Supporting Information High Temperature CO2-in-Water Foams ...
Supporting Information
High Temperature CO2-in-Water Foams Stabilized with Cationic Quaternary Ammonium Surfactants Yunshen Chen1, Amro S. Elhag1, Andrew J. Worthen1, Prathima P. Reddy1, Anne Marie Ou1, George J. Hirasaki2, Quoc P. Nguyen3, Sibani L. Biswal2 and Keith P. Johnston1* 1. McKetta Department of Chemical Engineering, the University of Texas at Austin, 2. Department of Chemical and Biomolecular Engineering, Rice University 3. Department of Petroleum and Geosystems Engineering, the University of Texas at Austin
Corresponding Author Keith P. Johnston Address: Department of Chemical Engineering, the University of Texas at Austin, Austin, TX, 78712 E-mail: [email protected] Telephone: 512-471-9602
A
B
ISCO pump Computer
Camera
Light source
Measurement cell Measurement cell Optical rail
Manual pump
Figure S1. Scheme (A) and apparatus photos (B) for IFT measurement at high pressures
Apparent viscosity of foam in smooth capillaries1 In Hirasaki and Lawson1’s model, foam flow in porous media is described as a bundle of interconnected capillaries. The apparent viscosity of foam in this capillary model is the sum of three contributions as shown on the right side of Equation S1: (1) the viscosity of liquid slugs between bubbles, (2) the resistance due to bubble deformation when a bubble passing through a capillary, and (3) the surface tension gradient owing to the sweep of surface active materials from the front to the back of a bubble when it moves. ଵ
ଵ
ߤ ሺ݊ ܴ ሻ 3ߤ ܷ ିଷ ݎ 3ߤ ܷ ିଷ ሺ1 − ݁ ିேಽ ሻ ଶ = ܮ௦ ݊ + 0.85 ݎ ൬ ൰ [ቀ ൗܴ ሻ + 1ቃ + ሺ݊ ܴ ሻ ൬ ൰ ඥܰ௦ ߤ ߛ ߛ ሺ1 + ݁ ିேಽ ሻ ቀ ൗܴ ቁ
(S1)
where Ls is length of liquid slugs, ݊ is lamellae density (the number of equivalent lamellae per unit length), rc is curvature radius of the gas-liquid interface, Rc is radius of capillary, U is gas phase velocity, Ns is a dimensionless number which describes the interfacial tension gradient effect, and NL is the dimensionless bubble length.1 From Equation S1, with an increase of gas phase velocity, ߤ decreases indicating shear thinning behavior for foam flow in each capillary channel in porous media.
Apparent viscosity (mPa.s)
0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 60
70
80 Foam quality (%)
90
100
Figure S2. Effect of foam quality on apparent viscosity of CO2- 22%TDS brine mixture without surfactant in a 75 µm2 calcium carbonate packed bed at 393 K ± 1K and 23 ± 0.69 MPa and total superficial velocity of 0.331 cm/s. The errors in pressure drop readings are ±15%.
Water saturation and limiting capillary pressure in porous media2 In water-wet porous media, water forms a meniscus that spans the pair of grains in contact with water as shown in Figure S3. When an aqueous phase and CO2 are injected simultaneously into pores initially water, the water saturation decreases such that the meniscus moves closer towards the contact point. This change results a smaller radius of curvature at the interface as shown in Figure S3. As the radius of curvature decreases, the capillary pressure increases until it reaches a“limiting capillary pressure”2 above which the capillary pressure exceeds disjoining pressure (Figure S4).3, 4 Here, lamellae become unstable and several lamellae rupture simultaneously to produce a foam with a coarser texture (as demonstrated at 98% foam quality in Figure 7) The increase of the average bubble size causes a decrease in the capillary pressure.2 Thus, as the coarser foam is displaced, the capillary pressure increases again which leads to further bubble to coalescence. This repeated coalescence and displacement of the coarse-textured foam keeps the average capillary pressure near the limiting capillary pressure.2
Figure S3. Effect of water saturation on the curvature of CO2-water interface in water-wet porous media: Rlow Sw and Rhigh Sw are the radii of the curvatures at relative low and high water saturation.
Figure S4. Stability of lamellae: disjoining pressure versus capillary pressure
References 1. Hirasaki, G. J.; Lawson, J. B., Mechanisms of Foam Flow in Porous Media: Apparent Viscosity in Smooth Capillaries. Society of Petroleum Engineers Journal 1985, 176-190. 2. Khatib, Z. I.; Hirasaki, G. J.; Falls, A. H., Effects of Capillary Pressure on Coalescence and Phase Mobilites in Foams Flowing Through Porous Media. SPE Reservoir Engineering 1988, 3, (3), 919-926. 3. Kovscek, A. R.; Radke, C. J., Fundamentals of Foam Transport in Porous Media. In Foams: Fundamentals and Application in the Petroleum Industry., Schramm, L. L., Ed. ACS Washington DC, 1994. 4. Aronson, A. S.; Bergeron, V.; Fagan, M. E.; Radke, C. J., The Influence of Disjoining Pressure on Foam Stability and Flow in Porous Media. Colloids and Surface A: Physicochem. Eng. Aspects 1994, 83, (2), 109120.
High Temperature CO2-in-Water Foams Stabilized with Cationic Quaternary Ammonium Surfactants Yunshen Chen1, Amro S. Elhag1, Andrew J. Worthen1, Prathima P. Reddy1, Anne Marie Ou1, George J. Hirasaki2, Quoc P. Nguyen3, Sibani L. Biswal2 and Keith P. Johnston1* 1. McKetta Department of Chemical Engineering, the University of Texas at Austin, 2. Department of Chemical and Biomolecular Engineering, Rice University 3. Department of Petroleum and Geosystems Engineering, the University of Texas at Austin
Corresponding Author Keith P. Johnston Address: Department of Chemical Engineering, the University of Texas at Austin, Austin, TX, 78712 E-mail: [email protected] Telephone: 512-471-9602
A
B
ISCO pump Computer
Camera
Light source
Measurement cell Measurement cell Optical rail
Manual pump
Figure S1. Scheme (A) and apparatus photos (B) for IFT measurement at high pressures
Apparent viscosity of foam in smooth capillaries1 In Hirasaki and Lawson1’s model, foam flow in porous media is described as a bundle of interconnected capillaries. The apparent viscosity of foam in this capillary model is the sum of three contributions as shown on the right side of Equation S1: (1) the viscosity of liquid slugs between bubbles, (2) the resistance due to bubble deformation when a bubble passing through a capillary, and (3) the surface tension gradient owing to the sweep of surface active materials from the front to the back of a bubble when it moves. ଵ
ଵ
ߤ ሺ݊ ܴ ሻ 3ߤ ܷ ିଷ ݎ 3ߤ ܷ ିଷ ሺ1 − ݁ ିேಽ ሻ ଶ = ܮ௦ ݊ + 0.85 ݎ ൬ ൰ [ቀ ൗܴ ሻ + 1ቃ + ሺ݊ ܴ ሻ ൬ ൰ ඥܰ௦ ߤ ߛ ߛ ሺ1 + ݁ ିேಽ ሻ ቀ ൗܴ ቁ
(S1)
where Ls is length of liquid slugs, ݊ is lamellae density (the number of equivalent lamellae per unit length), rc is curvature radius of the gas-liquid interface, Rc is radius of capillary, U is gas phase velocity, Ns is a dimensionless number which describes the interfacial tension gradient effect, and NL is the dimensionless bubble length.1 From Equation S1, with an increase of gas phase velocity, ߤ decreases indicating shear thinning behavior for foam flow in each capillary channel in porous media.
Apparent viscosity (mPa.s)
0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 60
70
80 Foam quality (%)
90
100
Figure S2. Effect of foam quality on apparent viscosity of CO2- 22%TDS brine mixture without surfactant in a 75 µm2 calcium carbonate packed bed at 393 K ± 1K and 23 ± 0.69 MPa and total superficial velocity of 0.331 cm/s. The errors in pressure drop readings are ±15%.
Water saturation and limiting capillary pressure in porous media2 In water-wet porous media, water forms a meniscus that spans the pair of grains in contact with water as shown in Figure S3. When an aqueous phase and CO2 are injected simultaneously into pores initially water, the water saturation decreases such that the meniscus moves closer towards the contact point. This change results a smaller radius of curvature at the interface as shown in Figure S3. As the radius of curvature decreases, the capillary pressure increases until it reaches a“limiting capillary pressure”2 above which the capillary pressure exceeds disjoining pressure (Figure S4).3, 4 Here, lamellae become unstable and several lamellae rupture simultaneously to produce a foam with a coarser texture (as demonstrated at 98% foam quality in Figure 7) The increase of the average bubble size causes a decrease in the capillary pressure.2 Thus, as the coarser foam is displaced, the capillary pressure increases again which leads to further bubble to coalescence. This repeated coalescence and displacement of the coarse-textured foam keeps the average capillary pressure near the limiting capillary pressure.2
Figure S3. Effect of water saturation on the curvature of CO2-water interface in water-wet porous media: Rlow Sw and Rhigh Sw are the radii of the curvatures at relative low and high water saturation.
Figure S4. Stability of lamellae: disjoining pressure versus capillary pressure
References 1. Hirasaki, G. J.; Lawson, J. B., Mechanisms of Foam Flow in Porous Media: Apparent Viscosity in Smooth Capillaries. Society of Petroleum Engineers Journal 1985, 176-190. 2. Khatib, Z. I.; Hirasaki, G. J.; Falls, A. H., Effects of Capillary Pressure on Coalescence and Phase Mobilites in Foams Flowing Through Porous Media. SPE Reservoir Engineering 1988, 3, (3), 919-926. 3. Kovscek, A. R.; Radke, C. J., Fundamentals of Foam Transport in Porous Media. In Foams: Fundamentals and Application in the Petroleum Industry., Schramm, L. L., Ed. ACS Washington DC, 1994. 4. Aronson, A. S.; Bergeron, V.; Fagan, M. E.; Radke, C. J., The Influence of Disjoining Pressure on Foam Stability and Flow in Porous Media. Colloids and Surface A: Physicochem. Eng. Aspects 1994, 83, (2), 109120.
