Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an Eulerian-Lagrangian marker particle technique

A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow

Characterization of the velocity field organization in heterogeneous media by conditional correlation

International audienceThe purpose of the present work is to quantify the correlation structure of simulated velocity fields in heterogeneous permeability fields and to discuss how to represent it in upscaled transport models. We investigate the velocity field correlation structure for multinormal log permeability fields. The simulated velocity distributions are analyzed in a Lagrangian framework, i.e., along the particles' paths.To quantify the different spatial organization of low- and high-velocity zones, we condition the estimated velocity correlation length and time on the initial particle velocity. The velocity correlation length is found to increase with the initial particle velocity, following a power law. Such an effect is likely due to the channeling of high-velocity zones, which implies that particles keep memory of their initial velocity over longer distances for high initial velocities than for low initial velocities. Two distinct regimes are identified for the velocity correlation time. For low initial particle velocity the correlation time is controlled by the large time needed to escape from the low- velocity zones. For high initial particle velocity it is controlled by the large time needed for particles to sample the whole velocity field, in particular low- velocity zones. One of the consequences of these results is that for such velocity fields the nonlinear dependence of both the correlation length and time on the particle initial velocity restricts the se of spatial or temporal Markovian assumptions for modeling velocity transitions in effective transport models

Upscaling of the acidizing process in heterogeneous porous media

Coupled fluid flow, reaction and transport in porous media has been the topic of research in various disciplines for the past few decades. Conventional approach assumes a homogeneous and isotropic porous media, and simplifies the nature of coupling between fluid and rock interactions. However, including the reality of the process, i.e. assuming heterogeneous and anisotropic porous media with fully coupled rock fluid interaction, can lead to more advanced understanding of the fundamental physics behind the problem and developing efficient industrial applications. In the oil and gas industry optimization of different well stimulation techniques such as matrix acidizing in order to enhance oil recovery requires an advanced understanding of fluid flow and also reaction in heterogeneous formations. This thesis is a contribution to development of more general governing equations describing the reactive flow and transport in heterogeneous formations.;The heterogeneity of the porous medium is introduced in the formulation through random permeability field that possess the characteristics of stationary stochastic process. The heterogeneity in permeability field affects the reservoir dynamics over a range of length and time scales by making pressure, concentration, diffusion and reaction coefficients stochastic random fields. Stochastic nature of these parameters helps us to be able to upscale the process while keeping the local information associated with heterogeneous nature of the porous media.;Conventional approaches to deal with this problem are homogenization and smoothing the heterogeneous properties of the formation using averaging based techniques such as up-gridding. However, these techniques do not carry the fundamental physics governing the process and cannot mimic the experimental observations such as acid front movement and instability of the reaction process. The local variations in rock and fluid properties are also ignored in these techniques which might lead to significant impacts in field scale application of acidizing as one of the major stimulation techniques.;In order to upscale the isothermal reaction process in a heterogeneous porous medium, according to the nature of the process, spectral-based small perturbation theory (Gelhar, 1993; Gelhar and Axness, 1983) is used among the various numerical and analytical upscaling techniques. The reaction is a nonlinear dissolution of an injected acid in a homogeneous liquid with constant density in a stationary mineral with constant porosity. In order to follow the acid front a moving coordinate is introduced. The upscaled governing equations are obtained with explicit macro-scale expressions for the coefficients and solved using time adaptive implicit finite difference technique. The results are compared with homogeneous models and sensitivity analysis of the upscaled equations is performed. Finally conclusions and results are discussed showing the importance of applying upscaling techniques to capture the impacts of heterogeneity on fluid dynamics

Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers

Dividimos el trabajo en tres bloques: En el primer bloque, se han revisado las técnicas de escalado que utilizan una media simple, el método laplaciano simple, el laplaciano con piel y el escalado con mallado no uniforme y se han evaluado en un ejercicio tridimensional de escalado de la conductividad hidráulica. El campo usado como referencia es una realización condicional a escala fina de la conductividad hidráulica del experimento de macrodispersión realizado en la base de la fuerza aérea estadounidense de Columbus en Misuri (MADE en su acrónimo inglés). El objetivo de esta sección es doble, primero, comparar la efectividad de diferentes técnicas de escalado para producir modelos capaces de reproducir el comportamiento observado del movimiento del penacho de tritio, y segundo, demostrar y analizar las condiciones bajo las cuales el escalado puede proporcionar un modelo a una escala gruesa en el que el flujo y el transporte puedan predecirse con al ecuación de advección-dispersión en condiciones aparentemente no fickianas. En otros casos, se observa que la discrepancia en la predicción del transporte entre las dos escalas persiste, y la ecuación de advección-dispersión no es suficiente para explicar el transporte en la escala gruesa. Por esta razón, se ha desarrollado una metodología para el escalado del transporte en formaciones muy heterogéneas en tres dimensiones. El método propuesto se basa en un escalado de la conductividad hidráulica por el método laplaciano con piel y centrado en los interbloques, seguido de un escalado de los parámetros de transporte que requiere la inclusión de un proceso de transporte con transferencia de masa multitasa para compensar la pérdida de heterogeneidad inherente al cambio de escala. El método propuesto no sólo reproduce el flujo y el transporte en la escala gruesa, sino que reproduce también la incertidumbre asociada con las predicciones según puede observarse analizando la variabilidad del conjunto de curvas de llegada.Li ., L. (2011). Upscaling and Inverse Modeling of Groundwater Flow and Mass Transport in Heterogeneous Aquifers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12268Palanci

On the Use of Entropy Production to Improve Mathematical Models and Numerical Methods for Non-Dilute Flow and Transport in Porous Media

Non-dilute flow and transport in porous media plays an important role in many natural and engineered systems, however a mature understanding is lacking. As environmental conditions change and water resources become scarcer, the need for a more complete understanding of non-dilute flow and transport will be necessary to address future challenges, for example, assessing impacts of climate change on fresh water supplies and examining mitigation strategies. The thermodynamically constrained averaging theory (TCAT) is an approach for developing mathematical models that ties together conservation and thermodynamic laws and connects all spatial scales. This approach is used to develop a new macroscale model for non-dilute flow and transport in porous media. This model is found to more accurately describe a set of non-dilute laboratory displacement experiments as compared to existing models. Through the development of the model, an entropy production rate is derived and a new numerical method is formulated that utilizes the entropy production rate to improve computational efficiency. The general framework of this new approach can be applied to other models where the entropy production rate is known. To further improve macroscale models and our understanding of non-dilute behavior, microscale simulations are performed. As TCAT relates all spatial scales, the microscale simulations are averaged to gain insight on macroscale behavior. The importance that density, viscosity, and activity have on macroscale transport is assessed and microscale velocity distributions are analyzed to explain gravity stabilization and macroscale transport behavior.Doctor of Philosoph

Improving convergence rates for low pressure material processing calculations

An enhanced solution strategy for the SIMPLER algorithm is presented for low pressure heat and mass transport calculations with applications in material processing. The accurate solution of highly diffusive flows requires an inflow boundary condition that preserves chemical species mass fluxes. The flux-preserving inflow boundary condition contains a scaling problem that causes the species equations to converge very slowly when using the standard SIMPLER algorithm. A gradient algorithm, coupled to a line-relaxation method, accelerates the convergence of the linear problem. Reformulation of the pressure-correction boundary conditions ensures that continuity is preserved in each finite volume at each iteration. The boundary condition scaling problem is demonstrated with a simple linear model problem. The enhanced solution strategy is implemented in a baseline computer code that is used to solve the multicomponent Navier-Stokes equations on a generalized, multiple-block grid system. Convergence rate acceleration factors of up to 100 are demonstrated for several material processing example problems

자연하천에서 물질 혼합해석을 위한 저장대에서의 정체시간분포 산정

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 서일원.자연하천에서 용존물질의 거동은 하천의 지형학적인 요인으로 형성된 저장대의 영향에 의해 흐름 영역의 특성만으로 해석될 수 없다. 이러한 저장대 효과를 분석하기 위해 지난 수십년동안 다양한 구조의 저장대 모형이 제시되어 왔다. 용존물질의 하류이송을 지체시키는 이러한 저장대의 영향을 고려하기 위해, 기존의 1차원 이송-분산 방정식을 바탕으로 다양한 형태의 저장대 모형이 개념적으로 제시되어 왔다. 이러한 모형의 타당성은 대부분 흐름영역에서 측정한 추적자의 농도-시간 곡선의 실측값으로부터 증명되어 왔다. 하지만, 흐름영역에서의 추적자 거동은 저장대의 영향보다 이송과 분산의 영향에 더욱 민감하기 때문에, 이는 저장대의 영향을 대표하기 어려우며, 저장대 모델링은 저장대의 영향의 실측값으로부터 검증되어야 한다. 하지만, 자연하천의 저장대는 그 형태가 다양하며 경계가 모호하기 때문에 실측값을 얻기 힘든 한계가 있다. 따라서, 본 연구에서는 이송, 분산의 영향과 저장대의 영향을 명시적으로 구분할 수 있는 모형을 제시하고, 역합성곱 기법을 적용하여 흐름영역에서 측정한 추적자의 거동으로부터 이송과 분산의 영향을 제외하여 저장대의 영향만을 측정할 수 있는 방법을 제시하였다. 측정한 저장대의 영향은 가장 대표적인 1차원 저장대 모형인 Transient Storage Model (TSM)의 모의 결과와 결정된 매개변수의 타당성을 검증하는데 활용되었다. 그 결과 TSM의 모의는 실제 하천의 저장대의 영향을 44%까지 과소평가하는 결과를 보였다. 또한, 자연하천에서 저장대가 수계 생물화학적 반응의 주요 영역이라는 점을 고려하여, 평가된 정체시간분포를 이용하여 여러 유기화학물질별 생화학적 반응에 의한 감쇠정도를 평가하는데 활용되었다.The solute propagation along stream flow cannot be interpreted only by hydrodynamic properties of surface flow due to the influence from surrounding storage zones of the stream. To analyze this unidentified storage effect, various transient storage models have been proposed for recent decades. The time dependent behavior of solute within the storage zone was often modeled a conceptualized retention time function added to conventional advection-dispersion equation. The validity of these models has been predominantly demonstrated with tracer breakthrough curves measured in surface flow. However, the storage effect is less responsible for the breakthrough curve behavior than in-stream flow dynamics. For model validation purpose, tracer behavior only within storage zones should be investigated. The present study is aimed at quantifying the time-dependent storage effect, herein termed the net retention time distribution (NRTD), from tracer measurements at the flow zone using a deconvolution technique with filtering in the Fourier domain. The results showed that the deconvolved NRTDs successively represented the temporal behavior of the tracer in the storage zones without significant distortion in the observed breakthrough curves. Using the estimates of NRTD, we evaluated the validity of first-order mass transfer and its parameters of the transient storage model (TSM), which is the most widely-used storage zone model. The simulation results of the parameter-optimized TSM underestimated the inherent storage effect by as much as an average 44 %. It is also noteworthy that the larger net retention time scale the channel has, the larger discrepancy the TSM’s exponential retention time function could yield.LIST OF FIGURES LIST OF TABLES LIST OF SYMBOLS LIST OF ABBREVIATIONS CHAPTER I. INTRODUCTION 1 1.1 Motivation 1 1.2 Problem Statement 3 II. THEORETICAL BACKGROUNDS 8 2.1 One-dimensional solute transport modeling 8 2.2 Conceptualization of storage mechanism 13 2.3 Determination of TSM parameters 23 2.4 Summary of literatural review 26 III. MATERIALS AND METHODS 27 3.1 Tracer experiments in a stream 27 3.1.1 Site description 27 3.1.2 Tracer Measurement 30 3.1.3 Preprocessing for Breakthrough Curves 31 3.2 Development of algorithm for storage effect quantification 32 3.2.1 Concept of residence time distribution 33 3.2.2 Convolutional Decomposition Equation (CDE) 34 3.2.3 Deconvolution technique with BTCs 39 3.2.4 Data stabilization for deconvolution 43 3.2.5 Parameter estimation 47 3.3 Net retention time distribution in TSM 52 3.4 Biodegradation of chemicals in streams 56 IV. RESULTS AND DISCUSSIONS 59 4.1 Tracer behavior in a stream 59 4.2 Net retention time distribution 66 V. APPLICATION 70 5.1 Evaluation of TSM simulation 70 5.2 Prediction of biodegradation of chemicals 78 IV. CONCLUSIONS 82 REFERENCES 85석

Stability and convergence based on the finite difference method for the nonlinear fractional cable equation on non-uniform staggered grids

Abstract(#br)In this article, a block-centered finite difference method for the nonlinear fractional cable equation is introduced and analyzed. The unconditional stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O ( Δ t α + h 2 + k 2 ) both for pressure and velocity are established on non-uniform rectangular grids, where α = min ⁡ { 1 + γ 1 , 1 + γ 2 } , Δ t , h and k are the step sizes in time, space in x - and y -direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis