Influência da pressão capilar em escoamentos bifásicos com espuma em meios porosos

Abstract

Foam injection is one of the studied methods for advanced oil recovery. This method has great potential for application in the Brazilian pre-salt reservoirs. The technique consists of injecting foam into the reservoir (or creating it in situ). This technique aims to reduce gas mobility to provide more uniform and efficient sweeping in the reservoir. Foam models are typically described as a system containing a conservation law for the mass of water and a balance law for the amount of foam. In previous works, assuming a fixed surfactant concentration, the authors present traveling wave solutions for this model. Inspired by adsorption phenomena, we proposed a modification for this model to consider a variable surfactant concentration. By analyzing this modified model analytically, looking for solutions in the form of traveling waves, we found that it may lead to non-physical solutions. Besides, the numerical and analytical obtained solutions did not match. This has motivated us to study the influence of capillarity on the first-order-kinetic model. In the present work, we discuss how the kinetic model behaves under two capillary pressure simplifications. In the first, we approximate the capillary diffusion in both system equations by a constant. In the second, we approximate the capillary diffusion in the water conservation equation by a constant and neglect the capillary diffusion in the foam balance, motivated by the fact that bubble diffusion in the gas phase is lower than water-gas diffusion. We look for analytical solutions in both cases as traveling waves and validate them with numerical simulations. The obtained solutions show abrupt drops in the foam texture. Such decay have already been described in the literature in simulations and assumed to be numerical errors. Other studies justify that this decay represent physical phenomena. In this context, the present work is one of the pioneers to describe that phenomenon analytically.