Foam is an attractive option in EOR for increasing oil recovery in mature water-flooded reservoirs. In this paper we use stochastic bubble population model and complex power law rheological model, to integrate foam physics into a flow simulator. Foam displacement is examined in layered reservoirs with and without isolating shale barrier between the layers and in stochastically distributed permeability fields. It is demonstrated that in isolated layers foam propagates faster in the high permeability layer and sweeps the low permeability layer only modestly. In communicating layers, sweep efficiency is improved significantly due to cross flow. In stochastic random permeability field, foam injection increases the liquid recovery by a factor of two in comparison to gas injection.


Foam is an excellent mobility control agent for Enhanced Oil Recovery (EOR) processes, such as gas (nitrogen, carbon dioxide, etc.) or steam injection [1–8]. Due to its unique microstructure, foam dramatically reduces gas mobility and considerably improves the vertical and areal reservoir sweep efficiency [1–4]. The ability to reduce fluid mobility forms the basis of profile correction used to improve water- or steam-flooding in highly heterogeneous (layered) formations [7]. Foam has also been used for gas blocking in oil wells [5] and of acid diversion in matrix stimulation operations [2]. In these near-wellbore applications foam is particularly attractive because it is inherently non-damaging and low cost, allowing easily recursive treatments in case of an unsuccessful operation [1–4].

The evaluation and implementation of foam processes rely on experiments, modeling and numerical reservoir simulations. This work is mainly concerned with the modeling and numerical simulation of foam. Several foam models have been proposed in the last three decades, including semi-empirical models [9], fractional flow models [10, 11], population balance model [12–315], and percolation theory [16]. Recently, Zitha [17] examined the strengths and limitations of the available models. In order to capture more realistically the physics of foam motion in porous media, Zitha [17] developed a new stochastic bubble population (SBP) foam model, with the main features described below:

Foam is a complex fluid, characterized by a yield stress and, above the yield stress, by a power law behavior. Its rheology can be described using a Herchel-Bulkley type of model where the constitutive parameters depend mainly on the bubble density, also referred to as the 'foam texture'. Since on a large scale foam generation occurs over a large number of randomly interconnected pores, bubble generation can be treated as a stochastic process. The kinetic of foam generation can thus be described by a simple exponential growth law involving only two unknown parameters that can be determined from core flow experiments. The SBP foam model was applied successfully to simulate different core-flow experiments [18, 19]. The simulation results showed a rather good match with fluid partitioning images obtained by X-ray computed tomography (CT) [18, 19]. Both experiment and simulations in layered cores showed that foam propagates faster in the high permeability layers [18].

In this paper, we build a novel multi-phase multi-dimension reservoir simulator based on the SBP foam model and provide a numerical analysis of foam flow in heterogeneous porous media. We examine several scenarios concerning the co-injection of liquid (surfactant solution) and gas (N2, CO2, etc.) in layered and randomly heterogeneous reservoirs. We show that foam performance, i.e. the amount of fluid recovery during foam injection, is higher with foam regardless of reservoir heterogeneity.

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