Network model for deep bed filtration

Lee, Jysoo; Koplik, Joel

doi:10.1063/1.1359747

Cited by 47 publications

(16 citation statements)

References 22 publications

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“…In order to determine the volume fractions of the different constituents in the porous medium, the system of equations to be solved consists in Equations (10) and (20), together with the boundary condition (13) and the initial conditions (14) and (15). In this system, the unknowns are f and d: The cement volume fraction in the fluid phase is then derived from the definition of d ¼ f c =f: The solid volume fraction increase due to filtration is derived from f according to f s ¼ 1 À f:…”

Section: General Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Modelling of cement suspension flow in granular porous media

Saada¹,

Canou²,

Dormieux³

et al. 2005

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYA theoretical model of cement suspensions flow in granular porous media considering particle filtration is presented in this paper. Two phenomenological laws have been retained for the filtration rate and the intrinsic permeability evolution. A linear evolution with respect to the volume fraction of cement in the grout has been retained for the filtration rate. The intrinsic permeability of the porous medium is looked for in the form of a hyperbolic function of the porosity change. The model depends on two phenomenological parameters only. The equations of this model are solved analytically in the onedimensional case. Besides, a numerical resolution based on the finite element method is also presented. It could be implemented easily in situations where no analytical solution is available. Finally, the predictions of the model are compared to the results of a grout injection test on a long column of sand.

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Section: General Equationsmentioning

confidence: 99%

“…Once d nþ1 is computed, the field f nþ1 is then calculated using (23). Starting from time t ¼ 0 for which the fields are prescribed by the initial conditions (14) and (15), the procedure is repeated for increasing values of t.…”

mentioning

confidence: 99%

Modelling of cement suspension flow in granular porous media

Saada¹,

Canou²,

Dormieux³

et al. 2005

Int. J. Numer. Anal. Meth. Geomech.

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“…Network models can be classified by their topology ranging in complexity from regular lattices to random networks with spatial correlations of pore sizes (e.g., Bryant and Blunt, 1992). Numerous authors have recognized the potential of network models for understanding filtration processes by directly modeling the pore scale flow of particle suspensions (Rege and Fogler, 1988;Imdakm and Sahimi, 1991;Datta and Redner, 1998a, b;Lee and Koplik, 2001). For example, Burganos et al (1992Burganos et al ( , 2001 have developed 2-D and 3-D regular lattice models where each link has a constricted tube geometry and particle infiltration is computed using trajectory analyses (after Tien and Payatakes, 1979).…”

Section: Introductionmentioning

confidence: 99%

Filtration in a Porous Granular Medium: 2. Application of Bubble Model to 1-D Column Experiments

Kim¹,

Whittle

2006

Transp Porous Med

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This paper describes the formulation of a quasi-1-D network model, referred to as the 'bubble model', and its application for simulating particle transport and filtration through a granular filter bed. The model comprises a series of homogeneous sites linked through bundles of cylindrical bonds that represent flow pathways through distributions of pores and pore throats. This model incorporates pore scale processes of particle sieving and infiltration are based on numerical simulations described in a companion paper. The modeling of infiltration is further refined based on detailed experimental observations and measurements of the filtration of a dilute suspension of acrylic particles through a column of glass beads reported by Yoon et al. (2005 Water Resour. Res., to appear). Their data distinguish (a) between the collection of particles on grain surfaces and at grain-tograin contact points, and (b) between particles that are fully entrapped and those that are hindered (temporarily collected) and can later become detached. These effects are represented by two parameters that characterize the probability of attachment and are linked to the surface roughness of the grains; one that describes the minimum particle size that can be fully entrapped, and one that describes the detachment rate. These parameters can be readily calibrated from conventional measurements of effluent concentration and effluent particle size distribution. Detailed comparisons with the data reported by Yoon et al.show that the proposed bubble model is able to achieve reliable predictions of the spatial distribution of particles within the filter bed following phases of particle injection and washing.

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“…in networks with different geometries including bundle of parallel tubes [8], square networks [14,16,23], triangular networks [3,27], cubic networks [2,17,33], bubble models [6,22], and the so-called three-dimensional physically representative networks [1,34].…”

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confidence: 99%

Clogging of Multigraphs as Toy Models of Filters

Goldsztein¹

2009

SIAM J. Appl. Math.

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Abstract. In this paper we model filters as networks of channels. As suspension (fluid with particles) flows through the filter, particles are trapped and clog channels. We assume there is no flow through clogged channels. The filter becomes impermeable after not all, but only a portion, of the channels clog. In this paper we compute an upper bound on the number of channels that clog. This bound is a function of properties of the network. Our results provide an understanding of the relationship between the filter pore space geometry and the filter efficiency. Fluid suspensions, or suspensions for short, are fluids with small solid particles in them. As suspension flows through a permeable porous material, some particles are trapped within the material. In fact, the function of the filters we consider in this paper is to clean suspensions by capturing particles.The removal of particles from fluid suspensions is of importance in a wide range of industrial and technological applications such as wastewater treatment [20], drinking water treatment, and other filtration processes [4,35]. Our studies are motivated by the filters used in the process known as deep bed filtration. In this process, as suspension flows through a filter, particles penetrate the filter and deposit at various depths [36]. As a result, the fluid suspension is cleaner when it exits the filter (i.e., the suspension exits the filter with fewer solid particles than it originally had when it entered the filter).Mathematical models for studying transport in porous media can be classified as either macroscale models [5,15,24,25,26,28,36] or pore-scale models (also known as microscale models) [9,21,31]. Macroscale models are those that model phenomena occurring at length scales much larger than the pore dimensions. On the other hand, pore-scale models, as the name suggests, model phenomena occurring at the length scale of the size of the pores. Within the pore-scale models, the class of network models is very popular. Network models are a class of models that represent the pore space in an idealized fashion, which can be channels, or pore bodies connected by pore throats. Our work belongs to the class of network models.Network models for studying transport in porous media were introduced by Fatt [10,11,12]. Donaldson [8] was the first one to use networks to study particle transport within porous media. The clogging of particles has been studied

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Network model for deep bed filtration

Cited by 47 publications

References 22 publications

Modelling of cement suspension flow in granular porous media

Modelling of cement suspension flow in granular porous media

Filtration in a Porous Granular Medium: 2. Application of Bubble Model to 1-D Column Experiments

Clogging of Multigraphs as Toy Models of Filters

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