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Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection

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Abstract

Fines migration induced by injection of low-salinity water (LSW) into porous media can lead to severe pore plugging and consequent permeability reduction. The deep-bed filtration (DBF) theory is used to model the aforementioned phenomenon, which allows us to predict the effluent concentration history and the distribution profile of entrapped particles. However, the previous models fail to consider the movement of the waterflood front. In this study, we derive a stochastic model for fines migration during LSW flooding, in which the Rankine-Hugoniot condition is used to calculate the concentration of detached particles behind and ahead of the moving water front. A downscaling procedure is developed to determine the evolution of pore-size distribution from the exact solution of a large-scale equation system. To validate the proposed model, the obtained exact solutions are used to treat the laboratory data of LSW flooding in artificial soil-packed columns. The tuning results show that the proposed model yields a considerably higher value of the coefficient of determination, compared with the previous models, indicating that the new model can successfully capture the effect of the moving water front on fines migration and precisely match the effluent history of the detached particles.

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Abbreviations

c :

suspended-particle concentration

C :

dimensionless suspended-particle concentration

C v :

coefficient of variation

f a :

fractional flow through accessible pores

f ns :

fractional flow through inaccessible pores

F d :

dragforce

F e :

electrostatic force

F g :

gravity

F L :

lifting force

h :

total pore concentration

h 0 :

initial total pore concentration

H :

pore size distribution

k :

permeability

k 0 :

initial permeability

k 1 :

conductance in single pore

l :

porous space dispersivity

l d :

level arm of drag force

l n :

level arm of normal force

L :

length of porous specimen

r 0 :

averaged radius of moving particles

r p :

radius of pore

r s :

radius of particle

s 1 :

cross area of single pore

S :

dimensionless captured-particle concentration

S cr :

dimensionless critical attached-particle concentration

S r :

dimensionless attached-particle concentration

t :

time

t 0 :

the moment corresponding to intersection of characteristic line and water front

U :

Darcy velocity

x :

linear coordinate

α :

drift delay factor

β :

power index

γ :

salinity

Λ:

dimensionless filtration coefficient

σ :

captured-particle concentration

σ 0 :

initial captured-particle concentration

σ r :

attached-particle concentration

φ 0 :

initial porosity

φ a :

accessible porosity

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Acknowledgements

The authors are grateful to Professor P. BEDRIKOVETSKY (The University of Adelaide) for the discussion of the analytical model.

Author information

Authors and Affiliations

  1. Unconventional Petroleum Research Institute, China University of Petroleum, Beijing, 102249, China

    Yulong Yang, Weifeng Yuan & Jirui Hou

  2. School of Chemical Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Zhenjiang You

  3. College of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China

    Jun Li & Yang Liu

Authors
  1. Yulong Yang
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  2. Weifeng Yuan
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  3. Jirui Hou
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  4. Zhenjiang You
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  5. Jun Li
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Corresponding author

Correspondence to Zhenjiang You.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 51804316, 51734010, and U1762211), the National Science and Technology Major Project of China (No. 2017ZX05009), and the Science Foundation of China University of Petroleum, Beijing (No. 2462017YJRC037)

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Yang, Y., Yuan, W., Hou, J. et al. Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection. Appl. Math. Mech.-Engl. Ed. 41, 491–506 (2020). https://doi.org/10.1007/s10483-020-2583-9

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  • DOI: https://doi.org/10.1007/s10483-020-2583-9

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2010 Mathematics Subject Classification

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