oe4625 Dredge Pumps and Slurry Transport Vaclav Matousek October 13, 2004

Transcription

1 oe4625 Vaclav Matousek October 13, Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport

2 2. SOIL-WATER MIXTURE AND ITS PHASES SOIL PROPERTIES LIQUID PROPERTIES MIXTURE PROPERTIES October 13,

3 SOIL PROPERTIES SIZE OF PARTICLE & SOIL DENSITY OF PARTICLE & SOIL October 13,

4 PARTICLE SIZE Classification and identification of soil Particle size distribution (PSD) Characteristic sizes October 13,

5 Classification & Identification Main type of soil Identification Particle size size in [mm] Boulders Granular - > 200 Non-cohesive Cobbles Coarse Gravel Medium 20 6 Fine 6 2 Coarse Sand Medium Fine Coarse Silt Cohesive Medium Fine Clay - < October 13,

6 Particle Size Distribution (PSD) sieve opening [mm] weight fraction [g] percentage of total weight, pi [%] cumulative % mass characteristic particle size, di [mm] October 13,

7 Particle Size Distribution (PSD) KLEI SILT ZAND G RIND Totaal dmf (%) zand a zand b zand c (µm) (µm) (µm) g e wic htsp e rc e nta g e o p d e z e e f d ro o g FIJN G RO F FIJN G RO F FIJN a b c ,001 0,002 0,005 0,01 0,02 0,05 0,1 0,2 0, ko rre ld ia m e te r in m m October 13,

8 Characteristic Sizes If a sample of soil is composed of particles of different sizes, the soil particles are represented by a characteristic size (diameter): Mass-median diameter : d 50 The 85%-diameter : d 85 Mean diameter : Decisive particle diameter: d d s mf i i i i i i = = i d p p i [mm] [mm] d p 1.00 [mm] d + d d + d = g e wic htsp e rc e nta g e o p d e ze e f d ro o g KLEI SILT ZAND GRIND FIJN GROF FIJN GROF FIJN 0,001 0,002 0,005 0,01 0,02 0,05 0,1 0,2 0, korreldia meter in mm a b c October 13,

9 Density of Submerged Soil (granular body) The density of a granular body is given by the density of solid particles and the density of liquid in the pores. Volume pores in gran. body The porosity of granular body n= [-] Total volume granular body he typical value of the sand-bed porosity is 0.4, 40 per cent of the total volume. The density of granular body ρsi = ρs(1-n) + ρf n [kg/m 3 ] The typical value of the soil density is 2000 kg/m 3 for a submerged sand bed. October 13,

10 Density and Porosity of Soil Density of solids [kg/m3] Density of soil in situ (wet) [kg/m3] Porosity n [%] silt loose clay packed clay sand with clay sand coarse sand with gravel clay boulders October 13,

11 LIQUID PROPERTIES DENSITY OF LIQUID VISCOSITY OF LIQUID October 13,

12 Density and Viscosity of Liquid The density and viscosty of liquid vary with temperature. Sensitivity to pressure can be neglected, the liquids are considered incompressible. The density of liquid Mass liquid ρ f = [kg/m 3 ] Volume liquid The typical value of the liquid density is 1000 kg/m 3 for tap water. The sea water is heavier, round 1025 kg/m 3. The dynamic viscosity of liquid (Newton s law of viscosity) The kinematic viscosity of liquid Shear stress τ µ f = = Velocity gradient dux dy Dynamic viscosity µ f ν f = = Density of liquid ρ f [Pa.s]. [m 2 /s]. October 13,

13 Density and Viscosity of Liquid Temperature T [ o C] Density, [kg/m 3 ] Dynamic viscosity, [Pa.s] Kinematic viscosity, [m 2 /s] Vapour pressure, [Pa] x x x x x x x x x x x x x x x x x x x x x 10 3 October 13,

14 MIXTURE PROPERTIES DENSITY OF MIXTURE SOLIDS CONCENTRATION IN MIXTURE October 13,

15 Solids Concentration in Mixture Mixture is composed of two phases: solids and liquid. The density of mixture is determined from the density of solid particles and the density of liquid. The proportion of the phases is given by the parameter called CONCENTRATION OF SOLIDS. Volume solids in mixture The concentration of solids in mixture C= [-]. v Total volume of mixture Remark: If the mixture is the granular bed, there is a direct relationship between the solids concentration and porosity in the bed: C v,bed = 1 n. Thus if the sand-bed porosity is 0.4, then the bed concentration is 0.6, 60 per cent of the bed volume is occupied by solid particles. October 13,

16 Density of Mixture MASS(mixture) = MASS(liquid) + MASS(solids) considering MASS = DENSITY (ρ) x VOLUME (U) and U m = U f + U s ρ m U m = ρ f U f + ρ s U s = ρ f (U m -U s ) + ρ s U s dividing by U m and considering C v = U s /U m gives finally ρ = ρ (1-C ) + ρ C [kg/m 3 ]. m f v s v Rearranging gives the relationship between the mixture density and the concentration of solids in mixture C = v ρ ρ m s ρ ρ f f [-]. October 13,

17 Delivered Concentration Solids concentration in flowing mixture: There are two possible Control Volumes: 1. CV is the length section of a pipe: C vi = U s,p /U m,p is the spatial concentration of solids; 2. CV is the volume moving with the flowing mixture: C vd = Q s /Q m is the delivered concentration of solids. October 13,

18 Delivered Concentration In pipe: 1. C vi = U s,p /U m,p Q m Q s 2. C vd = Q s /Q m = = U s / t. t/ U m = U s /U m in the tank U m C vi > = C vd U s October 13,

19 Delivered Concentration In pipe: 1. C vi = U s,p /U m,p 2. C vd = Q s /Q m Q s = 0 Q m C vi > 0 C vd = 0 U s = 0 U m October 13,

20 Delivered Concentration Practical Values Density of Delivered C vdsi Delivered C vd in situ mixture solid grains [-] [kg/m3] [-] CSD without submerged pump CSD with submerged pump Bucket wheel dredge with submerged pump Plain suction dredge Modern THSD during hopper loading (suction process) Modern THSD during hopper unloading (pumping to shore) October 13,

21 Slip Between Solids and Liquid Phases: mixture = liquid + solids In pipe: Q m = Q f + Q s i.e. V m.a = V f.a f + V s.a s Spatial concentration: C vi = U s,p /U m,p = A s.l/(a.l) = A s /A Delivered concentration: C vd = Q s /Q m = V s.a s /(V m.a) = (V s /V m ). C vi The slip ratio (= transport factor): V s /V m = C vd /C vi October 13,

22 Slip Ratio Practical Values At low C vd At high C vd Silt and finer solids Fine to medium sand Medium to coarse sand Coarse sand Fine gravel Boulders October 13,

23 CASE STUDY Consider that sand particles occupy 27 per cent of the total volume of a dredging pipeline. The rest is occupied by carrying water. The sand-water mixture is discharged from the dredging pipeline at a deposit site. The porosity of the sand in the deposit site n = 0.4. Determine the density ρ m of sand-water mixture in the pipeline and the weight concentration C w of solids in the mixture. Further, determine the in situ density ρ si and the spatial volumetric concentration of in situ sand, C vsi, in the deposit site and in the pipeline. October 13,

24 CASE STUDY Inputs: The spatial volumetric concentration of solids in mixture flow: C v = 0.27 The density of sand particles: ρ s = 2650 kg/m 3 The density of carrying water: ρ f = 1000 kg/m 3 Porosity of sand in a granular body: n = 0.4. October 13,

25 CASE STUDY Solution: a. Density of mixture (ρ m ) & weight concentration of solids in mixture (C w ) Eq. 2.9 determines the density of mixture ρ m = ρ f (1-C v ) + ρ s C v = 1000(1-0.27)+2650x0.27 = kg/m 3. Eq determines the weight concentration C w ρ s = Cv = ρm = 0.495, i.e % October 13,

26 CASE STUDY Solution: b. In-situ density (ρ si ) & in-situ volumetric concentration of soil (C vsi ) in a granular body (sand bed) According to Eq. 2.3 the porosity and thus n = ρs ρsi ρ ρ s f ρ si = ρ s (ρ f - ρ s ).n = x 0.4 = 1990 kg/m 3. In the sand bed the density of the sand-water mixture is equal to ρ si and thus C vsi =1 (see Eq. 2.11). October 13,

27 CASE STUDY Solution: c. The in-situ volumetric concentration in the pipeline Eq determines the volumetric concentration of in-situ material in the pipeline as C 1 n v C vsi = = 0.27 = 0.45, i.e. 45 %. October 13,