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8.1: Introduction

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  • The DHLLDV Framework is based on the philosophy that pressure/hydraulic gradients and Limit Deposit Velocities can only be determined based on the spatial volumetric concentration for uniform PSD’s, in contrary to most models from literature. For heterogeneous and homogeneous transport the spatial and transport volumetric concentrations are almost identical, but for the fixed and the sliding bed regimes the difference is substantial. To use the model the following steps have to be carried out:

    1. The hydraulic gradient curves and the relative excess hydraulic gradient curves for the fixed or stationary bed regime (FB), for the sliding bed regime (SB), for the heterogeneous flow regime (He) and for the homogeneous flow regime (Ho) have to be determined.

    2. The resulting curve, based on the algorithm according to Figure 8.1-1 has to be constructed.

    3. The Limit Deposit Velocity has to be determined. There are 3 possible Limit Deposit Velocities, the transition heterogeneous-homogeneous (HH) for very small particles, the transition fixed bed-heterogeneous (FH) for medium sized particles and the transition sliding bed-heterogeneous (SH) for coarse particles. Which one to apply depends on the algorithm according to Figure 8.11-1.

    4. The transport or delivered concentration curves are determined based on a holdup or slip factor function, where the Limit Deposit Velocity plays a very important role.

    5. The bed height and bed fraction are determined based on the Limit Deposit Velocity and the slip factor.

    Figure 8.1-1: The algorithm to determine the constant Cvs and Cvt curve for uniform sands and gravels.

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    In the following chapters the different steps are explained. All equation have two numbers, the first number refers to the location where the equation is derived or first used, and the second number is the equation number in this chapter.

    The book is accompanied with an Excel Workbook showing the DHLLDV Framework, and also many other models. This Excel Workbook can be downloaded from ResearchGate or send an email to