Influence of the irregular hole on the cement displacement efficiency in deep wells

Deep oil and gas reservoirs are greater in burial depth and there are more complex series of strata. And due to the influences of geological and engineering factors, the phenomenon of hole collapse or shrinkage occurs frequently. Applying experimental or theoretical method to study the cementing operation in irregular holes is of high cost and great difficulty. And the conventional numerical simulation can hardly track the sudden change characteristics of the displacement interface induced by the disturbance of hole collapse or shrinkage. To this end, this paper proposed the mathematical model of cement displacement based on phase field method. In this model, the interfacial tension is taken as the coupling variable, the Navier-Stokes equation is used to describe fluid flow, and the Cahn-Hilliard equation is used to track the change of the displacement interface. In this way, the problem that numerical simulation is unlikely to converge due to irregular hole is settled down. In addition, the evolution processes of flow field and displacement interface in the process of cementing were simulated by means of numerical method, and the influential mechanisms and laws of hole collapse or shrinkage on displacement efficiency were revealed. It is indicated from the simulation results that the disturbance of hole collapse or shrinkage can result in swirls. Speaking of hole enlargement section, the displaced fluid in the hole enlargement zone can be hardly “swirled out” when the swirling strength is lower, so that retention or dead displacement corner is generated. And when the hole enlargement rate is over 15%, the influence of hole collapse on the retention of displaced fluid gets greater and greater. In the shrinkage section, swirls can generate the phenomenon of slurry mixing in the downstream. And when the hole shrinkage rate is over 10%, the influence of hole shrinkage on slurry mixing gets greater and greater. In conclusion, by virtue of the phase field method, the problem that the numerical simulation of cement displacement is unlikely to converge due to irregular hole is solved, which is conducive to reveal the influential mechanisms of hole collapse or shrinkage on cement displacement.