General method of calculating annular laminar pressure drop of drilling fluids with different rheological models

Traditional annular laminar flow analysis method applied in drilling engineering has poor accuracy and does not apply to complicated rheological models. A general method of calculating annular laminar pressure drop of drilling fluids with different rheological models was proposed, compared with traditional method, and verified using experiment data in published articles. Based on annular slot flow model, the pipe flow equation was popularized in annular and an annular flow equation was established, and the relationship between annular flow and shear stress at pipe wall was established by combining annular flow equation and fluid's rheological equation. If annular flow is given, shear stress at pipe wall can be got, and then the annular pressure drop is also available. Compared with traditional methods, the general method is adapt to any rheological model of annular laminar flow, and has good universality, simple modeling process and high accuracy. The calculation results based on experiment data in published articles show: no matter the flow rate is high or low, the results of the general method match the measured results well, which makes up the error of traditional method.