Summary
Foam is used in the oil industry in a variety of applications, and polymer
is sometimes added to increase foam’s stability and effectiveness. A variety of
surfactant and polymer combinations have been employed to generate
polymer-enhanced foam (PEF), typically anionic surfactants and anionic
polymers, to reduce their adsorption in reservoir rock. While addition of
polymer to bulk foam is known to increase its viscosity and apparent stability,
polymer addition to foams for use in porous media has not been as
effective.
In this pore-level modeling study, we develop an apparent viscosity
expression for PEF at fixed bubble size, as a preliminary step to interpret the
available laboratory coreflood data. To derive the apparent viscosity, the
pressure-drop calculation of Hirasaki and Lawson (1985) for gas bubbles in a
circular tube is extended to include the effects of shear-thinning polymer in
water, employing the Bretherton’s asymptotic matching technique. For polymer
rheology, the Ellis model is employed, which predicts a limiting Newtonian
viscosity at the low-shear limit and the well-known power-law relation at high
shear rates. While the pressure drop caused by foam can be characterized fully
with only the capillary number for Newtonian liquid, the shear-thinning liquid
requires one additional grouping of the Ellis-model parameters and bubble
velocity.
The model predicts that the apparent viscosity for PEF shows behavior more
shear-thinning than that for polymer-free foam, because the polymer solution
being displaced by gas bubbles in pores tends to experience a high shear rate.
Foam apparent viscosity scales with gas velocity (Ug) with an exponent
[–α/(α+2)], where α, the Ellis-model exponent, is greater than 1 for
shear-thinning fluids. With a Newtonian fluid, for which α = 1, foam apparent
viscosity is proportional to the (–1/3) power of Ug, as derived by Hirasaki and
Lawson.
A simplified capillary-bundle model study shows that the thin-film flow
around a moving foam bubble is generally in the high-shear, power-law regime.
Because the flow of polymer solution in narrower, water-filled tubes is also
governed by shear-thinning rheology, it affects foam mobility as revealed by
plot of pressure gradient as a function of water and gas superficial
velocities. The relation between the rheology of the liquid phase and that of
the foam is not simple, however. The apparent rheology of the foam depends on
the rheology of the liquid, the trapping and mobilization of gas as a function
of pressure gradient, and capillary pressure, which affects the apparent
viscosity of the flowing gas even at fixed bubble size.
Introduction
When a gas such as CO2 or N2 is injected into a mature oil reservoir for
improved oil recovery, its sweep efficiency is usually very poor because of
gravity segregation, reservoir heterogeneity, and viscous fingering of gas, and
foam is employed to improve sweep efficiency with better mobility control (Shi
and Rossen 1998; Zeilinger et al. 1996). When oil is produced from a thin oil
reservoir overlain with a gas zone, a rapid coning of gas can drastically
reduce oil production rate, and foam is used to delay the gas coning (Aarra et
al. 1997; Chukwueke et al. 1998; Dalland and Hanssen 1997; Thach et al. 1996).
During a well stimulation operation with acid, a selective placement of acid
into a low-permeability zone from which oil has not been swept is desired,
which can be accomplished with use of foam (Cheng et al. 2002). For
environmental remediation of subsurface soil using surfactant, foam is used to
improve displacement of contaminant, such as DNAPL, from heterogeneous soil
(Mamun et al. 2002).
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
17 February 2006
- Meeting paper published:
22 April 2006
- Revised manuscript received:
12 June 2007
- Manuscript approved:
24 June 2007
- Version of record:
20 March 2008
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