Fig 4 - uploaded by You-Im Chang
Content may be subject to copyright.
Source publication
The effect of different interaction energy curves of DLVO theory on the permeability reduction in a filter bed is investigated by using the Brownian dynamics simulation method and the modified square network model to track the individual particles movement through the filter bed. When energy barrier exists and both particle and pore size distributi...
Context in source publication
Context 1
... overall description of the simulation procedure is presented in the algorithm shown in Fig. 4, and the values of corresponding parameters are given in Table 2. Simulations are performed on a two-dimensional network with N L =70×70, and the influent flow rate is kept at constant. The estimation of the permeability ratio K/K 0 based on the Brownian trajectory analysis and the stochastic simulation procedure for different types of ...
Similar publications
The track of individual particles moving through a filter bed is simulated by applying the Brownian dynamics simulation method and the modified square network model. The effect of the Raleigh-type size distribution of particles and pores on the permeability reduction of porous media is also investigated. We find that the pore size distribution of p...
Citations
... Straining usually occurs when pore throats are significantly small to allow the passing of a given colloid particle. Recent findings have suggested that the rate of colloid straining within saturated porous media is sensitive to the size and shape of colloid particle, the ratio of particle diameter to sand-grain diameter, pore-scale hydrodynamics and pore water chemistry, and the shape and surface roughness of the solid matrix [18][19][20]. ...
... Advection-dispersion theory has frequently been used to describe the straining of spherical and non-spherical colloidal particles and non-uniform colloid mixtures in saturated porous media. The mathematical form of this model consists of the two following equations [20]: ...
... As a result, the particle capture probability is decreased and the time for the network to be fully clogged is delayed. The trends of the simulated results are consistent with those of the experimental data ( Fig. 1) reported by Alexis A. Porubcan [20]. Pore size distribution parameter σb is lowly sensitive to Ce/C0 and pressure drop. ...
A straining-dominant filtration model based on a 2D square network is proposed. In this model, the colloid particle can be captured in a node only. The effects of network parameters (node size distribution parameters μn and σn and pore throat size distribution parameters μn and σb), particle concentration of influent (C0), and particle size distribution parameters (μr and σr) on straining-dominant deep bed filtration simulation are investigated. Four parameters (C0, μn, μb, and μr) significantly affect the simulated pressure drop and the normalized particle concentrations of effluent (Ce/C0). The increase in parameters μn and μb decreases pressure drop and increases Ce/C0, whereas the increase in parameters μr and C0 increases pressure drop and decreases Ce/C0. With the experimental condition and a 5% variation in parameters, parameters σn, σb, and σr are lowly sensitive to Ce/C0 and pressure drop. When the variation in σr is sufficiently large, the model simulation is significantly affected. The simulated normalized effluent concentrations and pressure drop are consistent with the experimental data under appropriate simulated conditions.
... are given in Figures 4 and 5 The rise of temperature enhances the flow turbulence in the inhomogeneous flow field in the pores of the porous medium. Also, the thermodynamic driving force increases with increasing temperature by the stochastic Brownian motion behavior of SPs, and the straining deposition becomes more prominent (Chang et al., 2004). The higher the temperature is, the higher the collision probability will be, and the longer the transport paths of particles become because of the detours in the porous medium. ...
... e., the repulsive electrical double layer forces) by the DLVO theory (García-García et al., 2006;Rosenbrand et al., 2012;Rosenbrand et al., 2015) and enhances the collisions between particles and between the particles and the surface of porous matrix, which finally reduces the size exclusion effect caused by preferential streams. The rise of temperature can also accelerate the irregular movement of particles by the Brownian motion (Chang et al., 2004), and prolong their transport paths and consequently reduce the migration velocity of SPs ( Figure 7a). There is a negative correlation between u/u 0 and T within the investigated temperature range from 15°C to 55°C, although the evolution process is somewhat different for low water velocities (e.g., v = 0.066 cm/s). ...
The main purpose of this study is to experimentally investigate the effect of temperature on the seepage transport of suspended particles (SP) with a median diameter of 10 − 47 µm in a porous medium for various seepage velocities. The results show that the rise of temperature accelerates the irregular movements of SPs in the porous medium and reduces their migration velocity. As a result, the pore volume corresponding to the peak value of the breakthrough curves is apparently delayed, and the peak value in the effluent is decreased. The migration velocity of SPs decreases with increasing particle size, regardless of the Darcy velocity and temperature. The longitudinal dispersivity of SPs decreases slightly with increasing temperature and then remains almost unchanged. Larger particles experience more irregular movements induced by the limit of pore size, which leads to a larger dispersivity. The deposition coefficient increases with increasing temperature, especially in the case of a high seepage velocity, and then tends to be stable. The deposition coefficient for large-sized particles is higher than that for small-sized particles, which can be attributed to the restriction of large-sized particles by the narrow pores in the porous medium. The recovery rate decreases slightly with the increase of temperature until a critical value is reached, beyond which it remains almost unchanged. In summary, temperature is a significant factor affecting the transport and deposition of SPs in the porous medium, and the transport parameters such as particle velocity, dispersivity and deposition coefficient.
... In order to describe the effect of spatial distribution of porosity on the particle or droplet behaviour along the porous structure the network model has been applied extensively for many years [8,15,7,2,4,14]. The complex filter can be represented by 2-D network model [21,22,13]. ...
... There are many types of network models such as square, hexagonal, triangular and random ones, which differ in the pattern of connected channels. In this study we choose a regular square lattice rotated around 45°to the flow axis [4]. This rotation makes the channels not to be aligned with the direction of the gravity force, which would enhance deposition rates [3]. ...
... The flow of fluid is maintained only through the cylindrical channels, and is described by Hagen-Poiseuille's law, Eq. (2). This equation can be used assuming that the flow in each channel is laminar and Reynolds number is less than unity [4,13]. Eq. (2) is presented in the following form ...
... Research on particle transport in porous media has been active since the 1960s (Gao, 2008). To understand the mechanisms of the formation damage process and its variation features under different conditions, multiple studies have been conducted using experiments (Barkman and Davidson, 1972;Todd et al., 1900;AI-Abduwani et al., 2003;Wong and Mettananda, 2010) and simulations (Sharma and Yortsos, 1987;Mdakm and Sahimi, 1991;Jalel, 1999;Siqueira and Petrobras, 2003;Chang and Chen, 2004;Civan, 2007). According to previous experimental work, a higher particle concentration, a larger particle size and a lower fluid velocity can result in much more severe impairment (Gao, 2007). ...
... Nomenclature σ unit particle retention concentration, dimensionless c particle concentration in suspension, dimensionless λ filtration coefficient, dimensionless δ, γ Weibull parameters, dimensionless x random number between 0 and 1, dimensionless α aspect ratio, dimensionless n c coordination number, dimensionless L length of pores and throats, m G shape factor of pore-throats, dimensionless P pressure value of a certain pore node, Pa μ viscosity of the fluid in network model, mPa s C particle concentration in injected water, dimensionless A cross-sectional area of the pores and throats, m 2 r p particle radius, m F b buoyancy forces that act on the particles, N F d drag forces that act on the particles, N V P volume of the particle, m 3 ρ density of particles or fluids, kg/m 3 D c drag coefficient, dimensionless u velocity of fluids or particles, m/s r max maximum inscribed radius value of pore-throats, m r min minimum inscribed radius value of pore-throats, m Subscripts p particle f fluid Generally, the pore-throat radius distribution follows certain types of distribution functions based on an analysis of the mercury intrusive experiment. Distribution functions such as the log-normal distribution, truncated Weibull distribution (Valvatne, 2004), and Raleigh distribution (Chang and Chen, 2004) have been used by researchers for constructing the network model. In our model, the truncated Weibull function is applied for assigning the porethroat radius, which can be written as ...
... Once the particle deposits in the pores or throats of the network model, the pressure drop will become larger, and the extra pressure drop can be estimated by applying the equation proposed by Happel and Brenner (Happel and Brenner, 1973;Chang and Chen, 2004 ...
... abbreviated as 2-D below). In our previous papers [9,10], we adopted the Brownian dynamic simulation method of solving Langevin type equations [11], and assumed that the porous media of the filter bed is unconsolidated, we had successfully tracked the motion of individual particles with Brownian motion behavior as they move through the filter bed, by using the 2-D models of the modified square network and the triangular network, respectively. Through this process, the temporal variations of the permeability reduction and the effluent concentration of particles, caused either by the straining or by the direct deposition of particles on the pore walls, were determined. ...
... Similar to our previous papers [9,10], with the consideration of the Brownian diffusion force in determining particle trajectories, the method of Brownian dynamics simulation is adopted in the present study. Assume that the distribution of the initial position (r in , h in ) of each particle is assigned by the random number generator in the flow field simulation (see Fig. 2). ...
... When the particle's Brownian motion behavior is not considered, termed as non-Brownian particle in the present paper, this Brownian diffusion force is excluded in Eq. (1). From those trajectories of influent particles in the network, the permeability reduction ratio K/K 0 in a percolation history can be determined by the method outlined in our previous papers [9,10]. In order to express the extent of permeability reduction as percolation proceeds, we use the permeability ratio K/K 0 as the function of the pore volumes of fluid injected into the filter bed. ...
This paper employs the Brownian dynamics simulation method to compare the particle breakthrough history and permeability reduction of porous media between Voronoi and regular triangular networks of the same coordination number. For the case of transporting Brownian particles through these two networks, it is found that their breakthrough concentrations are of the same value, but have different breakthrough moments and permeability reduction rates under either favorable or unfavorable deposition conditions. Same results are also obtained for the non-Brownian particles.
... This approach previously was used to simulate the filtration of the solid particle suspension during the flow through the porous media filters. For specific details, the reader may see the works (Payatakes, 1973;Burganos et al., 1991Burganos et al., , 1995Burganos et al., , 2001Chang et al., 2003Chang et al., , 2004. The shape of the porous coalescer structure is strictly limited to a 2D approach in the present work due to its suitability for CFD calculations. ...
Fibrous-bed coalescers are frequently used for separation of the suspension. The effectiveness of the process depends on the flow condition through the packed bed and its structure. The population balance equation was used for analysis of the evolution of the distribution of droplet diameter in the raw suspension due to the coalescence and breakage of droplets passing different sequences of the coalescer structures distinguished by the packing density of fibers in the layers of the coalescers. The results of calculations show the values of particular parameters, like droplet concentration, the mean diameter of the droplet and droplet size distribution in the population as the results of the process. The proposed model can be useful for the designing of the coalescer structures for their particular applications.
... However, for sand single media filter ( Figure 6), it is observed that the peak is slightly lower or closer to the surface of filter. When both the particle and pore size distribution are of the Raleigh type, it is reported that the straining of the particles with Brownian motion behavior at the small pores were enhanced, thus resulted in higher permeability reduction [9,10]. This suggests that most of the filtration process took place on the shallow surface of the filter. ...
Penurasan merupakan unit operasi utama bagi loji olahan air. Media penuras yang lazim digunakan adalah berbentuk butiran seperti pasir, antrasit, arang, magnetik, garnit dan tempurung kelapa. Prestasi penuras media berbentuk butiran telah terbukti berkesan. Walau bagaimanapun, keperluan media penuras alternatif yang kos efektif masih diperlukan memandangkan kos operasi dan kos pengeluaran air sentiasa meningkat dari semasa ke semasa. Dewasa ini kajian telahpun dijalankan terhadap potensi butiran arang tempurung kelapa sawit sebagai media penuras. Bahan ini merupakan sisa buangan pepejal yang terdapat dengan banyaknya hasil dari pemprosesan industri minyak sawit. Dalam kajian ini, pasir dan butiran arang tempurung kelapa sawit (BOPS) telah digunakan sebagai penuras satu-media dan penuras dua-media pada beberapa saiz efektif, Es (iaitu Es 0.4 dan 0.6 untuk pasir, Es 1.0 dan 2.0 untuk BOPS) dan kadar alir (iaitu 10 dan 15 m 3 /m 2 .jam). Prestasi penurasan adalah dipengaruhi oleh ketebalan penuras, kualiti air influen, kadar alir air dan saiz efektif media penuras. Keputusan menunjukkan bahawa penuras mampu menghasilkan kualiti air yang tinggi ( i.e. Es of 0.4 and 0.6 for sand, Es of 1.0 and 2.0 for BOPS) and flow rates ( i.e. 10 and 15 m 3 /m 2 .hr). The performances of filter are influenced by filter bed depth, influent water quality, flow rate and effective size. Result suggests that all the filters are capable of producing water with acceptable turbidity unit ( i.e. running time of BOPS/sand is four to nine times greater than single media filter).
Key words: Single media filter; dual media filter; sand; BOPS; turbidity; rapid filtration
... But, the Brownian motion behavior of microsized particles was not included in their models. We studied the Brownian particle's movement through porous media in a filter bed by using the Brownian dynamic simulation method [12][13][14] and the constricted tube model [15,16] to represent the pore geometry by 2-D network model (i.e., the Langevin-type approach). The temporal variations of the effluent concentrations and the pressure drop caused either by the straining or by the direct adhesion of colloidal particles onto the pore walls were successfully determined. ...
... The temporal variations of the effluent concentrations and the pressure drop caused either by the straining or by the direct adhesion of colloidal particles onto the pore walls were successfully determined. More importantly, when comparing with the available filter coefficient experimental data, our network model of using the Brownian dynamic simulation method yields less discrepancy than that of the convective diffusion model, especially under the unfavorable deposition conditions (i.e., in the presence of the electrostatic repulsive force of the DLVO theory) [13,14]. ...
... The details of the flow field distributions can be found in the reference work of Profs. Ramarao and Tien [22] and in our previous papers [13,23]. An illustrative example of the flow field in SCT at N Re =1.0 can be found in the supplement of the present paper. ...
From the viewpoint of colloidal transport phenomena, the individual drug particle’s movement through the tumor is studied
by using the square network model. The effects of drug concentration, arterial pressure, and interstitial pressure of the
tumor on the concentration breakthrough moment of drug particles are investigated by using the Brownian dynamics simulation
method. From the simulation results, we find that the present network model and the Brownian dynamics simulation method can
successfully analysis the therapeutic ranges achieved by the drug particles in the tumor at different magnitudes of the drug
concentration, the inlet blood velocity, the arterial pressures, and the interstitial pressures of the tumor. Because of the
high interstitial fluid pressure, the drug particles can only reach the peripheral region and cannot penetrate inside the
target tumor efficiently, and the decreased interstitial fluid pressure will lead more drug particles to penetrate inside
the tumor.
KeywordsDrug delivery–Brownian particle–Network model–Tumor
... Since the triangular network model of using SCT (sinusoidal constricted tube) gives the best accuracy on predicting the dynamic behavior of granular filtration when comparing with the available experimental data in our previous article, 5 hence here we use the triangular network to represent the porous media of the filter, and adopt the Brownian dynamic simulation method to track the individual particles as they move through the network. 9 All pores in the network and particles in the influent are assumed to be of the Raleigh type size distribution. 10 Then, the pore size distribution can be assigned randomly to the bonds in the network as follows, and 0 \ a i \ 1 where the random number a i can be generated by using the standard computer software of IMSL, 11 r f and r mean are the radius of filter grains and the mean radius of pores, respectively. ...
... where the values of B and C are dependent on the geometry of the collector, and their evaluation method can be found in chapter 5.8 of ref. 2. From those trajectories of influent particles in the network, the temporal variations of the effluent concentrations and the pressure drop in a filtration history can be obtained, 9 and therefore the values of the initial collection efficiency g 0 and the filter coefficient a shown in Eq. 1 can be determined consequently. ...
A new correlation equation for predicting the filter coefficient under unfavorable deposition conditions is presented. By adopting the triangular network model of using the Brownian dynamic simulation method, as the sum of four individual deposition mechanisms, e.g., the Brownian diffusion, the DLVO interactions, the gravitational force, and the interception, the correlation equation is obtained by regressing against a broad range of parameter values governing particle deposition in deep bed filtration. The new correlation equation is able to describe previous experimental results well, especially for those submicro particles with significant Brownian motion behavior. © 2008 American Institute of Chemical Engineers AIChE J, 2008
... The permeability reduction rate along the filter bed is dependent on several system parameters which have been the subject of numerous studies. The parameters are the fluid superficial velocity, the grain and particle sizes (Ison and Ives, 1969;Herzig et al., 1970;Yao et al., 1971), the geometry of collector (Tien and Payatakes, 1979), the interaction forces between particles and collector surfaces (Kim and Rajagopalan, 1982;Chang and Whang, 1998), and the pore size distribution (Sharma and Yortsos, 1987;Rege and Fogler, 1988;Imdakm and Sahimi, 1991;Chang et al., 2004). ...
... In our previous paper (Chang et al., 2004), with the adoption of the Brownian dynamic simulation method and the constricted tube model representing the geometry of porous media (see Fig. 1), we had successfully applied the twodimensional modified square network model to track the individual particles with Brownian motion behavior as they move through the filter bed (i.e., the Langevin-type approach). From this, which was caused either by the straining or by the direct deposition of particles on the pore walls, the temporal variations of the permeability reduction and the pressure drop were successfully determined. ...
... In the present study, we use the modified two-dimensional square network to represent the porous media of the filter, and adopt the Brownian dynamic simulation method to track the individual particles as they move through the network (Chang et al., 2004). All pores in the network and particles in the influent are assumed to be with the Raleigh-type size distribution (Sharma and Yortsos, 1987). ...
The track of individual particles moving through a filter bed is simulated by applying the Brownian dynamics simulation method and the modified square network model. The effect of the Raleigh-type size distribution of particles and pores on the permeability reduction of porous media is also investigated. We find that the pore size distribution of porous media has a more profound effect on the reducing of the permeability ratio than that of the particle size distribution especially at the initial period of filtration. Straining is the main mechanism to reduce the permeability at the initial period of injection for the case of Raleigh distribution of the pore size, and vice versa for the case of unique size value where the direct deposition mechanism becomes dominant.
