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A study of liquid drainage rate from foam with population balance equation: impact of bubble evolution

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Abstract

A significant challenge of foam injection is the stability of the foam in formations. In this study, the modeling of liquid drainage and the impact of some parameters (i.e., concentration of surfactants, nano-particles, and monovalent ions) on the liquid drainage rate and foam stability were investigated by using a population balance model. First, foam bubble size distribution was experimentally measured and used as input for the population balance model. The population balance equations were solved numerically, and the number density of bubble size distribution as a function of time was obtained. Then, the liquid drainage rate was calculated using volume balance equations. It is shown that the liquid drainage rate can be underestimated by neglecting the effect of gas bubble evolution over time. Thus, unrealistic (overestimated) foam stability is predicted. The results of this study provide an insight to the evaluation of foam stability for different solutions.

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Abbreviations

AEq :

Equivalent area of equivalent cylinder (m2)

D:

Average bubble diameters (m)

De :

Equivalent diameter of equivalent cylinder cross section (m)

G:

Gravity acceleration (\( \frac{\mathrm{m}}{{\mathrm{s}}^2} \))

G:

Diameter evolution rate (\( \frac{\mathrm{m}}{\mathrm{s}} \))

L:

Foam initial length (m)

M:

Drainage constant (\( \frac{1}{\mathrm{s}} \))

N:

Bubble number density (\( \frac{\mathrm{bubble}\ \mathrm{number}}{\mathrm{m}} \))

nD :

Dimensionless bubble number density

hi :

Interfacial height (m)

ht :

Foam height (m)

QGC :

Gas separation rate (\( \frac{{\mathrm{m}}^3}{\mathrm{s}} \))

tD :

Dimensionless time

Vf :

Foam volume (m3)

VfD :

Dimensionless foam volume

VGf :

Gas volume in foam (m3)

VL :

Liquid volume in foam (m3)

Vl0 :

Liquid initial volume (m3)

VLD :

Drained liquid volume (m3)

VlD :

Dimensionless liquid volume

Vtot :

Total initial volume (m3)

vB :

Stock’s velocity (\( \frac{\mathrm{m}}{\mathrm{s}} \))

Z:

Foam column height

Ε:

Gas volume fraction

ε0 :

Initial gas volume fraction

ρL :

Density of aqueous phase (\( \frac{\mathrm{kg}}{{\mathrm{m}}^3} \))

ρG :

Density of gas phase (\( \frac{\mathrm{kg}}{{\mathrm{m}}^3} \))

Δρ:

Density difference between gas and aqueous phase (\( \frac{\mathrm{kg}}{{\mathrm{m}}^3} \))

Μ:

Viscosity of aqueous phase (cP)

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Authors and Affiliations

  1. Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

    Yousef Shafiei, Mohammad Hossein Ghazanfari & Seyyed Mehdi Seyyedsar

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  1. Yousef Shafiei
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  2. Mohammad Hossein Ghazanfari
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  3. Seyyed Mehdi Seyyedsar
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Correspondence to Seyyed Mehdi Seyyedsar.

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Shafiei, Y., Ghazanfari, M.H. & Seyyedsar, S.M. A study of liquid drainage rate from foam with population balance equation: impact of bubble evolution. Colloid Polym Sci 296, 1097–1108 (2018). https://doi.org/10.1007/s00396-018-4323-x

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  • DOI: https://doi.org/10.1007/s00396-018-4323-x

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