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Кузьмина Людмила Ивановна

Московский институт электроники и математики им. А.Н. Тихонова

Профиль на hse.ru ↗ тел.: +7 (495) 772-95-90 | 15219
Публикаций
82
Языков
2
Наград
9
Конференций
15
Профиль Публикации (82) Курсы (3)

Профессиональные интересы

27.35.00 Математические модели естественных наук и технических наук. Уравнения математической физики27.35.59 Методы теории возмущений27.35.35 Математическая теория дифракции

Должности

  • Доцент — Московский институт электроники и математики им. А.Н. Тихонова, Департамент прикладной математики

Био

  • · Начала работать в НИУ ВШЭ в 2012 году.
  • · Научно-педагогический стаж: 49 лет.

Образование

  • 1994 · Ученое звание: Доцент
  • 1986 · Кандидат физико-математических наук: Ленинградский государственный университет им. А.А. Жданова, специальность 01.00.00 «Физико-математические науки», тема диссертации: Дифракция поверхностных волн на вертикальных преградах
  • 1980 · Аспирантура: Ленинградский государственный университет им. А.А. Жданова, специальность «дифференциальные уравнения и математическая физика»
  • 1976 · Специалитет: Ленинградский государственный университет им. А.А. Жданова, специальность «Прикладная математика», квалификация «Математик»
  • 1976 · Специалитет: Ленинградский государственный университет им. А.А. Жданова, факультет: прикладной математики-процессов управления, специальность «прикладная математика»

Опыт работы

  • · 2012: НИУ ВШЭ с года

Награды и поощрения

  • · Почетная грамота Министерства науки и высшего образования Российской Федерации (декабрь 2024)
  • · Благодарственное письмо первого проректора НИУ ВШЭ (январь 2021)
  • · Почетная грамота Высшей школы экономики (декабрь 2017)
  • · Благодарность Высшей школы экономики (июнь 2014)
  • · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2020–2022, 2019–2020, 2018–2020)
  • · Надбавка за регулярные публикации в международных рецензируемых научных изданиях (2025–2030, 2023–2028, 2021–2022)
  • · Надбавка за статью в зарубежном рецензируемом журнале (2014–2016)
  • · Надбавка за статью в зарубежном рецензируемом научном издании (2016–2018)
  • · Лучший преподаватель — 2022, 2015–2017

Конференции (15)

Показать все
  • · 2021: Innovations and Technologies in Construction (BUILDINTECH BIT 2021) (Белгород). Доклад: Filtration of 2-particles suspension in a porous medium
  • · 2020: VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) (Ташкент). Доклад: Asymptotics of inverse filtration problem in porous media
  • · 2020: XXIII International Scientific Conference on Advance in Civil Engineering: "CONSTRUCTION - THE FORMATION OF LIVING ENVIRONMENT" (FORM-2020) (Ханой). Доклад: Filtration of a highly concentrated suspension in a porous medium
  • · 2019: XXII International Scientific Conference “Construction the Formation of Living Environment” (FORM-2019) (Ташкент). Доклад: Global asymptotics of filtration in porous media
  • · 2019: XXVIII R-S-P Seminar «Theoretical Foundation of Civil Engineering» (Жилина). Доклад: Particle Capture in Porous Medium
  • · 2018: XXVII R-S-P Seminar, Theoretical Foundation of Civil Engineering (27RSP) (Ростов-на-Дону). Доклад: Deep bed filtration with multiple pore-blocking mechanisms
  • · 2018: XXI International Scientific Conference on Advanced in Civil Engineering (FORM 2018) (Москва). Доклад: Particle transport in a porous medium with initial deposit
  • · 2018: VII International Symposium Actual Problems of Computational Simulation in Civil Engineering (Новосибирск). Доклад: Modelling uniform asymptotics of the filtration problem in a porous medium
  • · 2017: XXVI R-S-P Seminar 2017 Theoretical Foundation of Civil Engineerin (Варшава). Доклад: Filtration model of the unsteady suspension flow in a porous medium
  • · 2016: XXV Russian-Slovak-Polish seminar «Theoretical Foundation of Civil Engineering» (Жилина). Доклад: Deep Bed Filtration Asymptotics at the Filter Inlet
  • · 2016: 5th International Scientific Conference “Integration, Partnership and Innovation in Construction Science and Education” (Москва). Доклад: Calculation of filtration of polydisperse suspension in a porous medium
  • · 2015: XXIV Russian-Slovak-Polish seminar (24RSP) «Theoretical Foundation of Civil Engineering» (Самара). Доклад: Asymptotic solution for deep bed filtration with small deposit
  • · 2014: 3rd International scientific-practical conference «Innovative Information Technologies» (Прага). Доклад: Learning Management System Lms In Mathematical University Courses
  • · 2013: Х Международная научная конференция "Новые информационные технологии и менеджмент качества" (Белек). Доклад: Система управления обучением LMS в преподавании математических дисциплин
  • · 2013: XX Всероссийская научно-методическая конференция "Телематика 2013" (Санкт-Петербург). Доклад: Использование системы LMS для контроля знаний по математическим дисциплинам: возможности и проблемы

Идентификаторы исследователя

Публикации (82)

Injectivity decline under suspension injection with Langmuir's fines capture: analytical model

2026 · ARTICLE · en

Injectivity decline due to injection of colloidal suspensions and emulsions occur in numerous areas of geo-energy production, geo- and environmental engineering. This phenomenon is attributed to colloidal capture by porous media resulting in permeability decrease. The shortcoming of the traditional analytical model predicting injectivity decline is the assumption of constant filtration coefficient (probability of the capture) leading to infinite retained particle concentration. This restricts the model application to short injection periods only. This paper derives explicit formulae for particle concentrations and well injectivity for Langmuirian filtration coefficient that decreases during injection and yields a limited retained concentration. The permeability damage occurs in well vicinity, which is significantly smaller than the drainage radius, so we use an asymptotic method for analytical modelling. It was shown that second-order asymptotic approximation provides sufficient accuracy for the prediction of the skin factor, its stabilization period, and damage radius. The explicit analytical formulae allow for multivariant sensitivity study for well impedance with respect to filtration and formation damage parameters. This study reveals that the most influential parameters are the permeability decline exponent and formation damage coefficient, while the initial filtration coefficient almost does not affect the impedance growth. Besides impedance, the analytical model provides formula for skin stabilization period and damage radius. Matching the field case data on well injectivity history by the lab-based asymptotic model exhibits high accuracy, which validates the asymptotic model for injectivity decline prediction.

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Фильтрация с эрозией осадка в пористой среде

2025 · ARTICLE · ru

Модели переноса и фильтрации мелких частиц в пористых средах используются в строительной индустрии при проектировании фундаментов, и подземных сооружений. Жидкость с частицами движется по каналам пористого грунта. При переносе частиц некоторые из них запираются в порах и образуют осадок. При медленном течении жидкости осажденные частицы, задержанные на стенках широких пор или в горловинах узких пор, остаются неподвижными. Жидкость и взвесь не могут оторвать осажденные частицы от мест седиментации. При увеличении скорости потока суспензии или коллоида часть осадка вымывается жидкостью-носителем и переносится по порам. Рассматривается одномерная модель переноса частиц в однородной пористой среде, учитывающая осаждение взвешенных частиц на каркасе и эрозию осадка. Модель задает связь взвешенных и осажденных частиц и баланс седиментации и эрозии осадка. При малой концентрации суспензии интенсивность образования и подъема осадка зависит от функции фильтрации и концентрации взвешенных частиц; эрозия осадка определяется количеством осажденных частиц на каркасе пористой среды. Приводятся аналитические решения модели и асимптотика в виде бегущей волны. Найдена предельная концентрация осадка при одновременном действии механизмов задержания и подъема частиц.

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PARTICLE TRANSPORT WITH FINITE FILTRATION TIME

2025 · ARTICLE · en

Abstract: Particle transport by a fluid flow occurs in many applied construction problems, including pumping mortar into porous soil, creating watertight diaphragm walls, and constructing dams and underwater structures. A model of deep bed filtration of suspensions and colloids in a homogeneous porous medium with a finite number of vacancies for retained particles is considered. A suspension of constant concentration is injected into the inlet of a porous medium containing clean water. If the sediment growth rate remains positive as the sediment concentration approaches the upper limiting value, the filtration process continues for a finite time. In this case, the filtration function that specifies the sediment growth rate in the mathematical model is not blocking. At each point of the porous medium, sedimentation begins from the moment the concentration front passes and ends after a finite period of time depending on the distance to the porous medium inlet. A global exact solution to the problem is constructed in the filtration domain, which consists of two zones. In the zone bordering the concentration front, the solution has a standard form, and in the zone adjacent to the upper limiting values of the concentrations of suspended and retained particles, it has the form of a traveling wave.

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Modelling of Filtration with Two Capture Mechanisms

2024 · CHAPTER · en

Filtering fluids with tiny particles in porous media occurs in many technological processes of environmental and civil engineering. To strengthen the foundation, a slurry is pumped into loose rock and, when hardened, strengthens it. Deep bed filtration is accompanied by the retention of particles. Various forces act on the particles and cause them to settle on the framework of the porous medium. The most common are the capture of particles in the inlets of narrow pores and attachment to the walls of wide pores. A model with two simultaneous particle capture mechanisms is considered. The problem is reduced to a standard model with an implicit aggregated filtration function. To simplify the calculations, it was previously proposed to use an approximate model with an explicit linear-constant filtration function. The linear-constant function has a break and does not optimally approximate the aggregated filtration function. The paper introduces a linear-fractional (hyperbolic) filtration function with a free parameter. The parameter is selected from the condition of the best approximation to the aggregated function. The system of equations in partial derivatives is integrated and reduced to a system of transcendental equations. It is shown that the solution to the model with a hyperbolic filtration function is closer to the true solution than the approximate solution with a linear-constant function.

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Long-term filtration of particles in a porous medium

2024 · CHAPTER · en

The formation of grout sediment in the pores of loose rock increases the water resistance of the soil and strengthens the foundation. A one-dimensional model of filtration in a porous medium considers the particles transport by the flow of a carrier fluid and the deposition of particles on the framework of a porous medium. The purpose of the work is to study the concentrations of suspended and settled particles of a suspension over a long time. Exact and asymptotic methods are used to obtain a solution to the model. The exact solution is presented in an implicit integral form. A set of solutions in the form of traveling waves with an arbitrary initial condition and their asymptotics are constructed. For the exact solution, an explicit second-order asymptotic solution for a long time is obtained as an expansion in decreasing exponents. Comparison of the asymptotic solution with the traveling waves makes it possible to choose a single traveling wave corresponding to the exact solution. The closeness of the traveling wave to the exact solution of the filtration model is verified numerically. The traveling wave found determines the explicit asymptotics of the concentration of deposited particles for a long time.

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Deep bed filtration model for cake filtration and erosion

2024 · ARTICLE · en

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition, namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion, the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

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Retention profiles of multiparticle filtration in porous media

2024 · ARTICLE · en

A one‐dimensional deep bed filtration model of a polydisperse suspension or colloid in a porous medium is considered. The model includes a quasilinear system of 2n equations for concentrations of suspended and retained particles of n types. The problem is reduced to a closed 3 × 3 system for total concentrations of suspended and retained particles and of occupied rock surface area, which allows an exact solution. The exact solution to the n‐particle problem is derived, the existence and uniqueness of the solution are proven, and the solution in the form of a traveling wave is obtained. The retention profiles (dependence of the deposit concentration on the coordinate at a fixed time) of different size particles and the total profile are studied. It is shown that the profile of large particles decreases monotonically, while the profile of small particles is nonmonotonic. Conditions for the monotonicity/nonmonotonicity of the intermediate particle profiles and the total profile are obtained. The maximum point of the small particles profile tends to infinity with unlimited growth of time, and the maximum points of nonmonotonic profiles of intermediate particles are limited. The asymptotical expansion of the maximum points of nonmonotonic profiles is constructed.

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An averaged model for colloidal transport to exhibit hyper-exponential particle retention

2024 · ARTICLE · en

Modelling of colloidal and nano-suspension transport in porous media has garnered significant attention due to the prevalence of these processes in many engineering applications. A number of experimental studies have reported retention profiles after coreflooding that are hyper-exponential, a feature that the traditional models for deep bed filtration are unable to capture. The aim of this work is the development of a model for binary particle transport which can account for hyper-exponential retention profiles (HERPs). Averaging of the multicomponent model results in a non-linear dependence of the capture rate on the suspended particle concentration. The averaged model demonstrates how nonlinear capture behaviour arises due to particle heterogeneity even when individual particle populations filter traditionally. The averaged model exhibits classical filtration behaviour at low concentrations as a result of selective particle filtration, with a more rapid degeneration to this behaviour when the difference between particle populations is larger. The model establishes that nonlinear capture behaviour, including the prediction of HERPs, occurs even for dilute particle suspensions given that particle heterogeneity is significant. An exact solution of the colloidal transport equations is presented for any non-linear suspension function and any step-wise-constant injected concentration. The binary suspension function cannot be written explicitly, and so we present asymptotic expansions for several limiting cases where the suspension function can be expressed directly. The asymptotic expansions show good agreement with the binary model, and correctly capture the HERPs calculated with the exact solution. Several laboratory tests exhibiting HERPs have been matched by the traditional, binary, and asymptotic expansion models. The traditional model significantly deviates from the laboratory data due to its inability to capture the hyper-exponential behaviour, while both the binary and asymptotic models capture this behaviour well.

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Non-linear filtration model with splitting front

2024 · ARTICLE · en

We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the front boundary of suspended particles and the front of the carrier fluid was observed. This article proposes a modification of the standard model that provides a description of the separation between the fluid front and the particle front. For this purpose, a non-smooth non-linear function depending on the concentration of the suspension is introduced into the deposit growth equation. In case of a non-smooth suspension function, the concentration of suspended particles at the front decreases to zero in a finite time. At this moment the united front splits into the front of pure injected water and the front of suspended and retained particles. The particle front moves slower than the pure water front. In case of a linear filtration function (Langmuir coefficient), an exact solution is constructed in a closed form. For the filtration problem with a suspension function in the form of a square root, explicit analytical formulae are obtained. In case of a non-smooth filtration function, the filtration time is finite. The curvilinear boundary separates the filtration domain, where concentrations increase with time, from the stabilization domain, where the concentrations of suspended and retained particles have reached their limits. The limit speeds of the stabilization border and of the particle front coincide.

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Model Of Cake Filtration In Porous Medium

2024 · ARTICLE · en

Strengthening of loose soil and creation of water-resistant underground walls are associated with filtration of small particles in a porous medium. Liquid solution pumped into a well under pressure spreads through hollow channels and strengthens the soil upon hardening. Many porous filters retain particles near the entrance. The particles deposited on the filter surface form a crust, which does not allow suspended particles to penetrate deep into the porous medium. A model of cake filtration - the formation of a surface crust during filtration of a monodisperse suspension in a homogeneous porous medium is considered. This model is a modification of the standard mathematical description of deep bed filtration with linear accessible fractional flow decreasing to zero. An exact solution is obtained using the method of characteristics. Asymptotics is constructed for a long time. It is shown that the dynamics and profiles of suspended and deposited particles concentrations exponentially decrease.

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Курсы (3)