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Exact Solutions for Nonlinear High Retention-Concentration Fines Migration

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Abstract

The paper discusses migration of natural reservoir fines lifted by high-rate or low-salinity water injection. The previous papers used linear analytical model, which is valid for low retention of mobilised fine particles in order to determine the model parameters from breakthrough fines concentration and pressure drop across the core during laboratory corefloods. The current work derives exact analytical solutions for the nonlinear case of high retention-concentration fines migration. The solution exhibits uniform profiles of suspended and retained concentrations ahead of the particle front and steady-state retained concentration behind the front. The obtained type curves allow distinguishing between linear and nonlinear fines migration. The laboratory data exhibit close agreement with the nonlinear model predictions, whereas the linear model poorly matches the laboratory data.

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Abbreviations

c :

Suspended particle concentration (\(\hbox {L}^{-3}\))

C :

Dimensionless suspended particle concentration

f :

Drift-delay factor

k :

Permeability (\(\hbox {L}^{2}\))

L :

Core length (L)

p :

Pressure (\(\hbox {MT}^{-2}\hbox {L}^{-1}\))

s :

Accessibility factor

S :

Dimensionless retained particle concentration

\(S_{m}\) :

Dimensionless maximum vacancy concentration

t :

Time (T)

U :

Darcy’s velocity (\(\hbox {LT}^{-1}\))

\(U_{s}\) :

Velocity of particles (\(\hbox {LT}^{-1}\))

x :

Dimensionless linear coordinate

\(\alpha \) :

Constant value of drift-delay factor

\(\beta \) :

Formation damage coefficient

\(\lambda \) :

Filtration coefficient (\(\hbox {L}^{-1}\))

\(\mu \) :

Dynamic viscosity (\(\hbox {ML}^{-1}\hbox {T}^{-1}\))

\(\sigma \) :

Concentration of retained particles

\(\sigma _{cr}\) :

Maximum retention function

\(\sigma _{m}\) :

Maximum vacancy concentration

\(\phi \) :

Porosity

f:

Front

0:

Initial value

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Acknowledgements

The authors are grateful to Prof Y Osipov (Moscow State University of Civil Engineering) and Dr Z You (the University of Adelaide) for discussion of the analytical model, and to Dr A Badalyan (the University of Adelaide) for providing the laboratory data. Many thanks are due to David H. Levin (Murphy, NC, USA) who provided professional English-language editing of this article.

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  1. University of Adelaide, Adelaide, Australia

    Y. Yang & P. Bedrikovetsky

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  1. Y. Yang
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Correspondence to P. Bedrikovetsky.

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Yang, Y., Bedrikovetsky, P. Exact Solutions for Nonlinear High Retention-Concentration Fines Migration. Transp Porous Med 119, 351–372 (2017). https://doi.org/10.1007/s11242-017-0885-1

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