Delft University of Technology
A comparison of graded PSD methods in slurry transport
Miedema, Sape
Publication date 2017
Document Version Final published version Citation (APA)
Miedema, S. (2017). A comparison of graded PSD methods in slurry transport. Poster session presented at 20th International Conference on Hydrotransport, Melbourne, Australia.
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A comparison of graded PSD methods in slurry transport.
Dr.ir. Sape A. MiedemaProblem definition:
Many models exist for single particle solids, but how to deal with graded solids? Solution:
Divide the graded solids into n fractions, determine the hydraulic gradient curves for each fraction and add up these curves weighed.
Requirements:
• The resulting hydraulic gradient curve should match experimental data.
• The PSD should be based on the spatial concentration.
• The method should give continues results.
• The method should converge to the single particle model for narrowly graded PSD’s.
4 models considered:
• The DHLLDV Framework.
• The original Wilson model for heterogeneous flow.
• The 4 Component Model (4CM) of Wilson & Sellgren.
• The Durand & Condolios method for heterogeneous flow.
Conclusions:
• The DHLLDV Framework method follows the requirements.
• The Wilson model also follows the requirements in the heterogeneous flow regime.
• The 4 Component Model (4CM) does not follow the requirements.
• The Durand & Condolios model does not follow the requirements.
Figure 1: The PSD’s used.
Figure 2: The DHLLDV Framework method.
Figure 3: A comparison of the 4 methods.
• The DHLLDV Framework, the original Wilson model and the 4CM model of Wilson & Sellgren give about the same hydraulic gradients under operational conditions. 0 10 20 30 40 50 60 70 80 90 100
1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00
% P a s s in g Particle Diameter (m)
Cumulative Grain Size Distribution
PSD Original Spatial PSD Remaining DHLLDV Framework PSD 4 CM Heterogeneous Fraction PSD Delivered © S.A.M. 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0 1 2 3 4 5 6 7 8 9 10 H y d ra u li c g ra d ie n t im , il (m w a te r/ m )
Line speed vls(m/sec)
Hydraulic gradient im, ilvs. Line speed vls, Graded
Liquid il curve Equivalent Liquid Model Homogeneous Sliding Bed Cvs=c d05=0.033 mm d15=0.100 mm d25=0.180 mm d35=0.282 mm d50=0.500 mm d65=0.888 mm d75=1.386 mm d85=2.500 mm d95=7.682 mm Limit Deposit Velocity Graded © S.A.M. Dp=0.1524 m, Rsd=1.585, Cvt=0.300, μsf=0.416 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0 1 2 3 4 5 6 7 8 H y d ra u li c g ra d ie n t im , il (m w a te r/ m )
Line speed vls(m/sec)
Hydraulic gradient im, ilvs. Line speed vls
Liquid il curve Limit Deposit Velocity 4 Component Model Wilson Heterogeneous Durand & Condolios Graded DHLLDV Graded Sand Cvs=c. DHLLDV Graded Sand Cvt=c. © S.A.M. Dp=0.1524 m, d=0.500 mm, Rsd=1.585, Cv=0.300, μsf=0.416
