# Transport of Polymer Particles in Oil–Water Flow in Porous Media: Enhancing Oil Recovery

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## Abstract

We study a heuristic, core-scale model for the transport of polymer particles in a two-phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when polymers are injected after the initial waterflood. We propose the recovery mechanism to be microscopic diversion of the flow, where injected particles can accumulate in narrow pore throats and clog it, in a process known as a log-jamming effect. The blockage of the narrow pore channels leads to a microscopic diversion of the water flow, causing a redistribution of the local pressure, which again can lead to the mobilization of trapped oil, enhancing its recovery. Our objective herein is to develop a core-scale model that is consistent with the observed production profiles. We show that previously obtained experimental results can be qualitatively explained by a simple two-phase flow model with an additional transport equation for the polymer particles. A key aspect of the formulation is that the microscopic heterogeneity of the rock and a dynamic altering of the permeability must be taken into account in the rate equations.

## Keywords

Enhanced oil recovery Trapped oil mobilization Polymer particles Log-jamming## List of symbols

- \(A_1, A_2\)
Constants for residual oil saturation change

- \(c_l\)
Mass concentration of polymer particles (\(\hbox {kg}/\hbox {m}^3\))

- \({\varvec{D}}_l\)
Diffusion matrix of polymer particles in water (\(\hbox {m}^2/\hbox {s}\))

- \(d_\mathrm{p}\)
Polymer particle diameter (m)

- \(\mathbf {g}\)
Gravity vector (\(\hbox {m}/\hbox {s}^2\))

- \(\mathbf{K}\)
Absolute permeability tensor (\(\hbox {m}^2\))

- \(K_\mathrm{B}\)
Boltzmann constant (\(\hbox {m}^2\,\hbox {kg}/\hbox {s}^2\,\hbox {K}\))

- \(k_l\)
Constant rate of clogging (\(\hbox {m}^{-1}\))

- \(k_r\)
Constant rate of unclogging (\(\hbox {s}^{-1}\))

- \(k_{r\alpha }\)
Relative permeability of phase \(\alpha \)

- \(n_o,n_w\)
Exponents for the relative permeabilities

- \(p_\alpha \)
Pressure of phase \(\alpha \) (Pa)

*R*Reaction rate \((\hbox {kg}/\hbox {m}^3\,\hbox {s}\))

- \(s_\alpha \)
Saturation of phase \(\alpha \)

*T*Temperature (K)

- \(\mathbf {u}_\alpha \)
Velocity of phase \(\alpha \, (\hbox {m}/\hbox {s})\)

## Greek letters

- \(\gamma \)
Constant for permeability change

- \(\delta \)
Heterogeneity factor

- \(\lambda _\alpha \)
Mobility of phase \(\alpha \, (\hbox {m s}/\hbox {kg})\)

- \(\mu _\alpha \)
Viscosity of phase \(\alpha \, (\hbox {kg}/\hbox {m s})\)

- \(\rho _\alpha \)
Mass density of phase \(\alpha \, (\hbox {kg}/\hbox {m}^3)\)

- \(\sigma \)
Volumetric concentration of accumulated particles

- \(\tau \)
Tortuosity

- \(\phi \)
Porosity

- \(\varphi \)
Clogging rate (\(\hbox {kg}/\hbox {m}^3\,\hbox {s}\))

- \(\psi \)
Unclogging rate (\(\hbox {kg}/\hbox {m}^3\,\hbox {s}\))

## Supplementary material

## References

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