**A Framework for Chemical Plant Safety Assessment under Uncertainty**

**Xiaoyan ZENG**, **Mihai ANIŢESCU**

Mathematics and Computer Science Division, Argonne National Laboratory

9700 South Cass Avenue, Building 221, Argonne, IL 60439-4844, U.S.A

**Candido PEREIRA**, **Monica REGALBUTO**

Chemical Sciences and Engineering Division, Argonne National Laboratory

9700 South Cass Avenue, Building 205, Argonne, IL 60439-4837, U.S.A

**Mihai Aniţescu dedicates his work on this article to the 60th birthday of Dr. Neculai Andrei. Neculai, thanks for your extraordinary work for the benefit of the numerical optimization community in Romania and everywhere.**

**Abstract**: We construct a framework for assessing the risk that the uncertainty in the plant feed and physical parameters may mask the loss of a reaction product. To model the plant, we use a nonlinear, quasi-steady-state model with stochastic input and parameters. We compute the probability that more than a certain product amount is diverted, given the statistics of the uncertainty in the plant feed, in the values of the chemical parameters, and in the output measurement. The uncertainty in the physical parameters is based on the one provided by the recently developed concept of thermochemical tables. We use Monte Carlo methods to compute the probabilities, based on a Cauchy-theorem-like approach to avoid making anything but the safest asymptotic assumptions, as well as to avoid the excessive noise in the region of low-probability events.

**Keywords**: Safety Assessment, Uncertainty, Chemical Process, Stream Methane Reforming, Active Thermochemical Tables, Monte Carlo Methods.

**Xiaoyan Zeng** has received the Bachelor degree in Applied Mathematics in 2000 and the Master degree in Applied Mathematics in 2003 in Wuhan University. She obtained the PhD in Applied Mathematics of Illinois Institute of Technology in 2008. She is currently working as a postdoctoral fellow in Mathematics and Computer Science Division at Argonne National Laboratory. Her research interests are in the areas of Monte Carlo and quasi-Monte Carlo methods, stochastic optimization and spline methods.

**Mihai Aniţescu** has obtained his Engineer (M.Sc.) Diploma in electrical engineering from the Polytechnic University of Bucharest in 1992 and his Ph.D. degree in applied mathematical and computational sciences from the University of Iowa in 1997. Between 1997 and 1999 he was the Wilkinson fellow in computational science in the Mathematics and Computer Science Division at Argonne National Laboratory. Between 1999 and 2002 he was an assistant professor of mathematics at the University of Pittsburgh, where he is currently an adjunct associate professor. Since 2002, he has been a computational mathematician In the Mathematics and Computer Science Division At Argonne National Laboratory. Dr. Anitescu is a Senior Editor for Optimization Methods and Software and a member of the editorial boards of Mathematical Programming series A. a series B. In 2009, Dr. Anitescu will be the member of the Organizing Committees of the SIAM Annual Meeting and of the International Symposium on Mathematical Programming.

**Candido Pereira** received his PhD in Chemical Engineering from the University of Pennsylvania. He is currently a Principal Engineer at Argonne National Laboratory where he leads the Process Simulation and Equipment Design Group, which develops computer codes and equipment designs for the treatment of spent nuclear fuel. He has been at Argonne since 1992, he has also worked on the Integral Fast Reactor program and on the development of hydrocarbon reforming systems for fuel cell applications.

**Monica Regalbuto** received her PhD in Chemical Engineering from Notre Dame University. She is currently Head of the Process Chemistry and Engineering Department, responsible for programmatic and financial management. She manages the activities of three research groups conducting research on spent fuel separations, process modeling and simulation, and repository waste form corrosion. Prior to joining Argonne she was a Senior Research Engineer at BP Amoco where she developed new technologies to reduce pollutants from gasoline combustion; she was also responsible for all separation needs at four refineries. In an earlier stint at Argonne, she developed material balance, solvent loading and speciation computer models for the TRUEX Program.

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**CITE THIS PAPER AS**:

Xiaoyan ZENG, Mihai ANIŢESCU, Candido PEREIRA, Monica REGALBUTO, **A Framework for Chemical Plant Safety Assessment under Uncertainty***, Studies in Informatics and Control*, ISSN 1220-1766, vol. 18 (1), pp. 7-20, 2009.

**1. Introduction**

Chemical plant safety is an issue that affects a large number of plants in the United States. Currently, more than 15,000 chemical plant sites in the United States are required to file a risk management plan with the U.S. Environmental Protection Agency [3]. Such plans consider both worst-case scenarios and alternative case scenarios. Such alternatives include the moderately abnormal release of controlled materials or illegal plant interference [17]. While sudden, massive release is likely detectable by safety measures in place, the same cannot be said of long-term, slow releases that can be confused with measurement noise or other uncertain information. In this paper, we present a novel framework that uses the plant model and prior statistical information about the uncertainty for estimating the risk posed by a diverting agent to a chemical plant. The diverting agent can be damage, an insufficient design, or an individual engaged in the illegal activity [3, 17].

For this initial application of our framework, we will assume that the chemistry is described by nonlinear equations, that is, that the reactions involved are in steady state [27]. This approximation is reasonable in the case where the chemical reactions have time constants that are much smaller than the typical frequencies in the input [9, 27]. However, to preserve a dynamical aspect of the inputs, which is essential for our work, we will employ a description of the chemical process whereby, due to our assumption of the chemical process having much smaller reaction times compared to the characteristic times over the input, the equilibration following the introduction of additional feed and extraction of the reaction products is instantaneous [9]. Therefore, our model will have discrete dynamics due to the progressive introduction of additional feed and extraction of the reaction products, but it will have no dynamics due to the chemistry. The equations of state are obtained by requiring that the reaction rates be zero and that the total mass of the individual components be conserved.

The key question that we are interested in answering is the following: Given the uncertainty in the input of a plant and in the physical parameters of the reaction, how confident can one be of the estimate of the amount of reaction product diverted from the plant?

**5. Conclusions and Future Research**

We have presented a model-based framework for assessing the risk of diversion of a given reaction product in a chemical plant in the presence of uncertainty. We have accounted for both feed and model parameter uncertainties. We have shown how the framework can be applied to chemical reaction models by tracking of hydrogen in the steam methane reforming reaction.

In future research, we will address the issue of obtaining superior estimates where we consider the entire covariance matrix that is obtained by our simulation. Therefore, in the language of this application, correlations between outputs would provide asymptotically sharper estimates than the one we have already obtained. In addition, we will be interested in formulating and solving the problem for the case with dynamics and a more faithful description of the input/output mechanism in the chemical plant (rather than all in – equilibration – all out, as we do at the moment). We will also apply quasi-Monte Carlo methods [15, 26] to sample the parameter to speed up the algorithm.

**Acknowledgments**

We are grateful to Dr. Branko Ruscic for providing access to and expertise in ATcT software. We are grateful to Dr. Manuela Serban for help with the SMR reaction setup. We are grateful to Prof. Dan Negrut for comments on our manuscript. This work was supported by the Department of Energy through contract DE-AC02-06CH11357.

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