The Method of Characteristics Applied to Oil Displacement by Foam

Abstract

Summary Solutions obtained by the method of characteristics (MOC) provide key insights into complex foam enhanced-oil-recovery (EOR) displacements and the simulators that represent them. Most applications of the MOC to foam have excluded oil. We extend the MOC to foam flow with oil, where foam is weakened or destroyed by oil saturations above a critical oil saturation and/or weakened or destroyed at low water saturations, as seen in experiments and represented in foam simulators. Simulators account for the effects of oil and capillary pressure on foam using algorithms that bring foam strength to zero as a function of oil or water saturation, respectively. Different simulators use different algorithms to accomplish this. We examine SAG (surfactant-alternating-gas) and continuous foam-flood (coinjection of gas and surfactant solution) processes in one dimension, using both the MOC and numerical simulation. We find that the way simulators express the negative effect of oil or water saturation on foam can have a large effect on the calculated nature of the displacement. For instance, for gas injection in a SAG process, if foam collapses at the injection point because of infinite capillary pressure, foam has almost no effect on the displacement in the cases examined here. On the other hand, if foam maintains finite strength at the injection point in the gas-injection cycle of a SAG process, displacement leads to implied success in several cases. However, successful mobility control is always possible with continuous foam flood if the initial oil saturation in the reservoir is below the critical oil saturation above which foam collapses. The resulting displacements can be complex. One may observe, for instance, foam propagation predicted at residual water saturation, with zero flow of water. In other cases, the displacement jumps in a shock past the entire range of conditions in which foam forms. We examine the sensitivity of the displacement to initial oil and water saturations in the reservoir, the foam quality, the functional forms used to express foam sensitivity to oil and water saturations, and linear and nonlinear relative permeability models.

Modeling of Liquid Injectivity in Surfactant-Alternating-Gas Foam Enhanced Oil Recovery

“…Liquid follows 1-GPV gas injection-Peaceman equation Liquid follows 10-GPV gas injection-Peaceman equation Liquid follows 20-GPV gas injection-Peaceman equation Liquid follows 1-GPV gas injection-radial-flow model Liquid follows 10-GPV gas injection-radial-flow model Liquid follows 20-GPV gas injection-radial-flow model Liquid follows 1-GPV gas injection-skin factor Liquid follows 10-GPV gas injection-skin factor Liquid follows 20-GPV gas injection-skin factor especially problematic in this regard. In fitting the effect of long-time gas injection on foam mobility near a gas-injection well in a field test, Rossen et al (2017) found that the Zanganeh model (Zanganeh et al 2011) did a reasonable job of representing foam mobility after many PVs of gas injection. In any event, a model fit with more-abrupt foam collapse at the limiting water saturation would have come closer to the predictions of the radial-flow model during gas injection in this study.…”

Three‐Phase Fractional‐Flow Theory of Foam‐Oil Displacement in Porous Media With Multiple Steady States

“…This result hinges on the nonlinearity of relative-permeability functions. In the simplified case of linear relative-permeability functions, shocks (equation ( 13)) occur along the same curve as spreading waves (equation ( 11)), but this is not the case in general (Lake et al, 2014;Namdar Zanganeh et al, 2011).…”

Tuning Foam Parameters for Mobility Control using CO2 Foam: Field Application to Maximize Oil Recovery from a High Temperature High Salinity Layered Carbonate Reservoir

“…Their experimental evidence indicates that apparent foam viscosity is strongly reduced at oil saturations greater than some critical oil saturation; below this saturation, foam is weakened proportionately to oil saturation. − Moreover, another factor to note is that foam dries out and at least partially collapses abruptly at a water saturation corresponding to limiting capillary pressure. , Mayberry et al made a few assumptions and restrictions to simplify the description of the three phase flow process. Some of the basic assumptions and restrictions are flow is rectilinear and one-dimensional in a horizontal porous medium, effects of gravity is neglected, immiscible displacement occurs, and three phases (oil, gas, and water) are present, properties depend only on phase saturations and not on pressure, phases are incompressible and porous medium is considered to be homogeneous, no chemical reaction, and no degradation of surfactant with time . Upon imposing these restrictions and using Darcy’s law with linear Corey-type relative permeability model in the equation for mass conservation of each of the three phases in porous media results in a homogeneous, reducible system of two first-order equations with two dependent variables …”