Parameter estimation for reactive transport by a Monte‐Carlo approach

Aggarwal, Mohit; Carrayrou, Jérôme

doi:10.1002/aic.10813

Cited by 10 publications

(10 citation statements)

References 12 publications

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“…can be expressed by The behaviors of parameters a , b , and c are obtained using the Monte Carlo simulation technique. The Monte Carlo simulation has been used successfully in many non‐linear and complex problems for parameter estimation . We used this technique to generate a large number of the physical problem realizations ( N = 10 6 ) based on the deterministic model presented in this article (i.e., the analytical model for the transient case [Eqs.…”

Section: Model Verificationmentioning

confidence: 99%

Mixing induced by buoyancy‐driven flows in porous media

Meybodi

2012

AIChE Journal

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A theoretical model for fluid mixing in steady and transient buoyancy-driven flows induced by laminar natural convection in porous layers is presented. This problem follows a highly nonlinear dynamics and its accurate modeling poses numerical challenges. Based on the Taylor dispersion theory, a one-dimensional analytical model is developed for steady and transient velocity fields. To investigate steady-state mixing, a unicellular steady velocity field is established by maintaining a thermal gradient across a porous layer of finite thickness. A passive tracer is then introduced into the flow field and the mixing process is studied. In the case of transient flows, as the convective flow grows and decays with time the behavior of the dispersion coefficient is characterized by a four-parameter Weibull function. The simple analytical model developed here can recover scaling relations that have been reported in the literature to characterize the mixing process in steady and transient buoyancy-driven flows.

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Section: Model Verificationmentioning

confidence: 99%

Mixing induced by buoyancy‐driven flows in porous media

Meybodi

2012

AIChE Journal

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“…Since the review article of Yeh and Tripathi [28], three ways are well known for reactive transport modelling: the global approach where both transport and chemical operators are solved simultaneously [9,10,22,24]; the iterative operator splitting approach where both operators are solved separately but coupled by Picard-like iterations [5,6,14,18,26]; and the non-iterative operator splitting approach where transport and chemistry operators are separately solved only one time per time step [1,2,27]. In this work, we present the non-iterative operator splitting approach.…”

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confidence: 99%

Looking for some reference solutions for the reactive transport benchmark of MoMaS with SPECY

Carrayrou

2009

Comput Geosci

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International audienceNumerical benchmark can be an efficient way to validate reactive transport codes. The reactive transport benchmark of GNR MoMaS is here presented and solved on its easy 1D version. The reactive transport code SPECY is presented with a brief description of its main numerical methods: discontinuous finite elements for solving advection, mixed hybrid finite elements for solving dispersion and Newton–Raphson method to linearise the equilibrium chemistry and respect of the chemically allowed interval and positive continuous fractions methods to increase the robustness of the chemistry resolution. By successive mesh and time step refinement, we use the reactive transport code SPECY to look for a reference solution to this problem

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“…Finding a global minimum for E(Θ) and not becoming trapped in a local minimum is the objective of maximum-likelihood estimation. Becoming trapped in a local minimum is a common problem for traditional nonlinear optimization algorithms [24,25], preventing determination of the parameters. In this study, the EMC method [26][27][28]35,36], which is also called parallel tempering [37], is used as an iterative minimization routine to overcome this problem.…”

Section: General Frameworkmentioning

confidence: 99%

“…Accordingly, an effective methodology is required to simultaneously estimate the reaction-rate constants of several minerals and/or diffusivity of elements from complex water-rock systems.However, multiple parameterizations from a coupled transport and reaction system, pertaining to the dissolution and precipitation of many minerals and the transport of aqueous species (ions and complexes), raise a difficult geochemical inverse problem due to computational difficulties. This is especially true when multiple parameters are to be estimated; estimation sometimes fails to converge to the global minima due to convergence to the local minima through error minimization [24,25]. Moreover, the data used for parameterization may be "noisy" due to analytical uncertainties, and therefore, the fitted parameters would also contain errors.…”

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Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

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Water-rock interaction in surface and subsurface environments occurs in complex multicomponent systems and involves several reactions, including element transfer. Such kinetic information is obtained by fitting a forward model into the temporal evolution of solution chemistry or the spatial pattern recorded in the rock samples, although geochemical and petrological data are essentially sparse and noisy. Therefore, the optimization of kinetic parameters sometimes fails to converge toward the global minimum due to being trapped in a local minimum. In this study, we simultaneously present a novel framework to estimate multiple reaction-rate constants and the diffusivity of aqueous species from the mineral distribution pattern in a rock by using the reactive transport model coupled with the exchange Monte Carlo method. Our approach can estimate both the maximum likelihood and error of each parameter. We applied the method to the synthetic data, which were produced using a model for silica metasomatism and hydration in the olivine-quartz-H 2 O system. We tested the robustness and accuracy of our method over a wide range of noise intensities. This methodology can be widely applied to kinetic analyses of various kinds of water-rock interactions.2 of 15 happen simultaneously. Even for monomineralic systems, such as feldspar-water or olivine-water systems in batch experiments, coupled reactions could occur, marked by the dissolution of the primary mineral and the formation of a secondary mineral [9,[20][21][22][23]. Accordingly, an effective methodology is required to simultaneously estimate the reaction-rate constants of several minerals and/or diffusivity of elements from complex water-rock systems.However, multiple parameterizations from a coupled transport and reaction system, pertaining to the dissolution and precipitation of many minerals and the transport of aqueous species (ions and complexes), raise a difficult geochemical inverse problem due to computational difficulties. This is especially true when multiple parameters are to be estimated; estimation sometimes fails to converge to the global minima due to convergence to the local minima through error minimization [24,25]. Moreover, the data used for parameterization may be "noisy" due to analytical uncertainties, and therefore, the fitted parameters would also contain errors. Such errors on rate constants are typically ignored to avoid the complex computations required to handle error propagation. Therefore, it would be ideal to develop a versatile method that can extract multiple kinetic parameters and associated errors from noisy laboratory datasets without becoming trapped in local minima.In this study, we present a novel method to estimate not only multiple reaction-rate constants, but also the diffusivity of aqueous species using only the dataset of spatial mineral distribution, and by combining the reactive transport model and the exchange Monte Carlo (EMC) method [26][27][28]. The latter is well-known as an improvement on Markov chain Monte Carlo (MCMC) ...

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Parameter estimation for reactive transport by a Monte‐Carlo approach

Cited by 10 publications

References 12 publications

Mixing induced by buoyancy‐driven flows in porous media

Mixing induced by buoyancy‐driven flows in porous media

Looking for some reference solutions for the reactive transport benchmark of MoMaS with SPECY

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

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