Inverse problems of elastoplastic filtration of liquid in a porous medium

Khuzhaerov, B. Kh.; Kholiyarov, E. Ch.

doi:10.1007/s10891-007-0068-y

Cited by 12 publications

(4 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We begin considering the second range given in (17). Taking m = 2 in (19), f 2 (η; α) can be represented by two linearly independent solutions of Kummer equations.…”

Section: Positive Similarity Solutionsmentioning

confidence: 99%

“…taking ϕ 1 (η) = M (α/2, N/2; − (1+γ) 4 η 2 ) and ϕ 2 (η) = U (α/2, N/2; − (1+γ) 4 η 2 ), complex solutions for the ODE in (17), the solution f 2 (η; α) can be written as follows:…”

Section: Positive Similarity Solutionsmentioning

confidence: 99%

“…where −1 < γ < 1. This equation was formulated in [4] as a nonlinear filtration theory model and since it's presentation it has been studied different framework in applied mathematics [8,17,20] and considered as a simple model of nonlinear parabolic equation [3,10,14,15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a family of exact solutions for a nonlinear diffusion equation

Pacheco

2014

Preprint

View full text Add to dashboard Cite

We present a complete description of the similarity solutions uα(x, t) = t −α/2 f ( x / √ t; α) for the following nonlinear diffusion equationThe behaviors of these solutions are obtained through the explicit representation of f (η; α), in terms of Kummer and Tricomi functions. Considering results about confluent hypergeometric functions, new methods to describe asymptotic and oscillatory behaviors of the similarity solutions are obtained. We prove that there exists an increasing and unbounded sequence of positive similarity exponents such that the associated profile f has a gaussian rate decay. These special similarity exponents are related with the zeros of Kummer and Tricomi functions. Finally, we indicate how to extend our results on more general nonlinear diffusion equations.

show abstract

“…We begin considering the second range given in (17). Taking m = 2 in (19), f 2 (η; α) can be represented by two linearly independent solutions of Kummer equations.…”

Section: Positive Similarity Solutionsmentioning

confidence: 99%

Section: Positive Similarity Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

On a family of exact solutions for a nonlinear diffusion equation

Pacheco

2014

Preprint

View full text Add to dashboard Cite

show abstract

“…At first, we derived the equations for filtering a suspension through a radial filter formed by an elastic-plastic cake. To model the elasticplastic properties of sediment, we used the general principles of elastic-plastic filtration developed in [30,31,[36][37][38][39]. First, the derivation of the filtration equations with increasing pressure was given, i.e., in the cake loading mode, and then in the unloading mode, i.e., when pressure is released.…”

Section: Introductionmentioning

confidence: 99%

An Axisymmetric Problem of Suspension Filtering with Formation of Elastic–Plastic Cake Layer

et al. 2022

View full text Add to dashboard Cite

The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake on the filter surface. It is supposed that the cake has elastic–plastic properties. Using the mass conservation equation and Darcy’s law, the suspension filtration equations at the elastic–plastic regime are derived, which characterize the partial irreversibility of the filtration characteristics when the system is unloaded after loading. An equation is also derived that describes the increase in the thickness of the cake. Problems of suspension filtering for the derived equations are posed and numerically solved. The role of partial irreversibility of deformation on the filtration characteristics is estimated. Distributions of compression pressure, the concentration of solid particles in the cake, relative permeability in the mode of primary and secondary loading of the system, as well as in the mode of unloading after the first loading are obtained. The growth dynamics of the cake thickness are also established. The parameters of plasticity in terms of particle concentration and permeability mainly affect the corresponding indicators, i.e., on the particle concentration distribution and on the relative permeability of the cake. It is shown, that depending on the change in the model parameters characterizing the elastic–plastic properties of the cake, the filtration characteristics change significantly. This indicates a significant effect of the elastic–plastic deformation of the cake on the suspension filtration characteristics.

show abstract

Determination of Relaxation and Flow Coefficients During Filtration of a Homogeneous Liquid in Fractured-Porous Media

Kholiyarov

Ernazarov

2023

Lecture Notes in Networks and Systems

View full text Add to dashboard Cite

Inverse problems of elastoplastic filtration of liquid in a porous medium

Cited by 12 publications

References 3 publications

On a family of exact solutions for a nonlinear diffusion equation

On a family of exact solutions for a nonlinear diffusion equation

An Axisymmetric Problem of Suspension Filtering with Formation of Elastic–Plastic Cake Layer

Determination of Relaxation and Flow Coefficients During Filtration of a Homogeneous Liquid in Fractured-Porous Media

Contact Info

Product

Resources

About