Digested sludge, Bingham model, Herschel-Bulkley model, shear banding, viscoelasticity.

Transcription

1 The anaerobi rheologial behaviour of digested sludge J.C. Baudez 1.2, F. Markis 2, N., Eshtiaghi 2, P. Slatter 2 1 Cemagref, UR TSCF, F-315 Montoldre, Frane 2 Rheology and Materials Proessing Centre, Dept. of Chemial Engineering, RMIT University, Vitoria, Australia, 31 Corresponding author: jean-hristophe.baudez@emagref.fr Abstrat Produing biogas energy from the anaerobi digestion of wastewater sludge is one of the most hallenging tasks faing engineers, beause they are dealing with vast quantities of fundamentally sientifially poorly understood and unpreditable materials; while digesters need onstant flow properties to operate effiiently. An aurate estimate of sludge rheologial properties is required for the design and effiient operation of digestion, inluding mixing and pumping. In this paper, we have determined the rheologial behaviour of digested sludge at different onentrations, and highlighted ommon features. At low shear stress, digested sludge behaves as a linear visoelasti solid, but shear banding an our and modify the apparent behaviour. At very high shear stress, the behaviour fits well to the Bingham model. Finally, we show that the rheologial behaviour of digested sludge is qualitatively the same at different solids onentrations, and depends only on the yield stress and Bingham visosity, both parameters being losely linked to the solids onentration. Keywords Digested sludge, Bingham model, Hershel-Bulkley model, shear banding, visoelastiity. Introdution Renewable energy is said to be one of the pillars of sustainable management. Biogas from the anaerobi digestion of sewage sludge an provide a lean, easily ontrolled soure of renewable energy from sewage sludge, replaing fossil fuels. However, an aurate estimate of sludge rheologial properties is required for the design and effiient operation of the pumping systems whih surround anaerobi digesters (Slatter, 1997, 23). Indeed Tarp and Melbinger (1967) showed the signifiant advantages of reyling and reirulating digested sludge to mix it with 1

2 exess sludge, among them an inrease in biogas prodution (Sperry, 1959). The mixture an be onentrated to a muh higher solid ontent than would be possible for the exess sludge alone, and reirulation also failitates improved mixing effiieny over mehanial stirring. However, the flow rate in the reirulation iruits has to be very large (Appels et al, 28) and rheology is needed to alulate head losses and pumping power (Slatter, 21). Exept for the work of Monteiro (1997) who showed that anaerobi digestion indues a derease of the rheologial harateristis of sludge, most investigations on sludge rheology were foused on ativated sludge. No reliable data, at high shear rate (within reirulation pipes), an be found in the literature for digested sludge while at low shear rate (within the digester), results are sare and not always usable. Most of these were obtained by applying shear rate ramps that gave distint peaks in the flow urve (for example, Ayol et al., 25), but Baudez (26) learly established that these peaks in the flow urves were prinipally instrument artefats, and not material harateristis. However, the work of Ayol et al. (25) pointed out that with very dilute sludge, the Ostwald model, i.e. a power law model with no yield stress, gave the best fit. From a physial perspetive, digested sludge appears to be a stable suspension with low settling rates (Namer and Ganzarzyk, 1993) and low surfae harge (Forster, 22), implying that interations are more steri than eletrostati. The most important onstituents in digested sludge are lipopolysaharides (Forster, 1983) whih are amphiphile lipids with both hydrophili and hydrophobi heads. These moleules displayed a very intriguing rheologial behaviour (Muñoz et al, 2), showing linear visoelastiy, non-newtonian visous flow and shear banding (Miller and Rothstein, 27). In this paper, our intention is to establish the basi harateristis of the rheologial behaviour of digested sludge, with the objetive of industrial appliations in digester mixing, pumping and pipe flows, meaning that we will fous on short-term behaviour. Short-term behaviour means we will not fous our researh on eventual thixotropi effets. As predited by the literature on amphiphile rheology, we show that digested sludge exhibits linear visoelasti behaviour at low shear stresses, followed by shear-banding phenomena at intermediate stresses, and finally a non- Newtonian fluid behaviour with a yield stress, modelled by a Hershel-Bulkley model at intermediate shear rates and by a Bingham model at very high shear rates. We also highlight the fat that the rheologial behaviour is qualitatively the same at different solid onentrations, allowing us to define a master-urve for whih the dimensionless parameters are the yield stress and the Bingham visosity. Material and methods The digested sludge was sampled at the Mount Martha waste water treatment plant (Melbourne, Vitoria, Australia) at the outlet of the digester number 1. Its initial solid onentration was at 18.5g.L -1 and was also gently onentrated to 25.5, 32 and 49g.L -1 by using a Buhner vauum. Sludge samples were stored at 4 C for 3 days befor e experiments, in order to redue temporal variability. Indeed, even after anaerobi digestion, sludge may not be fully stabilised and organi 2

3 hanges may still our. By storing the sludge sample for suh an extended period, the potential for omposition hanges is redued; and we an assume that we used exatly the same material throughout all our experiments. Rheologial measurements were performed with a DSR2 instrument from Rheometri Sientifi, onneted to a temperature ontrolled water bath. The rheometer was equipped with a up and bob geometry (inner diameter: 29mm, outer diameter: 32mm, length: 44mm). Temperature was kept at 25 C. To avoid evaporation, sludge was ove red with a thin film of immisible Newtonian oil. Before eah measurement, sludge was presheared for 1 minutes at a shear rate of 1s -1 then left at rest for 1 minutes. This proedure allowed us to erase material memory and to have reproduible measurements. Then, different tests were performed: Shear stress sweep, by applying a linear ramp of inreasing stress over time. In this test, we hanged the time of rest between preshear and shear, from 1 to 6 minutes in order to investigate strutural hanges ourring during rest; Creep test, by applying onstant shear stress and measuring the orresponding shear strain, at different shear stresses in the linear visoelasti regime and above; Dereasing stress ramp to determine the flow urve, starting at a high stress orresponding to a shear rate of approximately 1s -1 or lower for the less onentrated sludge (to avoid turbulent onditions). Results and disussion Starting from rest, the shear stress sweep first eliits a linear visoelasti response from the digested sludge up to a ritial shear stress τ above whih the material apparently starts to flow (Fig. 1). In the linear visoelasti region, the behaviour is modelled by a generalised Kelvin-Voigt model, with a wide relaxation time spetrum modelled by a strethed exponential: γ 1 G ( ( ) m ( t) = τ 1 exp ( λt) G where γ represents the strain, τ the stress and λ = with G and µ the usual parameters of a µ Kelvin-Voigt model. Assuming that the sludge is flowing in its liquid regime above the ritial shear stress following a Hershel-Bulkley model (Monteiro, 1997), the additional strain an be expressed as: 1 n 1 n t t t a x a t a n ( t) = τ τ γ du dx ( t t ) n & γ = = t = t K (2) t K ( n + 1) K (1) 3

4 where a is the slope of the shear stress ramp and t the time suh that the shear stress equals the yield stress of the Hershel-Bulkley model τ = a t. Thus, the total strain, whih predits the experimental data (Fig. 1), an be expressed as: ( ( ) n b ( t t ) n 1 + ( t) = τ 1 exp ( λt) γ (3) G with b = an ( n + 1) K Applying this to the experimental data gave a flow behaviour index for the Hershel-Bulkley model, n, greater than 1 (Fig. 1), meaning that the digested sludge ould apparently be a shear-thikening liquid above τ, whih is unusual. Creep tests onfirmed a hange in the behaviour above τ. Below τ, the strain slowly inreased with time, while above τ, the inrease is faster (Fig. 2), both following a power law with time. However, even for stresses higher than τ (Fig. 2) the shear strain follows a power-law with a power-law index less than 1, indiating that the shear rate is a dereasing funtion of time: there is no steady state and so, sludge is restruturing and not flowing (otherwise, the shear rate would have been onstant over time for a onstant shear stress). The value τ annot therefore be onsidered as a lassial yield stress above whih digested sludge flows in its liquid regime. These power-law relationships between strain and time are in fat a onsequene of a strutural relaxation proess whih ours during reep (Baudez, 28). When the time of rest between the preshear and the stress sweep inreases, the behaviour is globally the same, with first a linear visoelasti behaviour (Fig. 3) but the ritial shear stress, τ dereases with inrease of the time of rest, the global elastiity dereases, the mean relaxation time (inverse of λ ) inreases and the strain orresponding to τ dereases (Fig. 4): the longer the time of rest, the smaller the linear visoelasti range. At rest, the digested sludge struture beame weaker and weaker (derease of τ and elastiity) but onurrently the relaxation time inreased, indiating an evolution from a visoelasti material towards a more elasti solid (the derease of µ is faster than the derease of G ). Sine this is physially impossible, this observed apparent behaviour is not representative of the true material behaviour but derives from erroneous interpretation of raw data. Above τ, experimental results showed the visosity is globally dereasing, whih is inonsistent with the apparent shear-thikening behaviour noted earlier, but osillations of visosity regarding shear stress are reported (Fig. 5). These osillations indiated loal minima in the flow urve where apparent shear rate oasionally dereased while shear stress inreased. If we assume the relationship between loal shear rate and loal shear stress is monotoni, then we an write: ( τ ) & γ = f where f is the inverse funtion of the behaviour law. 4

5 In a Couette geometry, the shear rate an be expressed as: ( ω) R2 & γ R f ( τ ) loal loal & γ loal = r ω = dr ω = R dr (4) r 1 r R1 r where ω is the angular veloity, R 1 the inner radius and R R1 the thikness of the sheared region. The maximum value of R R1 is R2 R1, where R 2 is the outer radius. The apparent shear rate is alulated from the measured angular veloity, the only raw data measured by the rheometer. The shear rate given by the rheometer is alulated with the assumption of a full shear within the gap. So, if the apparent shear rate dereased, it means the angular veloity dereased. However, beause f is a monotoni funtion, this derease of ω is rather the onsequene of a derease of the effetive gap R R1, implying that shear banding has ourred during the measurement. Suh behaviour (shear banding and visoelasti behaviour) has to be taken into aount in digester design and operation, beause shear banding means that there is oexistene of both sheared and unsheared zones in the digester, these last being useless, unmixed, dead zones. Aording to Moller et al. (28), the width of the flowing band an be diretly related to the marosopially imposed shear rate. At high shear rates, the whole gap is sheared and when the applied stress is muh higher than τ, the sludge flows normally, with no apparent perturbation effets, allowing us to have ahieve reproduible measurements (Fig. 6) with the orresponding smooth lassial shape of the flow urve. As expeted, the higher the onentration, the thiker the sludge (Fig. 7) but depending on the shear rate range, different well-known models an be used to desribe the rheologial behaviour of digested sludge. At high shear rates, a basi Bingham model is suffiient (Fig. 8) while at low and intermediate shear rates, Hershel-Bulkley and power-law models are more appropriate (Fig 9). They all represent the same material but an only be used in a speifi range of validity, regarding the omplexity of the proess to be modelled. Thus, for pumping where shear rates are very high, a Bingham model would be appropriate sine it deals with simple harateristis, i.e. a yield stress and a onstant rheogram slope above it. From a more general point of view, in the liquid regime we an summarize the rheologial behaviour of digested sludge as a shear-thinning yield stress fluid with a plateau visosity at high shear rates: (& γ ) & γ with η( & γ ) α τ = τ + η & γ τ = τ + K & γ = τ + η & γ & γ η & γ K & γ n n 1 Moreover, at low and intermediate shear stresses, ( ) ( ) Thus, for the sake of simpliity, we define the rheologial behaviour of digested sludge as follows: n 1 ( & γ + α ) & γ τ = τ + K (5) 182 On our range of data, i.e. below 1s -1, this model was suessful. However, if γ& << K 1 n α, the 183 Hershel-Bulkley model is suffiient to model the behaviour, whih orresponds to a shear rate 5

6 smaller than 565s -1 for the most onentrated sludge and smaller than 145 s -1 for the less onentrated sludge as shown below (Table 1). Table 1: Shear rate above whih the Hershel-Bulkley model is not suitable Conentration [%] Equation (5) an also be expressed as: n τ = τ + K & γ + α & γ τ K n α = 1+ & γ + & γ τ τ τ τ = 1+ β Γ τ α K τ Γ = & γ, β = τ τ α n + Γ n Limit shear rate [s-1] In suh a dimensionless form, all the flow urves are similar, independent of solids onentration (Fig. 1). From a physial point of view, this result means that there is some similarity of the network of interations within the sludge at different onentrations, whih is at the origin of the similarity of its marosopi behaviour. In suh suspensions, interations an be lassified into two main groups (Baudez and Coussot, 21): hydrodynami interations (between solid partiles and surrounding fluid, here basially represented by the Bingham visosity) and non-hydrodynami interations (between solid partiles, basially represented by the yield stress). Inreasing the onentration doesn t hange the nature of these interations, but rather modifies their relative intensity. The dimensionless form smoothed these differenes beause both kinds of interations in this form will approah unity. On our range of onentrations, yield stress and Bingham visosity inrease with the solid onentration (Fig. 11) respetively following a power-law and an exponential law of the following form, whih is in agreement with the literature, both for the yield stress (Baudez, 28) and the Bingham visosity (Sanin, 22): ( φ φ ) m τ = α (7) ( β φ) k = µ exp (8) 2 where φ is the lowest onentration below whih there is no yield stress, m is related to the fratal dimension of sludge flos (Baudez, 28) and µ is the visosity of the liquid medium. (6) 6

7 We found that the value µ is twie that of pure water, whih an be explained by the large amount of dissolved matter present, whih may inrease the supernatant visosity. Conlusion In this paper, we have shown that digested sludge is a shear-thinning yield stress fluid, presenting flow instabilities at low shear rates, manifesting as shear banding. At low shear stress, below the yield stress, digested sludge behaved as a visoelasti solid. When the applied stress is inreased, above a ritial shear strain, whih dereases with the restruturing, shear banding appears. Then, at higher stresses, digested sludge behaves like a yield stress fluid and an be modelled using both the Hershel-Bulkley and Bingham plasti models over a wide range of shear rates. This behaviour was similar at different onentrations and yield stress followed a power-law with the onentration while the Bingham visosity followed an exponential law with onentration. By reduing the rheologial parameters with the yield stress and the Bingham visosity, whih have to be measured separately, a master urve was obtained. This result means that the rheologial behaviour of the digested sludge at any onentration an be dedued from this master urve. However, further work has to be done on shear banding. This behaviour will have to be taken into aount in digester design and proess operations, in order to avoid dead zones in the digester. Aknowledgements The authors aknowledge the Cemagref-RMIT agreement for our ollaboration Referenes Appels, L., Baeyens, J., Degrève, J., Dewil, R., 28. Priniples and potential of the anaerobi digestion of waste-ativated sludge. Progress in Energy and Combustion Siene Volume 34, Issue 6, Deember 28, Pages Ayol, A., Filibeli, A;, Dentel, S.K., 26. Evaluaion of onditioning responses of thermophili- mesophili anaerobially and mesophili aerobially digested biosolids using rheologial properties. Water Siene and Tehnology, 54, 5, Baudez, J.C, Coussot, P., 21. Rheology of aging, onentrated, polymeri suspensions - Appliation to pasty sewage sludges. J. Rheol. 45(5): Baudez, J.C., 26. About peak and loop in sludge rheogram. Journal of Environmental Management, 78, Baudez, J.C., 28. Physial aging and thixotropy in sludge rheology. Applied Rheology, 18,

8 Forster, C.F., Bound water in sewage sludge and its relationship to sludge surfaes and sludge visosities. J. Chem. Teh. Biol., 33B: Forster, C.F., 22. The rheologial and physio-hemial harateristis of sewage sludge". Enzyme and Mirob. Teh., 3(3): Miller, E., Rothstein, J.P., 27. Transient evolution of shear banding in wormlike mielle solutions. J. Non-Newtonian Fluid Meh. 143, Moller, P. C. F,Rodts, S. Mihels, M. A. J. and Bonn,D., 28. Shear banding and yield stress in soft glassy materials. Phys. Rev. E 77, Monteiro, P.S., The influene of the anaerobi digestion proess on the sewage sludges rheologial behaviour. Wat. Si. Teh., 36 (11): Munoz, J., Alfaro, M.C., 2. Rheologial and phase behaviour of amphiphili lipids. Grasas y aeites, vol. 51, pp Namer, J. J. Ganzarzyk, L., 1993.Settling Properties of Digested Sludge Partile Aggregates. Water Researh, 27, Sanin, F.D., 22. Effet of solution physial hemistry on the rheologial properties of ativated sludge. Water SA, 28: Slatter P The rheologial haraterisation of sludges. Wat. Si. Teh. 36(11), Slatter P. 21. Sludge pipeline design, J. Wat. Si. Teh. 44(1): Slatter P. 23. Pipeline transport of thikened sludges. Water 21: Tropey, W. N. and Melbinger, N. R., Redution of Digested Sludge Volume by Controlled Reirulation. Journal Water Pollution Control Federation 39(9): Sperry, W.A., Gas Reirulation at Aurora, Illinois, Sewage and Industrial Wastes vol. 31, n 6. 8

9 272 Captions Figure 1: Strain-stress behaviour of the 4.9% digested sludge. The dashed lined orresponds to the model of (1) with G=.62Pa, λ= s -1, m=.34, b=.35s -2, t =315.5s, orresponding to a stress equals to 2.13Pa and n=

10 Figure 2: Creep test below, above and equal to the ritial shear stress. Here, the ritial stress is 2.5 Pa for the 4,9% sludge. The insert is a fous on the strain at the highest strain at longer time, following a power-law with an index smaller than Figure 3: strain stress behaviour when a stress sweep is applied after different time of rest. 1

11 Figure 4: Evolution of the Kelvin-Voigt model parameters as a funtion of the time of rest

12 Figure 5: stress-visosity variations highlighted osillations with the 4.9% digested sludge Test 1 Test 2 Test 3 Shear stress [Pa] Shear rate [s -1 ] Figure 6: Repeatability of the measurements

13 Figure 7: Flow urves regarding the onentration of the digested sludge Shear stress [Pa] Shear rate [s-1] Figure 8: At high shear rates, the rheologial behaviour an be basially modelled with a Bingham plasti model

14 Figure 9: At low and intermediate shear rates, the Hershel-Bulkley model or power-law model are the most suitable. The dashed line represents the power-law model τ 2 & γ.45 = Figure 1: Dimensionless flow urves of the digested sludge at different onentrations. 14

15 Figure 11: Evolution of the yield stress and the Bingham visosity regarding the onentration. The parameters of the equations (7) and (8) are respetively a=.19 Pa, φ =1.17%, m=1.89 and µ =.18 Pa.s, β =