This paper proposes a robust methodology to calibrate steady-state models of foam flow through porous reservoirs from foam displacements on core samples. The underlying approach is an equivalence between foam mobility and foam lamellas density (or texture) at local-equilibrium. This calibration methodology is applied to foam displacements at different qualities and velocities on a series of sandstones. Its advantage lies in a deterministic transcription of flow measurements into texture data, by comparison with commonly-applied least-square-fit methods that may yield non unique solutions.Scaling trends of foam parameters with porous medium permeability are then identified and discussed 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, these scaling laws can increase the reliability of reservoir simulators for the assessment of foam-based improved recovery processes in heterogeneous reservoirs.

Models for simulating foam-based displacements in enhanced oil recovery (EOR) processes fall into two categories: population-balance (PB) models that derive explicitly foam texture, or bubble size, evolution in porous media from pore-level mechanisms related to lamellas generation and coalescence, and semi-empirical (SE) models that account implicitly for foam texture effects through a gas mobility reduction factor that depends on fluid saturation, interstitial velocity, surfactant concentration, and other factors. 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 each considered parameter on foam behavior. This paper develops a method for identifying the SE models from the physics of foams as derived from PB models at local equilibrium (LE). The identification of both foam flow models leads to a method for calibrating SE models from the PB model translation of foam flow data. Application to a set of foam quality-scan experiments at fixed total flow rate shows that the SE and PB models at LE match equally well the measurements and generate almost the same results in both the so-called high-and low-quality regimes. We demonstrate that the two approaches are equivalent at local equilibrium and differ only in the way in which the complex dynamic mechanisms of lamellas are handled. This physical approach of foam flow could circumvent some difficulties in the direct calibration of SE models from foam mobility (or apparent viscosity) data.

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 behavior 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.

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