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Statistics of Flow and the Scaling of Ceramic Water Filters

Article  in  Journal of Environmental Engineering · July 2014

DOI: 10.4028/www.scientific.net/AMR.1132.267

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Statistics of Flow and the Scaling of Ceramic Water FiltersEbenezer Annan1; Kabiru Mustapha2; Olushola S. Odusanya3; Karen Malatesta4; and Winston O. Soboyejo5

Abstract: According to the World Health Organization (WHO), there was an increase in the number of people that have access to safedrinking water between 2006 and 2010. Such trends can be accounted for partly by the increasing usage of ceramic water filters that canremove microbial pathogens from water. However, the initial flow rates in such filters are often limited to ranges between 1 and 3 L=h. In thispaper, six frustum-shaped ceramic water filters of the same clay:sawdust composition were tested. Each ceramic water filter was filled withwater and allowed to filter 20 times. Each time, the flow rate and water level were measured for a consecutive 12 h. Permeability values wereestimated for each run of the ceramic water filters. Statistical analysis was performed on flow rates (in the first hour), mean flow rates, andestimated permeability values. The flow rate values (in the first hour) for the six ceramic water filters were found to be between 1.4 and3.0 L=h. An effective permeability was obtained for ceramic water filters with a range of microscale and nanoscale pore sizes. The statisticalvariations in the flow rates and effective permeabilities were elucidated along with the potency of a multiple ceramic water filter system forscale-up studies in serving communities that need portable water. DOI: 10.1061/(ASCE)EE.1943-7870.0000862. © 2014 American Societyof Civil Engineers.

Author keywords: Ceramic water filter; Permeability; Flow rate statistics; Scale-up filters; Multiple filter system.

Introduction

It is estimated that 1.8 million deaths per year and 61.9 milliondisability-adjusted life-years are attributed to the drinking of unsafewater and poor sanitation (WHO/UNICEF 2000). The WHO alsosuggests that over 99.8% of the deaths are caused by unsafe water,sanitation, and hygiene in developing countries (WHO/UNICEF2000). Furthermore, in developing countries, most of the childhoodmortality occurs in children who are less than 5 years old (WHO/UNICEF 2004).

Those who have access to improved water may also experiencecontamination between the source and the point of use. Hence, thekey is to ensure that people have access to improved water at thepoint of use. This is crucial for the achievement of the MillenniumDevelopment Goals (MGDs) of halving the number of peoplewithout access to improved water supply and sanitation by the year2015 (WHO/UNICEF 2004). To achieve this target, it is importantto explore point-of-use water purification methods (Murcott 2006;

Sobsey 2002) that can improve the health and well-being of peoplein rural/urban areas in the developing world.

Several point-of-use treatment systems (Murcott 2006; Sobsey2002) can be used to provide microbiological, chemical, orphysical water treatment. They include (1) disinfection [chlorina-tion, solar disinfection (SODIS), solar pasteurization, ultravioletirradiation with lamps, and boiling] (Liu and Fitzpatrick 2010),(2) particle filtration (cloth fiber, ceramic filter, biosand, and otherslow sand filter technologies) (Heather et al. 2010; Yakub et al.2013), (3) adsorption media (granular activated carbon andactivated alumina or clay) (Liu and Fitzpatrick 2010; Yakub andSoboyejo 2013), (4) combined system (combined flocculationand disinfection or filtration) (Liu and Fitzpatrick 2010; Prestonet al. 2010), and (5) other approaches (plain sedimentation settling,safe storage, flocculation with iron or alum salts, and membraneprocesses) (Preston et al. 2010; Davies et al. 2010). Within therange of possible water treatment methods, water filters are oneof the most highly rated systems for the removal of turbidity(Van Halem et al. 2009; Brown et al. 2009; Brown and Sobsey2010), fluoride removal (Yakub and Soboyejo 2013), and bacteriainactivation (Van Halem et al. 2009; Brown et al. 2009; Brown andSobsey 2010; Oyanedel-Craver and Smith 2008; Yakub et al.2013). Filters are advantageous because they are relatively inexpen-sive (Van Halem et al. 2009; Brown et al. 2009).

Ceramic water filters are produced from a mixture of clays andsawdust. The mixtures are then molded into pot shapes using steelmolds that are subjected to hydraulic pressure. After drying, thegreen bodies are treated at approximately 850°C (Yakub andSoboyejo 2013; Yakub et al. 2013; Van Halem 2006). Duringthe heating process, the carbonaceous materials are burnt at temper-atures between 400 and 500°C and sintered between 800 and 900°C(Yakub and Soboyejo 2013; Yakub et al. 2013; Van Halemet al. 2009; Brown et al. 2009; Brown and Sobsey 2010;Oyanedel-Craver and Smith 2008; Van Halem 2006). They are thenfurnace-cooled (to minimize thermal shock) and dipped in water for24 h. After dipping to saturation, the filters are soaked in colloidalsilver or silver nitrate (Yakub and Soboyejo 2013; Yakub et al.2013; Van Halem et al. 2009; Brown et al. 2009; Brown and Sobsey2010; Oyanedel-Craver and Smith 2008; Van Halem 2006) to

1Ph.D. Candidate, African Univ. of Science and Technology, P.M.B.681, Garki - Abuja, Federal Capital Territory, Nigeria; and AssistantLecturer, Univ. of Ghana, Accra, Ghana. E-mail: eannan@ug.edu.gh

2Ph.D. Candidate, African Univ. of Science and Technology, P.M.B.681, Garki - Abuja, Federal Capital Territory, Nigeria. E-mail:mustkabir@googlemail.com

3Deputy Director, Biotechnology Laboratory, Sheda Science and Tech-nology Complex (SHESTCO), P.M.B. 186, Garki - Abuja, Federal CapitalTerritory, Nigeria. E-mail: shola2@hotmail.com

4Lecturer and Research Specialist II, Dept. of Mechanical and Aero-space Engineering, Princeton Univ., 1 Olden St., Princeton, NJ 08544.E-mail: kmalates@princeton.edu

5Professor, Dept. of Mechanical and Aerospace Engineering, PrincetonUniv., 1 Olden St., Princeton, NJ 08544; Professor, Dept. of MaterialsScience and Engineering, African Univ. of Science and Technology,P.M.B. 681, Garki - Abuja, Federal Capital Territory, Nigeria (correspond-ing author). E-mail: soboyejo@princeton.edu

Note. This manuscript was submitted on August 21, 2013; approved onMay 8, 2014; published online on July 10, 2014. Discussion period openuntil December 10, 2014; separate discussions must be submitted for in-dividual papers. This paper is part of the Journal of Environmental En-gineering, © ASCE, ISSN 0733-9372/04014039(11)/$25.00.

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introduce a coating layer that disinfects microbial pathogens (Dies2003). Although the use of ceramic water filters has been promotedby nongovernmental organizations such as Potters for Peace (Liuand Fitzpatrick 2010), the current understanding of the flow andpermeability in ceramic water filters is limited (Liu and Fitzpatrick2010; Dies 2003; Lantagne 2002; Swanton 2008).

Prior work on flow through porous ceramic water filters has beencarried out by Van Halem (2006), Yakub (2012), Yakub et al.(2013), Schweitzer et al. (2013), and Bear (1972). The Darcy equa-tion (Bear 1972) is very instrumental in flow studies. Van Halemet al. (2009), Yakub (2012), and Yakub et al. (2013) used Darcyflow concepts to model the flow through porous ceramic water fil-ters. Yakub (2012) also considered the flow through the sides andbase of frustum-shaped ceramic water filters. Flow characteristics offrustum-shaped ceramic water filters with varying sawdust:claycontent were also studied by Yakub et al. (2013). However, the ear-lier models did not fully explore the statistical variations in theDarcy flow parameters and the applicability of the Darcy flowmodel under scenarios in which the filters are used multiple times.

The most recent publication on flow modeling—Schweitzeret al. 2013—deduced equations that can be used to compute theflow rate of frustum-shaped and parabolic-shaped ceramic waterfilters (with uniform thickness of the sides and bottom). They per-formed tests on ceramic water filters for three runs (every 8 h=day).This indeed suggested that, barring clogging, increasing thefrequency of loading of the filter or runs may increase the volumeof water produced. The hydraulic conductivities obtained intheir work (k¼ 1.2 × 10−7 m=s for parabolic-shaped ceramic waterfilters and k¼ 0.78 × 10−7 m=s for frustum-shaped ceramic waterfilters) were found to be comparable to previous estimates in theliterature (Oyanedel-Craver and Smith 2008; Van Halem 2006).

However, the dependence of flow rate on permeability or thehydraulic pressure head has not been statistically fully exploredunder enough multiple loadings or runs. Therefore, the objectivesof this paper are to (1) explore and expand variations in flow rate (inthe first hour) values and permeability (in the first hour) values for20 runs of six frustum-shaped ceramic water filters, (2) give insightinto the spread of flow rate (in the first hour) values and permeabil-ity (in the first hour) values using statistical distribution tools,(3) understand the behavior or spread of the mean flow rate valuesand effective permeability values using statistical tools within thecontext of Darcy’s equation, and (4) assess the scale-up potential ofceramic water filters in serving a community. The implications ofthe results are then discussed.

Analytical Modeling

Schweitzer et al. (2013) modeled the flow through ceramic waterfilters. In their analysis, they assumed uniform thickness for thewalls and bottom of the frustum-shaped ceramic water filter.Schweitzer and co-workers initiated their modeling by theDarcy equation (Bear 1972). The modified Schweitzer et al.(2013) modeled equation is presented for the flow rate offrustum-shaped ceramic water filters. The equation is made generalby allowing for differences in the thicknesses of the walls andbottom of the ceramic water filter. Fig. 1 shows the parametersof the flow through the ceramic water filter.

The flow rates for the bottom and sides of the ceramic waterfilter following the similar procedure of Schweitzer et al. (2013)are given in Eqs. (1) and (3)

Qb ¼Kμπr2oρghðtÞ

tbð1Þ

where ρ = density of fluid (in this case, water); πr2o = area; g = theacceleration due to gravity; hðtÞ = the height of the waterhead; tband ts = the respective thicknesses of the bottom and sides of theceramic water filter; Qs and Qb = the respective flow rates throughthe sides and bottom of the ceramic water filter; and θ = angle ofinclination at the corners. The flow through an annular elementalong the sides of the filter is given by

Qs ¼2πKρgμts

ZhðtÞ

0

ðh − yÞðro þ y tan θÞdy ð2Þ

Integration of Eq. (2) gives

Qs ¼πKρgtsμ

�roh2ðtÞ þ

tan θh3ðtÞ3

�ð3Þ

The total flow, Q, through the sides and bottom of the filter is,therefore, given by the sum of Eqs. (1) and (3)

Q ¼ KμπρghðtÞ

�r2otb

þ rohðtÞts

þ h2ðtÞ3ts

tan θ

�ð4Þ

Thus, a more general expression for the flow rate through thefrustum-shaped ceramic water filter following the Schweitzer et al.(2013) derivation procedure (Yakub 2012; Yakub et al. 2013) isgiven in Eq. (4). This is expressed as a function of the height ofthe waterhead in the ceramic water filter. The height of the waterlevel in the ceramic water filter is a function of time, which dependson the volumetric flow rate and the filter geometry. The volume ofwater, VðtÞ, contained in the frustum-shaped ceramic water filter atany given time is given as

VðtÞ ¼ π

�R2hðtÞ þ Rh2ðtÞ tan θþ h3ðtÞtan2θ

3

�ð5Þ

The expressions obtained for hðtÞ were generally found to be ofthe form

h3ðtÞfα3t − β3g þ h2ðtÞfα2t − β2g þ hðtÞfα1t − β1g ¼ 0 ð6Þ

where α1, α2, α3, β1, β2, and β3 are all constants defined in thefollowing equation, and t is defined as time.

tb

h(t)

y

ts

θ

r(y)

Fig. 1. Schematic of frustum-shaped ceramic water filter

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α1 ¼KπρgR2

μtb; β1 ¼ πR2;α2 ¼

KπρgRμts

;

β2 ¼ R tan θ; α3 ¼tan θ3

�Kπρgμts

�; β3 ¼

tan2θ3

ð7Þ

Eq. (6) shows that hðtÞ can converge. The measured flow rateplot versus the time-dependent values of hðtÞwas used to determinepermeability values and was then consequently used in the fittingprocess.

Materials and Methods

Ceramic Water Filter Preparation

Two types of clays were used in the fabrication of the filters. They areEwuya and Iro clays, which were mined from Abeokuta, Ogun State,Southern Nigeria. The sawdust was obtained from a saw mill inSapon Market, Abeokuta-Nigeria. The clays and the sawdust weresieved through 1-mm pores. They were then mixed in thevolume ratios of 50% clay and 50% sawdust. Two liters of waterwere added before molding into a frustum shape (Oyanedel-Craverand Smith 2008; Yakub 2012). The water was added in a smallincremental amount until the clay mixture coalesced into a clay ballwhose surface is not cracked and also does not stick on the boardor sides of the mixing machine. The molded shapes were thenair-dried for 2 weeks before firing. The firing involved heatingfrom room temperature (approximately 25–30°C) to 850°C,followed by furnace cooling in air. The firing was done in a kiln (withthermocouple measurement of temperature). During heating, thesawdust was burnt off at a temperature of approximately 500°C(Yakub 2012; Yakub et al. 2013; Plappally et al. 2011). The initialheating rate of 45°C=h was increased to 100°C=h for the firingprocess.

Porous Material Characterization

X-ray diffraction (XRD) analysis was carried out on the as-receivedclays and the sintered product. X-ray diffraction was performedusing an XPERT-PRO diffractometer (PANalytical BV, Almelo,Netherlands) with theta/theta geometry. The system was operatedin a cobalt tube at 35 kVand 50 mA. The goniometer was equippedwith an automatic divergence slit and a PW3064 spinner stage. TheXRD patterns of all specimens were recorded in the 10-degree to50-degree, 2θ range, with a step size of 0.017 degrees and acounting time of 14.1565 s per step. Qualitative phase analysiswas conducted using X’pert HighScore Plus search match software(PANalytical B.V., Almelo, Netherlands).

X-ray fluorescence (XRF) spectroscopy of the clay sampleswas also conducted to determine the chemical compositions.The XRF data were collected using a Thermo Fisher ARL9400XP+ Sequential XRF spectrometer equipped with a WinXRF soft-ware package. The samples were milled in a tungsten-carbidemilling pot to achieve particle sizes of less than 75 microns.The samples were then dried at 100°C and roasted at 1,000°C todetermine loss on ignition (LOI) values. A gram of the samplewas mixed with 6 g of lithium teraborate flux and fused at1,050°C to make a stable fused glass bead. For trace elementanalyses, the sample was mixed with a polyvinyl acetate (PVA)binder and pressed into a pellet using a 10-t press.

Flow Experiments

The ceramic water filters were soaked in water for 12 h prior tothe flow experiments. This was done to avoid transient flow

phenomena during the early stages of the flow experiments (Yakubet al. 2013). The saturated ceramic water filters were then mountedin the receptacles and filled with 9 L of tap water at the start of theexperiments. The flow through the filters was then measured byrecording the volume of water discharged from the ceramic waterfilter after each hour. The waterhead, h, was also measured. Thewaterhead, h, is a function of time and is usually represented ashðtÞ in equations. Six ceramic water filters were used in this sectionof the research. Each ceramic water filter was loaded with water 20times, and flow experiments were performed at each loading or runto determine the variability in the flow parameters. In this way, themeans and standard deviations of the permeabilities and flow rateswere obtained along with the statistical distributions that providedthe reasonable characterization of the measured flow rates.

Multiple Filter Studies

Five ceramic water filters were connected such that both the fillingsof the filters and outflows were connected in parallel. The paralleloutflows were then connected to a common pipe, thus creating acommon discharge outlet. The system had a main supply that wasfilled with water and was connected to the filtration system. Eachceramic water filter was initially ensured to be filled with 9 L ofwater before starting the timer. The volume of water that flowed outof the common outlet at hourly time intervals was recorded andcontinued for 12 h.

Results and Discussion

X-Ray Diffraction and X-Ray Fluorescence Analyses

Figs. 2(a–c) show the XRD diffraction patterns obtained for theclays. These show the minerals in the Ewuya and Iro clays. TheEwuya clay contained mostly kaolinite and silica, while the Iro clayhad silica, mica, and montmorillonite prior to firing. However, afterfiring, the fired clays were found to also contain allophane (alumi-num silicate hydrate and potassium silicate hydroxide) [Fig. 2(c)].

Table 1 provides the chemical compositions of the Ewuya andIro clays. The major differences between the Ewuya and Iro clayswere in the Al2O3 and SiO2 contents. The Ewuya clay containsapproximately 74.43% by weight SiO2 and 11.46% by weightAl2O3, and the Iro clay has 61.88% by weight SiO2 and15.14% by weight Al2O3. The more plastic Iro clay had a higherAl2O3 content of approximately 15.14% by weight compared to theEwuya clay, which contained approximately 11.46% by weightAl2O3. Conversely, the Iro clay contained approximately61.88% by weight SiO2 compared to the Ewuya clay, which con-tained approximately 74.43% by weight SiO2. Hence, the mixingof the Ewuya and Iro clays produced a composite clay with inter-mediate silica and alumina contents that optimized the plasticityand the thermal shock resistance of the clay mixtures during hy-draulic pressing and sintering, respectively.

Flow through Ceramic Filters

Figs. 3(a–f) show the mean flow rates obtained for the 20 runs foreach ceramic water filter of the six ceramic water filters that weretested. The individual flow rates were found to be between approx-imately 1.4 and 3.0 L=h during the first hour of the flow. However,the flow rates decreased with increasing time. This was due to thedecrease in the hydraulic pressure and possibly clogging or unclog-ging for increasing flow durations (Van Halem 2006; Schweitzeret al. 2013; Yakub 2012). Fig. 3 shows the measured flow ratevariations for different durations with their analytical modeled

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plots. These clearly show that the flow rates vary significantly as afunction of time and variations in the individual filters. Also, for asingle ceramic water filter, no clear trend was observed for mea-sured flow rate from one run to the next run over the entire 20 runs.Furthermore, the variations in the flow rates would be expectedto result in variations in the permeabilities extracted from the over-all flow data (Yakub and Soboyejo 2013; Yakub et al. 2013;

Davies et al. 2010; Brown et al. 2009; Brown and Sobsey 2010;Oyanedel-Craver and Smith 2008; Van Halem 2006).

The mean flow rate of water discharge for the six filters was2.3 L=h during the first hour of discharge. The effective permeabil-ity of each ceramic filter was also obtained by fitting the measuredflow rate data to Eq. (4). The permeability values for the six filterswere found to be between approximately 0.44 × 10−14 and2.54 × 10−14 m2, with an average value of 1.19 × 10−14 m2 (hy-draulic conductivity; k¼ 1.46 × 10−7 m=s). The average effectivepermeability value is found to be very comparable to permeabilityvalues found for ceramic water filters from Cambodia(1.37 × 10−7 m=s) and Ghana (1.3 × 10−7 m=s) in Van Halem’s(2006) work. Also, the average effective permeability computedis well within the hydraulic conductivity range (1.15 × 10−7 to5.01 × 10−7 m=s) obtained by Oyanedel-Craver and Smith(2008) for three ceramic water filters. Furthermore, Yakub et al.(2013) found permeability values between approximately0.1 × 10−14 and 5.0 × 10−14 m2. A linear dependence of the flowon the permeability exists, which therefore suggests that the effec-tive permeability approach captures the trends in the flow rate data.

Figs. 4(a–f) and 5(a–f) show the variability in the permeabilitiesand flow rates, respectively, for the six filters that were each testedover 20 runs. In each case, the filters exhibited statistical variationsattributable to pore clogging and unclogging and changes incrack sizes within the porous structures (Schweitzer et al. 2013;Van Halem 2006; Dies 2003; Yakub 2012; Plappally et al.2011). The variations in the flow rates were found to be reasonably

α α

Note: R – Silica, S – Mica, T – Montmorillonite

Note: U – Aluminum silicate hydrate, V – Potassium aluminum silicate hydroxide

(a) (b)

(c)

Fig. 2. X-ray diffraction patterns of clays showing peak minerals identified: (a) Ewuya clay; (b) Iro clay; (c) fired clay

Table 1. X-Ray Fluorescence Results of Clays

% composition Ewuya clay Iro clay

SiO2 74.43 61.88TiO2 1.00 0.80Al2O3 11.46 15.14Fe2O3 4.51 8.84MnO 0.09 0.08MgO 0.24 1.19CaO 0.22 0.53Na2O 0.14 0.33K2O 1.13 0.84P2O5 0.02 0.01Cr2O3 0.01 0.02NiO <0.01 <0.01V2O5 0.01 0.02ZrO2 0.09 0.05CuO <0.01 <0.01LOI 6.12 10.20Total 99.47 99.93

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characterized by normal distributions that fitted the measured ex-perimental data. The mean flow rate and the effective permeabilityvalues spreads for the 20 runs of each filter are plotted (with fittednormal distribution) in Figs. 6 and 7 respectively. The distributionof the flow rate (in the first hour and mean) and permeabilities (inthe first hour and mean) obtained for 20 runs are fairly normallydistributed, and this is confirmed using the Kolmogorov-Smirnovnormality test and the OriginPro software statistical tool.

Furthermore, the average flow rates obtained for the six filterswere found to increase with increasing permeability values. At the0.05 level, all data drawn for the flow rate (in the first four) andthe permeabilities were significantly normally distributed. Ceramic

water Filters F4 and F6 were found to have effective permeabilityP-values fairly close to the chosen 0.05 alpha value. This, therefore,depicts a weak dependence in terms of the distribution being nor-mally distributed. The mean flow rate P-values of ceramic waterFilter F6 was found to be 0.03 and thus failed the normality test.Tables 2 and 3 give the P-values computed using the Kolmogorov-Smirnov normality test and the OriginPro software statistical tool.

Scale-up Potential

The scale-up filtration system experiments conducted suggest thatit is possible to scale up the number of water filtration systems to

(a) (b)

(c) (d)

(e) (f)

Fig. 3. Comparison of experimental flow rates to model simulation for ceramic water filters: (a) Filter F1; (b) Filter F2; (c) Filter F3; (d) Filter F4;(e) Filter F5; (f) Filter F6

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serve rural communities. Fig. 8 shows the arrangement of theceramic water filters in the multiple filter studies. The cumulativewater discharge over time obtained is plotted in Fig. 9. An averageflow rate of 7 L=h (in the first hour) was found for five ceramicwater filters connected in parallel. The system was able to producea total volume of 23 L of water, with decreasing waterhead, withinthe first 5 h (refer to Fig. 9). Therefore, with an average flow rate of7 L=h and considering the WHO guidance for daily safe drinkingwater of 2 L per day, the volume of water that flowed out of thecommon outlet (at maximum waterhead for 10 continuous h,7 L=h × 10 h ¼ 70 L) can serve a community of 35 people. Such

a system will prove capable of producing safe drinking water foreight different households (four members) for a day. Even with de-creasing waterhead for a continuous 12 h, the average flow rate was4.5 L=h, producing 37 L of water (extrapolation from Fig. 9).Based on the parameters obtained from this study, at maximumwaterhead for 10 h, a community of 525 people could be servedby 15 multiple-filter systems. These 15 systems should be locatedat accessible positions in the community. It is important to charac-terize the individual ceramic water filters of the multiple-filter sys-tem in terms of flow well. Moreover, the number of filters used inthe multiple-filter system can be increased to serve even larger

(a) (b)

(c) (d)

(e) (f)

Fig. 4.Histogram of flow rates (in the first hour) with normal distribution fit for ceramic water filters: (a) Filter F1; (b) Filter F2; (c) Filter F3; (d) FilterF4; (e) Filter F5; (f) Filter F6

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communities. The results obtained from this study, therefore, sug-gest the possibility of having a combined multi-filter system that isconnected to water obtained from a borehole or a polluted source.However, one problem with such multi-filter systems is that if oneceramic water filter unit is cracked or not functioning well, the en-tire water discharged is contaminated. Furthermore, as a way ofreducing the total number of ceramic water filters in multiple-filtersystems, larger ceramic water filters can be produced. These can bedesigned by considering the fracture toughness, pressure-induced

strength, and Darcy’s flow equation. The key condition for oper-ation without fracture would be to ensure that the stress intensityfactor, K, applied to the cracks in the ceramic water filters is lessthan the fracture toughness (KIC).

Implications

The implications of the aforementioned results are quite significant.First, they show that the variations in the flow rates across the water

(a) (b)

(c) (d)

(e) (f)

Fig. 5. Histogram of permeability values (in the first hour) with normal distribution fit for ceramic water filters: (a) Filter F1; (b) Filter F2; (c) FilterF3; (d) Filter F4; (e) Filter F5; (f) Filter F6

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filters are well-characterized by normal distributions during the firsthour of flow. Furthermore, the effective permeability values asso-ciated with the 20 consecutive flows through the filters underinvestigation were well-characterized by normal distributions. Thissuggests that 20 consecutive filter tests can be used to establish thevariability in the initial flow rates and permeabilities of the filters.The initial flow rates are easier to estimate, especially within ruralvillage settings in which ceramic water filters were fabricated andused. However, they do not capture the overall trends in the flowover the period of discharge. Hence, the effective permeabilities are

needed to determine a material parameter that captures the effectiveflow through the porous structures of the filters. However, theserequire more detailed analyses of flow data that are probably wellbeyond the capabilities of most ceramic water filter factory engi-neers. Hence, simple software is needed to enable engineers toestablish the variability in the effective permeabilities forefficient applications in quality control.

In any case, the correlations established between the effectivepermeabilities and the flow rate after the first hour suggest thateither the permeability or flow rate approach may be used to

(a) (b)

(c) (d)

(e) (f)

Fig. 6. Histogram (with normal distribution fit) of mean flow rates for ceramic water filters: (a) Filter F1; (b) Filter F2; (c) Filter F3; (d) Filter F4;(e) Filter F5; (f) Filter F6

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(a) (b)

(c) (d)

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Fig. 7. Histogram (with normal distribution fit) of effective permeabilities for ceramic water filters: (a) Filter F1; (b) Filter F2; (c) Filter F3; (d) FilterF4; (e) Filter F5; (f) Filter F6

Table 2. Normality Test Analysis of Ceramic Water Filters for Flow Rate and Permeability

Filter parameter

Filter F1a Filter F2a Filter F3a Filter F4a Filter F5a Filter F6a

K1b Q1c K2b Q2c K3b Q3c K4b Q4c K5b Q5c K6b Q6c

P-value 0.87 1.00 0.26 0.40 1.00 1.00 0.91 0.94 0.94 0.63 1.00 1.00Normality test PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd

Note: The normality test was verified at an alpha α-value of 0.05.aFilters F1–F6 are porous clay ceramic water filters.bKn (where n is an integer from 1 to 6) are permeability histogram data in the first hour of flow.cQn (where n is an integer from 1 to 6) are flow rate histogram data in the first hour of the flow experiment.dPNT = passed the Kolmogorov-Smirnov normality test.

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characterize and test the filters. Further work is clearly needed tocharacterize the statistical variations in the flow rate parametersat different stages of the filter life. There is also a need to establishthe acceptable variances in filter flow rates and permeabilities

over periods of 2–3 years in which most ceramic water filters areexpected to provide filtered water at rates between approximately1 and 3 L=h. These are clearly the challenges for future work.

Conclusions

This paper presents the results of combined analytical and exper-imental study of flow through frustum-shaped ceramic water filters.The statistical variations in flow rates were found to be well-described by normal distributions. The average flow rate was2.3 L=h for first-hour use at maximum waterhead, with the effec-tive permeabilities for the six filters ranging between 0.44 × 10−14and 2.54 × 10−14 m2. Permeabilities for the first hour of use can bededuced from the Darcy equation. The flow through frustum-shaped ceramic water filters was well-described by Darcy’s equa-tion. The results suggest that reasonable filtered water can beobtained by adopting filter testing methods that involve the useof 20 tests in the establishment of the statistical variations in flowrates and effective permeabilities for effective filter quality control.The average flow rate and effective permeabilities were found to bewell-characterized by the normal distribution. The linear depend-ence of flow rates (in the first hour) on the measured permeabilities

Table 3. Normality Test Analysis of Ceramic Water Filters for Mean Flow Rates and Effective Permeabilities

Filter parameter

Filter F1a Filter F2a Filter F3a Filter F4a Filter F5a Filter F6a

K1b Q1c K2b Q2c K3b Q3c K4b Q4c K5b Q5c K6b Q6c

P-value 0.52 0.72 0.85 0.18 0.61 0.35 0.07 0.20 0.32 0.45 0.07 0.03Normality test PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd PNTd FNTe

Note: The normality test was verified at an alpha α-value of 0.05.aFilters F1–F6 are porous clay ceramic water filters.bKn (where n is an integer from 1 to 6) are permeability histogram data in the first hour of flow.cQn (where n is an integer from 1 to 6) are flow rate histogram data in the first hour of the flow experiment.dPNT = passed the Kolmogorov-Smirnov normality test.eFNT = failed the Kolmogorov-Smirnov normality test.

Fig. 8. Multi-filter scale-up system

Fig. 9. Volume of water discharged for scale-up system

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suggests that filter quality may be assessed using either flow rate orpermeability measurements.

The multiple-filter study also shows that a combination of filtersmay be used to provide drinking water for communities of differentsizes. Since the overall flow rates from multiple-filter systems scalewith the number of filters, the filter sizes and the number of filterscan be scaled to provide adequate drinking water for communities.Furthermore, the multiple filters can be placed in strategic locationswithin rural communities to provide easy access to safe drinkingwater in rural/urban communities in developing countries.

Acknowledgments

Ebenezer Annan’s Ph.D. research at the African University ofScience and Technology (AUST), Abuja, Federal Capital Territory,Nigeria, was sponsored by the Next Generation of Academics inAfrica (NGAA) project at the University of Ghana, Accra-Ghana.The NGAA project is a Carnegie cooperation of the New York–U.S.A. funding project at the University of Ghana, Ghana. Theauthors are also grateful to the World Bank STEP-B Program,the African Centers of Excellence Program, the African Develop-ment Bank, and the Princeton Grand Challenge Program for finan-cial support. The authors would like to thank the staff at Mateng,Nigeria Limited, Abeokuta-Nigeria, for their support in the fabri-cation of ceramic water filters used in this research.

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