non-Newtonian Flow In Porous Media Research Articles

A model for non-Newtonian flow in porous media at different flow regimes

Polymeric liquids are of great practical importance for porous media flow as they can be used to improve the sweep of water in the reservoir and therefore improve the recovery of oil. Due to the non-Newtonian behavior of these liquids, they are extremely challenging to model. In this paper, we present a model that is capable of describing the most commonly observed flow regimes in porous media: (i) Newtonian, (ii) Shear thinning, (iii) Shear thickening, and (iv) Mechanical degradation. The novel feature of our model is that the time constants for the shear thinning and shear thickening behavior are related to variations in reservoir properties and conditions, thus making it possible to translate lab results to larger scale without introducing new fitting parameters. Furthermore, we present a way to estimate polymer mechanical degradation in porous media. In our model, the polymer degradation rate is linked to the effective pore radius (using a Kozeny-Carman type equation), shear stress, and polymer molecular weight, M w . The degradation results in a lower M w , while the polymer volumetric concentration is unaffected. The model is applied to a series of laboratory core flood experiments conducted with partially hydrolyzed polyacrylamide, HPAM, of different initial M w ranging from 5 to 20 MDa in seawater, and core permeability varied from 137 to 2019 mD. The flow rate is varied approximately three orders of magnitude and covers the shear thinning, shear thickening, and degradation flow regimes. We show that our model is able to reproduce experimental rate-dependent flow resistance, as well as viscosity of effluent samples. An important aspect supporting the use of the model as a predictive tool is that all the simulations with a given brine have made use of a single set of input parameters to describe the observed shear thickening and degradation behavior. Simulation of a second experimental series using low salinity brine required a separate set of input parameters for the shear thickening and shear degradation. The onset of shear thickening was not affected while shear thickening was reduced and degradation appeared to be slower.

COMPUTATIONAL TECHNIQUES FOR MODELING NON-NEWTONIAN FLOW IN POROUS MEDIA

Modeling the flow of non-Newtonian fluids in porous media is a challenging subject. Several approaches have been proposed to tackle this problem. These include continuum models, numerical methods, and pore-scale network modeling. The latter proved to be more successful and realistic than the rest. The reason is that it captures the essential features of the flow and porous media using modest computational resources and viable modeling strategies. In this article we present pore-scale network modeling techniques for simulating non-Newtonian flow in porous media. These techniques are partially validated by theoretical analysis and comparison to experimental data.

A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains

In the present study, the Lattice Boltzmann Method (LBM) is applied to simulate the flow of non-Newtonian shear-thinning fluids in three-dimensional digitally reconstructed porous domains. The non-Newtonian behavior is embedded in the LBM through a dynamical change of the local relaxation time. The relaxation time is related to the local shear rate in such a way that the power law rheology is recovered. The proposed LBM is applied to the study of power-law fluids in ordered sphere packings and stochastically reconstructed porous domains. A linear relation is found between the logarithm of the average velocity and the logarithm of the body force with a curve slope approximately equal to the inverse power-law index. The validity of the LBM for the flow of shear thinning fluids in porous media is also tested by comparing the average velocity with the well known semi-empirical Christopher–Middleman correlation. Good agreement is observed between the numerical results and the Christopher–Middleman correlation, indicating that the LBM combined with digital reconstruction constitutes a powerful tool for the study of non-Newtonian flow in porous media.

Predictive network modeling of single-phase non-Newtonian flow in porous media

The majority of complex fluids used in oil-field applications are polymeric solutions exhibiting shear-thinning (pseudoplastic) behavior in solution. We study the flow of power-law fluids in porous media using network modeling. We use realistic representations of porous media that capture the geometry and topology of sands and sandstones as input to our flow model. The bulk rheology (variation of viscosity with shear rate) is used to define a relationship between pressure drop and average flow velocity in each pore. We then compute the variation of average velocity with apparent viscosity for the whole network. We successfully predict the results of four experiments from different sources in the literature. The predictions are superior to those using simplified capillary bundle models and involve no adjustable parameters, but are limited to polymer exhibiting simple shear-thinning behavior and require a detailed description of the pore space of interest.

Non‐Newtonian flow (through porous media): A lattice‐Boltzmann method

We introduce a new two‐dimensional microscopic model for the simulation of non‐Newtonian fluids. The model is based on the recently introduced lattice‐gas and lattice‐Boltzmann models of fluid dynamics, which simulate Newtonian fluids by simple interactions on the particle level. The model has the advantage of easy treatment of complex boundaries and multiphase fluids. We use the new model to study non‐Newtonian flow in porous media, and find that flux is related to force by a simple scaling law.

Two-phase flow of a shear thinning fluid in reservoir rock

The flow of a purely viscous rheologically complex fluid as the aqueous phase in two-phase flow in a porous medium is developed. The relationship relative permeability vs. saturation is related to the pore-size distribution of the medium using a “bundle of capillaries”, generalized to allow for flow paths of various diameters and lengths. The pore size distribution is determined by a capillary pressure vs. saturation curve. A weighted shear rate and saturation-dependent viscosity function is used to calculate the aqueous phase flow rate from the multiphase Darcy equation using conventional water relative permeability values. A similar approach can be applied to the hydrocarbon phase if one suspects the displaced phase is rheologically complex. The viscosity function is represented by the empirical power law model. However, the viscosity function may also be represented by a variation of the generalized scale-up method for single-phase non-Newtonian flow in porous media. The analysis predicts interactions between advance rate, rheology, shear rate, reservoir rock morphology, and the displacing phase saturation. Some predicted interactions are absent in the case of a Newtonian/Newtonian fluid pair. The analysis is extended to a consideration of the mobility ratio referenced with respect to the displacement front between the aqueous and hydrocarbon phases. The predicted relationship between the apparent viscosity of the aqueous phase and the saturation level suggests sharp changes in polymer phase mobility can occur over rather small intervals of saturation. These results are used to develop a modified fractional flow expression for non-Newtonian two-phase flow. Fractional flow for a non-Newtonian/Newtonian fluid pair is illustrated for a shear thinning aqueous phase using the properties of a xanthan gum solution.

Non-Newtonian flow in porous media

The conditions for expecting a similarity solution on the lines of d'Arcy's Law for non-Newtonian flow in porous media are examined. A modified d'Arcy Law can be expected for a power law fluid. If the viscometric data does not indicate a power law fluid one cannot find a simple solution for calculating pressure drop flow rate behaviour from rheological parameters. The reason for this can be due to a number of causes of which viscoelasticity is only one. For this reason it is probably easier to find the relationship by simple experiment, and to extend the results to analyse technically important problems such as filtration and three-dimensional flow.