling in the mentioned subjects. The models were derived based on the principles of mass balance (including diffusion/dispersion), Darcy's law, and heat of conduction with minimum convective heat transfer analysis. The majority of the models were based on steady-state flow conditions with a scarcity of models considering unsteady-state conditions. The inverted triangle (linear) and the curved geometries defined the vapour chamber shapes with a lack of curved studies in the hybrids of warm vapour extraction (VAPEX) and non-condensable gas (NCG) with steam. The lateral chamber spreading stage was common in the creation of each model. Limited studies in rising and declining chamber stages were noted especially in the warm VAPEX and hybrids of warm VAPEX and non-condensable gases with steam, enhancing more comprehensive modelling studies that distinguish stages in future works. Hybrids of warm VAPEX and NCG with steam models were discovered to lack validations. A paucity of model uncertainty parameters tuning to match experiments, simulations, and field studies was revealed promoting parameter-tuning sensitivity analysis to estimate most components of uncertainty in the equations and further driving mechanisms exploration in the subsequent research. Modelling modifications are also suggested including sensible heat consideration in the steam heat balance equations that utilized latent heat only.