Abstract. We present a new numerical method to approximate the solutions of an Euler-Poisson model, which is inherent to astrophysical flows where gravity plays an important role. We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations, paying particular attention to the gravity source term involved in the latter equations. In order to approximate this source term, its discretization is introduced into the approximate Riemann solver used for the Euler equations. A relaxation scheme is involved and its robustness is established. The method has been implemented in the software HERACLES [29] and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.

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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.