An Effective Continuum Model for the Gas Evolution in Internal Steam Drives

Abstract

Summary We derive an effective continuum model to describe the nucleation and subsequent growth of a gas phase from a supersaturated liquid in a porous medium, driven by heat transfer. The evolution of the gas results from the reduction of the system pressure at a constant rate. The model addresses two stages before the onset of bulk gas flow, nucleation, and gas-phase growth. The problem arises in internal steam drive—for example, of the type recently discussed in blowdown experiments in carbonate rocks (Dehghani et al.,1 Dehghani and Kamath2). Important quantities, such as the fraction of pores that host activated sites, the deviation from thermodynamic equilibrium, the maximum supersaturation, and the critical gas saturation depend crucially on the nucleation characteristics of the medium. We use heterogeneous nucleation models in the form of pre-existing gas, trapped in hydrophobic cavities, to investigate the nucleation behavior. Using scaling analysis and a simpler analytical model, we show that the relevant quantities during nucleation can be expressed in terms of a simple combination of dimensionless parameters, which include rate effects. The subsequent evolution of the gas phase and the approach to the critical gas saturation are also described using numerical and analytical models. The theory predicts that the maximum supersaturation in the system is a weakly increasing function of the decline rate. This function depends sensitively on the probability density function of the nucleation cavity sizes. It also predicts that the final nucleation fraction, and thus the critical gas saturation, is a power law of the decline rate. The theory for both nucleation and phase growth is then compared with available experimental data.