Calibrating and Scaling Semi-empirical Foam Flow Models for the Assessment of Foam-Based EOR Processes (in Heterogeneous Reservoirs)

Models for simulating foam-based displacements fall into two categories: population-balance (PB) models that derive explicitly foam texture or bubble size from pore-level mechanisms related to lamellas generation and coalescence, and steady-state semi-empirical (SE) models that account implicitly for foam texture effects through a gas mobility reduction factor. This mobility reduction factor has to be calibrated from a large number of experiments on a case-by-case basis in order to match the physical effect of parameters impacting foam flow behaviour such as fluids saturation and velocity. This paper proposes a methodology to set up steady-state SE models of foam flow on the basis of an equivalence between SE model and PB model under steady-state flow conditions. The underlying approach consists in linking foam mobility and foam lamellas density (or texture) data inferred from foam corefloods performed with different foam qualities and velocities on a series of sandstones of different permeabilities. Its advantages lie in a deterministic non-iterative transcription of flow measurements into texture data and in a separation of texture effects and shear-thinning (velocity) effects. Then, scaling of foam flow parameters with porous medium permeability is established from the analysis of calibrated foam model parameters on cores of different permeability, with the help of theoretical representations of foam flow in a confined medium. Although they remain to be further confirmed from other well-documented experimental data sets, the significance of those scaling laws is great for the assessment of foam-based enhanced oil recovery (EOR) processes because foam EOR addresses heterogeneous reservoirs. Simulations of foam displacement in a reservoir cross section demonstrate the necessity to scale foam SE models with respect to facies heterogeneity for reliable evaluation.