Exact solutions for two-phase colloidal-suspension transport in porous media

Borazjani, Sara; Bedrikovetsky, Pavel

doi:10.1016/j.apm.2016.12.023

Cited by 31 publications

(9 citation statements)

References 40 publications

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“…The developed averaging approach can be applied for two‐phase suspension‐colloidal‐nanotransport in porous media (Borazjani & Bedrikovetsky, ). For particles suspended in aqueous phase and attached to the surface, the splitting method separating two‐phase multicomponent system into one‐phase solute system and one equation for phase saturation yields one‐phase solute system (, ) (Borazjani et al, ).…”

Section: Discussionmentioning

confidence: 99%

Exact Upscaling for Transport of Size‐Distributed Colloids

Bedrikovetsky

Osipov

Кузьмина

et al. 2019

Water Resources Research

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The article investigates one-dimensional (1-D) suspension-colloidal transport of size-distributed particles with particle attachment. A population balance approach is presented for computing the particle transport and capture by porous media. The occupied area of each attached particle is particle size-dependent. The main model assumption is the retention rate dependency of the overall vacancy concentration for all particle sizes. For the first time, we derive an exact averaging (upscaling) procedure resulting in a closed system of large-scale equations for average concentrations of suspended and retained particles and of occupied rock surface area. The resulting large-scale 3 × 3 system significantly differs from the traditional 2 × 2 deep bed filtration model. However, the traditional model becomes a particular case that corresponds to an equal occupied area for all particles. The averaging yields the appearance of two empirical suspension and site occupation functions, which govern the kinetics of particle retention and site occupation, respectively. One-dimensional flow problems for the averaged equations are essentially nonlinear. However, they allow for exact solutions. We derive novel exact solutions for three 1-D problems: continuous injection of particulate colloidal suspension, injection of colloidal suspension bank with particle-free chase drive, and fines migration induced by high-rate flows. The analytical model for continuous injection closely matches three series of laboratory tests on nanofluid transport.

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Section: Discussionmentioning

confidence: 99%

Exact Upscaling for Transport of Size‐Distributed Colloids

Bedrikovetsky

Osipov

Кузьмина

et al. 2019

Water Resources Research

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“… . The solution of the filtration problem (18)-(19) is compared with the numerical solutions of problems (1)- (2) and (9), obtained by the finite difference method with the second order approximation by integrating over a rectangular grid cell…”

Section: Discussionmentioning

confidence: 99%

“…There are various filtration models of monodisperse and polydisperse suspensions [7], [8]. In a number of important special cases, it is possible to obtain an exact or asymptotic solution of the problem [9], [10]. In the general case the model have no explicit analitic solution and numerical methods have to be used.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of filtration in porous rock

Safina

2019

E3S Web Conf.

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The filtration problem is one of the most relevant in the design of retaining hydraulic structures, water supply channels, drainage systems, in the drainage of the soil foundation, etc. Construction of transport tunnels and underground structures requires careful study of the soil properties and special work to prevent dangerous geological processes. The model of particle transport in the porous rock, which is based on the mechanical-geometric interaction of particles with a porous medium, is considered in the paper. The suspension particles pass freely through large pores and get stuck in small pores. The deposit concentration increases, the porosity and the permissible flow of particles through large pores changes. The model of one-dimensional filtration of a monodisperse suspension in a porous medium with variable porosity and fractional flow through accessible pores is determined by the quasi-linear equation of mass balance of suspended and retained particles and the kinetic equation of deposit growth. This complex system of differential equations has no explicit analytical solution. An equivalent differential equation is used in the paper. The solution of this equation by the characteristics method yields a system of integral equations. Integration of the resulting equations leads to a cumbersome system of transcendental equations, which has no explicit solution. The system is solved numerically at the nodes of a rectangular grid. All calculations are performed for non-linear filtration coefficients obtained experimentally. It is shown that the solution of the transcendental system of equations and the numerical solution of the original hyperbolic system of partial differential equations by the finite difference method are very close. The obtained solution can be used to analyze the results of laboratory research and to optimize the grout composition pumped into the porous soil.

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“…4 partial deposit concentrations (0, ); 1, 2 i S t i  tend to the maximum limit values with increasing time. These limits are the roots of the filtration coefficients (14). A new nonlinear model of long-term deep bed filtration with variable porosity and permeability and several pore blocking mechanisms is considered, including pore clogging by single particles and arched bridges of different configurations.…”

Section: Numerical Calculationmentioning

confidence: 99%

“…For some filtration models, exact solutions are obtained [13][14][15], in the absence of a global exact solution, asymptotics are constructed [16][17][18], if there are no analytical solutions, numerical methods are used [19,20].…”

Section: Introductionmentioning

confidence: 99%

Deep bed filtration with multiple pore-blocking mechanisms

Кузьмина

Osipov

2018

MATEC Web Conf.

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A one-dimensional model for the deep bed filtration of a monodisperse suspension in a porous medium with variable porosity and permeability and multiple pore-blocking mechanisms is considered. It is assumed that the small pores are clogged by separate particles; pores of medium size, exceeding the diameter of the particles, can be blocked by arched bridges, forming stable structures at the pore throats. These pore-blocking mechanisms - size-exclusion and different types of bridging act simultaneously. Exact solutions are obtained for constant coefficients, on the concentrations front and at the porous medium inlet.

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Exact solutions for two-phase colloidal-suspension transport in porous media

Cited by 31 publications

References 40 publications

Exact Upscaling for Transport of Size‐Distributed Colloids

Exact Upscaling for Transport of Size‐Distributed Colloids

Numerical solution of filtration in porous rock

Deep bed filtration with multiple pore-blocking mechanisms

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