Analytical model for straining-dominant large-retention depth filtration

Bedrikovetsky, Pavel; You, Zhenjiang; Badalyan, Alexander; Osipov, Yu. V.; Кузьмина, Людмила Ивановна

doi:10.1016/j.cej.2017.08.031

Cited by 58 publications

(27 citation statements)

References 44 publications

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“…The calculation of filtration problems (1)-(4), (5)- (6) and 20 [11]. x S x t  a) general view; b) enlarged view for 100 100.01 t  ; c) enlarged view for 500 500.01 t  .…”

Section: Calculation Resultsmentioning

confidence: 99%

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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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“…The calculation of filtration problems (1)-(4), (5)- (6) and 20 [11]. x S x t  a) general view; b) enlarged view for 100 100.01 t  ; c) enlarged view for 500 500.01 t  .…”

Section: Calculation Resultsmentioning

confidence: 99%

“…At the concentration front the solution ( , ) C x t has a discontinuity of the first kind, the solution ( , ) S x t is continuous and has discontinuous derivatives. In [11] it is shown that from the system of equations (1)-(4) it is possible to obtain the equation…”

Section: A Mathematical Modelmentioning

confidence: 99%

Numerical solution of filtration in porous rock

Safina

2019

E3S Web Conf.

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“…Exact upscaling of the population balance equations for transport of monosized colloids yields unique solution for the downscaling problem (Bedrikovetsky et al, ). Filtration function h ( s ) defines the pore size distribution.…”

Section: Discussionmentioning

confidence: 99%

“…The upscaling of population balance equations for monosized particles and size exclusion capture yields two traditional equations ( and ) for deep bed filtration (Bedrikovetsky, ). Moreover, due to exact averaging procedure, the upper‐scale exact 1‐D solutions allow for downscaling (Bedrikovetsky et al, ). Yet the upscaled equations for multisized particle transport with attachment are not available.…”

Section: Introductionmentioning

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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“…The oldest digital core models are the abstract capillary bundle model and the random pore network model; however, the concept of digital cores was unknown when these models were initially created. The capillary bundle model approximates the pore space of the rock by using capillary tubes of varying radii [34][35][36]. Although this method is extremely abstract with respect to the pore network of a rock, it is valuable for evaluating the seepage characteristics of conventional reservoirs and primary tight-pored sandstone reservoirs [37,38].…”

Section: Introductionmentioning

confidence: 99%

Challenges and Prospects of Digital Core-Reconstruction Research

et al. 2019

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The simulation of various rock properties based on three-dimensional digital cores plays an increasingly important role in oil and gas exploration and development. The accuracy of 3D digital core reconstruction is important for determining rock properties. In this paper, existing 3D digital core-reconstruction methods are divided into two categories: 3D digital cores based on physical experiments and 3D digital core stochastic reconstructions based on two-dimensional (2D) slices. Additionally, 2D slice-based digital core stochastic reconstruction techniques are classified into four types: a stochastic reconstruction method based on 2D slice mathematical-feature statistical constraints, a stochastic reconstruction method based on statistical constraints that are related to 2D slice morphological characteristics, a physics process-based stochastic reconstruction method, and a hybrid stochastic reconstruction method. The progress related to these various stochastic reconstruction methods, the characteristics of constructed 3D digital cores, and the potential of these methods are analysed and discussed in detail. Finally, reasonable prospects are presented based on the current state of this research area. Currently, studies on digital core reconstruction, especially for the 3D digital core stochastic reconstruction method based on 2D slices, are still very rough, and much room for improvement remains. In particular, we emphasize the importance of evaluating functions, multiscale 3D digital cores, multicomponent 3D digital cores, and disciplinary intersection methods in the 3D construction of digital cores. These four directions should provide focus, alongside challenges, for this research area in the future. This review provides important insights into 3D digital core reconstruction.

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Analytical model for straining-dominant large-retention depth filtration

Cited by 58 publications

References 44 publications

Numerical solution of filtration in porous rock

Numerical solution of filtration in porous rock

Exact Upscaling for Transport of Size‐Distributed Colloids

Challenges and Prospects of Digital Core-Reconstruction Research

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