Optimizing the rheological properties of silica nano-modified bentonite mud using overlaid contour plot and estimation of maximum or upper shear stress limit.

An optimization based statistical (response surface) approach was used to evaluate the rheological properties of bentonite mud treated with silica nanoparticles. The overlaid contour plot established the feasible region for the various factor settings from multiple regression equations. The steepest method was used to further determine the optimal factor settings for minimum rheological properties and this was established at 6.3 wt.% bentonite content and 0.94 wt.% silica nanoparticles. The rheological properties of the bentonite mud containing and without silica nanoparticles was evaluated using a Hyperbolic (new) model and related with other oil industry based models: Herschel Bulkley, Sisko, Casson. The hyperbolic rheological model estimated the rheological behaviour of the nano-modified mud satisfactorily while also predicting a shear stress limit for the nano-modified mud. The maximum shear stress limit values for 6.3, 13 and 15 wt.% mud were 14.59, 61.74 and 107.4 Pa respectively. Upper shear stress values obtained from a 1.5 wt.% silica nanoparticle modified 6.3, 13 and 15 wt.% bentonite mud were 22.27, 72.62 and 171.3 Pa respectively, which represents an increment of 34.5 to 37.4% in the upper limit of shear stress. The effect of silica nanoparticles on the upper shear stress limit was quantified using a response surface design

Anomalous temperature behavior in clay swelling due to ion-ion correlations

We show, experimentally and theoretically, that swelling of both natural and refined clays has an anomalous temperature behavior depending on counterion valency. In an aqueous clay dispersion dominated by monovalent counterions the swelling pressure increases with temperature as expected from entropic arguments. In a clay with predominantly divalent counterions, the opposite behavior is found. The explanation is due to the fact that ion-ion correlations increase with temperature. Ion-ion correlations are important at strong electrostatic coupling and in an aqueous solution the dielectric permittivity, $\epsilon_r$ , drops with increased temperature, T, in such a way that the product $\epsilon_r T$ also decreases. Thus, the net effect is an increased coupling