Numerical calculation of pressure gradient of helical flow of power-law fluid in eccentric annulus

The pressure gradient of helical flow of drilling fluid that can be regarded as power-law fluid in eccentric annulus is studied in this paper to rationally design hydraulic parameters of drilling. The governing equations of helical flow of power-law fluid in eccentric annulus are transformed by the undetermined coefficients method, the pressure gradient formula for this flow is obtained. Taking CMC aqueous solution which can be regarded as a power-law fluid for an example, the pressure gradient of this flow is numerically calculated by using the finite difference method and the influences of the rotation velocity of inner cylinder, the eccentricity and the flow rate on the pressure gradient are analyzed. The results show the eccentricity and the flow rate are main influential factors. Comparing the pressure gradient calculated by the numerical solution of axial velocity given in this paper with that calculated by the analysis solution, they coincide well, which shows that the formula and the numerical calculation method of pressure gradient of helical flow for power-law fluid in eccentric annuls are correct and can be applied further.