This paper investigates application of SQP optimization algorithms to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs. full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.

This paper investigates application of SQP optimization algorithms to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs. full space methods. The suitable choices between these various strategies are assessed informally through a case study.

eCalc is the name of a software tool for high-quality emission forecasting. eCalc allows integration of subsurface and operational knowledge and calculates emission forecasts directly relating drainage strategy to operational strategies and equipment. Emissions directly relating to reservoir drainage (CO2 in particular) vary with the reservoir production rates and pressures, and the process assumptions. Emissions from drilling, flaring and mobile vessels may be included for integrated bookkeeping. eCalc is a holistic asset prognosis tool for calculation of the total emissions allowing break-down into single emission sources. eCalc has integrated energy functions to be used for modeling the energy usage of various process equipment such as pumps, compressors, generators, and turbines. The energy functions are models that relate input variables to energy consumption. The input variables are typically rate and pressures. For the compressor models, it uses compressor curves and thermodynamical models to calculate the shaft work needed for the predicted compression work through a single or a series of compressors. Also, it has built in models for future low-pressure projects, for less mature tie-in projects and new builds where vendor data is not available. In addition, there is also support for energy functions based on tables generated by external software (e.g. Unisim, Hysys). The flexibility of the software allows evaluating varying subsurface drainage strategies combined with process modifications in an integrated calculation. The tabulated energy functions, or likewise thermodynamical calculations, allow for a fast and easy to use calculation tool that can be used in multi-realization systems like the fast model update environment. eCalc is batch callable in Unix and can thus be easily integrated in workflows. eCalc also allows integration with external software, like for example numerical optimizers. eCalc uses process knowledge to mimic anti-surge and minimum flow without needing iterative solvers. Depending on where the operating point is relative to the chart, eCalc implements control strategies to automatically mimic process control. Eg if the operating point is in the surge domain, eCalc adds mass rate to the rate input to move to a point on the control line. A forward model results which is at the core of the calculations. It is not intended to replace the commercial process simulation software but allows subsurface personnel access to simplified process calculations and therefore opens the possibility for a better cross-disciplinary working environment. The integrated tool makes mutual information exchange between operations, subsurface and sustainability disciplines easy. The engineering approach with real physical models, capacities and data provides a high-quality emission forecast suitable for the long term. eCalc has been implemented on nearly all Norwegian installations (Espelid et al, 2022) and three generic examples are included in this paper.

In this paper a control relevant nonlinear dynamic model of grate sintering is presented. The model is designed for control purposes for use in future model predictive control MPC strategies. A m ulti-model approach i s utilized where the model is presented as a convex combination of locally a ne models. The model performance is compared to global models listed in the literature by simulations and by comparison to industrial plant data. I n troductionThe metallurgical process of sintering prepares the iron ore to form suitable feed for the blast furnace. Granulated ore and coke are mixed, moistened with water and micro-pelletized to form the charge. The charge is loaded onto a grate and leveled to form a bed which i s ignited by a gas-fueled ignition hood. A heat wave and coke combustion zone travels down through the bed under the in uence of a suction pressure. Hot gas from the combustion zone passes through moist charge deeper in the bed where water evaporates. The process can be divided in ve subsequent zones; heat exchange, fusion, combustion, drying and over-moist charge. This is illustrated in gure 2 a. The main purpose of sintering is to convert weakly-bounded granules into a partially fused porous sinter cake suitable for feeding to the blast furnace. Sintering is a complex process involving ow o f gas through a packed bed, heat and mass transfer between gas and solids, heterogeneous chemical reactions and melting of solids.Several models of the sintering process is presented in the literature 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . These models are presented as nonlinear PDE's, and mainly focus on reproducing important process quantities. There are few reported results on model based control of the sintering process. Kwon et al. 9 uses a linear MPC scheme with an identi ed input output model to control the burn-through point o f t r a veling grate sintering. The reported real-time experiments and simulations demonstrates that the chosen MPC algorithm performs well. In the present w ork, the problem of controlling production rate and quality is directly addressed by identifying a model from designed experiments. As argued below there is an economic criteria restricted by constraints involved, and investigating MPC as a means to control grate sintering is motivated. We seek to exploit the underlying structure of the sintering process to develop a structured model which later on can be utilized to develop a robust control strategy for the sintering process. In the present approach the global nonlinear PDE model is approximated by a convex combination of locally linear or a ne models. The local zone models are interconnected by both boundary values and propagation of zone positions as sintering proceeds. The interconnection of the zones are handled by the multi-modeling techniques of Johansen and Foss 10 . This method gives smooth interpolation of zones and is chosen since exact zone boundaries are uncertain and overlap. Early attempts to model the sintering process divided the process into zones 1 . This ...

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