The targeted reservoir for foam mobility control is usually layered or heterogeneous. However, a major limitation of existing foam models is that there are no dependencies of the foam modeling parameters on permeability, even though the permeability is accounted inherently only through changes in gas-water capillary pressure and shear rate. This results in considerable errors in predicting the foam mobility at largely varying permeabilities, which prevents users from simulating correctly the conformance achievable with the help of foam in heterogeneous reservoirs.
Developing a foam simulator with systematic permeability-dependencies of foam properties is a key enabler for the rigorous simulation of foam floods in the field. An advanced population-balance foam model has been developed with reasonable physical mechanisms associated with the effect of permeability on the bubble density, foam generation and stability in porous media. The derivations indicate that the gas viscosity scaling constant increases with permeability exponentially, while the upper limit of foam texture, the foam generation coefficient, and the limiting capillary pressure decrease exponentially as the permeability increases. All these factors collectively affect the foam mobility. The upper limit of foam texture and the foam generation coefficient share the same power-law exponent with permeability because of the similar fundament. As a result, three additional power-law exponents are needed to correlate with permeability in the new model.
To verify the correlations of the parameters with the permeability change, an automated regression program was applied to fit the resistance factors of several groups of foam flood experiments with foam quality scans at different permeabilities. The newly developed permeability-dependency functions showed its great competency in matching all the experimental data in a wide range of permeability. The optimized parameters are largely consistent with the theoretical exponents of the power-law functions of the aforementioned physical properties correlated to permeability, but also suggest extra modifications. In particular, the exponent for the limiting capillary pressure is about -0.5, which is equivalent to that the limiting water saturation is approximately independent of the permeability according to the Leverett J-function. As a result, the new functions of permeability dependencies for the foam-model parameters in the population-balance model enables the foam modeling with only a single input of foam parameters at a referenced permeability. A 2D layered reservoir case was used to test the new permeability functions, which shows the significant difference in terms of the oil recovery and the injector BHP between whether considering the permeability effect or not.
This paper proposed, for the first time, a systematic methodology to account for the critical permeability effect to simulate foam flooding in heterogeneous reservoirs. This is a key advance in consideration of the major limitation of existing reservoir simulators using fixed or ad-hoc foam-model parameters throughout the entire reservoir. This new model enables the reservoir engineers to simulate and optimize the foam performance in real fields with better accuracy of foam physics in porous media.