The Limit Deposit Velocity model, a new approach

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In slurry transport of settling slurries in Newtonian fluids, it is often stated that one should apply a line speed above a critical velocity, because blow this critical velocity there is the danger of plugging the line. There are many definitions and names for this critical velocity. It is referred to as the velocity where a bed starts sliding or the velocity above which there is no stationary bed or sliding bed. Others use the velocity where the hydraulic gradient is at a minimum, because of the minimum energy consumption. Most models from literature are one term one equation models, based on the idea that the critical velocity can be explained that way.

Here the following definition is used: The critical velocity is the line speed below which there may be either a stationary bed or a sliding bed, depending on the particle diameter and the pipe diameter, but above which no bed (stationary or sliding) exists, the Limit Deposit Velocity (LDV). The way of determining the LDV depends on the particle size, where 5 regions are distinguished.

These regions for sand and gravel are roughly; very small particles up to 0.014–0.040 mm (d < δv), small particles from δv–0.2 mm, medium particles in a transition region from 0.2–2.00 mm, large particles > 2 mm and very large particles > 0.015·Dp. The lower limit of the LDV is the transition between a sliding bed and heterogeneous transport. The new model is partly based on physics and correlates well with experiments from literature.

Azamathulla, H.M., Ahmad, Z., 2013. Estimation of critical velocity for slurry transport through pipeline using adaptive neuro-fuzzy interference system and gene-expression programming. Journal of Pipeline Systems Engineering and Practice, 131–137.

Berg, C.H., 1998. Pipelines as transportation systems. In: Proceedings of the European Mining Course. IHC-MTI, Kinderdijk, the Netherlands.

Charles, M.E., 1970. Transport of solids by pipeline. Hydrotransport 1. BHRA, Cranfield.

Davies, J.T., 1987. Calculation of critical velocities to maintain solids in suspension in horizontal pipes. Chemical Engineering Science, 42, 7, 1667–1670.

Durand, R., 1953. Basic Relationships of the Transportation of Solids in Pipes - Experimental Research. In: Proceedings of the International Association of Hydraulic Research. Minneapolis.

Durand, R., Condolios, E., 1952. Etude experimentale du refoulement des materieaux en conduites en particulier des produits de dragage et des schlamms. [Experimental study of the discharge pipes materieaux especially products of dredging and slurries]. Deuxiemes Journees de l'Hydraulique, 27–55. (In French.)

Fuhrboter, A., 1961. Über die Förderung von Sand-Wasser-Gemischen in Rohrleitungen. [On the advances of sand - water mixtures in pipelines]. Mitteilungen des Franzius-Instituts, H. 19.(In German.)

Garcia, M.H., 2008. Sedimentation Engineering (Vol. 110). ASCE Manuals & Reports on Engineering Practise No. 110.

Gibert, R., 1960. Transport hydraulique et refoulement des mixtures en conduites. [Hydraulic transport and discharge pipes of mixtures]. Annales des Ponts et Chausees, 130, 3, 307–374, 130, 4, 437–494. (In French.)

Gillies, R.G., 1993. Pipeline flow of coarse particles, PhD Thesis. University of Saskatchewan, Saskatoon.

Gogus, M., Kokpinar, M.A., 1993. Determination of critical flow velocity in slurry transporting pipeline systems. In: Proceeding of the 12th International Conference on Slurry Handling and Pipeline Transport. British Hydraulic Research Group, Bedfordshire, UK, pp. 743–757.

Graf, W.H., Robinson, M., Yucel, O., 1970. The critical deposit velocity for solid-liquid mixtures. Hydrotransport 1. BHRA, Cranfield, UK, pp. H5-77–H5-88.

Hepy, F.M., Ahmad, Z., Kansal, M.L., 2008. Critical velocity for slurry transport through pipeline. Dam Engineering, 19, 3, 169–184.

Jufin, A.P., Lopatin, N.A., 1966. O projekte TUiN na gidrotransport zernistych materialov po stalnym truboprovodam. [TUiN project on hydrotransport of grain materials in steel tubes]. Gidrotechniceskoe Strojitelstvo, 9, 49–52. (In Russian.)

Kokpinar, M.A., Gogus, M., 2001. Critical velocity in slurry transport in horizontal pipelines. Journal of Hydraulic Engineering, 127, 9, 763–771.

Lahiri, S.K., 2009. Study on slurry flow modelling in pipeline. National Institute of Technology, Durgapur, India.

Miedema, S.A., 2012a. Constructing the Shields Curve: Part A Fundamentals of the Sliding, Rolling and Lifting Mechanisms for the Entrainment of Particles. Journal of Dredging Engineering, 12., 1–49.

Miedema, S.A., 2012b. Constructing the Shields Curve: Part B Sensitivity Analysis, Exposure & Protrusion Levels, Settling Velocity, Shear Stress & Friction Miedema, S.A., 2014 Velocity, Erosion Flux and Laminar Main Flow. Journal of Dredging Engineering, 12, 50–92.

Miedema, S.A., 2014. An analytical approach to explain the Fuhrboter equation. Maritime Engineering, 167, 2, 1–14.

Miedema, S.A., 2015a. A head loss model for homogeneous slurry transport. Journal of Hydrology and Hydromechanics, 1, 1–12.

Miedema, S.A., 2015b. Head loss model for slurry transport in the heterogeneous regime. Journal of Ocean Engineering, 12., 50–92.

Miedema, S.A., 2015c. The Slip Ratio or Holdup Function in Slurry Transport. Dredging Summit and Expo 2015. WEDA, Houston, Texas, USA, p. 12.

Miedema, S.A., Matousek, V., 2014. An explicit formulation of bed friction factor for sheet flow. In: Proc. 15th International Freight Pipeline Society Symposium, IFPS, Prague, Czech Republic, p. 17.

Miedema, S.A., Ramsdell, R.C., 2013. A head loss model for slurry transport based on energy considerations. In: Proc. XX World Dredging Conference, WODA, Brussels, Belgium, p. 14.

Miedema, S.A., Ramsdell, R.C., 2014a. An analysis of the hydrostatic approach of wilson for the friction of a sliding bed. WEDA/TAMU. WEDA, Toronto, Canada, p. 21.

Miedema, S.A., Ramsdell, R.C., 2014b. The Delft Head Loss & Limit Deposit Velocity Model. In: Hydrotransport, BHR Group, Denver, USA, p. 15.

Newitt, D.M., Richardson, M.C., Abbott, M., Turtle, R.B., 1955. Hydraulic conveying of solids in horizontal pipes. Transactions of the Institution of Chemical Engineers, 33, 93–110.

Oroskar, A.R., Turian, R.M., 1980. The hold up in pipeline flow of slurries. AIChE, 26, 550–558.

Parzonka, W., Kenchington, J.M., Charles, M.E., 1981. Hydrotransport of solids in horizontal pipes: Effects of solids concentration and particle size on the deposit velocity. Canadian Journal of Chemical Engineering, 59, 291–296.

Poloski, A.P., Etchells, A.W., Chun, J., Adkins, H.E., Casella, A.M., Minette, M.J., Yokuda, S., 2010. A pipeline transport correlation for slurries with small but dense particles. Canadian Journal of Chemical Engineering, 88, 182–189.

Ramsdell, R.C., Miedema, S.A., 2013. An overview of flow regimes describing slurry transport. In: WODCON XX, WODA, Brussels, Belgium, p. 15.

Sanders, R.S., Sun, R., Gillies, R.G., McKibben, M., Litzenberger, C., Shook, C.A., 2004. Deposition velocities for particles of intermediate size in turbulent flows. In: Hydrotransport 16, BHR Group, Santiago, Chile, pp. 429– 442.

Schiller, R.E., Herbich, J.B., 1991. Sediment Transport in Pipes. Handbook of Dredging. McGraw-Hill, New York.

Shook, C.A., Gillies, R.G., Sanders, R.S., 2002. Pipeline Hydrotransport with Application in the Oil Sand Industry. SRC Publication 11508-1E02, Saskatchewan Research Council, Saskatoon, Canada.

Souza Pinto, T.C., Moraes Junior, D., Slatter, P.T., Leal Filho, L.S., 2014. Modelling the critical velocity for heterogeneous flow of mineral slurries. International Journal of Multiphase Flow, 65, 31–37.

Thomas, A.D., 1979. Predicting the deposit velocity for horizontal turbulent pipe flow of slurries. International Journal of Multiphase Flow, 5, 113–129.

Thomas, A.D., 2014. Slurries of most interest to the mining industry flow homogeneously and the deposit velocity is the key parameter. In: HydroTransport 19, BHR Group, Denver, Colorado, USA, pp. 239–252.

Thomas, D.G., 1962. Transport characteristics of suspensions: Part VI. Minimum velocity for large particle size suspensions in round horizontal pipes. A.I.Ch.E. Journal, 8, 3, 373–378.

Thomas, D.G., 1965. Transport characteristics of suspensions: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. Journal of Colloidal Sciences, 20, 267–277.

Turian, R.M., Hsu, F. L., Ma, T.W., 1987. Estimation of the critical velocity in pipeline flow of slurries. Powder Technology, 51, 35–47.

Wasp, E.J., Slatter, P.T., 2004. Deposition velocities for small particles in large pipes. In: Proc. 12th International Conference on Transport & Sedimentation of Solid Particles, Prague, Czech Republic, pp. 20–24.

Wasp, E.J., Kenny, J.P., Aude, T.C., Seiter, R.H., Jacques, R.B., 1970. Deposition velocities transition velocities and spatial distribution of solids in slurry pipelines. In: Hydro Transport 1, paper H42, BHRA Fluid Engineering, Coventry, pp. 53–76.

Wasp, E.J., Kenny, J.P., Gandhi, R.L., 1977. Solid liquid flow slurry pipeline transportation. Transactions Technical Publications.

Wilson, K.C., 1979. Deposition limit nomograms for particles of various densities in pipeline flow. In: Hydrotransport 6, BHRA, Canterbury, UK, p. 12.

Wilson, K.C., Judge, D.G., 1976. New techniques for the scale-up of pilot plant results to coal slurry pipelines. In: Proceedings International Symposium on Freight Pipelines, University of Pensylvania, Washington DC, USA, pp. 1–29.

Wilson, K.C., Judge, D.G., 1977. Application of analytical model to stationary deposit limit in sand water slurries. In: Dredging Technology, BHRA Fluid Engineering, College Station, Texas, USA, pp. J1 1–12.

Wilson, K.C., Addie, G.R., Clift, R., 1992. Slurry Transport using Centrifugal Pumps. Elsevier Applied Sciences, New York.

Wilson, W.E., 1942. Mechanics of flow with non colloidal inert solids. Transactions ASCE, 107, 1576–1594.

Yagi, T., Okude, T., Miyazaki, S., Koreishi, A., 1972. An Analysis of the Hydraulic Transport of Solids in Horizontal Pipes. Nagase, Yokosuka, Japan. Report of the Port & Harbour Research Institute, Vol. 11, No. 3.

Zandi, I., Govatos, G., 1967. Heterogeneous flow of solids in pipelines. Proc. ACSE, J. Hydraul. Div., 93(HY3), 145–159.

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