The coupled model of transient non-equilibrium interphase mass transfer rate of sliding bubble and two-phase flow in variable gradient drilling

Abstract

The aim of this research is to investigate the influence of key parameters of variable gradient drilling by injecting hollow-glass spheres (Referred to as HGS, it is a low-density and micron-sized hollow glass sphere) on the interphase mass transfer rate of the surface boundary layer of the sliding bubble in the annulus and the flow law of the two-phase flow in the wellbore after the gas intrusion occurred. Firstly, the key parameters of variable-gradient drilling, such as HGS volume fraction, HGS density, the depth of the filter separator, were coupled with the model of non-equilibrium interphase mass transfer rate and the mathematical model of two-phase flow to establish a new two-phase flow model of transient non-equilibrium interphase mass transfer for variable-gradient drilling. Secondly, the existing classic model and measured data were used for comparative analysis with the model in this paper, and then the accuracy of the model in this paper was verified. Thirdly, based on the on-site data, the numerical calculations and sensitivity analysis were carried out using the model in this paper. Finally, a comparative analysis of the interphase mass transfer rate was performed under equilibrium and non-equilibrium conditions. In addition, the influence on non-equilibrium interphase mass transfer rate of surface boundary layer of the bubble, bottom hole pressure, overflow rate and overflow rate exerted by different separator positions, HGS volume fraction, HGS density, and pumping rate was studied. The results indicated that the interphase mass transfer rate under the non-equilibrium condition was lower than that under the equilibrium condition when the both were at the same well depth or at the same circulation time. The interphase mass transfer rate enhanced with the increase of pumping rate, the depth of filter separator and HGS density, but decreased with the increase of HGS volume fraction. The bottom-hole pressure was negatively correlated with the depth of the filter separator and the volume fraction of HGS, on the contrary, it was positively correlated with the HGS density. Similarly, the gas void fraction, overflow rate and overflow were positively correlated with the depth of filter separator and HGS volume fraction, but negatively correlated with the HGS density. This research can provide a certain theoretical reference for variable gradient drilling.