Particles sedimenting in viscoelastic drilling muds [electronic resource]
Keywords: Mechanical Engineering.

Suspensions of solids in polymeric solutions are pumped to help prop open the fracture during the drilling of oil and gas wells. These high-density solids in suspension sediment in the presence of shear flow in the orthogonal direction as they are pumped. Experimental data [Tonmukayakul et al. , US Patent Application US20110219856 (2011); van den Brule and Gheissary, J. Non-Newton. Fluid Mech. 49 (1993) 123-132] have shown that both shear thinning and the elasticity of the suspending polymeric solutions affect the settling rate of the solids. The mechanism by which the elasticity of the carrying fluid affects the settling rate is not well understood. In the present work, simulations of viscoelastic flow past a single, torque-free sphere with a cross shear flow are used to study the effect of the shear-thinning and elasticity of the carrying fluid on the sphere's settling rate. We study sedimentation in two different fluids i.e. a Boger fluid and shear-thinning guar gum solutions. The FENE-P constitutive model is used to represent a viscoelastic Boger fluid, with parameters obtained by fitting rheological data. A twofold increase in drag, i.e. a decrease in settling rate, is obtained with increase in the cross shear Weissenberg number, Wi < 15, even though the shear viscosity of the solution decreases modestly over this same range. At small Weissenberg number, Wi < 2, the simulations remain in quantitative agreement with the experiments. At higher Weissenberg number, the numerical results remain in qualitative agreement with settling experiments although the magnitude of the simulated decrease in settling rate is smaller than that observed in experiments. The detailed physical mechanism for the increase in the drag experienced by the sphere in the simulations is presented and we show that the viscous shear stress is the primary cause of the increase in sphere drag. The weakly elastic guar gum solutions are modeled using the Giesekus constitutive model. The drag on the sphere decreases with an increase in the shear Weissenberg number that is in qualitative agreement with the experiments. The decrease in the drag is primarily due to the decrease in the polymer drag component because of shear-thinning of the polymers. The competing effects of the shear-thinning and elasticity of the guar gum solutions is presented. The effect of walls on the drag coefficients in Boger fluids is also investigated. It is demonstrated, that the effect of the increase in the drag coefficients with Wi is accentuated as the interactions with the wall grows stronger. The wall interactions lead to an increase in viscous shear stresses downstream of the sphere, which causes the increase in the drag. In the second part of the thesis, we investigate the flow through porous media. Simulations are performed for creeping flow through periodic and random arrays of spheres and cylinders. We use the inelastic power-law model for examining the effects of shear-thinning and shear-thickening of the fluid on the drag coefficients. The drag coefficients are calculated over a broad range of volume fractions and power-law indices. The simulation results at small volume fractions show good agreement to the theoretical scaling for small volume fractions [Singh et al. , J. Fluid Mech., 713 (2012), 491-527]. The simulation results at high volume fractions also show good agreement with the lubrication theory results. The effects of viscoelasticity on the drag in porous media are then analyzed by using the FENE-P model as constitutive equation for the fluid. The drag coefficients are calculated for moderate Reynolds number between 0 and 100. The introduction of polymers leads to a drastic increase in the drag coefficients as Re is increased for both periodic as well as random arrays of cylinders. The drag increase is primarily due to the increase in form drag. The mechanism for the increase in the form drag is analyzed and discussed.