THEORY FOR HOPPER SEDIMENTATION.

Transcription

1 THEORY FOR HOPPER SEDIMENTATION. Dr.ir. S.A. Miedema 1 Prof.ir. W.J. Vlablom ABSTRACT. The edimentation proce in the hopper of a Trailing Suction Hopper Dredge (TSHD) i very complex. However it i debatable whether for etimation purpoe it i neceary to model the procee involved in detail. For etimation purpoe a black box approach may uffice. Baed on the turbulent diffuion theory of Camp (1936, 1946) and Dobbin (1944) for edimentation tank, a method ha been developed decribing the edimentation and thu the overflow loe in hopper. The Camp theory conider particle of one diameter, but here the grain ditribution i conidered, which i the bai for calculating the overflow loe. In the time domain, a homogeneou flow above the and bed i aumed. Uing Camp a a firt criterion, it i poible to determine which percentage of particle of a pecified diameter will ettle and which particle will have too mall a ettling velocity to ettle. A econd criterion i the cour velocity. If the velocity above the bed i greater than the cour velocity of a particle of a pecified diameter, that particle will be re upended. Both criteria will reult in overflow loe. Given a pecified mixture flow into the hopper, once the overflow loe are known, the loading curve can be determined. Since non-linearitie are involved, the calculation are carried out in the time domain. The model i implemented in a computer program, which alo calculate the tratification of the grain ditribution in the hopper and the grain ditribution of the material leaving the hopper through the overflow a a function of time. Thi paper i a follow-up of the paper of Vlablom and Miedema (1995) at WODCON XIV. Some of the equation have been modified reulting in different loading curve. The implementation of cour ha changed and a dicuion about two-dimenional turbulent diffuion model ha been added. INTRODUCTION. The edimentation proce in TSHD' ha not been the ubject for many publication. Although reearch ha been carried out, there i not a good prediction model available. Model that exit are baed on ediment flow in river or on edimentation tank. Camp (1946) and Dobbin (1944) developed a theory for ideal ettling tank. In thee tank an entrance zone, a ettling zone and an overflow zone can be ditinguihed. Settled grain will be removed periodically, o the tank will not be filled until the overflow level i 1 Aociate Profeor, Chair of Dredging Technology, Delft Univerity of Technology Profeor, Chair of Dredging Technology, Delft Univerity of Technology

2 reached a with TSHD'. Another difference with TSHD' i that the entrance and the overflow zone are not ued for the ettling proce. In the hopper of a TSHD, although an entrance and an overflow zone exit, the hopper a a whole will be ued for the ettling proce. In the hopper of a TSHD the flow velocity above the ediment i much higher then it i in a ettling tank. With a few adaptation however the Camp and Dobbin theory can be applied to TSHD'. Thee adaptation are: - The hopper a a whole i ued for the edimentation proce. - The edimentation proce continue until the hopper i economically full. - The overflow level may change during the edimentation proce. - A grain ize ditribution will be ued. To undertand the adapted model, firt the ettling of grain will be conidered. With thi knowledge the ideal ettling bain will be dicued. Before implementing the Camp and Dobbin theory to a TSHD, the loading cycle of the TSHD will be explained. With ome cae tudie the ue of the model a applied to TSHD' will be dicued. THE SETTLING VELOCITY OF GRAINS. The ettling velocity of grain depend on the grain ize, hape and pecific denity. It alo depend on the denity and the vicoity of the fluid the grain are ettling in, it alo depend upon whether the ettling proce i laminar or turbulent. In general, the ettling velocity v can be determined with the following equation: ( q w) 4 g ρ ρ d ψ v = (1) 3 ρw Cd The Reynold number of the ettling proce determine whether the proce i laminar or turbulent. The Reynold number can be determined by: Re = v d ν () The drag coefficient C d depend upon the Reynold number according to: 4 Re < 1 Cd = (3) Re < Re < 000 Cd = (4) Re Re Re > 000 C d = 0. 4 (5) Stoke, Budryck and Rittinger ued thee drag coefficient to calculate ettling velocitie for laminar ettling (Stoke), a tranition zone (Budryck) and turbulent ettling (Rittinger) of and grain. Thi give the following equation for the ettling velocity:

3 Laminar flow, d<0.1 mm, according to Stoke. v = 44 q w d ρ ρ (6) Tranition zone, d>0.1 mm and d<1 mm, according to Budryck. 3 ( ( ρ ρ ) d ) q w 1 v = 8.95 (7) d Turbulent flow, d>1, according to Rittinger. v = q w d 87 ρ ρ (8) In thee equation the grain diameter i in mm and the ettling velocity in mm/ec. Since the equation were derived for and grain, the hape factor for and grain i ued for determining the contant in the equation. The hape factor can be introduced into the equation for the drag coefficient by dividing the drag coefficient by a hape factor ψ. For normal and thi hape factor ha a value of 0.7. The vicoity of the water i temperature dependent. If a temperature of 10 i ued a a reference, then the vicoity increae by 7% at 0 and it decreae by 30% at 0 centigrade. Since the vicoity influence the Reynold number, the ettling velocity for laminar ettling i alo influenced by the vicoity. For turbulent ettling the drag coefficient doe not depend on the Reynold number, o thi ettling proce i not influenced by the vicoity. Other reearcher ue lightly different contant in thee equation but, thee equation uffice to explain the baic of the ettling proce in hopper dredge. The above equation calculate the ettling velocitie for individual grain. The grain move downward and the ame volume of water ha to move upward. In a mixture, thi mean that, when many grain are ettling, an average upward velocity of the water exit. Thi reult in a decreae of the ettling velocity, which i often referred to a hindered ettling. However, at very low concentration the ettling velocity will increae becaue the grain ettle in each other hadow. Richardon and Zaki determined an equation to calculate the influence of hindered ettling for volume concentration Cv between 0 and 0.3. The coefficient in thi equation i dependent on the Reynold number. The general equation yield: vc β = ( 1 Cv) (9) v The following value for β hould be ued: 3

4 Re<0. β=4.65 Re>0. and Re<1.0 β=4.35 Re Re>1.0 and Re<00 β=4.45 Re -0.1 Re>00 β=.39 THE IDEAL SETTLEMENT BASIN. The ideal ettlement bain (Fig. 1 & ) conit of an entrance zone where the olid/fluid mixture enter the bain and where the grain ditribution i uniform over the croection of the bain, a ettlement zone where the grain ettle into a ediment zone and a zone where the cleared water leave the bain, the overflow zone. It i aumed that the grain are ditributed uniformly and are extracted from the flow when the ediment zone i reached. Each particle tay in the bain for a fixed time and move from the poition at the entrance zone, where it enter the bain toward the ediment zone, following a traight line. The lope of thi line depend on the ettling velocity v and the flow velocity above the ediment o. Figure 1 how a top view of the ideal ettlement bain. Figure how the ide view and Figure 3 the path of individual grain. All particle with a diameter d0 will ettle, if a particle with thi diameter entering the bain at the top, reache the end of the ediment zone. Particle with a larger diameter will all ettle, particle with a maller diameter will partially ettle. The ettling velocity of a grain with diameter d0 can be determined by: v o H = o = L With: Q W L (10) o = Q W H (11) The ettling velocity vo i often referred to a the hopper load parameter. A mall hopper load parameter mean that mall grain will ettle. From figure 3 the concluion can be drawn that grain with a ettling velocity greater then vo will all reach the ediment layer and thu have a ettling efficiency of 1. Grain with a ettling velocity maller then vo will only ettle in the edimentation zone, if they enter the bain below a pecified level. Thee grain have a ettling efficiency of v/vo. If the fraction of grain with a ettling velocity 4

5 5

6 greater then vo equal p o, then the ettling efficiency for a grain ditribution can be determined by integrating the grain ettling efficiency: r g v = (1) v o po r = ( 1 p ) r dp b o + g 0 (13) Thi i illutrated in figure 5, howing a grain ditribution curve, but intead of uing the grain diameter on the horizontal axi, the ettling velocity divided by the hopper load parameter i ued. The hatched area i equal to the total ettling efficiency r. Until now the flow velocity ditribution ha been conidered uniform. If thi ditribution i not uniform, a hown in figure 4, it can be hown that the ettling efficiency doe not change (Camp 1946, de Koning 1977). For the ideal ettlement bain laminar flow i aumed. Turbulent flow will reduce the ettling velocity of the grain and thu the total ettling efficiency. Whether turbulent flow occur, depend on the Reynold number of the flow in the bain. Uing the hydraulic diameter concept thi number i: Re = Q ν ( W + H) (14) For a given flow Q and vicoity ν the Reynold number depend on the width W and the height H of the bain. A large width and height give a low Reynold number. However thi doe not give an attractive hape for the bain from an economical point of view, which explain why the flow will be turbulent in exiting bain. Dobbin (1944) and Camp (1944, 1946) ue the two-dimenional turbulent diffuion equation to determine the reulting decreae of the ettling efficiency. c c εz c c z ( ) = εz + vc ( ) + + εx x z z z x (15) Auming a parabolic velocity ditribution intead of the logaritmic ditribution, neglecting diffuion in the x-direction and conidering the ettling velocity independent of the concentration reduce the equation to: ( k h z ) t c c c ( ) = εz + v x z z (16) 6

7 Becaue of the parabolic velocity ditribution, the turbulent diffuion coefficient εz i a contant. A further implification i obtained if the velocity i aumed contant throughout the depth, meaning that the contant of the parabola k approache zero. In thi cae the turbulent diffuion equation become: c c c c = = εz + v (17) t x z z Huiman (1995) in hi lecture note, derive the diffuion-diperion equation in a more general form, including longitudinal diperion. c ( c) c c + = εx + v c+ εz t x x x z z (18) Auming a teady and uniform flow, the longitudinal diperion coefficient i independent of x and the ettling velocity v independent of z. Thi reduce the equation 18 to: c c c c = ε + v + ε x z z z x x (19) By mean of computation Huiman (1995) how that the retarding effect of diperion may be ignored for the commonly applied width to depth ratio 3 to 5. Thi reduce equation 19 to equation 17 of Dobbin and Camp. Groot (1981) invetigated the influence of hindered ettling and the influence of different velocity ditribution uing the following equation: c c vc ( ) c c = vc ( ) + c + ε( xz, ) (0) x z c z z z The velocity ditribution, the diffuion coefficient ditribution and the ditribution of the initial concentration did not have a ignificant influence on the computed reult, but the reult were very enitive on the formulation of hindered ettling. Thi formulation of coure influence the ettling velocity in general. Equation 17 can be olved analytically uing eparation of variable. The boundary condition ued by Camp and Dobbin decribe the rate of vertical tranport acro the water urface and the ediment for x= and the concentration ditribution at the inlet, thee are: 7

8 ε c + v z c = 0 at the water urface ε c + v z c = 0 at the ediment for x=, for the no-cour ituation ( ) c= f z at the entrance for x=0 Thi method, reulting in figure 6, give the removal ration due to turbulence for a ingle grain. The removal ratio can be determined by ummation of a erie. Solving equation 17 give (v H/ ε z ) a the independent parameter on the horizontal axi and the removal ratio (v/v o =ettling efficiency) on the vertical axi. Uing a parabolic velocity ditribution thi can be ubtituted by: v H v 3 8 v = = 1 ε κ λ z o o with: κ = 0.4 and λ = 0.03 (1) rb=rg*rt Fig. 6: Total ettling efficiency for individual grain v/o Grain ettling efficiency v/vo=0.1 v/vo=0. v/vo=0.3 v/vo=0.4 v/vo=0.5 v/vo=0.6 v/vo=0.7 v/vo=0.8 v/vo=0.9 v/vo=1.0 v/vo=1.1 v/vo=1. v/vo=1.3 v/vo=1.4 v/vo=1.5 v/vo=1.6 v/vo=1.7 v/vo=1.8 v/vo=1.9 v/vo=.0 v/vo=.5 v/vo=3 v/vo=3.5 v/vo=4 v/vo=4.5 v/vo=5 It i however of interet how the removal ratio (ettling efficiency) of a grain can be plit up in a part determined by laminar flow in the bain according to equation (1) and a part 8

9 caued by turbulence. Vlablom and Miedema (1995) give relation for the effect of turbulence only (fig. 7), a derived by Miedema (1991): r r r rt r r TanH r Log v g g g = + r g () g g g o For value of v/vo greater then 1 the following equation hould be ued. r r r rt r r TanH r Log v g g g = + r g g g g o (3) Equation and 3 have been revied ince Vlablom and Miedema (1995) to match the reult of equation 17 more cloely. For other value of the vicou friction factor λ, the contant.5 hould be taken a: Log(0.03/λ) The reulting bain ettling efficiency i equal to the grain ettling efficiency time the turbulence ettling efficiency, according to figure 6. The total ettling efficiency for the bain can now be determined by: 1 rb= rg rt dp 0 (4) rt Fig. 7: Turbulence ettling efficiency for individual grain v/o Grain ettling efficiency v/vo=0.1 v/vo=0. v/vo=0.3 v/vo=0.4 v/vo=0.5 v/vo=0.6 v/vo=0.7 v/vo=0.8 v/vo=0.9 v/vo=1.0 v/vo=1.1 v/vo=1. v/vo=1.3 v/vo=1.4 v/vo=1.5 v/vo=1.6 v/vo=1.7 v/vo=1.8 v/vo=1.9 v/vo=.0 v/vo=.5 v/vo=3 v/vo=3.5 v/vo=4 v/vo=4.5 v/vo=5 9

10 phae 1 phae Fig. 8: The hopper dredge cycle. phae 3 phae 5 phae 6 phae 7 phae Load in ton phae Time in min Total load Effective (itu) load Tonne Dry Solid Overflow loe Maximum production When the height of the ediment increae and the hopper load parameter remain contant, the horizontal flow velocity above the ediment alo increae. Grain that have already ettled will be re upended and leave the bain through the overflow. Thi i called couring. The cour velocity for a grain with a diameter d i according to Camp (1946): = 8 (1 n ) µ ( ρ - ρ ) g d λ ρ q w w (5) Grain that are re upended due to cour, will not tay in the bain and thu have a ettling efficiency of zero. In thi equation λ i the vicou friction coefficient mobilized on the top urface of the ediment and ha a value in the range of , depending upon the Reynold number and the ratio between the hydraulic diameter and the grain ize (urface roughne). The value of λ hould be chooen equal to the value in equation 1. The poroity n ha a value in the range , while the friction coefficient µ depend on the internal friction of the ediment and ha a value in the range of for and grain. To prevent cour for a pecified grain diameter, the flow velocity ha to be maller then the cour velocity. The total ettling efficiency change due to cour, according to: 10

11 1 r = r r dp b g t p (6) If the ettling proce doe not occur in ome part of the bain, owing to a concentrated inflow of mixture, vortexe, etc. the effective hopper load parameter will increae and the ettling efficiency will decreae. The homogeneity of the flow depend on the tability of the flow. The tability i indicated by the Froude number of the bain. Thi Froude number i: ( ) Q W+ H Fr = 3 3 g W H (7) A higher Froude number indicate higher tability to the flow in the bain. Thi reult in a narrow bain with a mall height. With repect to turbulence the demand for a high Froude number conflict with the demand for a mall Reynold number, which i aociated with a wide deep bain. THE LOADING CYCLE OF A HOPPER DREDGE. The loading cycle i conidered to tart when the hopper i filled with oil and tart to ail to the dump area. Thi point in the loading cycle wa choen a the tarting point to how the optimal load in a graph. The loading cycle then conit of the following phae: Phae 1: The water above the overflow level flow away through the overflow. The overflow i lowered to the ediment level, o the water above the ediment can alo flow away. In thi way minimum draught i achieved. Sailing to the dump area i tarted. Phae : Continue ailing to the dump area. Phae 3: Dump the load in the dump area. Phae 4: Pump the remaining water out of the hopper and ail to the dredging area. Phae 5: Start dredging and fill the hopper with mixture to the overflow level, during thi phae 100% of the oil i aumed to ettle in the hopper. Phae 6: Continue loading with minimum overflow loe, during thi phae, according to equation 6, a percentage of the grain will ettle in the hopper. The percentage depend on the grain ize ditribution of the and. Phae 7: The maximum draught (CTS, Contant Tonnage Sytem) i reached. from thi point on the overflow i lowered. Equation 6 i till valid. Phae 8: The ediment in the hopper i riing due to edimentation, the flow velocity above the ediment increae, reulting in cour. Thi i the caue of rapidly increaing overflow loe. 11

12 5000 Fig. 9: The loading curve for an 0.1 mm d50 and phae 6 phae 7 phae 8 Load in ton phae Time in min Total load Effective (itu) load Tonne Dry Solid Overflow loe Maximum production Thee phae are hown in fig. 8. The way each phae occur in the cycle, depend on the type of hopper dredge, the working method and of coure, the type of oil to be dredged. The edimentation in the hopper occur during the phae 5, 6, 7 and 8. During phae 5 the hopper i filled with mixture until the overflow level i reached. During thi phae 100% of the oil i aumed to tay in the hopper and ettle. When the overflow level i reached, phae 6, depending on the grain ditribution, a pecified percentage of the oil will not ettle and will leave the hopper via the overflow. During thi phae couring doe not have much influence on the edimentation proce. When the maximum weight of the hopper content i reached, the overflow will be lowered continuouly in order to keep the weight of the hopper content contant at it maximum. When the ediment level rie, phae 8, the flow velocity above the ediment increae and couring will re upend ettled particle. The overflow loe increae with time. The tranition between phae 5 and 6 i very harp, a i the tranition between the phae 6 and 7 for the graph of the total load, but thi doe not exit in the graph of the effective load (fig. 8). However, the tranition between the phae 7 and 8 i not necearily very harp. When thi tranition occur depend on the grain ditribution of the oil dredged. With very fine and thi tranition will be near the tranition between phae 6 and 7, o phae 7 i very hort or may not occur at all. With very coare and and gravel couring i minimal, o phae 8 i hardly preent. In thi cae the ediment level may be higher then the overflow 1

13 level. With ilt the phae 7 and 8 will not occur, ince after reaching the overflow level the overflow loe will be 100% Fig. 10: The loading curve for an 0.3 mm d50 and phae 6 phae 7 phae 8 Load in ton phae Time in min Total load Effective (itu) load Tonne Dry Solid Overflow loe Maximum production So far the total load in the hopper ha been decribed. A contractor i, of coure, intereted in the "Tonne Dry Solid" (TDS) or itu cubic meter. The total load or gro load conit of the ediment with water in the pore and a layer of water above the ediment. The TDS conit of the weight of the oil grain only. The net weight in the hopper conit of the weight of the ediment, including the weight of the pore water. If the poroity of the ediment i conidered to be equal to the in-itu poroity, then the volume of the ediment in the hopper equal the removed itu-volume. Although, in practice, there will be a difference between the in-itu poroity and the ediment poroity, here they will be conidered equal. The net weight can be calculated according to: W = W - W h w V = V - V h w (8) (9) V ρ = W - V ρ and V = V - V (30) h w w w h 13

14 V ρ = W - (V - V ) ρ (31) h h w V ( ρ - ρ )= W - V ρ (3) w h h w V = (W - V ρ ) h h w ( ρ - ρ ) w W = V = (W - V ρ ) ρ ρ ( ρ - ρ ) h h w w (33) (34) TDS = W ρ (W - V ) ρ ρq h h ρw ρ w q = (35) ρ ρ ρ ( ρ - ρ ) q w q w The net weight (itu weight) according to equation 34 can be approximated by the total weight of the load in the hopper minu the weight of the ame volume of water and the reult multiplied by. For the TDS thi factor i about 1., according to equation 35. Thi i of coure only valid for a pecific denity of the ediment of ton per cubic meter Fig. 11 The loading curve for a 1.0 mm d50 and phae 6 phae 7 phae 8 Load in ton phae Time in min Total load Effective (itu) load Tonne Dry Solid Overflow loe Maximum production 14

15 With thee equation the hopper cycle for the net weight and the TDS can be derived, thi i hown in the figure 8 to 11. The hopper dredge i optimally loaded, when the effective load (weight) or the TDS divided by the total cycle time dw/dt reache it maximum. Thi i hown in figure 8 to 11 and i the reaon for the tarting point of the loading cycle in figure 8. THE CALCULATION MODEL. The previou paragraph explain the baic of the ettling velocity of grain, the ideal ettlement bain and the loading cycle of a hopper dredge. Thee baic theorie will now be applied to the edimentation proce in a hopper. Conider a rectangular hopper of width W, height H and length L. A mixture with a mixture denity ρm and with a pecified grain ditribution i being dredged. Depending on the operational condition uch a dredging depth, the pump ytem intalled and the grain ditribution and mixture denity, a mixture flow Q will enter the hopper. If the poroity n of the ediment i known, the flow of ediment can be determined according to: The ma flow of the mixture i: Q ρ Q ( ρ (1 - C ) + ρ C ) (36) m = w v q v The ma flow of the olid i now: ( ρ - ρ ) m w Q ρ = Q C ρ (37) q ( ρ - ρ ) v q q w From thi, the ma flow of ediment i: dw dt = Q C ( ρ + e ρ ) r b (38) v q w With: n e = (1 n) (39) Part of thi ma flow will ettle in the hopper and another part will leave the hopper through the overflow. The ratio between thee part depend on the phae of the loading proce. During phae 5 the hopper i loaded to the overflow level, o the ma flow into the hopper will tay in the hopper. Thi mean that the total ettling efficiency during thi phae equal 1. During phae 6 the loading continue until the maximum load in the 15

16 hopper i reached. If couring doe not occur, the ma flow that will ettle into the ediment can be calculated with equation 38, where the ettling efficiency hould be determined with equation Fig. 1: Grain ditribution of ediment () and overflow (o), for an 0.1 mm d50 and % Grain diameter in mm Time in minute after the tart of the hopper loading proce (o=overflow left, =ediment right). 0riginal 15 (o) 5 (o) 35 (o) 45 (o) 55 (o) 65 (o) 75 (o) 85 (o) 15 () 5 () 35 (o) 45 () 55 () 65 () 75 () 85 () During phae 7 the loading continue, but with a CTS, the overflow i lowered to enure that the total weight in the hopper remain contant. A cour doe not yet occur, the above equation i till valid. During phae 8 couring occur. If couring doe occur, the ma flow that will ettle into the ediment can be calculated alo with equation 38, but the ettling efficiency hould be determined with equation 6. Scouring i the caue of increaing overflow loe. Scour depend upon the velocity of the flow above the ediment. Since in a hopper the ediment i not removed, the ediment level rie during the loading of the hopper. Thi mean that the height of the mixture flow above the ediment decreae during the loading proce, reulting in an increaing flow velocity. The cour velocity can now be determined by: = Q B H w (40) 16

17 100 Fig. 13: Grain ditribution of ediment () and overflow (o), for an 0.3 mm d50 and % Grain diameter in mm Time in minute after the tart of the hopper loading proce (o=overflow left, =ediment right). 0riginal 15 (o) 0 (o) 5 (o) 30 (o) 35 (o) 40 (o) 15 () 0 () 5 (o) 30 () 35 () 40 () With: W H = H H = H w ρ B L (41) The height H i a contant for a Contant Volume Sytem (CVS), but thi height change for a CTS, becaue the overflow i lowered from the moment, the maximum weight in the hopper i reached. If a maximum weight Wm i conidered, the height of the layer of water above the ediment for a CTS can be determined by: H w = W ρ H B L m ρ w B L (4) The hopper loading curve can now be determined by firt calculating the time required to fill the hopper (phae 6), given a pecified mixture flow Q. From the mixture denity ρm the ma and given a pecified poroity, the volume of the ediment can be calculated. From thi point the calculation are carried out in mall time tep (phae 7 and 8). In one time tep, firt the height of the ediment and the height of the water layer above the ediment are determined. The height of the water layer can be determined with equation 17

18 41 for a CVS hopper and equation 4 for a CTS hopper. With equation 40 the cour velocity can now be determined. Uing equation 5 the fraction of the grain that will be ubject to cour can be determined. If thi fraction p i zero equation 4 ha to be ued to determine the ma flow that will tay in the hopper. If thi fraction i not equal to zero equation 6 ha to be ued. Equation 38 can now be ued to determine the ma flow. Thi ma flow multiplied by the time tep reult in an increment of the ediment ma that i added to the already exiting ma of the ediment. The total ediment ma i the tarting point for the next time tep. Thi i repeated until the overflow loe are 100%. When the whole loading curve i known, the optimum loading time can be determined. Thi i hown in Figure 8, where the dotted line jut hit the loading curve of the effective (itu) load. The point determined in thi way give the maximum ratio of effective load in the hopper and total cycle time. THE HOPPER OF A TRAILING SUCTION HOPPER DREDGE AS AN IDEAL SETTLEMENT BASIN. A tated before, the ideal ettlement bain i a rectangular bain with an entrance zone, a ettlement and edimentation zone and a overflow zone. The hopper geometry and configuration aboard of the TSHD can be quite different from the ideal ituation, o a method to chematie the hopper dimenion i required. 1. The height H of the hopper can be defined bet a the hopper volume divided by the hopper area L W. Thi mean that the bae of the ideal hopper, related to the maximum overflow height i at a higher level than the hip' bae. Thi aumption reult in a good approximation at the final phae (7 and 8) of the loading proce, while in phae 6 of the loading proce the hopper i filled with mixture and o the material tay in the hopper anyway.. Near the loading chute of the hopper or in cae where a deep loading ytem i ued, the turbulence of the flow reult in a good and ufficient ditribution of the concentration and particle ize ditribution over the cro-ection of the hopper, o the entrance zone can be kept mall. For example between the hopper bulkhead and the end of the loading chute. 3. In the ideal ettlement bain there are no vertical flow velocitie except thoe reulting from turbulence. However in reality vertical velocitie do occur near the overflow, therefore it i aumed that the overflow zone tart where the vertical velocitie exceed the horizontal velocitie. An etimate of where thi will occur can eaily be made with a flow net. 4. Although the preence of beam and cylinder rod for the hopper door doe increae the turbulence, it i the author opinion, that an additional allowance i not required, neither for the hopper load parameter, nor for the turbulence parameter. 18

19 100 Fig. 14: Grain ditribution of ediment () and overflow (o), for a 1.0 mm d50 and % Grain diameter in mm Time in minute after the tart of the hopper loading proce (o=overflow left, =ediment right). 0riginal 15 (o) 0 (o) 5 (o) 30 (o) 35 (o) 40 (o) 15 () 0 () 5 (o) 30 () 35 () 40 () CASE STUDIES. To give an impreion of the behaviour and the enitivity of the Camp and Dobbin model, three cae are calculated with the computer program TSHD (Miedema 1991). The rectangular hopper ued, ha a length L, of 46.3 m, a width W, of 9.8 m and a height H, of 6.0 m. At the entrance zone the mixture enter the hopper at a flow rate of approximately 4.6 m3/ec and a mixture denity of 1.5 ton/m3. The hopper ha a deign denity of 1.48 ton/m3. The hopper loading cycle conit of ailing to the dump area (phae 1 + ); 10 min., dumping (phae 3); 15 min., ailing back to the dredging area (phae 4); 10 min., filling the hopper up to the overflow level (phae 5); about 10 min. and continue loading until the optimum loading cycle production i reached (phae 6, 7 and 8). The hopper i of the CTS type (de Koning 1977), o the overflow will be lowered when the maximum weight i reached. The flow rate and mixture denity are choen relatively high to emphaie the overflow loe. The calculation are carried out with three and. A and with a d50 of 100 µm (and A), a and with a d50 of 300 µm (and B) and a and with a d50 of 1000 µm (and C). The grain ditribution are determined by integration of a Gau ditribution, where the d50 i equivalent to the mean value and (d50-d85) i equivalent to the variance of the Gau ditribution. The cumulative grain ditribution i determined at 100 grain 19

20 diameter. Thi way the total ettling efficiency, according to equation 5, can be determined accurate enough. For each grain diameter at each time tep, the fraction that ettle and thu the fraction that leave the hopper through the overflow can be determined. The reult of thi i, that the cumulative grain ditribution of the and at the top of the edimentation zone and of the and leaving through the overflow can be generated. For determining the cour velocity, a poroity n of 0.4, a friction coefficient µ of (30 ) and a vicou friction coefficient λ of 0.03 are ued. For and A the total loading cycle i hown in figure 8. Figure 9 i a cloe-up of the phae 5, 6, 7 and 8. Figure 1 how the original grain ditribution (the thick olid line in the middle), at the left of the original ditribution, the grain ditribution of the and leaving the hopper at time interval of 5 min. and at the right of the original ditribution, the grain ditribution at the top of the edimentation zone, alo at interval of 5 min. The dotted line in figure 8 and 9 how optimal loading. In the graph the loading i continued for everal minute after thi optimal point to emphaie the overflow loe. Figure 10 and 13 give the ame information for and B and Figure 11 and 14 give thi information for and C. Thee figure how that the optimal loading time decreae with an increaing grain diameter. The overflow loe alo decreae with an increaing grain diameter, which i evident. The tendencie a they are calculated match practice, however the model ha to be tuned to every pecific dredge to be a tool for etimating purpoe. CONCLUSIONS AND DISCUSSION. The Camp and Dobbin model can be ued to etimate loading time and overflow loe, however, the model hould be tuned with meaurement of the overflow rate in ton/ec a well a the particle ize ditribution in the overflow, a a function of time. The model can then alo be ued for the calculation of the decaying of the overflow plume in the dredging area. If the model i ued for the calculation of the production rate of the dredge a ditinction ha to be made whether the production i expreed in T.D.S./ec or in m3/ec. In the firt cae the theory can be applied directly, while in the econd cae it ha to be realied, that the overflow loe in T.D.S./ec do not alway reult in the ame overflow lo in m3/ec, ince fine particle may ituate in the void of the bigger one. The lo of fine doe not reduce the total volume, but increae the void ratio. Although the fine leave the hopper in thi cae, they do not reult in a reduction of the volume of the ettled grain. Thoe fraction which can be conidered to apply to the overflow loe and thoe which do not, can be etimated from the difference between the real particle ize ditribution and the optimal particle ize ditribution, giving a maximum dry denity, the o called Fuller ditribution. If the gradient of the ditribution curve for the fine i le teep then the correponding gradient of the Fuller ditribution, than that fraction of fine will not 0

21 effectively contribute to the overflow loe if they are expreed in m3/ec. In uch a cae, in-itu, the fine were ituated in the void of the courer grain. If the gradient i 100 Fig. 15: Fuller' method Cumulative grain ditribution in % Sqrt(d/dmax) Fuller PSD however teeper, the fine alo form the grain matrix and the volume of ettled grain will decreae if the fine leave the hopper through the overflow. Figure 15 give an example of the Fuller ditribution compared with a real grain ditribution. In the model a number of aumption are made. Except from numerical value for the parameter involved, the Camp and Dobbin approach i ued for the influence of turbulence, while eperately the influence of cour i ued intead of uing it a a boundary condition. During phae 8 of the loading proce cour dominate the overflow loe. Thi of coure depend on the way cour i modelled. In the cae tudie equation 5 according to Camp (1946) i ued. Whether thi i correct will be one of the ubject of further reearch. Until now it i very difficult to get correct data from the field to verify thi theory. It i not only neceary to have loading curve, but alo grain ditribution of the ediment and in the overflow, which are hard to obtain. LITERATURE. 1

22 Camp, T.R. 1936, "Study of rational deign of ettling tank". Sen. Work Journal, Sept. 1936, page 74. Dobbin, W.E. 1944, "Effect Of Turbulence On Sedimentation". ASCE Tran , page 69. Camp, T.R. 1946, "Sedimentation and the deign of ettling tank". ASCE Tran. 1946, page 895. Camp, T.R. 1953, "Studie of edimentation deign". Sen. Ind. Wate, jan Huiman, L., "Theory of ettling tank". Delft Univerity of Technology Groot, J.M. 1981, "Rapport Beunbezinking. Bokali (From lecture note of v/d Schrieck 1995). Koning, J. de 1977, "Contant Tonnage Loading Sytem of Trailing Suction Hopper Dredge'". Proc. Modern Dredging, The Hague, The Netherland Miedema, S.A. 1981, "The mixture flow and ettlement of particle in Trailing Suction Hopper Dredge". Report Sc0/81/103 (in Dutch), Delft Univerity of Technology, Miedema, S.A. 1991, "T.S.H.D.". Computer program for the calculation of hopper loading cycle, Delft, Huiman, L. 1995, "Sedimentation and Flotation". Lecture Note, Delft Univerity Of Technology Vlablom, W.J. & Miedema, S.A. 1995, "A theory for determining edimentation and overflow loe in hopper". Proc. WODCON XIV, Amterdam NOMENCLATURE. Cd Drag coefficient - Cv Volumetric concentration - d Grain diameter m d Grain diameter (cour) m e Void ratio - g Gravitational contant (9.81) m/ec H Height of bain m H Height of ediment layer in bain m Hw Height of water layer in bain m L Length of bain m n Poroity - po Fraction of grain that ettle partially (excluding turbulence) - p Fraction of grain that do no ettle due to cour - pt Fraction of grain that ettle partially (including turbulence) - Q Mixture flow m3/ec rb Settling efficiency for bain - rg Settling efficiency individual grain - rt Turbulence ettling efficiency for individual grain -

23 o Flow velocity in bain m/ec Scour velocity m/ec v Settling velocity m/ec vc Settling velocity with hindered ettling m/ec vo Hopper load parameter m/ec Vh Volume of ediment + water in hopper ton V Volume of ediment in hopper ton Vw Volume of water in hopper ton W Width of bain m Wh Weight of ediment + water in hopper ton W Weight of ediment in hopper ton Ww Weight of water in hopper ton α Factor (cour) - β Power for hindered ettling - λ Friction coefficient - ρ m Denity of a and/water mixture ton/m3 ρ q Denity of quart ton/m3 ρ Denity of ediment ton/m3 ρ w Denity of water ton/m3 ψ Shape factor - ν Kinematic vicoity m/ec 3