Comparing Model and Experimental Results of the Volume of Filtrate during Sludge Dewatering

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1 Open Access Library Journal 018, olume 5, e4650 ISSN Online: ISSN Print: Comparing Model and Experimental Results o the olume o Filtrate during Sludge Dewatering Sheikh Yusu, Joel Ademiluyi Department o Civil Engineering, University o Nigeria, Nsukka, Nigeria How to cite this paper: Yusu, S. and Ademiluyi, J. (018) Comparing Model and Experimental Results o the olume o Filtrate during Sludge Dewatering. Open Access Library Journal, 5: e Received: May 8, 018 Accepted: July 6, 018 Published: July 9, 018 Copyright 018 by authors and Open Access Library Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). Open Access Abstract The results o the experiment o dewatering analysis carried out on a municipal sludge were recorded. Similarly, analytical mathematics was used to develop an equation to calculate volume o iltrate. The two results were plotted in graphs and comparisons were made. The results show very close relationships between the two results. In act in most cases the two results were almost overlapping. For example ater 3, 6, 9, 1, 15 hours, the volumes o iltrates are: m 3 (model), m 3 (experiment), (model), (experiment), (model), (experiment), (model), (experiment) and (model), (experiment). This has shown that the experiment was carried out very well and that, mathematical equations can be used directly in order to calculate the volume o iltrate and the values can be nearly the same with model results. Subject Areas Civil Engineering Keywords Municipal Sludge, Dewatering, olume o Filtrate, Analytical Mathematics 1. Introduction 1.1. Wastewater Wastewater can have a number o deinitions. Domestic wastewater is deined as wastewater rom household water use, while industrial wastewater is rom industrial practices only. In reality, the term wastewater clearly encompasses domestic, commercial, industrial, agricultural components and also aecal sludge, DOI: /oalib Jul. 9, Open Access Library Journal

2 S. Yusu, J. Ademiluyi these are sometimes covered separately in order to clariy or highlight the importance o the individual components or wastewater streams [1]. The presence o contaminants in sewage sludge arising rom municipal discharges is the most challenging problem and may be the deciding actor in determining the choice o a utilization dewatering option []. 1.. Sludge Sludge is a semi-solid material produced by various biological and chemical processes in water and wastewater treatment plants that needs urther treatment prior to its disposal into the environment. More importantly, the water in sludge is not only in one orm in terms o its binding characteristics to solids. According to [3] the orm o water in sludge determines the eectiveness o sludge treatment operations to separate the water associated with the solids. Municipal sludge can be obtained rom open drains, while in some cases sludge originates rom the process o treatment o wastewater and is separated rom the treatment process by sedimentation or lotation. Sewage sludge consists o water and solids that can be divided into mineral and organic solids. The act remain that a simple technique close to nature and very eective in wastewater treatment is dewatering in drying beds. Reerence [4], the principal advantages o drying beds are low costs, inrequent attention required, and high solids content in the dried product, especially in arid climates. The main purpose o a drying bed is to achieve dewatering; i.e. a physical separation between liquid and solids.. Literature Review.1. Sludge Dewatering The orm o water in sludge determines the eectiveness o sludge treatment operations to separate the water associated with the solids. Beore ultimate disposal, the water content o sludge should be decreased both rom environmental and economical point o view [5]. Sludge dewatering, commonly achieved through vacuum/pressure iltration or centriugation, is a paramount process in water and wastewater treatment systems as it reduces the volume o sludge, and consequently, the costs or transporting the sludge to its ultimate disposal site. Cake ilters commonly used in wastewater treatment works include pressure ilters, vacuum ilters and centriugal ilters [6]. In this research however, no pump is used, rather the sludge is allowed to percolate onto a ilter made o sand and gravel. The characterization o the sludge to be dewatered is the key actor or the design and operation o sludge ilters [4]. The problem o sludge generation, storage, treatment and disposal is a serious one especially in developing countries where there are no enough sewers or even none in most o our cities, and the wastewater is not treated accordingly. Thereore the collection, treatment and disposal o sludge is an issue that is supposed to be taken serious especially i one look at the hazards involved in terms o degradation o the environment and spreading o waterborne diseases [7]. Sludge iltration theories and derived DOI: /oalib Open Access Library Journal

3 S. Yusu, J. Ademiluyi equations have been made on experimental assumptions and conditions. Reerence [], each researcher is making eort to modiy already existing theory in order to introduce a completely new concept or evaluating sludge iltration equation. A careul study o researchers works on this topic, have shown that most o them do reer to Carman s equation as the basis o their research... Filtration Theories..1. Filtration Based on Cake Resistance This was pioneered by Almy and Lewis [6] that was in 191 when they iltered chromium hydroxide. They suggested this equation: dv n m kp dt = (.0) This constituted the basic law o iltration, where m and n are indeinite powers o the relationships, which the rate o low d v possesses with pressure P dt and volume respectively. Since Poiseuille s law and Darcy s law both deal with low and considering sand bed as a bundle o capillaries, Carman proposed the ollowing equation: Cµ r µ R t = + (.1) PA PA... Modiication o Carman s Equation Reerence [6], in 1974, Anazodo objected to Carman s equation on its ormulation point o view. He argued that the approximation o compressible ilter cakes to rigid bundles o capillary tubes or to non-compressible sand-bed did not make sense. He then used dimensionless analysis to come up with the ollowing equation: A Cr A pc r t = (.) Cr µ Since the relationship between and t has been established to be parabolic, Anazodo substituted = 1/ to obtain this equation: 5 PA t = (.3) 1 1 µcr Reerence [6] reported that Gale and White advocated that Anazodo s partial equation should be written as: 1 bt b 3 = Pµ A Cr (.4) So that relationship between and A should be experimentally determined. Reerence [8], conducted an investigation to determine experimentally the values o the exponent b which relates the volume o iltrate to the area o iltration. They suggested that the total area o iltration should be used in Carman s equation, while the eective area o iltration should be used in the dimensional DOI: /oalib Open Access Library Journal

4 S. Yusu, J. Ademiluyi equation or sludge iltration. They came up with these equations: and PAt1.8t = (.5) µcr1.18 PA e.76 t = (.6) µ Cr 0.4 ( )..3. Theory Based on Filtration Coeicient Hal on his own part developed an equation that established the act that iltration ollows the parabolic relationship until the cake reaches 80% iltration [6]. He proposed this equation: δγ i Ci = (.7) µ Co S ( )..4. Theory Based on the Concept o SDN Even though the speciic resistance parameter is a good measure o sludge iltrability, it does not have constant unit. In the light o the above, a dimensionless number reerred to as the sludge dewaterability number was developed by [8], and it has ound to be a very good measure o sludge iltrability. It is given as: where: Cc = Concentration o cake (kg/m 3 ) C = Concentration o iltrate (kg/m 3 ) C o = Concentration o sludge (kg/m 3 ) H 0 = Initial headloss (m) H = Change in headloss (m) SDN = Sludge Dewaterability Number t = Time o iltration = olume o iltration (m 3 ) ( o ) 0 H C C H + (.8) tcc t..5. Resistance to Filtration The iltration equation according to [9]: Q P = A µ R + αc A ( ) (.9) considers the overall resistance to low o iltrate to be made up o contributions rom the ilter medium R, and rom the cake with speciic resistance α. Normally R is ound to depend on the operating pressure; the two intercepts may correspond to dierent values o R at the two pressures. Although these porosities and permeabilities are o unused materials, the relative values may be useul or comparing behaviors under iltration conditions. Permeability K p normally is the property reported rather than the resistivity that has been discussed here. It is DOI: /oalib Open Access Library Journal

5 S. Yusu, J. Ademiluyi deined by the equation Q = K P L p µ (.10) A where L is the thickness. Thus the resistivity o the medium includes its thickness. The relation o the above equation to resistivity is: R L = (.11) K p..6. Theory o Filtration Reerence [10] as iltration proceeds, a porous cake o solid particles is built up on a porous medium, usually a supported cloth. Because o the ineness o the pores the low o liquid is laminar so it is represented by the equation d A P Q = = (.1) dt µ R The resistance R is made up o those o the ilter cloth R and that o the cake R, which may be assumed proportional to the weight o the cake. Accordingly: d A P Q = = t µ R R ( + ) d c where: c = wt o solids/volume o liquid (kg/m 3 ) μμ = viscosity (N sec/m ) P = pressure dierence (N/m ) A = iltering surace (m ) = volume o iltrate (m 3 ) Q = rate o iltrate accumulation (m 3 /sec). At constant pressure Equation (.13) is integrated as: A P αc t R µ A (.13) = + (.14) The above equation can be written in linear orm as: t C = µ R + µα A P P A (.15) The constants R and a derivable rom the intercept and slope o the plot o t/ against. I the constant pressure period sets in when t = 0 t and = 0, the equation becomes: t t µ µαc = R A P A P ( ) 0 (.16) At a constant rate o iltration Equation (.16) can be written as: A P Q = = t µ R αc A ( + ) (.17) DOI: /oalib Open Access Library Journal

6 S. Yusu, J. Ademiluyi The above equation can be re-arranged in linear orm as ollows: P P c = = µ R + µα (.18) Q t A A The constants again are ound rom the intercept and slope o the linear plot o P/Q against. Ater the constants have been determined, Equation (.18) can be employed to predict iltration perormance under a variety o constant rate conditions. For instance, the slurry may be charged with a centriugal pump with a known characteristic curve o output pressure against low rate [9]. 3. Methodology In order to carry out this research work, sewage sludge was collected rom an open unlined drain along Layin Wanki in Unguwar Sarki area, Kaduna, Kaduna North Local Government o Kaduna State. The sample was collected equally along the length o the open drain in order to get a composite sample. Even though it is a municipal wastewater, but there is need to mention that there are people along the street, who are engaged in washing o clothes, locally. The wastewater rom their activities is also included in this sludge. About 15 litres o sludge was poured on to the drying bed which was located on a corridor o the Water Laboratory o the Department o Civil Engineering Kaduna Polytechnic, Kaduna The drying bed was made with a glass so that it is transparent. The length is 1.5 m and width is 0.5 metres. The ilter medium consists o coarse sand and gravel. The sand has a depth o 0.3 m and the same depth is the gravel (0.3 m). The depth above the sand (where the sludge is slowly allowed in) is 0. m. In this research, the wastewater was allowed to percolate onto the drying bed or 15 days, and the volume o the iltrate was taken (and recorded) ater every 4 hours, throughout the duration. From the results obtained, the t/v was calculated and a graph o volume and t/v, and t were plotted. A sand layer is placed on top o the gravel. The sand layer enhances drainage and prevents clogging, as it keeps the sludge rom lodging in the pore spaces o the gravel. The diameter o the sand is crucial as sand with a larger diameter ( mm) can result in the relatively ast accumulation o organic matter, thereby increasing the risk o clogging, In order to reduce this risk a sand with a smaller diameter ( mm) is use. The municipal sludge was passed through the ilter in order to get a dry solid known as cake. The mathematical equation will be developed using advanced calculus [11]. In order to develop equation or the volume o iltrate collected there is need to reer to [1], which is: dc = Q0C0 QC (3.0) dt where Q 0 is the rate o sludge low (m 3 /sec) Q is the rate o volumetric increase o the iltrate (m 3 /sec) C 0 is the concentration o the sludge (kg/m 3 ) DOI: /oalib Open Access Library Journal

7 S. Yusu, J. Ademiluyi C is the concentration o the iltrate (kg/m 3 ) dc is the small change in the cake concentration (kg/m 3 ) is the volume o itrate in m 3 olume o Filtrate Equation ( ) Considering a situation where sludge is applied on the surace o ilter and it was dewatered. I Q and C are considered to be unctions o time while C 0, Q 0 are considered to be constant, then integrating, Equation (3.0), we will have: d C = ( Q C QC 0 0 ) d t (3.1) I is considered to be constant, ater inal collection, then Equation (3.1) becomes: But according to [1] d = 0 0 d ( ) ( ) d (3.) t QC t Q t C t t = Qt Thereore Equation (3.), becomes: C QC t t C t t d = 0 0 d ( ) d (3.3) Integrating Equation (3.3), Equation (3.4) will be: 1 C= QCt 0 0 C ( t) dt (3.4) t Integrating by part: 1 d t =, U = C ( ) t, log ( t) du = dc t Thereore: uv vdu C = Q0C0t C ( t) log ( t) log ( t) dc ( t) dt =, ( ) ( ) ( ) ( ) ( ) C = QCt 0 0 C t log t log t dc t dt (3.5) Neglecting rate o change in C, Equation(3.6), becomes: C = QCt 0 0 C ( t) log ( t) (3.6) But [1], said: Qt= 0 0 Thereore Equation (3.6) becomes: ( ) ( ) C = C 0 0 C t log t (3.7) Re-organizing the above equation, Equation (3.7) becomes: Since according to [1]: Thereore ( ( ) log ( )) 0 0 C+ C t t = C (3.8) 0 = + c DOI: /oalib Open Access Library Journal

8 ( ( ) log ) 0 ( ) c S. Yusu, J. Ademiluyi C+ C t t = C + (3.9) Re-organizing the above equation, Equation (3.9), will be : 4. Discussions o Results ( ( ) log ( )) 0 ( ) C+ C t t = C + (3.10) c ( ) ( ) ( ) C = C0 + c C t log t (3.11) ( ) ( ) C = C 0 + C 0 c C t log t ( ) ( ) C C 0 = C 0 c C t log t ( ) = ( ) ( ) C C0 C 0 c C t log t ( ) log ( ) ( ) = C C t t C C 0 c 0 ( ) log ( ) ( ) = C C t t C C (3.1) 0 c 0 Considering the graphs plotted in Figures 1-3, it can be observed that the dierences between the model and experimental results are so near to each other, and in act in Figure, the two results overlapped. This indicates the nearness o the two results and conirmed that, one can either use the model or experiment way to get a good result o volume o iltrate. The results obtained rom the research work have indicated a very good arrangement o the ilter. Also the practical work was monitored eiciently. These two events made the work very successul, thus giving a very good result (Tables 1-3). Figure 1. Time vs Table 1. Time versus model and experimental. Time (Model) (Experimental) DOI: /oalib Open Access Library Journal

9 S. Yusu, J. Ademiluyi Figure. Cake versus Table. Cake versus model and experimental. Cake (Model) (Experimental) Figure 3. Concentration versus model and experimental. Table 3. Concentration versus model and experimental Co (Model) (Experimental) Conclusion and Recommendation 5.1. Conclusion The analysis carried out in this research has shown that mass balance equation DOI: /oalib Open Access Library Journal

10 S. Yusu, J. Ademiluyi can be used in order to develop an equation or the volume o iltrate. Also good and reliable laboratory work can lead to a good result. This can be concluded by comparing the model and experimental results that are almost the same. 5.. Recommendation From the laboratory analysis, it can be recommended that: 1) The medium o the dry bed ilter should be arranged in such a way to avoid clogging within a short time; because this will make the dewatering process to be delayed and cost more, as the ilter has to be cleaned within a short period o time. ) Drops o iltrate should be monitored properly at every time. This will help to monitor the eiciency o the ilter. 3) The process should be carried out in-doors to avoid external orces, such as wind that may blow away the drops rom entering the collecting vessel. 4) More research should be carried out where period o iltration is increased and the time interval o recording the iltrate is decreased. For example the dewatering process can be increase to a month and the recording time be made ater 1 hours. The process should be monitored to see whether it is more eicient, than the one carried out in this research. Reerences [1] Corcoran, E., Nellemann, C., Baker, E., Bos, R., Osborn, D. and Savelli, H. (Eds.) (010) Sick Water? The Central Role o Wastewater Management in Sustainable Development. A Rapid Response Assessment. UNEP/UNHABITAT. [] Ademiluyi, J.O. and Arimieari, L.W. (01) Evaluating the Speciic Resistance o Conditioned Sludge Filtration o Natural Driving Bed. International Journal o Current Research, 4, Issue 0. [3] Metcal & Eddy, Inc. (003) Wastewater Engineering: Treatment, Disposal, Reuse. McGraw-Hill, New York. [4] Koné, D., Coie, O., Zurbrügg, C., Gallizzi, K., Moser, D., Drescher, S. and Strauss, M. (007) Helminth Eggs Inactivation Eiciency by Faecal Sludge Dewatering and Co-Composting in Tropical Climates. Water Research, 41, [5] Tchobanoglous G, Burton, F.L. and Stewel, H.D. (00) Wastewater Engineering: Treatment and Cause. 4th Edition/Revised. McGraw-Hill, New York. [6] Ademiluyi, J.O. (1986) Developments in the Constant acuum Cake Filtration Theory. Paper presented at the Engineering Section o the Science Association o Nigeria Conerence, 6-9 April University o Lagos. [7] Huisman, L. and Wood, W.E. (1974) Slow Sand Filtration (ol. 16). World Health Organization, Geneva. [8] Ademiluyi, J.O., Egbuniwe, N. and Agunwamba, J.C. (1987) Dimensionless Number as an Index o Sludge Dewatering. Journal o Engineering or Development, 4, -4. [9] Tiller, F.M. (1978) Theory and Practice o Solid-Liquid Separation. University o Houston, Houston. [10] Ademiluyi, J.O. (1990) Eect o Shear, Filter Medium, Sludge Ageing and Sequence o Chemical Addition o Sludge Dewaterability Number (SDN). AJST Series A, 8, No.. DOI: /oalib Open Access Library Journal

11 S. Yusu, J. Ademiluyi [11] Bird, J. (007) Engineering Mathematics. 5th Edition, Newnes, Linacre House, Jordan Hill, Oxord, UK. [1] Ademiluyi, J.O., Agunwamba, J.C. and Egbuniwe, N. (1989) Mass Balance Filtration Equation. Waste Management, 9, DOI: /oalib Open Access Library Journal