# Preface

- Page ID
- 29488

In dredging, trenching, (deep sea) mining, drilling, tunnel boring and many other applications, sand, clay or rock has to be excavated. The productions (and thus the dimensions) of the excavating equipment range from mm^{3}/sec - cm^{3}/sec to m^{3}/sec. After the soil has been excavated it is usually transported hydraulically as a slurry over a short (TSHD’s) or a long distance (CSD’s). Estimating the pressure losses and determining whether or not a bed will occur in the pipeline is of great importance. Fundamental processes of sedimentation, initiation of motion and erosion of the soil particles determine the transport process and the flow regimes. In all cases we have to deal with soil and high density soil water mixtures and its fundamental behavior.

The book covers horizontal transport of settling slurries (Newtonian slurries). Non-settling (non-Newtonian) slurries are not covered.

Although some basic knowledge about the subject is required and expected, dimensionless numbers, the terminal settling velocity (including hindered settling), the initiation of motion of particles, erosion and the flow of a liquid through pipelines (Darcy Weisbach and the Moody diagram) are summarized. In the theory derived, the Zanke (1977) equation for the settling velocity is used, the Richardson & Zaki (1954) approach for hindered settling is applied and the Swamee Jain (1976) equation for the Darcy-Weisbach friction factor is used, Moody (1944). The models developed are calibrated using these basic equations and experiments.

An overview is given of experiments and theories found in literature. The results of experiments are considered to be the physical reality. Semi empirical theories based on these experiments are considered to be an attempt to describe the physical reality in a mathematical way. These semi empirical theories in general match the experiments on which they are based, but are also limited to the range of the different parameters as used for these experiments. Some theories have a more fundamental character and may be more generic as long as the starting points on which they are based apply. Observing the results of many experiments gives the reader the possibility to form his/her own impression of the processes involved in slurry transport.

Flow regimes are identified and theoretical models are developed for each main flow regime based on constant volumetric spatial concentration. The 5 main flow regimes are the fixed or stationary bed regime, the sliding bed regime, the heterogeneous regime or the sliding flow regime and the homogeneous regime. It is the opinion of the authors that the basic model should be derived for a situation where the amount of solids in the pipeline is known, the constant volumetric spatial concentration situation.

A new model for the Limit Deposit Velocity is derived, consisting of 5 particle size regions and a lower limit. Based on the Limit Deposit Velocity a (semi) fundamental relation is derived for the slip velocity. This slip velocity is required to determine constant volumetric transport concentration relations based on the constant volumetric spatial concentration relations. These relations also enable us to determine the bed height as a function of the line speed.

The concentration distribution in the pipe is based on the advection diffusion equation with a diffusivity related to the LDV.

Finally a method is given to determine relations for non-uniform sands based on the superposition principle.

The last chapter is a manual on how to reproduce the Delft Head Loss & Limit Deposit Velocity model.

The DHLLDV Framework is based on numerous experimental data from literature, considered to be the reality.

This book is supported by the website www.dhlldv.com containing many additional graphs and tables with experimental data. The website also has spreadsheets and software implementing the model.

The name Delft in the title of the DHLLDV Framework is chosen because most of the modelling is carried out at the Delft University of Technology and in my home in Delft.

Another book by the author is: The Delft Sand, Clay & Rock Cutting Model Available on https://textbooks.open.tudelft.nl/index.php/textbooks

**Modeling is an attempt to approach nature without having the presumption to be nature.**