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An Investigation of Polymer Adsorption in Porous Media Using Pore Network Modelling

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Abstract

Polymer injection in hydrocarbon reservoirs has been of great interest in petroleum engineering as an enhanced oil recovery method. In order to have a reliable injection plan, an accurate estimation of polymer behaviour is required to control the fluid flow in porous media. However, it is difficult to calculate the flow properties of polymer solutions—known as non-Newtonian fluids—in porous media, due to variable viscosity at different shear rates. Adsorption of polymer molecules onto the rock surface decreases the available cross-sectional area of polymer solution, therefore at a constant rate, the shear rate increases. As a result, it is important to investigate how polymer adsorption can affect the polymer solution flow behaviour in porous media. Moreover, prior to any polymer injection plan, the amount of adsorbed polymer should be calculated, due to the high cost of polymers. In the present study, pore network modelling was used to investigate the effect of polymer adsorption on flow behaviour of polymer solutions in porous media. To achieve this goal, a simple pore was constructed to adequately represent the real structure of the porous medium. It was then validated by simulation of Newtonian fluid flow in the network and comparison of the calculated flow properties with the experimental data. After validation, the pore network was used for simulation of non-Newtonian fluid flow in porous media. The experimental apparent viscosity of non-Newtonian fluid was used for verification of the procedure and the developed network. The apparent viscosity of non-Newtonian was calculated successfully using macroscopic properties of the rock sample and measured bulk properties of non-Newtonian fluid. The effect of polymer adsorption on calculation of non-Newtonian fluid apparent viscosity was then investigated. It was shown that the polymer adsorption process plays an important role in calculation of polymer solution apparent viscosity. The results reveal that polymer adsorption cannot be neglected, especially in near well-bore areas where the adsorption is high. Finally, the effect of wettability in calculating the total amount of adsorbed polymer volume was studied. The results suggest that neglecting the rock’s wettability can result in an overestimation or underestimation of the amount of adsorbed polymer.

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Abbreviations

\(\hbox {A}_{\mathrm{ow}}\) :

Oil-wet area \((\hbox {m}^{2})\)

\(\hbox {A}_{\mathrm{ww}}\) :

Water-wet area \((\hbox {m}^{2})\)

\(\hbox {AC}_{\mathrm{cat-ow}}\) :

Adsorption coefficient of cationic polymer on oil-wet surface \((\hbox {mg/m}^{2})\)

\(\hbox {AC}_{\mathrm{cat-ww}}\) :

Adsorption coefficient of cationic polymer on water-wet surface \((\hbox {mg/m}^{2})\)

C:

Consistency Index \((\hbox {Pa s}^{\mathrm{n}})\)

\(\hbox {C}_{\mathrm{p}}\) :

Polymer concentration (ppm)

f :

The fraction of mixed-wet pores and throats (fraction)

\(\hbox {F}_{\mathrm{rr}}\) :

Permeability reduction factor (fraction)

K:

Rock permeability (D)

\(\hbox {K}_{\mathrm{w}}\) :

Permeability of rock before polymer treatment (md)

\(\hbox {K}_{\mathrm{wp}}\) :

Permeability of rock after polymer treatment (md)

L:

The length of circular capillary (m)

n:

Shear-thinning exponent in Power Law model (dimensionless)

\(\hbox {P}_{\mathrm{c}}\) :

Capillary pressure (Pa)

\(\hbox {P}_{\mathrm{c,max}}\) :

Maximum capillary pressure reached during primary drainage (Pa)

\(\hbox {P}_{\mathrm{c}}^*\) :

Threshold capillary pressure for water film collapse (Pa)

\(\Delta \hbox {P}\) :

Pressure drop across circular capillary (Pa)

\(\hbox {Q}_{\mathrm{N}}\) :

Newtonian fluid flow rate \((\hbox {m}^{3}\hbox {/s})\)

\(\hbox {Q}_{\mathrm{NN}}\) :

Non-Newtonian fluid flow rate \((\hbox {m}^{3}\hbox {/s})\)

r:

Radius of circular capillary (m)

q:

Darcy velocity (m/s)

\(\hbox {S}_{\mathrm{wi}}\) :

Irreducible water saturation (fraction)

Z:

Average coordination number (dimensionless)

\(\alpha \) :

Scaling factor for adjusting calculated apparent viscosity (1/m)

ø:

Rock porosity (fraction)

\({\sigma }\) :

Interfacial tension, IFT (mN/m)

\(\mu _{\mathrm{app}}\) :

Apparent viscosity (Pa s)

\(\mu _N\) :

Newtonian fluid viscosity (Pa s)

\(\mu _{o}\) :

Oil viscosity (Pa s)

\(\mu _{w}\) :

Water viscosity (Pa s)

\(\mu _{0}\) :

Non-Newtonian fluid viscosity in lower Newtonian region (Pa s)

\(\mu _\infty \) :

Non-Newtonian fluid viscosity in upper Newtonian region (Pa s)

\(\dot{\gamma }\) :

Shear rate (1/s)

\(\updelta \) :

Weibull distribution parameter

\(\upomega \) :

Weibull distribution parameter

\(\uptau _{\mathrm{rz}}\) :

Shear stress (Pa)

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Authors and Affiliations

  1. Institute of Petroleum Engineering, Heriot Watt University, Edinburgh, UK

    Shokoufeh Aghabozorgi

  2. Institute of Petroleum Engineering, University of Tehran, Tehran, Iran

    Shokoufeh Aghabozorgi & Behzad Rostami

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  1. Shokoufeh Aghabozorgi
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  2. Behzad Rostami
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Correspondence to Shokoufeh Aghabozorgi.

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Aghabozorgi, S., Rostami, B. An Investigation of Polymer Adsorption in Porous Media Using Pore Network Modelling. Transp Porous Med 115, 169–187 (2016). https://doi.org/10.1007/s11242-016-0760-5

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