High purity distillation columns and multi-stream heat exchangers (MSHXs) are critical units in cryogenic air separation plants. This article focuses on modeling approaches for the primary section of a super-staged argon plant. A fullorder stage-wise model for distillation columns in air separation units (ASUs) that considers key process phenomena is presented, followed by a reduced-order model using a collocation approach. The extent of model reduction that can be achieved without losing significant prediction accuracy is demonstrated. A novel moving boundary model is proposed to handle MSHXs with phase change. Simulation results demonstrate the capability of the proposed model for tracking the phase change occurrence along the length of the heat exchanger. Dynamic simulation studies of the integrated plant show that the thermal integration between the feed and product streams captured in the primary heat exchanger is critical to accurately capture the behavior of ASUs.

This paper describes the development of a dynamic model for an industrial steelmaking electric arc furnace (EAF). The model is sufficiently detailed so as to describe the melting process and chemical reactions and account for reagent and energy additions. The lack of knowledge of reaction mechanisms due to the complex nature of the reacting system is overcome by modeling the process as equilibrium zones with mass transport limitations. An important objective of developing this model is to ensure that it can be used within an optimization framework, thus particular consideration is given to the continuity of model equations and the robustness of the model over a wide range of conditions. Parameter estimation is carried out using industrial data and the model performance illustrated through simulation studies.

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In this study population, MRI did not add any additional information beyond MDCT in identifying unstable cervical spine injuries. Magnetic resonance imaging frequently detected ligamentous injuries, none of which were found to be unstable at the time of detection, during the course of admission, or on follow-up. Magnetic resonance imaging provided beneficial clinical information and guided surgical procedures in patients with neurological deficits or radicular pain. An MDCT study with sagittal and coronal reconstructions negative for acute injury in patients without an abnormal motor examination may be sufficient alone for clearance.

in Wiley InterScience (www.interscience.wiley.com).The main objective of this work is the development of a computational procedure for determining optimal operating strategies for an industrial electric arc furnace (EAF). These goals are achieved by incorporating a detailed mechanistic model into a mathematical optimization framework. The model used in this work includes mass and energy balances, and contains sufficient detail to describe the melting process, chemical changes, and material and energy flows. Mathematical optimization is used to determine the optimal input trajectories based on an economic criterion; process limitations are accounted for by including them within the optimization problem as constraints. This optimization procedure considers trade-offs between all the process inputs and processing time, so as to maximize the profit. Several case studies illustrating the use of mathematical optimization in the enhancement of process performance are given.

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