Prediction of Xanthan Rheology in Porous Media

Abstract

ABSTRACT The flow behavior of xanthan in porous media has been investigated experimentally, and also theoretically using effective medium theory. In the experimental portion of this study, the rheology of a commercially-available xanthan broth was characterized in porous media and viscometers and compared for a wide range of polymer concentrations (300 to 1600 ppm), effective brine permeabilities (40 to 800 md), residual oil saturations (0 to 29%), temperatures (25° and 80°C), and rock lithologies (sandstones and carbonates). An apparent shear rate equation having no adjustable parameters was developed and proved to be effective in relating the flow behavior of a given polymer solution in porous media at one set of conditions to the behavior at all other porous media conditions tested as well as to the rheology in a viscometer. Although the shear rate dependence on flow velocity (first order) and effective permeability (negative one-half order) agrees with that predicted by traditional capillary bundle model approaches, the value of the experimentally determined constant coefficient is larger than those predicted by the models. The basis for the shear rate equation employed above has been studied theoretically with the assumption that the xanthan solution rheologies approximately follow the power-law relation. The apparent viscosity for a power-law fluid flowing in a porous medium is derived employing the effective medium approximation of percolation theory. In this approach, a porous medium is modeled as a network of capillary tubes, in which the radii of tubes are randomly distributed using a prescribed probability distribution. The apparent viscosity expression obtained is similar to that from the capillary bundle model, but the coefficient values are different, as observed experimentally. This difference is a consequence of the connectivity of flow channels and their variable cross-section. Due to its shear-thinning nature, a power-law fluid flows mainly through the wide channels of porous media, and largely bypasses small-scale pore channels of the porous body. The capillary bundle model cannot describe this tendency of a shear-thinning fluid.