Stochastic analysis of effective rate constant for heterogeneous reactions

Lichtner, Peter C.; Tartakovsky, Daniel M.

doi:10.1007/s00477-003-0163-3

Cited by 61 publications

(38 citation statements)

References 17 publications

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“…Regarding reactive solutes concentrations, Lichtner and Tartakovsky (2003) apply a pdf formulation to a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase in a batch. Upon considering both linear and nonlinear kinetic rate laws, they found an approximation for an effective rate constant describing the change in mean concentration with time.…”

Section: Introductionmentioning

confidence: 99%

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

2008

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This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space-time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in Math Geosci the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.

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Section: Introductionmentioning

confidence: 99%

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

2008

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“…Up-scaling of laboratory reaction rates to the continuum scale is also problematic in the context of matrix dissolution. Lichtner and Tartakovsky (2003) found that volume-averaging methods to upscale reaction rate constants for quartz dissolution resulted in effective reaction rate constants that varied as a function of time, which they attributed to heterogeneous distribution of grain sizes.…”

Section: Models Of the Acidizing Processmentioning

confidence: 99%

Pore-Network Modeling of Carbonate Acidization

Tansey

2014

SPE Annual Technical Conference and Exhibition

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Carbonate reservoirs represent a significant portion of global hydrocarbon reserves. Injecting strong acids around the wellbore of carbonate wells can significantly increase near-wellbore permeability. A pore-network model is developed to capture permeability response of carbonates to acid stimulation. A novel pore-scale mass-transfer coefficient and pore-merging criterion are developed using finite element simulations. Preliminary results are able to reproduce the expected trends in permeability increase and capture the gamut of different dissolution regimes. Future work will focus primarily on using advanced subdomain coupling techniques to simulate much larger domain sizes to investigate the effects of domain size and determine a representative elementary volume.

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“…They are used to describe phenomena as diverse as migration of reactive contaminants in the environment [2], immiscible finite times [27]. Even when accurate, MDEs yield only the first few statistical moments of system states rather than their full probability density functions (PDFs).…”

Section: Introductionmentioning

confidence: 99%

Cumulative distribution function solutions of advection–reaction equations with uncertain parameters

2014

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We derive deterministic cumulative distribution function (CDF) equations that govern the evolution of CDFs of state variables whose dynamics are described by the first-order hyperbolic conservation laws with uncertain coefficients that parametrize the advective flux and reactive terms. The CDF equations are subjected to uniquely specified boundary conditions in the phase space, thus obviating one of the major challenges encountered by more commonly used probability density function equations. The computational burden of solving CDF equations is insensitive to the magnitude of the correlation lengths of random input parameters. This is in contrast to both Monte Carlo simulations (MCSs) and direct numerical algorithms, whose computational cost increases as correlation lengths of the input parameters decrease. The CDF equations are, however, not exact because they require a closure approximation. To verify the accuracy and robustness of the large-eddydiffusivity closure, we conduct a set of numerical experiments which compare the CDFs computed with the CDF equations with those obtained via MCSs. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties of the two input parameters, such as their correlation lengths and variance of the coefficient that parametrizes the advective flux.

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Stochastic analysis of effective rate constant for heterogeneous reactions

Cited by 61 publications

References 17 publications

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

Pore-Network Modeling of Carbonate Acidization

Cumulative distribution function solutions of advection–reaction equations with uncertain parameters

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