Many slurry correlation models have been developed. It is important to understand the assumptions and limitations of each, and select the most appropriate model applicable to the situation at hand.
A qualitative study.
A qualitative study.
Durand and Condolios (1952)
Empirical model. The experiments were carried out mostly on sand and gravel with a d50 between 0.18 mm and 22.5 mm in pipes with a DP from 40 mm to 580 mm, and volumetric concentrations Cvt from 2% to 22%. Durand and Condolios did not perform experiments at low flows. Their experiments were conducted in "medium" pipe diameters. The main issues are: 1) the wrong use of the particle Froude number vs the drag coefficient, 2) the wrong use of the relative submerged density in the particle Froude number, 3) the wrong power of the particle Froude number and 4) the use of the wrong graph for the limit deposit velocity coefficient in the Durant and Condolios equations.
Worster and Denny (1955)
Empirical model. Worster, R. C., & Denny, D. F. (1955) Hydraulic transport of solid materials in pipelines. Institution of Mechanical Engineers (London), 563-586.
Empirical model. Newitt carried out experiments in a DN25 pipe using sand particle sizes of 0.0965 mm, 0.203 mm, 0.762 mm and a gravel with size 4.5 mm, 3.2-6.4 m. The Newitt model distinguishes a heterogeneous regime and a sliding bed regime. The friction factor for a sliding bed is likely to be different than the figure Newitt presented for his 1" pipe. Be careful of the limitations of an empirical model based on experience within a small pipe!
Newitt, D. M (1955) Hydraulic conveying of solids in horizontal pipes. Transactions of the Institution of Chemical Engineers Vol 33, 93-110.
Empirical model. Gibert analysed data from Durand and Condolios' 1952 tests and summarised the results. Gibert maintained that for the limit deposit velocity coefficient FL the correction factor of about 1.1 should be used.
Furhboter, A. (1961) Uber die Forderung von Sand-Wasser-Gemischen in Rohrleitungen. Mitteilungen des Franzius-Instituts, H. 19.
Jufin and Lopatin (1966)
Jufin, A. P. and Lopatin, N. A. (1966). O projekte TUiN na gidrotransport zernistych materialov po stalnym truboprovodam. Gidrotechniceskoe Strojitelstvo, 9., 49-52.
Zandi and Govatos (1967)
Empirical model. Zandi and Govatos criticised Durand and Condolios' model. Zandi, I., and Govatos, G. (1967). Heterogeneous flow of solids in pipelines. Proc. ACSE, J. Hydraul. Div., 93(HY3)., 145-159.
Graf and Acaroglu (1968)
Babcock criticised Durand and Condolios' model. Babcock, H. A. (1970). The sliding bed flow regime. Hydrotransport 1. Bedford, England: BHRA.
Zandi, I. (1971). Hydraulic transport of bulky materials, Advances in Solid-Liquid Flow in Pipes and its Applications. (pp. 1-38). Oxford: Pergamon Pres.
Charles and Stevens (1972)
Wasp (1970, 1977)
Wasp is the mainstay. At given flow conditions the model determines the degree of heterogeneity of the solid's particles. It then determines the friction losses contributions of the vehicle (supporting pseudo-homogeneous slurry) which suspends the heterogeneous solids. The total friction loss is calculated by summing losses due each. Main downfall is that the model assumes Newtonain behaviour of the vehicle. Multi-layer model. Waste, E. G., Kenny, J. O., Aude, T.C., Seiter, R.H., and Jacques, R. B. (1970). Deposition velocities transition velocities and spatial distibution of solids in slurry pipelines. Hydro Transport 1, paper H42. (pp 53-76). Coventry: BHRA Fluid Engineering.
Turian and Yuan (1977)
Empirical model. Turian, R.M. and Yuan, T.F. (1977) Flow of slurries in pipelines. AIChE Journal, 23, 232-243.
This correlation is generally not thought to be conservative. It is based on smaller particles than Oroskar and Turian. It is an empirical model.
This model is subject to a 180 μm lower limit on particle size. It applies to slurries which have a narrow PSD. Note that there are several errors in the mathematical equations.
2-layer model that allows for a stationary or sliding bed layer with a liquid layer above it.
Oroskar and Turian (1980)
The Oroskar and Turian correlation is an industry-derived model focussing on particles larger than 100 μm. It applies to slurries which have a narrow PSD.
This model is subject to a 90 μm lower limit on particle size. It applies to slurries which have a narrow PSD. This model assumes Stokes or intermediate-range hindered settling. There is no consideration of settling under turbulent flow.
Doron, P., and Barnea, D. (1987). Slurry flow in horizontal pipes, experimental and modelling. International Journal of Multiphase Flow, Vol. 13, No. 4., 535-547.
Refer to Shah SN, and DL Lord. 1991. "Critical Velocity Correlations for Slurry Transport with Non-Newtonian Fluids." AIChE Journal 37:6, 863-870.
This model is subject to a 230 μm lower limit on particle size. It applies to slurries which have a narrow PSD. This model has no pipe size limit. Refer to Bae KS, H Lee CG Park and CS Lee. 1991. "Empirical Correlation for the Minimum Transport Velocity of Multidisperse Slurries in Horizontal Pipes." Korean Journal of Chemical Engineering 8(2):120-124.
Gillies and Shook (1991)
This model is subject to a 150 μm lower limit on particle size. It applies to slurries which have a narrow PSD. This model has been developed for distributions containing fine-particle (<74 μm) carrier fluids, but the definition of "fine" is arbitrary. Gillies and Shook introduced the concept of homogeneous and heterogeneous fractions. Refer to Gillies RG, and CA Shook. 1991. "A Deposition Velocity Correlation for Water Slurries." Canadian Journal of CHemical Engineering 69(5):1225-1228.
There is an updated that has been issued (by Gillies and Shook) in 2000.
Shook and Roco (1991)
Multi-level model. The model assumes that the suspended solids are distributed uniformly across the entire pipe, and that the lower layer also contains the solids that contribute Coulombic friction.
Wilson et al (1992)
Wilson criticised Durand and Condolios' model. Wilson, K. C., Addie, G. R., and Clift, R. (1992) Slurry Transport using Centrifugal Pumps. New York: Elsevier Applied Sciences.
Doron and Barnea (1993)
Doron, P., and Barnea, D. (1993). A three layer model for solid liquid flow in horizontal pipes. International Journal of Multiphase Flow, Vol 19, No. 6., 1029-1043.
Multi-level model. Matousek, V. (1997). Flow Mechanism of Sand/Water Mixtures in Pipelines, PhD Thesis. Delft, Netherlands: Delft University of Technology.
Wilson, K. C., Addie, G. R., Clift, R., Sellgren, A. (1997) Slurry Transport using Centrifugal Pumps. Glasgow, UK: Chapman & Hall
Kaushal and Tomita (2002)
This model uses solids loading to calculate apparent viscosity. It applies to slurries which have a narrow PSD. The basis for the Jewett viscosity correlation is a correlation for Newtonian, non-interacting, spherical, dilute, uniform particles. It is based on the Thomas correlation. The Jewett viscosity correlation does not consider how suspending phase and particle chemistry impact bulk rheology.
Multi-level model. This model is good for slurries with coarse particles. This model is used in AFT Fathom's slurry module.
Rojas and Saez (2010)
Gillies and Shook (2010)
2-layer model, settling slurries. Extends an existing model for applicability to solids concentration >35 Cv. Randall G. Gillies, Clifton A Shook. "Modelling high concentration settling slurry flows", The Canadian Journal of Chemical Engineering volume (2000) 78(4).
Poloski PNNL (2010)
This model corresponds well with experimental data for slurries with Archimedes numbers <80. Adam P. Poloski, Arthur W. Etchells. "A pipeline transport correlation for slurries with small but dense particles". The Canadian Journal of Chemical Engineering (2010) 88(2): 182-189.
Rojas and Saez (2012)
2-layer model. Top layer of a flowing suspension, and a bottom bed of stationary or moving particles. Wide range of particle density and particle size distribution. Mario R. Rojas and A. Eduardo Saez, Two-Layer Model for Horizontal Pipe Flow of Newtonian and Non-Newtonian Settling Dense Slurries, Ind. Eng. Chem. Res. (2012) 51(20).
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