Modeling and Simultation of Arsenate Fate and Transport in a Distribution System Simulator

Klosterman, Stephen; Murray, Regan; Szabo, Jeff; Hall, John S.; Uber, James G.

doi:10.1061/41203(425)62

Cited by 11 publications

(12 citation statements)

References 6 publications

(8 reference statements)

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“…The physics is described by the Langmuir adsorption model

\begin{matrix} \partial_{t} D + v \partial_{x} D & = - \frac{1}{r_{h}} f (D, A), \\ \partial_{t} A & = f (D, A) \end{matrix}

with

f (D, A) = \frac{1}{\frac{1}{k_{1}} + \frac{1}{k_{f}} (S_{\max} - A)} (D (S_{\max} - A) - K_{eq} A),

where D is the concentration of dissolved arsenate and A the concentration of arsenate adsorbed at the pipe wall. We adopt realistic parameter values from

\begin{matrix} v & = 10 m / \min, & r_{h} & = 50 l / m^{2}, \\ k_{1} & = 0.2 l / (mg \min), & S_{\max} & = 100 mg / m^{2}, \\ K_{eq} & = 0.0537 mg / l, & k_{f} & = 2.4 l / (m^{2} \min), \end{matrix}

and consider the system on the approximately positively invariant Ω given by D ∈[0,1]mg/l and A ∈[0,100]mg/m 2 . To discretize time and space, we decouple the advection and the reaction step with the Trotter formula .…”

Section: Application: Inference Of Arsenate Sourcementioning

confidence: 99%

A new network approach to Bayesian inference in partial differential equations

Kohler

Marzouk

Müller

et al. 2015

Int. J. Numer. Meth. Engng

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SUMMARYWe introduce a novel numerical approach to parameter estimation in partial differential equations in a Bayesian inference context. The main idea is to translate the equation into a state-discrete dynamic Bayesian network with the discretization of cellular probabilistic automata. There exists a vast pool of inference algorithms in the probabilistic graphical models field, which can be applied to the network.In particular, we reformulate the parameter estimation as a filtering problem, discuss requirements for according tools in our specific setup, and choose the Boyen-Koller algorithm. To demonstrate our ideas, the scheme is applied to the problem of arsenate advection and adsorption in a water pipe: from measurements of the concentration of dissolved arsenate at the outflow boundary condition, we infer the strength of an arsenate source at the inflow boundary condition.

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“…The physics is described by the Langmuir adsorption model

\begin{matrix} \partial_{t} D + v \partial_{x} D & = - \frac{1}{r_{h}} f (D, A), \\ \partial_{t} A & = f (D, A) \end{matrix}

with

f (D, A) = \frac{1}{\frac{1}{k_{1}} + \frac{1}{k_{f}} (S_{\max} - A)} (D (S_{\max} - A) - K_{eq} A),

where D is the concentration of dissolved arsenate and A the concentration of arsenate adsorbed at the pipe wall. We adopt realistic parameter values from

\begin{matrix} v & = 10 m / \min, & r_{h} & = 50 l / m^{2}, \\ k_{1} & = 0.2 l / (mg \min), & S_{\max} & = 100 mg / m^{2}, \\ K_{eq} & = 0.0537 mg / l, & k_{f} & = 2.4 l / (m^{2} \min), \end{matrix}

Section: Application: Inference Of Arsenate Sourcementioning

confidence: 99%

A new network approach to Bayesian inference in partial differential equations

Kohler

Marzouk

Müller

et al. 2015

Int. J. Numer. Meth. Engng

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“…[6][7][8][9][10]. In this case the bulk live heterotrophic bacteria were chosen to represent the biocontaminant.…”

Section: Simulation Experimentsmentioning

confidence: 99%

Quality model for integrated security monitoring and control in water distribution systems

Zubowicz

Arminski

Brdyś

2012

Proceedings of the 10th World Congress on Intelligent Control and Automation

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This article addresses the problem of drinking water distribution system (DWDS) security in the terms of water quality which in the era of terrorist threat is of high importance to the public. The contribution of this paper is the development of the so called security module to extend a multi-species water quality model. This gives an insight to the situation in DWDS not only under normal operational conditions but also in case of a malicious attack on water quality. Moreover the security inputs are formally introduced to the model structure. This module enables simulation of both bacterial and/or chemical water contamination in DWDS environment. Previously defined inputs are utilised in proposed experiments by an attacking agent to influence the DWDS quality. The purpose of model development is to enable water scientists and water authorities to simulate the contamination propagation pathways and mechanisms throughout the network without omitting the 'natural' water chemistry effects. A simple simulation example for the exemplary DWDS illustrates the model performance for two distinct contamination scenarios.

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“…We adopt realistic parameter values from [26,37], whereas in Figure 6(d) the pattern size is extended by W = {−1, 0} to V = {−1, 0}. It is observed that in this example increasing the pattern size does not improve the result if compared to the Monte Carlo case, but increasing the state space resolution has a notable effect.…”

Section: Arsenate Fate In Water Pipementioning

confidence: 99%

“…Consider the advection and adsorption of arsenate in drinking water pipes, a topic that has attracted a lot of attention in the water supply community lately [39,26]. We describe a water tank on a hill and a pipe to a consumer in a valley.…”

Section: Arsenate Fate In Water Pipementioning

confidence: 99%

Cellular Probabilistic Automata---A Novel Method for Uncertainty Propagation

Kohler¹,

Müller²,

Wever

2014

SIAM/ASA J. Uncertainty Quantification

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Abstract. We propose a novel density based numerical method for uncertainty propagation under distinct partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method using the example of initial value uncertainties under deterministic dynamics and show that it is consistent. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations.

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Modeling and Simultation of Arsenate Fate and Transport in a Distribution System Simulator

Cited by 11 publications

References 6 publications

A new network approach to Bayesian inference in partial differential equations

A new network approach to Bayesian inference in partial differential equations

Quality model for integrated security monitoring and control in water distribution systems

Cellular Probabilistic Automata---A Novel Method for Uncertainty Propagation

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