Water Research 39 (2005) 1858–1868
Energy demand in sludge dewatering
C.P. Chu
a, D.J. Lee
a,, C.Y. Chang
ba
Department of Chemical Engineering, National Taiwan University, 1, Sec. 4 Roosevelt Road, Taipei, Taiwan, 10617, ROC
bGraduate Institute of Environmental Engineering, National Taiwan University, Taipei, Taiwan, 10617, ROC
Received 26 April 2004; received in revised form 12 December 2004; accepted 9 February 2005 Available online 18 April 2005
Abstract
This work investigates the energy required to dewater a suspension, i.e., activated sludge dewatered by centrifugation or consolidation.Total energy input to the suspension from the dewatering device, bond strength between adjacent water and solid surface, and intra-cake friction loss were evaluated for original and flocculated sludges.In centrifugal dewatering, most energy input during the initial stage was consumed by overcoming process irreversibility other than intra-cake friction, and, thereby, had a low energy efficiency.To increase centrifuge speed or to flocculate the sludge at optimal flocculant dosage would yield a high-energy input.In the consolidation test, most energy input at the initial stage was consumed in breaking down the bond strength until the moisture content reduced to less than the critical content.During subsequent dewatering stages, friction loss became the dominant source of energy loss.Dewatering sludge with high-energy efficiency is beneficial to optimally operate a dewatering process.
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Keywords: Energy; Efficiency; Bond strength; Friction loss; Centrifugation; Consolidation; Flocculation
1. Introduction
Energy consumption rate is an essential parameter determining the economy of dewatering a suspension by applying a solid–liquid separation (SLS) device.Profes-sionals acquired knowledge by experience regarding energy cost for specific SLS processes.The minimum energy required to achieve a dewatering operation is both of academic and practical interest since the extent to which a given process deviates from an ideal dewatering operation can be estimated.To reduce the process irreversibility provides ways of maximizing energy efficiency (Bejan, 1996).Restated, if the ratio of real energy input to minimum energy requirement defined energy efficiency, then the process dewatering
performance could be evaluated based on energy economy aspect.
Water with high water-to-solid bond strength can be referred to as sludge ‘‘bound water’’ (Vesilind, 1994). Various methods have been proposed for measuring bound water content (Heukelekian and Weisberg, 1956;
Lee et al., 1975;Haschemeyer et al., 1977;Lewicki et al., 1978; Karr and Keinath, 1978; Katsiris and Kouzeli-Katsiri, 1987; Herwijn et al., 1992; Robinson and Knocke, 1992; Lee and Hsu, 1995). Kopp and Dichtl (2000, 2001a, b) proposed the correlation between the moisture distribution in sludge and the efficiency of sludge dewatering in full-scale plant.Chen et al.(1997, 1999)proposed a continuous scheme that considers the water–solid bond strength as a physically relevant classification index to assess the status of water in sludge.Driving ‘‘freed’’ water out of the suspension requires sufficient energy to overcome irreversible internal processes, such as cake and filter media fluid
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friction.Modified Darcy’s law is typically used to describe this friction force (Lee and Wang, 2000).The sum of the bond strength and associated friction loss yielded the theoretically minimum amount of work needed to dewater a suspension, t.
Removing water from a suspension requires that (1) the bond strength between the adjacent water and the solid surface are broken down, without physically moving the water from its original position near the solid surface; and (2) that this water is moved from its original position in suspension to outside the system through the sludge cake and the filter medium.The energy needed to separate the adjacent water from the solid surface is denoted by EB, and the energy required
to force this water through the filter cake and filter medium is EF.Therefore, the minimum energy
require-ment to dewater a sludge is ðEBþEFÞ.If the energy
consumed by the dewatering device ðEVÞis higher than
this minimum energy requirement, and the difference is ðEVðEBþEFÞÞ, presented the irreversibility yielded by
other process non-ideality.This work estimated the minimum energy needed to dewater a suspension, and used an activated sludge as the test example.Bond strength of water ðEBÞ was estimated by utilizing the
method proposed byChen et al.(1997).Then, pressure and volume work done on the suspension ðEVÞ and
friction loss during the consolidated dewatering or centrifugal dewatering ðEFÞ were theoretically derived
and evaluated based on experimental data.The removal
process of moisture in suspension was schematically shown in Fig.1.In this figure, o is the solid volume coordinate per unit area of filter media, including cake, sediment, and supernatant, and where os is the total
solid volume above unit filter medium.
2. Energy demand in dewatering
2.1. Energy input
A mechanical dewatering device removes water from a suspension by supplying energy at a power level P. Consider that only some of the energy input is adopted during dewatering, characterized by an average effi-ciency of Zave, then the input energy can be expressed as
EV¼Zave
Z t 0
P dt, (1)
where EVis total energy input received by sludge, and t
is the dewatering time.
The mechanical work received by the sludge (solids and water that remain in the dewatering device) from the external environment is attributable to the change in volume of the sludge under shear owing to the removal of filtrate (Herwijn et al., 1992):
dEV¼ ðpSYSþdpSYSÞðV þ dV Þ pSYSV ,
¼pSYSdV þ V dpSYS, ð2Þ
Fig.1. The schematics of the moisture removal process.EV: p V work done by the surroundings, EB: energy needed to release the
where pSYSis the pressure exerted by the surroundings
to the sludge.Therefore, based on the solid volume unit area of the filter, pressure–volume work can be expressed as qEV qo ¼HV¼pSYS qV qoþV qpSYS qo ,
¼pSYSðo; tÞq VS½1 þ eðo; tÞ
qo þVS½1 þ eðo; tÞ
qpSYSðo; tÞ
qo , ð3Þ
where VS is the total solid volume, and e is the void
ratio.Then the total mechanical work received by sludge over time ½0; t is EV¼VS Z oS 0 pSYS qe qo þ ð1 þ eÞ qpSYS qo do.(4)
The lost work during a dewatering test, ðEV ðEFþEBÞÞ, is a result of the irreversible processes
other than the intra-cake friction, and the friction between cake and device’s wall (Zhao et al., 2003a, b), filter medium loss, or expansion work by water at the drainage port.The ratio ðEFþEBÞ=EVð¼ZÞ is the
energy efficiency for dewatering the sludge based on the total work received by the sludge.The work done by the surroundings is EV=Zave (Eq.(1)) and the overall
energy efficiency by the surroundings to suspension dewatering is ðEFþEBÞ=RP dt ¼ ZZave.In the next
sections methods for evaluating EV, EB and EF are
addressed.
2.2. Bond strength EB
The bond strength between water and solid phase, HB, can be estimated by the TGA/DTA scheme
proposed by Chen et al.(1997).Its procedures are briefly summarized as follows: The TGA and DTA tests, which are conducted simultaneously, evaluate, respec-tively, the heat flow Q and the mass loss rate ðmÞ of a sample.Under thermal equilibrium conditions, specific enthalpy applied in water evaporation can be evaluated with ðDH ¼ Q=m; kJ=kgÞ.As DH ¼ DHfg, the standard
enthalpy change for the bulk water, the evaporated water shows the same energy level as bulk water. According toTsang and Vesilind (1990), this water is the non-bound, or free water, in the sample.If, conversely, DH4DHfg, the difference, DH DHfg, can
be attributed to the existence of the solid phase of the sample, defined as the bond strength of the water ðHB; kJ=kgÞ.Water exhibiting increased bond strength
requires high enthalpy for its separation from the solid surface.The total energy, then, required to break down the bond strength of a slurry to water content of W is
EB¼VSrS
Z W 1
ðHBÞdW ; (5)
where W is residual water in the remaining slurry (cake and suspension) per unit solid mass.By this definition the moisture content W approaches infinity for all diluted suspension, and is zero for completely dehy-drated cake.
2.3. Friction loss EF
Friction loss owing to fluid outflow from the slurry is denoted as EF.Drag force acting on the fluid passing
through solid volume do can be stated as
dFF¼ASYS
m KqL
do, (6)
where ASYSis the filter area, m is the filtrate viscosity, K
the local permeability of the cake, and qLis the internal flow rate.Therefore, the energy loss attributable to the friction loss can be estimated as
dEF do ¼HF¼ASYS Z oS 0 m KqL h i do (7)
or as an equivalent (Chu and Lee, 2002):
EF¼ASYS Z oS 0 Z oS 0 m KqL do do.(8)
As stated, TGA/DTA tests can evaluate HB, with the
reference state ðEB¼0Þ at W ! 1 (free water has no
bond strength with solid surfaces).To evaluate HVand
HF, the reference state was chosen as EV¼EF¼0 at
oS¼0 (no cake limit) corresponding to the initial water
content value of slurry.To evaluate EVand EFrequires
information on how the cake will deform (pSYSe
relation in Eq.(4)) and how the fluid will flow through (K o relation in Eq.(8)) the stressed slurry, respec-tively.The pSYSe relation and K o relation for
centrifugation and consolidation tests are separately discussed as the following demonstrative examples.
2.4. Centrifugation
During centrifugal dewatering, the centrifugal force ðpCentÞrepresents the system pressure ðpSYSÞ.Assuming that the cake thickness in the centrifuge is thin, av can
be used to represent the porosity distribution in the centrifugated cake.Considering the radii of various interfaces that developed in the centrifugated sludge, rgl,
rls, rsc, and rcm represent air-supernatant interface,
supernatant–suspension interface, suspension–cake in-terface, and cake–media inin-terface, respectively (Chu and Lee, 2002).Then
EV¼
ASYSO2
2 ½G1ðtÞ þ G2ðtÞ, (9) where G1ðtÞ and G2ðtÞ are functions of rotational radii
that change over time (Appendix A), and presents the surface area of the centrifuge to sludge dewatering.
Energy consumption increases with the rotational speed. The differentiation of EV with respect to W gives the
specific p V work, HV.
With the centrate flow rate ðqLðtÞÞ obtained and interface positions noted in the centrifugal test, EF can
be estimated as (Chu and Lee, 2002)
EF¼ASYSmrSaavð1 avÞqLðrcmrscÞ2, (10)
where aav is the average specific resistance of the
centrifugated cake.Based on this model, if only the interface positions, rgl; rls; rsc, and rcm, can be tracked
with the filtrate flow rate, then EV and EF can be
subsequently estimated.
2.5. Consolidation
During sludge consolidation, the solid pressure ðpSÞ describes the system pressure pSYS.During the
consolidation test, pressure drop in the cake was substantial and, hence, the detailed pSe relation (rheological behavior) for stressed cake is required.
Lee and Wang (2000) summarized numerous correla-tions for the pSe relations proposed in the literature. Since the parameters in the various proposed correla-tions are determined by data fitting, adopting different forms of correlations of pSe relation does not significantly impact the predictions of the cake con-solidation behavior.
By considering the cake as a visco-elastic object and adopting the analytical model proposed byShirato et al. (1974), the expression of EVcan be stated as
EV¼C1p2ExprC2ð1 þ e1ÞpExpr.(11)
The functions C1and C2are functions of dewatering
time (Appendix B), and e1 is the void ratio of the
suspension before dewatering.It is clear that the energy consumed by consolidation increases with consolidation pressure.
Furthermore, friction drag loss can be stated using the Darcy’s law as EF¼ASYS Z oS 0 Z oS 0 qpL qo do do, ¼ASYS Z oS 0 Z oS 0 qpS qo do do. Or equivalently, HF¼ dEF dos ¼pExprASYSC2 VS .(12)
All parameters in Eqs.(9–12) can be estimated by fitting dewatering data to consolidation dewatering. Experiments described in Section 3 demonstrate the use of these equations to estimate energy consumption during sludge dewatering.
3. Experimental
3.1. Sample
An activated sludge sample taken from the waste-water treatment plant of Neili Bread Plant, Presidential Enterprise Co., Taoyuan, Taiwan was tested within 2 h after sampling.The COD and SS data of the super-natant drawn from the sludge, measured via EPA Standard Methods, were 22.6 and 14.3 mg l1, respec-tively.The weight percentage of dried solid of sludge, determined by weighing and drying at 102 1C, was 0.83% w/w.
Cationic polyelectrolyte, polymer T-3052, was ob-tained from Kai-Guan Inc., Taiwan. The polymer T-3052 is a polyacrylamide with an average molecular weight of 107, and a charge density of 20%.The original activated sludge was employed in flocculation.Sample sludge was first put into the mixing vessel.The polymer solution was then gradually poured into the mixing vessel by stirring at 200 rpm for 5 mins followed by 50 rpm for another 20 mins.The zeta potential for the original sample was negative, and was neutralized at 60 mg l1 (Zeter-Meter System 3.0, Zeter-Meter Inc., USA).
3.2. TGA/DTA test
Details for the TGA/DTA tests that can be found in
Chen et al.(1997)are herein briefly summarized for the sake of completeness.The thermal analyzer (SETAR-AM, 77A-92) was employed to record thermographs with argon (Ar) utilized as the carrying gas, in which the TGA and DTA tests were performed simulta-neously.From the DTA peak, energy flow rate into the sample cell can be estimated after calibration. The weight and time data represent the rate change of sample weight.
The sample was first vacuum filtered to remove some free water.Next, for the sake of uniformity, the resulting filter cake was completely blended, from which the sludge sample was randomly taken.Under each condi-tion, three independent tests were performed and their averages reported.The sample employed was limited to approximately 10 mg to minimize possible effects of non-uniform temperature distribution and mass transfer resistance within the sample body. Shie et al.(2004)
utilized the same TGA test adopted herein and noted that the intrinsic chemical kinetics of sample pyrolysis could be realized with an initial sample mass of around 10 mg.The mass transfer limitation hence plays no significant role for the TGA test conducted herein.The temperature was raised from room temperature to a fixed temperature of 80 1C.With TGA and DTA data, the bond strength versus residual water content was calculated.
3.3. Dewatering test
The arm-suspension centrifuge proposed byChu and Lee (2001) was employed in the centrifugal tests.This centrifuge facilitates direct observations on the filtrate amounts and cake thickness under the centrifugal field, and, hence, provides rheological information of the centrifugated cake under stress.Rotational speed ranged between 400 and 1000 rpm, with an acceleration at the filter medium of 32–200 g.
A constant head piston press (Triton Electronics Ltd., type 147) was employed in the consolidation tests.The sludge was placed in a stainless steel cylinder, 7.62 cm in diameter and 20 cm high.A hydraulic pressure of 1400–3000 psi was exerted on the piston to force water out of the sludge sample.Time evolution of the filtrate weight was then automatically recorded with an electronic balance connected to a personal computer. Given these data and solid density, time evolution for cake porosity was subsequently obtained. Chang and Lee (1998) provided the details for the consolidation experiment.
4. Results and discussion
4.1. TGA/DTA test
Fig.2a shows the TGA/DTA results for the floccu-lated (40 g/kg) sludge sample.The sample weight (TGA), rate of change (DTG), thermocouple output voltage (DTA), and reference cell temperature ðTcellÞ
were demonstrated to be functions of time.The sample mass decreased as the cell temperature increased, signaling the loss of water in response to input thermal energy.A period of near-constant DTG existed, corresponding to the amount of free water in the sludge. The falling-rate period followed the near-constant DTG period.Water removed during the falling-rate period exhibited an increased resistance to evaporation.
Fig.2bshows HBversus residual water W curves for
the sludge samples.The residual water content ðW Þ was directly calculated from the TGA data.Also, the HB
increased when the residual water content decreased.At W 430 kg kg1DS, the bond strength was close to 1 kJ/ kg (Herwijn et al., 1992).When the water content was less than 0.5 kg kg1DS, the bond strength exceeded 1000 kJ/kg, and was significantly close to that for chemisorption/chemical reactions.
At a 25-mg l1 dose, the optimal dose of the sludge identified using filtration test (shown later), HB for
Wo4 kg kg1DS was reduced, indicating that the adjacent water was loosened and became easier to be removed by flocculation.An overdose at 40 mg l1 of polymer also reduced HB for W 42:6 kg kg1DS
compared to the original sludge.But the polymer did
not significantly lower the bond strength for Wo2 kg kg1DS.Restated, an overdose of polymer would facilitate the release of some of the ‘‘easily removed’’ water, but could not release the tightly bound fraction of water.This result might be partly attribu-table to the adsorption of water on the excess flocculant molecules (Chu and Lee, 1999).
The HB curves, as shown in Fig.2b, presented the
bond strength required to ‘‘release’’ water from solid surfaces in the tested sludge.Based on this curve, the energy required to release 1 kg of water from a sludge with a water content of 4 kg kg1DS to a ‘‘free-water’’ state was roughly 60 kJ for the original sludge and less than 4 kJ for the 25-mg l1-flocculated sludge.Further dewatering to remove 1 kg of water from the sludge with a water content of 2 kg kg1DS required 140 kJ for the
original and 20 kJ for the 25-mg l1-flocculated sludges. Further dewatering consumed more energy than the initial dewatering stage.
Time (sec) 0 2000 4000 6000 Tcell ( ° C) ; TG (%) ; DTA ( µ V) -100 -50 0 50 100 DTG (m g /min ) -2 0 2 Tcell DTG DTA TG I II III W, kg/kg 0 HB , kJ/kg 0 100 200 300 400 500 600 700 800 900 1000 Original sludge 25 ppm 40 ppm 1 2 3 4 5 (a) (b)
Fig.2. (a) The TGA/DTA test for wastewater sludge (40 g/kg DS) and (b) the bond energy versus residue water in wastewater sludge, original and flocculated.
4.2. Centrifugal dewatering
The centrifugal rate was low for the original sludge at 400-rpm centrifugation, as shown inFig.3a.Increasing the centrifugal acceleration or adding polyelectrolyte facilitated the dewatering rate.The dose of 25 mg l1 provided the best dewatering rate, while an overdose of 40 mg l1 reduced the dewatering rate (Fig.3b).The optimal dose for the present sludge was 25 mg l1in the centrifugal test, as mentioned in preceding sections.
Fig.4 shows the HVdata during centrifugation with
polyelectrolyte dose and centrifugal speed parameters. The work by the centrifuge on the sludge increased as centrifugal acceleration increased, and, thereby, water content decreased.Also, at the optimal dose of 25 mg l1, as identified in Fig.4b, the HV was lower
than under- or overdosed regime at high W , and was higher than the other two at low W (o60 kg kg1DS). External work by the centrifuge to remove 1 kg of water from the sludge was comparably low, ca.1 kJ/kg at 400 rpm and 5–9 kJ/kg at 1000 rpm.
The EFdata calculated accounted for less than 5% of
EV, indicating that most of the friction loss did not
occur in line with the intra-cake flow.These data were not shown here for the sake of brevity.
4.3. Consolidation dewatering
Fig.5illustrates the consolidation curves.The original sludge had a low consolidation rate.To remove 280 g of filtrate from the original sludge required 1000 s, while the dose of 5 mg l1 polyelectrolyte reduced the corre-sponding consolidation time to 120–160 s, depending on the consolidation pressure.A further increase in dosage to 25 mg l1 demonstrated the best dewatering result,
around 30 s to remove 280 g of filtrate at 3000 psi.An overdose of 40 mg l1 polyelectrolyte yielded a slightly reduced dewatering rate.The optimal dose identified in the consolidation test corresponded to that in the centrifugal test (25 mg l1).
Fig.6 shows the EV data under consolidation, with
the polyelectrolyte dose and the consolidation pressure applied as parameters.The external work performed by the piston increased with increased consolidation pressure and with decreased water content.Also, at the optimal dosage of 25 mg l1, as identified inFig.5b, the HVwas lower than the under- or overdosed regime
at W ¼ 1:7 9:0 kg kg1DS.This experimental result did not correspond to that in centrifugation test (Fig.4). At 25-mg l1 dosage and consolidation pressure of 2200 psi, external work performed by the consolidation tester was not significant until W ¼ 3:2 kg kg1DS.The 25-mg l1-flocculated sludge was, hence, easily dewa-tered to a residual water of 3.2 kg kg1using consolida-tion.The original sludge, on the other hand, required external work greater than 100 kJ to dewater the sludge at 2200 psi to a water content of 4.2 kg kg1DS.The current flocculation conditioning effectively enhanced the sludge dewaterability by reducing the bond strength between water and the solid phase.
The estimated HF data were generally lower than
10% of HVand were, thereby, not shown in the figures
for sake of simplicity.
5. Discussion
HVbHF as demonstrated in the current
centrifuga-tion and consolidacentrifuga-tion tests.The resistance of internal flow through filter cake did not dominate.
The HB curves were also plotted onFigs.4 and 6for
comparison.During the initial stage of centrifugal dewatering, water content was high, and corresponded to low HB.Restated, the adjacent water is easily
removed from the solid surface at this moisture content level.The HVprovided by the centrifuge was even lower.
Most energy input was therefore utilized to overcome
time (s) 10 100 1000 Filtrate volume (cm 3) 0 10 20 30 40 50 60 Ori AS; 400 rpm Ori AS; 700 rpm Ori AS; 1000 rpm 5 mg l-1; 400 rpm 5 mg l-1; 700 rpm 5 mg l-1; 1000 rpm (a) time (s) 10 100 1000 Filtrate volume (cm 3) 0 10 20 30 40 50 60 25 mg l-1; 400 rpm 25 mg l-1; 700 rpm 25 mg l-1; 1000 rpm 40 mg l-1; 400 rpm 40 mg l-1; 700 rpm 40 mg l-1; 1000 rpm (b)
Fig.3. Dewatering curves of centrifugated sludge: (a) original and 5-mg l1flocculated and (b) 25- and 40-mg l1flocculated.
process irreversibility other than intra-cake friction.The dewatering rate was, thereby, not correlated with the HB2W curve until the latter was reduced to less than
20–30 kg kg1DS.At high rotational speeds or at the
optimal dose of flocculant, HVwas high, indicating that
the process was highly irreversible.This experimental result was likely due to the deterioration of the well-developed network structure of optimally flocculated sludge cake under the centrifugal field.Releasing adjacent water from solid surfaces did not affect the dewatering rate under this scenario.With a low W regime, HB increased rapidly during dewatering.Since
the HVW curves exhibited a lower slope than the
HBW curve, dewatering ceased at HV¼HB
.More-over, although the dewatering rate was quickest with optimal dose or with the fastest rotational speed (Fig.3), the corresponding energy demand is maximized.Con-sequently, a compromise between process time and energy demand is needed.
The current consolidation tester can provide a much higher HV on sludge than the tested centrifuge.
Depending on the polyelectrolyte dose, the HB was
close to HV until a critical water content level was
reached, then HV4HB.For instance, the HV for
consolidating original sludge at 3000 psi was close to HB up to W ¼ 4 kg kg1DS, or at 1400 psi up to
W ¼ 7 kg kg1DS.Therefore, most energy consumed during consolidation test was utilized to release adjacent water from solid surfaces since the HBis high at low-W
regime.Other process irreversibility was relatively small.
time (s) 10 100 1000 Filtrate volume (cm 3) 0 100 200 300 400
Ori AS; 1400 psi Ori AS; 2200 psi Ori AS; 3000 psi 5 mg l-1; 1400 psi 5 mg l-1; 2200 psi 5 mg l-1; 3000 psi (a) time (s) 10 100 1000 Filtrate volume (cm 3) 0 100 200 300 400 25 mg l-1; 1400 psi 25 mg l-1; 2200 psi 25 mg l-1; 3000 psi 40 mg l-1; 1400 psi 40 mg l-1; 2200 psi 40 mg l-1; 3000 psi (b)
Fig.5. Dewatering curves of consolidated sludge: (a) original and 5-mg l1flocculated and (b) 25- and 40-mg l1flocculated.
W, kg/kg 0 20 40 60 80 100 HV , HB , kJ/kg 0 2 4 6 8 10 1,000 rpm 700 rpm 400 rpm 40 40 25, 40 0 0 0 25 25 mg l-1 0, 5 25 40 HB curves
When Wo4 kg kg1DS at 3000 psi or Wo7 kg kg1DS at 1400 psi, HVbecame higher than HB.The majority of
energy consumed was applied to overcome internal frictions and possible particle re-orientation in the cake. The HV had become so large that further dewatering
through mechanical means below W ¼ 3:4 kg kg1DS was practically impossible.Lee and Hsu (1995)regarded this water content as the bound water identified by adopting the consolidation test.The HV(or HB) versus
W curves for flocculated sludge resembled, in character, those for original sludge.Just, as HBwas reduced at an
optimal dosage (25 mg l1), the corresponding H
V
curves in Fig.7shifted leftward to the low-W regime. The HVW curves followed closely the HBW curve
at W 41:9 or 45.5 kg kg1DS under 3000 or 1400 psi, respectively.The critical amount of water reduced at the optimal dosage, indicating that the cake became dryer when the consolidation reached mechanical equilibrium. The ratio of ððEFþEBÞ=EVÞ estimated how far the
system deviated from an ‘‘ideal’’ dewatering system.Fig. 7 presents this deviation based on the data shown in
Figs.4 and 6.If this ratio approaches unity, the energy
0 20 40 60 80 100 HV , HB , kJ/kg 0 20 40 60 80 100 W, kJ/kg 0 0 20 40 60 80 100 (a) (b) (c) HB HB HB HV 1400 psi 3000 psi 2200 psi HV 1400 psi 3000 psi 2200 psi HV 1400 psi 3000 psi 2200 psi 2 4 6 8
Fig.6. The HVinput during consolidation and the HB(bold) curves of sludges: (a) original sludge, (b) 25-ppm sludge and (c) 40-ppm
consumption rate ðEVÞ is close to the minimum energy
demand ðEBþEFÞ, and hence the energy efficiency to
dewatering is high.Centrifugation tests confirmed an increasing ratio while W was reducing.Consolidation tests exhibited a decreasing ratio with low W values. Also, the curves shown in Fig.7 shifted left after flocculation, or increased consolidated pressure/centri-fugal acceleration.The energy efficiency for dewatering depended on dewatering methods, dewatering pressure, and the state of flocculation.Regardless of the applied dewatering processes, a plateau regime of efficiency of around 95% existed on the ratio versus W curves. Initially, the average solid content was low (large W ). The fast dewatering rate through the filter media and the deterioration of cake structure under stress consumed most of the input energy, resulting in a low-energy efficiency.Since during the final stage the cake was highly compressible and had been satisfactorily com-pressed markedly close to filter media (Lee et al., 2000), the water that had been removed experienced marked resistance through the skin layer, and again yielded low-energy efficiency.The low-energy economy could be max-imized to operate closely at the high-Z plateau regime.
6. Conclusions
This work examined the minimum amount of mechanical work required to dewater a suspension, and considered the total energy input received by the
suspension from the dewatering device ðEVÞ, the bond
strength between the adjacent water and solid surfaces ðEBÞ, and the intra-cake friction loss ðEFÞ.To remove
water, the bond strength was first broken, and then water was removed from the cake, thus providing an estimate of minimum work needed to dewater a sludge as EBþEF.An activated sludge was taken as the test
sample.The bond strength of water was estimated with the thermal method proposed byChen et al.(1997), with excess enthalpy employed to evaporate water to be as the bond strength.Friction loss was assessed using a modified Darcy’s law, which required information on suspension rheology and dewatering rate as model parameters.The forms of EV and EF were evaluated
by applying centrifugal dewatering and pressure con-solidation as the demonstration examples.
During the preliminary stage of centrifugal dewater-ing, most of the energy input was used to overcome the process irreversibility other than the intra-cake friction, such as cake structure deterioration, that lead to low-energy efficiency.Increasing the centrifugal speed or to flocculate at optimal dosage required high-energy input. Since the centrifuge could not provide sufficiently high levels of energy, dewatering ceased when the breakdown of bond strength became important in dewatering. During the consolidation test, most input energy was consumed in breaking down bond strength up to a critical residual water content.Further dehydration exceeding this critical water content required extremely high-energy input.To consolidate at higher pressure or
W, kg/kg-DS 1 10 (E B + EF )/ EV 0.0 0.2 0.4 0.6 0.8 1.0 25 mg l-1 25 mg l -1 Ori Ori Centrifugation Consolidation Plateau - regime 700 rpm 1,000 700 1,000 kpsi 3.0 2.2 3.0 2.2
to flocculate at optimal dosage yielded low critical water content levels.The ratio of ððEFþEBÞ=EVÞproved how
far the system deviated from an ‘‘ideal’’ dewatering system.This ratio increased with decreasing residual water content during centrifugation, and, conversely decreased at consolidation.A plateau regime of high-efficiency was noted in all tests in which the energy efficiency could be maximized.
Acknowledgment
This work was supported by the National Science Council, ROC.
Appendix A. Derivation of Eq. (9)
The centrifugal force acting on the sludge could be estimated as follows (Tiller and Hsyung, 1993):
pCent¼O2 Z rls rgl rLr dr þ Z rsc rls rSlurryr dr " þ Z rcm rsc ðrLr þ Drð1 ÞrÞ dr , ðA:1Þ
where Dr is the density difference between the solid and the liquid, is the local porosity of the wet cake, and rgl; rls; rsc, and rcm are the rotational radii of
air–-supernatant interface, air–-supernatant–suspension interface, the suspension–cake interface, and the cake–media interface, respectively.Changing the coordinate system of Eq.(A.1) into a material coordinate o, we can reach the following equation:
qEV qr ¼pCent qV qrþV qpCent qr , ¼ Z r 0 qpCent qr dr ASYS þASYSðrcmrglÞ qpCent qr . ðA:2Þ
The substitution of Eq.(A.1) into Eq.(A.2) yields
EV¼ ASYSO2 2 ½G1ðtÞ þ G2ðtÞ, (A.3) where G2¼ ðrcmrglÞ½rLðr2lsr2glÞ þrSlurryðr2scr2lsÞ þ ðrLþDrð1 avÞÞðr2cmr 2 scÞ, ðA:5Þ
where av is the average porosity in the centrifugated
cake, and all interfaces were functions of time.
Appendix B. Derivation of Eq. (11)
Shirato et al.(1974)analytically derived the distribu-tions of pressure and void ratios in a consolidated cake as follows: pSþpL¼pExpr, (B.1) pS¼pExpr 1 þ sin po 2oS ½D1expðh1tÞ þ D2expðh2tÞ , (B.2) e ¼ e1aE Z t 0 qpS qt dt aCZc Z t 0 ½pSðo; tÞ pS1exp½Zcðt tÞdt, ðB:3Þ
where pExpr is the consolidation pressure and e1 is the
initial void ratio ðt ¼ 0Þ of suspension.Other parameters in Eqs. (B.2) and (B.3) are defined as follows:
j ¼ B 1 B; aE¼ 1 mrSaavCe ; aC¼faE, (B.4a2c) h1¼ C 2 1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2CeZcp 2 o2 S s , h2¼ C 2 þ 1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2CeZcp 2 o2 S s , ðB:4d2eÞ C ¼ bZcþZcþCep 2 4o2 S ; D1¼ pCeðZcþh1Þ2 4o2 Sh1½ðZcþh1Þ2þbZ2c , (B.4f2g) D2¼ p2C eðZcþh2Þ2 4o2 Sh2½ðZcþh2Þ2þbZ2c , (B.4h)
where pL is the liquid pressure, the B the ratio of secondary consolidation to the total consolidation, Zc the creep factor, and Ce the consolidation coefficient
(Chang and Lee, 1998).
Substituting Eqs. (B.1)–(B.4) into Eq. (4) leads to the following form of EV: EV¼VS aEaCZcp2ExprF1½F2þ1 ½F2D1D2 n g, ð1 þ e1ÞpExprF2 o , ¼C1p2ExprC2ð1 þ e1ÞpExpr, ðB:5Þ G1¼ rL½2r3 glþrlsðr2ls3r2glÞ þrSlurry½2r3lsþrscðr2sc3r2lsÞ þ ðrLþDrð1 avÞÞ½2r3scþrcmðr2cm3r2scÞ 3 , (A.4)
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