Foam Simulation Faces Several Numerical Challenges
Authors: Wilson Adam 
Published: February 2015

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 166232, ’Numerical Challenges in Foam Simulation: A Review,’ by W.R. Rossen, SPE, Delft University of Technology, prepared for the 2013 SPE Annual Technical Conference and Exhibition, New Orleans, 30 September-2 October. The paper has not been peer reviewed.
Foam simulation brings various numerical challenges. Some of these problems are largely cosmetic, creating, for instance, fluctuating fluxes and pressure gradient but no significant effect on final recovery. Others severely influence the whole progress of the flood. This paper discusses the origin of the challenges, how to recognize them, how they can be mitigated, and whether they arise from a correct representation of foam physics or are the unintended result of attempts to solve other numerical problems.
Introduction
Injected gas [carbon dioxide (CO2), hydrocarbon gas, nitrogen, or steam] can be very effective at displacing oil in enhanced- oil-recovery (EOR) processes, but ultimate recovery suffers from poor sweep efficiency. Poor sweep efficiency arises from reservoir heterogeneity, viscous instability, and gravity override of gas. Foam can address all three causes of poor sweep efficiency. Foam is a dispersion of gas separated by water films called lamellae that separate the gas into bubbles; the lamellae are stabilized by surfactant. Thus, foam requires the presence of gas, water, and surfactant.
Two fundamental approaches exist for representing the effect of foam on gas mobility. Population-balance models introduce lamella density (number of lamellae per unit volume of gas phase) as a separate variable and perform a balance on lamellae at each location in the formation, along with material balances on water, gas, surfactant, and oil. Thus, an additional partial-differential equation must be solved at each location and timestep, along with those for saturations of the phases. The model then represents gas mobility as a function of lamella density and other factors.
Local-equilibrium (LE) models assume that the processes of lamella creation and destruction are always and everywhere at local steady state. It is possible to adapt a population-balance model to LE by setting the expressions for lamella creation and destruction equal to each other. Most LE models, however, represent the effect of bubble size implicitly in relations for gas mobility as a function of water and oil saturations, surfactant concentration in the aqueous phase, and other factors.
Foam can be injected in at least four ways:
1. In coinjection, gas and aqueous surfactant solution are injected simultaneously from a single well. Foam forms in the surface facilities where the fluids meet, in the tubing, or shortly after the fluids enter the formation.
2. In surfactant-alternating-gas (SAG) injection, gas and surfactant solution are injected in separate slugs from a single well. Foam forms in the formation where gas meets previously injected surfactant solution or when surfactant solution meets previously injected gas.
3. It is possible to dissolve some surfactants directly into supercritical CO2. Then, there is no need to inject aqueous surfactant solution; injected CO2 with dissolved surfactant forms foam as it meets water in the formation.
4. Surfactant solution and gas can be injected simultaneously from different sections of a vertical well (gas injected below the surfactant solution) or from parallel horizontal wells (gas injected from the lower well). As far as we know, this approach has not been tested with foam in the field.
Simulating each of these injection methods involves particular challenges.