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In this present work, cement slurry flowing in well annuli with narrow or varied radial sizes is investigated, whose purpose is to precisely calculate the equivalent circulating density (ECD) during well cementing in the petroleum industry. The theoretical Metzner-Reed (MR) method and the direct numerical simulation (DNS) are applied to calculate the cementing ECD for different types of cement slurries by considering both the Bingham and Power-Law rheological models. The cementing ECD calculated by the theoretical MR method is verified to be in accordance with the DNS result. Moreover, for the narrow annulus, the cementing ECD is demonstrated to be sensitive to the rheological model. In addition, based on the obtained DNS results, the accuracies of the cementing ECD calculated by three commercial software, including DRILL BENCH (DB), LANDMARK (LM), and PVI, are compared, to determine their corresponding adaptability for different rheological models. According to the detailed comparisons, LM shows the highest accuracy in calculating the cementing ECD for the Power-Law fluid, while PVI is optimal for the Bingham fluid. However, sharp fluctuations of the calculation errors are observed when DB is applied. [ABSTRACT FROM AUTHOR]