Adaptive Fup multi-resolution approach to flow and advective transport in highly heterogeneous porous media: Methodology, accuracy and convergence

Gotovac, Hrvoje; Cvetković, Vladimir; Andričević, Roko

doi:10.1016/j.advwatres.2009.02.013

Cited by 28 publications

(64 citation statements)

References 51 publications

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“…Other improved Monte Carlo (MC) methodology aspects are: (a) the Fup Regularized Transform (FRT) for data or function (e.g., log-conductivity) approximations in the same multiresolution way as FCT, but computationally more efficient, (b) Adaptive Fup Collocation method (AFCM) for approximation of the flow differential equation, (c) particle tracking algorithm based on the Runge-Kutta-Verner explicit time integration scheme and FRT, and (d) MC statistics represented by Fup basis functions. All aforementioned MC methodology components are summarized in Gotovac et al [2009].…”

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

“…The following relationship is applied for computing values of the disconnected field (Figure 1b) with the same statistics as a multi-Gaussian field ( Figure 1c) used in Gotovac et al [2009Gotovac et al [ , 2010:…”

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

“…[29] Our recently presented simulation methodology, referred to as Adaptive Fup Monte Carlo Method (AFMCM) [Gotovac et al, 2007[Gotovac et al, , 2009[Gotovac et al, , 2010, supports the Eulerian-Lagrangian formulation and separates the flow from the transport problem. It consists of the following common steps [Rubin, 2003]: (1) generation of logconductivity realizations with predefined correlation structure, (2) numerical approximation of the log-conductivity field, (3) numerical solution of the flow equation with prescribed boundary conditions to produce head and velocity approximations, (4) evaluation of the transport variables for a large number of trajectories, (5) repetition of steps 2-4 for all realizations, and (6) statistical evaluation of transport variables.…”

Section: Flow Simulationsmentioning

confidence: 99%

“…[60] The AFMCM methodology [Gotovac et al, 2009] is based on Fup basis functions with compact support (related to the other localized basis functions such as splines or wavelets) and the Fup Collocation Transform (FCT), which is closely related to the Discrete Fourier Transform. It provides a multiresolution representation of any signal, function or set of data using only a few Fup basis functions and resolution levels on nearly optimal adaptive collocation grids, that are capable of resolving all spatial and/or temporal scales and frequencies.…”

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

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Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Cvetković

Gotovac

2013

Water Resources Research

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[1] Diffusive mass transfer in rock fractures is strongly affected by fluid flow in addition to material properties. The flow-dependence of matrix diffusion is quantified by a random variable (''transport resistance'') denoted as b [T/L] and computed from the flow field by following advection trajectories. The numerical methodology for simulating fluid flow is mesh-free, using Fup basis functions. A generic statistical model is used for the transmissivity field, featuring three correlation structures: (i) highly connected non-multiGaussian; (ii) poorly connected (or disconnected) non-multi-Gaussian ; and (iii) multiGaussian. The moments of b are shown to be linear with distance, irrespective of the structure, after approximately 10 integral scales of ln T. Percentiles of b are found to be linear with the mean b when considering all three structures. Taking advantage of this property, a potentially useful relationship is presented between b percentiles and the fracture mean water residence time that integrates all structures with high variability; it can be used in discrete fracture network simulations where T statistical data on individual fractures are not available.Citation: Cvetkovic, V., and H. Gotovac (2013), Flow-dependence of matrix diffusion in highly heterogeneous rock fractures, Water Resour. Res., 49,[7587][7588][7589][7590][7591][7592][7593][7594][7595][7596][7597]

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Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

Section: Flow Simulationsmentioning

confidence: 99%

Section: Appendix B: Numerical Simulationsmentioning

confidence: 99%

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Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Cvetković

Gotovac

2013

Water Resources Research

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“…The application of Fup basis functions has been demonstrated in signal processing [14], for solving the integral Fredholm equations [13], in initial value problems [9], and in the collocation methods for boundary value problems [10]. Recently, Fup basis functions were applied to the Monte-Carlo methodology and stochastic processes of flow and transport in heterogeneous porous media [11].…”

Section: Introductionmentioning

confidence: 99%

Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

Gotovac¹,

Gotovac

2009

Journal of Computational Physics

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On the upscaling of chemical transport in fractured rock

Cvetković

Gotovac

2014

Water Resources Research

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The impact of flow heterogeneity on chemical transport from single to multiple fractures is investigated. The emphasis is on the dynamic nature of the specific surface area (SSA) due to heterogeneity of the flow, relative to a purely geometrical definition. The flow-dependent SSA is interpreted probabilistically, following inert tracer particles along individual fractures. Upscaling to a fracture network is proposed as a time domain random walk based on the statistics of SSA for single fractures. Statistics of SSA are investigated for three correlation structures of transmissivity: multi-Gaussian and two non-multi-Gaussian. The mean of SSA stabilizes after $20 fractures at different values depending on whether the cubic or quadratic hydraulic law is assumed. The results are tested against comprehensive DFN simulations based on sitespecific data but also against direct estimates from a wider range of tracer tests. The proposed time domain random walk methodology sets bounds for SSA in a 75% confidence interval as $1800 1/m and 27,000 1/m, with a median of 14,000 1/m; these values capture reasonably well both the DFN simulation and tracer test SSA data. Presented results may be particularly relevant when quantifying uncertainty of reactive transport modeling in fractured rock.

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Adaptive Fup multi-resolution approach to flow and advective transport in highly heterogeneous porous media: Methodology, accuracy and convergence

Cited by 28 publications

References 51 publications

Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

On the upscaling of chemical transport in fractured rock

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