Journal Article

Shear Rate Determination from Pore-Scale Flow Fields

Berg, Steffen, van Wunnik, John

2017

Overview

Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order to predict the Darcy-scale effective viscosity μ eff required for practical applications often, semi-empirical correlations such as the Cannella or Blake–Kozeny correlation are employed. These correlations employ an empirical constant (“ C -factor”) that varies over three orders of magnitude with explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons for this dependency are not very well understood. The semi-empirical correlations are derived under the assumption that the porous media can be approximated by a capillary bundle for which exact analytical solutions exist. The effective viscosity μ eff ( v Darcy ) as a function of flow velocity is then approximated by a cross-sectional average of the local flow field resulting in a linear relationship between shear rate γ and flow velocity. Only with such a linear relationship, the effective viscosity can be expressed as a function of an average flow rate instead of an average shear rate. The local flow field, however, does in general not exhibit such a linear relationship. Particularly for capillary tubes, the velocity is maximum at the center, while the shear rate is maximum at the tube wall indicating that shear rate and flow velocity are rather anti-correlated. The local flow field for a sphere pack is somewhat more compatible with a linear relationship. However, as hydrodynamic flow simulations (using Newtonian fluids for simplicity) performed directly on pore-scale resolved digital images suggest, flow fields for sandstone rock fall between the two limiting cases of capillary tubes and sphere packs and do in general not exhibit a linear relationship between shear rate and flow velocity. This indicates that some of the shortcomings of the semi-empirical correlations originate from the approximation of the shear rate by a linear relationship with the flow velocity which is not very well compatible with flow fields from direct hydrodynamic calculations. The study also indicates that flow fields in 3D rock are not very well represented by capillary tubes.

• Publisher: Springer Netherlands,Springer Nature B.V
• Subject: Additives / Approximation / Aqueous solutions / Capillary tubes / Civil Engineering / Classical and Continuum Physics / Correlation / Dependence / Digital imaging / Earth and Environmental Science / Earth Sciences / Empirical analysis / Exact solutions / Flow simulation / Flow velocity / Fluid flow / Geotechnical Engineering & Applied Earth Sciences / Hydrogeology / Hydrology/Water Resources / Industrial Chemistry/Chemical Engineering / Local flow / Mathematical analysis / Newtonian fluids / Oil recovery / Porosity / Porous media / Rheological properties / Rheology / Sandstone / Shear flow / Shear rate / Three dimensional flow / Viscosity