This paper presents a theoretical model of two-phase flow of mixtures of water and solids in vertical pipelines. Simplified equations for approximate calculations have been also derived. Using the equations of two-phase flow presented in this paper, cases for different systems of vertical hydraulic transport can be calculated. Model was validated by comparison with the experimental results from industrial hydraulic systems for transport of coal from underground mines. Also presented are some examples of analyses of head loss and slip velocity changes in function on concentration of solids in mixture, diameter of the pipe and diameter of solids.


Transport in pipelines belong to for years intensively developed methods of bulk transportation. Progress in this field forced more and more intense scientific research (Sobota, Plewa 2000). A large number of factors, which influence phenomena that occur by multiphase flows, resulted in construction of simplified equations, being valid only for specific type of flow or composition of a mixture. However, industrial practice has proven that such an approach does not ensure sufficient accuracy of calculations by design of industrial hydrotransport systems. Moreover, simplified equations do not allow to carry on deeply penetrating theoretical analyses, which could lead to creation of new solutions or methods, i.e. in the range of minimization of energy losses or pipe wear. Obviously such a problems exist in pipeline systems, which have lift height of few hundreds meters or even few kilometers. Such a systems operate in coal mines for haulage of coal in deep sea mining projects. Specificity of extraction of minerals from sea floor requires use of such a methods, which are highly reliable and easy to control. The most reliable are such a deep sea mining systems, which do not contain moving parts (valves, pistons, impellers) in their transportation devices.

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