There are a lot of models available in literature, mostly based on experiments in small diameter pipes. But how do these models behave for the current pipe diameter? The following two graphs show the relation of the hydraulic gradient i_m versus the line speed v_ls and the relation of the relative excess hydraulic gradient E_rhg versus the hydraulic liquid i_l gradient of 22 models. The models include the homogeneous equivalent liquid model (ELM) and the detailed DHLLDV models. For small pipe diameters (D_p=0.15 m) the models are relatively close, but for large pipe diameters they deviate a lot.

The Hydraulic Gradient versus the Line Speed for 22 Models

The Relative Excess Hydraulic Gradient versus the Hydraulic Gradient for 22 Models

It is also interesting to compare the models based on flow regimes. It is not usefull to compare models of different flow regimes, since the physics are completely different. The following two graphs show the relation of the hydraulic gradient i_m versus the line speed v_ls and the relation of the relative excess hydraulic gradient E_rhg versus the hydraulic liquid i_l gradient of a number of sliding bed models.

The Hydraulic Gradient versus the Line Speed for Fixed Bed & Sliding Bed Models

The Relative Excess Hydraulic Gradient versus the Hydraulic Gradient for Fixed Bed & Sliding Bed Models

The Hydraulic Gradient versus the Line Speed for Heterogeneous & Homogeneous Models

The Relative Excess Hydraulic Gradient versus the Hydraulic Gradient for Heterogeneous & Homogeneous Models