Influence of Cement Concentration on Gas Migration in a Cement Slurry

Gas invasion into a freshly cemented wellbore annulus from the surrounding geological formation can cause loss of isolation, leaking, or other environmental issues. Cement slurries behave as complex nonlinear fluids that may exhibit viscoelasticity, thixotropy, yield stress, shear-thinning effects, etc... In this work, laboratory scale room temperature experiments, representative of the flow of gas invading wellbore cement are simulated. A column of cement slurry undergoes continuous air injection from the bottom. The flow of the slurry and the air bubbles are modeled relying upon the volume of fluid (VOF) approach, in which the interfacial interactions between the immiscible gas and the cement slurry is described through the surface force technique to account for the net tensile force acting on the interface. The cement slurry is considered as a suspension and the spatio-temporal distribution of the cement particles is described by using a convection-diffusion equation for the particle transport flux due to mechanisms such as the compactness and collision of the grains, the gravity, and the change in the viscosity. The effective viscosity of the slurry is based on the Herschel-Bulkley fluid model, modified by the volume fraction of the cement particles by using a polynomial expression or a function depending on the maximum packing fraction. We also look at the dependence of the yield stress on the volume fraction of the cement particles and the water-to-cement ratio. These equations are implemented as customized non-Newtonian viscosity libraries and are solved in OpenFOAM. The results of the air bubble property distributions along with their average rising velocities are discussed with respect to the baseline slurry (Herschel-Bulkley fluid) and the viscosity dependence on the cement volume fraction, over a range of gas injection flow rate.