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Modified Particle Detachment Model for Colloidal Transport in Porous Media

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Abstract

Particle detachment from the rock during suspension transport in porous media was widely observed in laboratory corefloods and for flows in natural reservoirs. A new mathematical model for detachment of particles is based on mechanical equilibrium of a particle positioned on the internal cake or matrix surface in the pore space. The torque balance of drag, electrostatic, lifting and gravity forces, acting on the particle from the matrix and the moving fluid, is considered. The torque balance determines maximum retention concentration during the particle capture. The particle torque equilibrium is determined by the dimensionless ratio between the drag and normal forces acting on the particle. The maximum retention function of the dimensionless ratio (dislodging number) closes system of governing equations for colloid transport with particle release. One-dimensional problem of coreflooding by suspension accounting for limited particle retention, controlled by the torque sum, allows for exact solution under the assumptions of constant filtration coefficient and porosity. The explicit formulae permit the calculation of the model parameters (maximum retention concentration, filtration and formation damage coefficients) from the history of the pressure drop across the core during suspension injection. The values for maximum retention concentration, as obtained from two coreflood tests, have been matched with those calculated by the torque balance on the micro scale.

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Abbreviations

A 132 :

Hamaker constant, J

C m :

Molar concentration of ith ion, L−3

c :

Suspended particle concentration, L−3

C :

Dimensionless suspended particle concentration

D e :

Dielectric constant

D :

Erosion front velocity, LT−1

F :

Force, N

h :

Separation length between particle and grain, L

H :

Thickness of rectangular pore channel, L

J :

Normalized pressure drop on the core

k :

Absolute permeability, L2

k det :

Particle detachment coefficient

k r :

Dimensionless factor of permeability reduction due to particle retention

k B :

Boltzmann constant, ML−2T−2K−1

L :

Core (reservoir) length, L

m :

Growth coefficient of the normalized pressure drop

n :

Number concentration of pores in the rock, L−2

p :

Pressure, MT−2L−1

P :

Dimensionless pressure

PVI:

Pore volume injected (dimensionless unit for time t D)

r :

Radius of a particle or of a pore, L

S :

Dimensionless retention concentration

t :

Time, T

T :

Absolute temperature, K

u :

Interstitial velocity in porous space, LT−1

U :

Darcy’s velocity in porous media, LT−1

V :

Eenergy of interaction, ML2T−2

x :

Coordinate, L

z :

Valence of ith ion

Z :

Ratio between the grain–particle separation distance and particle radius

β :

Formation damage coefficient

\({\varepsilon}\) :

Ratio between the drag and normal forces without retained particles

\({\varepsilon_{\rm p}}\) :

Ratio between the drag and normal forces at the presence of retained particles

\({\varepsilon_{0}}\) :

Free space permittivity, C−2J−1L−1

κ :

Inverse Debye length, L−1

κ C :

Coulomb dry friction coefficient

λ′:

Dimensional filtration coefficient, 1/L

λ:

Dimensionless filtration coefficient

μ :

Dynamic viscosity, ML−1T−1

ν :

Number concentration of ith ion far away from the surface, L−3

ρ :

Density of carrier fluid, ML−3

σ :

Concentration of retained particles

σ LJ :

Atomic collision diameter, L

\({\phi}\) :

Porosity

χ :

Correction factor in lifting formula

ψ :

Surface potential, mV

ω :

Correction factor in equation for drag force

BR:

Born (for energy potential)

c:

Cake

cr:

Critical (maximum) retained concentration

d:

Drag

DLR:

Double layer repulsion (for energy potential)

e:

Electric

l:

Lifting

g:

Gravity

i :

Index for ion

LVA:

London–van der Waals (for energy potential)

n:

Normal (for force)

s:

Suspended (of particles)

p:

Pore

0:

Initial condition or initial value (for permeability)

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Authors and Affiliations

  1. Australian School of Petroleum, University of Adelaide, Adelaide, Australia

    Pavel Bedrikovetsky

  2. State North Fluminense University of Rio de Janeiro UENF, Rio de Janeiro, Brazil

    Fernando D. Siqueira

  3. CENPES, Petrobras Research Center, Rio de Janeiro, Brazil

    Claudio A. Furtado & Antonio Luiz S. Souza

Authors
  1. Pavel Bedrikovetsky
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  2. Fernando D. Siqueira
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  3. Claudio A. Furtado
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  4. Antonio Luiz S. Souza
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Correspondence to Pavel Bedrikovetsky.

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The paper is dedicated to memory of Vladimir Markovich Entov.

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Bedrikovetsky, P., Siqueira, F.D., Furtado, C.A. et al. Modified Particle Detachment Model for Colloidal Transport in Porous Media. Transp Porous Med 86, 353–383 (2011). https://doi.org/10.1007/s11242-010-9626-4

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