PARTICLE TRANSPORT AND DEPOSITION IN POROUS STRUCTURES: EFFECTS OF PARTICLE PROPERTIES, POROSITY AND REYNOLDS NUMBER

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1 ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA PARTICLE TRANSPORT AND DEPOSITION IN POROUS STRUCTURES: EFFECTS OF PARTICLE PROPERTIES, POROSITY AND REYNOLDS NUMBER S. Kuz*, J. Pinela*, A. H. Reis* +, A. F. Miguel*, M. Aydin** * Évoa Geophysics Cente, Rua Romão Ramalho, 59, Évoa, Potugal ** Dept Mech. Engineeing, Istanbul Technical Univesity, Gumussuyu, Istanbul, Tukey + ah@uevoa.pt phone: fax: Keywods: paticle deposition, poous stuctue, pemeability Keywods: paticle deposition, pemeability, poosity, ceeping flow Abstact Since expeiments ae expensive and often difficult to pefom eliable computational fluid dynamics (CFD) models save time and money when applied to tanspot and deposition of aeosol paticles. In this wok, we simulate paticle tanspot and deposition in poous stuctues with diffeent poosity. The esulting ai-flow pattens as well as paticle tanspot and deposition ae analyzed fo diffeent inlet flows and paticle with diffeent popeties (i.e., density and diamete). We compute paticle tajectoies and the deposition fo diffeent conditions. In addition, the loss of pemeability due to deposition is evaluated. 1 Intoduction Thee is a geat deal of inteest in paticle tanspot and deposition in poous media due to thei common occuence in many fields of science and technology. Examples included ai filtation [1-3], tanspot of pollutants, bacteia and viuses in goundwate [4,5], paticle migation with poe blocking in both petoleum and geothemal esevois [6,7] etc. A diect consequence of deposition is the eduction of poosity (and pemeability) of the poous media. This eduction is dependent on seveal system paametes, such as the fluid supeficial velocity, the paticle sizes and the geometic chaacteistics of the poous media [1-3]. Geneally, the tanspot and deposition of paticles in poous media ae studied based on expeiments and numeical simulations. Expeiments ae especially suited to obtain the amount of paticles deposited but do not eveal details about deposition pattens. Computational fluid dynamics (CFD) simulation is a useful and non-invasive tool of obtaining paticle deposition and detailed paticle deposition pattens. Numeical simulations ae usually handled by Euleian o Lagangian appoaches. In Euleian appoach, paticle tanspot is govened by the convective-dispesive equation [1]. In Lagangian appoach, the fluid flow field is fist calculated and tajectoy of an individual paticle eleased in the flow is descibed accoding to the paticle equation of motion [8]. In the pesent study, a numeical analysis has been conducted to chaacteize the paticle tanspot and deposition in poous stuctues having diffeent poosities. We exploe the effect of paticle chaacteistics and flow field on the deposition. Ou effots have focused on the tanspot of solid paticles and wate doplets with diametes anging fom 1 and 10 µm. This is justified by the fact that in a ecent epot issued by the Wold Health Oganisation [9] is povided a clea summay of the existing medical evidence linking seious health poblems and fatalities to exposues especially to sub 10 µm diamete paticles. Numeical analyses epoted in this pape apply to ceeping flow, and paticles ae assumed not to affect the flow fields. Flow fields wee solved in an Euleian gid system and paticle 1

2 S. Kuz, J. Pinela, A. H. Reis, A. F. Miguel, M. Aydin tajectoies wee calculated by the Lagangian method. 2 Numeical method and model system The geometic model is shown in Fig.1. It consists of a two-dimensional poous stuctue fomed by egulaly placed ovelapping solid cicles with constant adius. These cicles having adius between 1.1 and 9.4 mm ae used fo decoating the undelying lattices fo pedictions of pemeability as a function of poosity. Details ae pesented in [10]. whee u f is the fluid velocity, t is the time and, m and u ae the mass and velocity of the paticle, espectively. Fig. 1. Geomety of poous stuctue 2.1 Flow field and paticle tacking The numeical solution of fluid flow equations and paticle tanspot equation ae caied out using a commecial finite-volume-based pogam, FLUENT [11]. Steady state flow fields ae solved in an Euleian gid system and paticle tajectoies ae calculated by the Lagangian method [10]. The non-slip bounday conditions ae set along the solid cicles with constant adius (Fig. 1). The developed velocity pofile is pescibed at the inlet while outflow bounday conditions ae set at the exit. The cell size of the gid whee high gadients of velocity ae expected to occu has been vaied to ensue a gid independent solution. Once the steady flow field is obtained, paticle tajectoies ae calculated by integating the equation of paticle motion with espect to time. The govening equation fo paticle motion is m ( du / dt) f ( u u ) + F + F ( t ) f = (1) s b Fig. 2 Contous of velocity in the poous stuctue (Re=0.1): poosity 0.4, poosity 0.9 Eq. (1) epesents a foce balance on the paticle, whee m( du / dt) (left-hand side) is the esultant of foces acting on a paticle (ighthand side). The fist tem on the ight-hand side epesents the viscous dag foce due to the motion of the paticle elative to the suounding fluid. The fiction coefficient f = 3πµ d / Cs is assumed to be govened by Stoke s law coected by the Cunningham facto. The second tem is a lift foce due to shea. Finally, the thid tem denotes a andom foce F ( t ) aising fom Bownian collisions. 2

3 PARTICLE TRANSPORT AND DEPOSITION IN POROUS STRUCTURES: EFFECTS OF PARTICLE PROPERTIES, POROSITY AND REYNOLDS NUMBER Paticle paths ae obtained by integating the govening equation. The integation time step is computed based on a specified length scale (L) and the velocity of the paticle and of the continuous phase as L t = u + u f. Integation with espect to time of Eq. 1 yields the velocity of the paticle at each point along the tajectoy, with the tajectoy itself pedicted by d dt u = (2) Paticles ae assumed to deposit when the cente of the paticle eaches a distance fom the wall coesponding to the paticle adius. simulation is pefomed fo Reynolds numbes anging fom and Results and discussion In ode to employ the flow simulation model as a pedictive tool fo paticle deposition, the esults of ou simulations have been compaed with studies available in liteatue. Velocity field within the poous stuctue, fo poosities 0.4 and 0.9, is epesented in Fig. 2 as a contou map. In both situations, these obtained velocity contous ae qualitatively consistent with the esults found in the liteatue [12]. Fig. 3 Typical tajectoies of cabon black and wate doplets (Re=0.01; paticle size 1 µm; poosity 0.4) Cabon black (ρ p =2250 Kg/m 3 ) and wate doplets (ρ p =0.55 kg/m 3 ) paticles of sizes 0.1, 1 and 10 µm ae consideed. The numeical Fig. 4 Typical tajectoies of cabon black paticles (Re=0.2; paticle size 1 µm): poosity 0.4, poosity 0.9 The tajectoies of paticles acoss the poous stuctue ae shown in Figs. 3 to 5. These figues show that the paticle tajectoies ae diectly influenced by: flow field, poosity of poous stuctue, size and density of the paticles. 3

4 S. Kuz, J. Pinela, A. H. Reis, A. F. Miguel, M. Aydin Based on the paticles tajectoies we ae able to obtain the amount of paticles deposited within the poous stuctue. Pecentages of deposited paticles ae documented in Figs. 6 and 7. Fig. 6 Pecentage of wate doplets deposited inside the poous stuctue fo poosities of 0.4 and 0.6. Fig. 5 Typical tajectoies of wate doplets (Re=0.2; poosity 0.4)): paticle size 1 µm, paticle size 10 µm. A compaison between these figues indicates that deposition within the poous stuctue is mainly detemined by the size and density of the paticles. Incease in size and density inceases the chance of paticles to get captued inside the poous stuctue. Figs 6 and 7 also show that an incease in the Reynolds numbe favous the pecentage of paticles escaped though the poous stuctue (i.e., deposition is moe likely to occu fo vey small Reynolds numbes). Besides, the poosity of the stuctue also plays an impotant ole in the amount of paticles deposited. Decease in poosity inceases the chance of paticles to get deposited in the poous stuctue. Fig. 7 Pecentage of cabon black paticles deposited inside the poous stuctue fo poosities of 0.4 and 0.9. Fo a boad ange of applications (e.g., filteing), the most impotant tanspot popety of poous stuctues is pemeability [1-3]. The vaiation of the filte pemeability with the poosity is shown in Fig. 8. As expected, these plots show that deposition of lage paticles has a stong influence on the pemeability. This influence is moe impotant fo stuctues having low poosity. 4

5 PARTICLE TRANSPORT AND DEPOSITION IN POROUS STRUCTURES: EFFECTS OF PARTICLE PROPERTIES, POROSITY AND REYNOLDS NUMBER K / K _ w i t h o u t p a t i c l e s K/K_without paticles Poosity Poosity Fig. 8 Ratio of the pemeability of a poous stuctue loaded with cabon black paticles to unloaded (clean) vesus the poosity ( 1µm; 10 µm) 4 Conclusion We have simulated paticle tanspot and deposition in poous stuctues with diffeent poosities. The effects of paticle diamete, density and velocity of fluid wee analyzed. The deposition of heavie and lage size paticles was found to be consideable in all conditions studied. On the othe hand, lighte paticles wee found to deposit most at lowe Reynolds numbe and in the poous stuctues of small poosity. Finally, the ole of deposition on the vaiation of the pemeability of the poous stuctue was examined. The loss of pemeability is shown to be vey sensitive to the paticle popeties. Acknowledgments The eseach epoted in this pape was suppoted by the Foundation fo Science and Technology (FCT) unde gant POCTI/EME/59909/2004. Refeences [1] Bejan A, Dince I, Loente S, Miguel A F and Reis A H. Poous and Complex Flow Stuctues in Moden Technologies, Spinge-Velag, New Yok, 2004 [2] Miguel A F. Poous Media and Filtation. In: Emeging Technologies and Techniques in Poous Media, Kluwe Academic Publishes, New Yok, pp , 2004 [3] Reis A H, Miguel A F. Analysis of Filte Pefomance as function of Paticle Diamete, Filte Intenal Suface and Filte Poe Size Distibution. In: Applications of Poous Media. CGE, Evoa, pp , 2004 [4] Lo I M C, Law W K W, Shen H M. Risk assessment using stochastic modeling of pollutant tanspot in landfill clay lines, Wate Science and Technology, Vol. 39, pp , 1999 [5] Schijven J F, Hassanizadeh S M. Removal of viuses by soil passage: oveview of modelling, pocesses and paametes. Citical Reviews in Envionmental Science and Technology, Vol. 30, pp , 2000 [6] Maini B, Wassmuth F, Schamm L L. Fines migation in petoleum esevois. Suspensions: Fundamentals and applications in the petoleum industy. ACS Advances in Chemisty Seies, Vol. 251, pp , 1996 [7] Kühn M, Venoux J F, Kellne T, Isenbeck-Schöote M., Schulz H D. Onsite expeimental simulation of bine injection into a clastic esevoi as applied to geothemal exploitation in Gemany. Applied Geochemisty, Vol. 13, pp , 1998 [8] Uijttewaal W S J, Oliemans R V A. Paticle dispesion and deposition in diect numeical and lage eddy simulations of vetical pipe flows, Phys. Fluids, Vol. 8, pp , 1996 [9] Wold Health Oganization (WHO) Health isk of paticulate matte fom long ange tansbounday ai pollution: peliminay assessment. Wold Health Oganization Regional Office fo Euope, Bilthoven Division [10] Pinela J., Kuz S, Aydin M, Miguel A F, Reis A H. Pemeability-poosity elationship assessment by 2-D numeical simulation, ISTP-16, Pague, 2005 (submitted) [11] FLUENT 6 Use s Guide, Fluent Inc.,

6 S. Kuz, J. Pinela, A. H. Reis, A. F. Miguel, M. Aydin [12] Chouikh R, Guizani A, Mafilej M. Numeical study of lamina natual convection flow aound an aay of two hoizontal isothemal cylindes, Int. Comm. Heat Mass Tansfe, Vol. 26, No, 3, pp ,