Mathematical modeling of nano-particle transport in oil well cement cracks

Abstract

Transport of nanoparticles (NPs) in fluids was analyzed in this study for sealing cement and micro-annuli fractures with nano-silica gels. Analytical models were developed to analyze NPs transport in cracks. The effects of gravitational, capillary, and viscous forces on NPs transport in oil well cement sheath cracks were investigated. It was found that the effect of gravitational force on the NPs transport in cracks is negligible owing to the small particle size. Gravity should not cause segregation of solid and liquid phases. Capillary force can induce spontaneous imbibition of nano-fluids that carries NPs into cement cracks. The imbibition rate is crack size-, fluid viscosity- and time-dependent. NPs can be effectively carried into cracks by viscous force. The viscous pressure gradients required for transporting NPs into the cement cracks are in the range between 0.04 psi/ft and 0.1 psi/ft at a convection flow rate of 1 gpm, depending on crack width and fluid viscosity. For a 500-ft long crack, the viscous pressure drop should be in a range from 20 psi to 50 psi, which is manageable in field operations.