A new mathematical model and experimental validation on foamy-oil flow in developing heavy oil reservoirs

To model foamy-oil flow in the development of heavy oil reservoirs, three depletion experiments were conducted with foamy oil treated as a pseudo-single-phase flow. In this pseudo single phase, dispersed bubbles are viewed as a part of the oil, and the redefined effective permeability varies with the changes of pressure depletion rate, oil viscosity, and gas saturation. A mathematical expression for the effective permeability was developed based on experiments, where the viscosity of foamy oil is assumed to be approximately equal to the saturated oil under equivalent conditions. The compressibility coefficient of foamy oil is treated as a volume-weighted compressibility coefficient of that of oil and gas phases. A new mathematical model for foamy-oil flow was proposed with consideration of foamy-oil supersaturation. To validate the mathematical model, the oil recovery and the production gas-oil ratio (GOR) calculated by the new model, conventional black oil model, supersaturation model and pseudo-bubble-point (PBP) model were all compared with those of the experimental data. The new model provided a substantially improved fit to the experimental data compared with the rest three models, which verifies the suitability of the mathematical model presented for simulating foamy-oil flow in the development of heavy oil reservoirs.