Real-time optimization models

Some recent applications have benefited from advances in computing and computational techniques. Steady-state simulation is being used off-line for process analysis, design, and retrofit process simulators can model flow sheets with up to about a million equations by employing nested procedures. Other applications have resulted in great economic benefits these include on-line real-time optimization models for data reconciliation and parameter estimation followed by optimal adjustment of operating conditions. Models of up to 500,000 variables have been used on a refinery-wide basis. 

A real-time optimization (RTO) system determines set point changes and implements them via the computer control system without intervention from unit operators. The RTO system completes all data transfer, optimization c culations, and set point implementation before unit conditions change and invahdate the computed optimum. In addition, the RTO system should perform all tasks without upsetting plant operations. Several steps are necessaiy for implementation of RTO, including determination of the plant steady state, data gathering and vahdation, updating of model parameters (if necessaiy) to match current operations, calculation of the new (optimized) set points, and the implementation of these set points. 

There is a need for methods that can determine global optima for arbitrary nonlinear functions, and that can handle extremely large nonlinear models for real-time optimization (on the order of millions of variables). 

Other synonyms for steady state are time-invariant, static, or stationary. These terms refer to a process in which the values of the dependent variables remain constant with respect to time. Unsteady state processes are also called nonsteady state, transient, or dynamic and represent the situation when the process-dependent variables change with time. A typical example of an unsteady state process is the operation of a batch distillation column, which would exhibit a time-varying product composition. A transient model reduces to a steady state model when d/dt = 0. Most optimization problems treated in this book are based on steady state models. Optimization problems involving dynamic models usually pertain to optimal control or real-time optimization problems (see Chapter 16)... 

In plant operations planning each refinery model produces target operating conditions, stream allocations, and blends across the whole refinery, which determines (a) optimal operating conditions, flows, blend recipes, and inventories and (b) costs, cost limits, and marginal values to the scheduling and real-time optimization (RTO) models. 

Diagram showing the combination of real-time optimization and model predictive control in a computer control system. 

Fatora III, F. C. Gochenour, G. B. and Kelly, D. N., "Modeling Ethylene Plants for Real-Time Optimization Applications", Paper Presented at the National AIChE Meeting (April 1992). 

Workstations. Workstations are the most powerful computers in the system, capable of performing functions not normally available in other units. A workstation acts both as an arbitrator unit to route internodal communications and as the database server. An operator interface is supported, and various peripheral devices are coordinated through the workstations. Computationally intensive tasks, such as real-time optimization or model predictive control, are implemented in a workstation. Operators supervise and control processes from these workstations. Operator stations may be connected directly to printers for alarm logging, printing reports, or process graphics. 

Another situation when the use of the statistical model can be a good choice over the RSM is when the deterministic model is excessively complex. For example, when the process is described by a distributed parameters model, the steady-state mass and energy balances are differential equations. The use of differential equations as constraints in an optimization problem makes its solution difficult and increases the incidence of convergence problems. In this case, solving the optimization problem using the statistical model is much simpler. The statistical model can also be used when the computational effort to solve the optimization problem using the deterministic model is too high, as can be the case for real-time optimization problems. 

It should be noted that the optimization problems solved for levels 2 and 3 begin to merge as the plantwide optimization begins to set targets for the unit operations in many process units. This large-scale, frequent optimization of operating conditions is known as real-time optimization (RTO). RTOs are run approximately every 30 minutes to 1 hour, with the resulting optimal setpoints downloaded to model predictive controllers (MPC). 

Although the MPC paradigm encompasses several different variants, each one with its own special features, all MPC systems rely on the idea of generating values for process inputs as solutions of an on-line (real-time) optimization problem. That problem is constructed on the basis of a process model and process measurements. Process measurements provide the feedback (and, optionally, feedforward) element in the MPC structure. Figure 1 shows the structure of a typical MPC system. It makes it clear that a number of possibilities exist for the following ... 

Model Parameterization Tailored to Real-time Optimization... 

Keywords Measurement-based optimization Real-time optimization Plant-model mismatch Model adaptation Model parameterization. 

Real-time optimization (RTO) schemes improve process performance by adjusting selected optimization variables using available measurements. The goal of this closed-loop adaptation is to drive the operating point towards the true plant optimum in spite of inevitable structural and parameter model errors. RTO methods can be classified in different ways. This section presents one such classification based on the parameters that can be adapted, as illushated in Fig. 1 note that repeated numerical optimization is used in the methods of columns 1 and 2, but not in those of column 3. 

Van Den Bergh, J., Model Reduction for Dynamic Real-Time Optimization of Chemical Processes, PhD Thesis, Delft University of Technology, The Netherlands, 2005. 

In the framework of real-time optimization, measurements are used to compensate for effects of uncertainty. The main approach uses measurements to update the parameters of a process model. In contrast, the constraint-adaptation scheme uses the measurements to bias the constraints in the optimization problem. In this paper, an algorithm combining constraint adaptation with a constraint controller is presented. The former detects shifts in the set of active constraints and passes the set points of the active constraints to the latter. In order to avoid constraint violation, the set points are moved gradually during the iterative process. Moreover, the constraint controller manipulates linear combinations of the original input variables. The approach is illustrated for a simple case study. 

The use of online data together with steady-state models, as in Real Time Optimization applications, requires the identification of steady-state regimes in a process and the detection of the presence of gross errors. In this paper a method is proposed which makes use of polynomial interpolation on time windows. The method is simple because the parameters in which it is based are easy to tune as they are rather intuitive. In order to assess the performance of the method, a comparison based on Monte-Carlo simulations was performed, comparing the proposed method to three methods extracted from literature, for different noise to signal ratios and autocorrelations. 

Petroleum shortage is an important issue. Improving the efficiency of refineries by optimising their operation is one of the measures that must be implemented. In order to do so using computational tools available, like Real Time Optimization (TTTO), it is mandatory to use data obtained in steady-state operation. This justifies the need for steady-state detection procedures, because the adaptation of process models to data obtained exclusively in steady state operation leads to better solutions (Bhat Saraf, 2004). 

Real Time Optimization. This module receives the values of the variables of the plant, performs reconciliation on these values. This node has a steady state (mathematical, physically based) model of the plant. An optimization is made using that model every hour or so. The optimization results are sent to the lower level, the supervisory control. These results are the new set points of the controlled variables. The best operating point of the plant (which means a set of set points values) is calculated in each optimization. The optimization takes into account constraints on the variables (limited change in manipulated variables, safety, quality, etc. constraints in controlled variables). The node uses as well a historian module with past data of the plant. 

Doe PD, Booker JD, Innes TC and Oliver AR (1996) Optimal lumber seasoning using acoustic emission sensing and real time strain modelling. Proceedings, 5th lUFRO International Wood Drying Conference, Quebec City, Canada, 209-12 Dohr AW (1953) Mechanical properties of Brazilian Parana pine. Southern Lumberman, 5(232,4) 39-42... 

Forbes, J.F. Marlin, T.E. Design cost a systematic approach to technology selection for model-based real-time optimization systems. Comput. Chem. Eng. 1996, 20 (6/7), 717-734. 

Fraleigh, L.M. Guay, M. Forbes, J.F. Sensor selection for model-based real-time optimization relating design of experiments to design cost. J. Process Control 2003, 13, 667-678. 

Halim, A. Detection and Diagnosis of Plant-Model Mismatch for Real-Time Optimization. M.Sc. thesis, University of Alberta, Edmonton, 2003. 

Model predictive control is based on real-time optimization of a cost function. Consequently, CPM methods that focus on the values of this cost function can be developed. The MPC cost function T(A ) is... 

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