Research Area: Improved recovery# Modelling of Rheological Properties of Polymeric Liquids for Improved Oil Recovery using Microscopic Physics

Project Number: 6370
### Objective

Project Duration: 01.07.18 - 30.06.22

Project Director: Aksel Hiorth

Division Head: Kent Holing

Technical contact person, Statoil: Thomas Ramstad

Investigate and extend microscopic physics-based models of polymeric liquids in order to describe, explain, and predict non-Newtonian phenomena in complex flows relevant for improved oil recovery applications:

**1.** Based on advanced thermodynamics, develop extended polymer fluid models, taking effects such as high temperature, solvent salinity and mechanical degradation into account.

**2.** Solve the realistic equations of non-Newtonian fluid dynamics for idealized geometries and calibrate the results to rheological experiments.

**3.** Solve the physically realistic equations of non-Newtonian fluid dynamics for complex and time-dependent flow patterns using the lattice Boltzmann method, and use the results to construct effective engineering theories for flows through porous media.

**Background **

According to Norwegian Petroleum Directorate, the most promising method of improved oil recovery (IOR) on the Norwegian Continental Shelf is polymer combined with low salinity flooding for enhanced IOR. The essence of this method is adding high-molecular-weight polymer to the injected water. This significantly increases the apparent viscosity of water, which leads to improved sweep efficiency and allows to recover more oil from the reservoir.

Polymer solutions contain macromolecules and therefore possess very specific properties. Unlike oil or water, obeying the laws of classical, or Newtonian, fluid dynamics, macromolecular fluids do not obey these laws: They are non-Newtonian.

To predict the motion of any fluid, one needs to solve the equations of fluid dynamics, known as the (generalized) Navier-Stokes equations. One of the key physical quantities included in these equations is the stress tensor, describing how forces are distributed inside the fluid. For Newtonian fluids, the stress tensor has a simple form and can be calculated provided the the viscosity of the fluid is known. For non-Newtonian fluids, it is more difficult to evaluate the stress tensor. It can be found from a so-called constitutive equation, which in turn must be derived by means of non-equilibrium thermodynamics.

Using correlations for non-Newtonian fluid properties obtained from laboratory experiments does not allow for realistic polymeric flow modelling: correlations are only valid at conditions at which they are measured, while the conditions in the reservoir are highly varied.

Available computational packages cannot be effectively used in modelling polymer enhanced IOR procedures. They support only "generalized Newtonian" constitutive equations, which do not work for flows in complex geometries, like porous rocks, and for time-dependent flows.

Thus, realistic modelling of polymeric flows must involve understanding the nature of macromolecular fluids, derivation of the constitutive equations based on microscopic physics, and solving them together with the equations of fluid motion. Development of such methods will drastically increase the predictive power of engineering calculations, allowing to spare time and resources spent in the laboratory, together with increasing the efficiency of IOR procedures.

Left: Visualized streamlines of a Newtonian flow through a porous medium obtained using the lattice Boltzmann method. Right: Typical apparent dynamics of polymeric flow through a porous medium -- flow resistance factor as a function of the volume flow rate. This behaviour cannot be explained by current polymeric flow modelling procedures.

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