Simultaneous modular model

Use of the reduced space SQP mentioned in Section 15.1 has facilitated the implementation of simultaneous modular optimization. The modeling equations representing the individual modules are not explicitly made part of the optimization problem. Instead, the equations are solved by taking successive steps using Newton s... 

The older modular simulation mode, on the other hand, is more common in commerical applications. Here process equations are organized within their particular unit operation. Solution methods that apply to a particular unit operation solve the unit model and pass the resulting stream information to the next unit. Thus, the unit operation represents a procedure or module in the overall flowsheet calculation. These calculations continue from unit to unit, with recycle streams in the process updated and converged with new unit information. Consequently, the flow of information in the simulation systems is often analogous to the flow of material in the actual process. Unlike equation-oriented simulators, modular simulators solve smaller sets of equations, and the solution procedure can be tailored for the particular unit operation. However, because the equations are embedded within procedures, it becomes difficult to provide problem specifications where the information flow does not parallel that of the flowsheet. The earliest modular simulators (the sequential modular type) accommodated these specifications, as well as complex recycle loops, through inefficient iterative procedures. The more recent simultaneous modular simulators now have efficient convergence capabilities for handling multiple recycles and nonconventional problem specifications in a coordinated manner. 

Umeda and Nishio ( J3) using fully linearized models compared the sequential modular and simultaneous modular approaches and concluded each architecture had its area of applicability. 

Simultaneous-modular methods attempt to combine the features of the sequential-modular and equation-oriented approaches to make use of models developed for the forater and to include (he flexibility of the latter.3 For more information, the reader is referred to the recent review by Biegler.3 ... 

In Simultaneous-Modular approach the solution strategy is a combination of Sequential-Modular and Equation-Oriented approaches. Rigorous models are used at units level, which are solved sequentially, while linear models are used at flowsheet level, solved globally. The linear models are updated based on results obtained with rigorous models. This architecture has been experimented in some academic products. 

A chemical process plant consists of many unit operations connected by process streams. Each process unit may be modelled by a set of equations (ODEs, PDEs, DAEs, algebraic equations), which include material, energy and momentum balances, phase and chemical equilibrium relations, rate equations and physical property correlations. These equations relate the outlet stream variables to the inlet stream variables for a given set of equipment parameters. At present, there are three approaches of flowsheet calculations the sequential modular, the equation oriented approach and the simultaneous modular strategy. 

Modular simulators are frequently constructed on three levels. The lowest level consists of thermodynamics and other physical property relations that are accessed frequently for a large number of flowsheeting utilities (flash calculations, enthalpy balances, etc.). The next level consists of unit operations models as described above. The highest level then deals with the sequencing and convergence of the flowsheet models. Here, simultaneous... 

Before leaving this section we consider a slightly different optimization problem that may also be expensive to solve. In flowsheet optimization, the process simulator is based almost entirely on equilibrium concepts. Separation units are described by equilibrium stage models, and reactors are frequently represented by fixed conversion or equilibrium models. More complex reactor models usually need to be developed and added to the simulator by the engineer. Here the modular nature of the simulator requires the reactor model to be solved for every flowsheet pass, a potentially expensive calculation. For simulation, if the reactor is relatively insensitive to the flowsheet, a simpler model can often be substituted. For process optimization, a simpler, insensitive model will necessarily lead to suboptimal (or even infeasible) results. The reactor and flowsheet models must therefore be considered simultaneously in the optimization. 

Note that this formulation illustrates an interesting trade-off for the optimization problem. In the modular mode the optimization problem remains fairly small and function evaluations (e.g., the reactor model) are expensive. With the simultaneous formulation, the model becomes a set of equations whose right-hand sides are much cheaper to evaluate, but the size of the optimization problem increases. Nevertheless, Vasantharajan and Biegler (1988b) showed that, even without SQP decomposition, the simultaneous approach for the reactor was 38% cheaper for the entire flowsheet optimization than the modular approach. Moreover, the number of function evaluations for the reactor model decreased by over an order of magnitude. 

An alternative to the sequential modular approach is to solve the equations modeling all of the units in a process flowsheet simultaneously this is known as the equation-based approach. Advantages to the sequential modular approach include (1) specialized numerical techniques tailored to each unit operation can be used, and (2) the numerical failure of one unit operation may still yield usable flowsheet information. Advantages to the equation-based... 

When there are multiple recycles present, it is sometimes more effective to solve the model in a simultaneous (equation-oriented) mode rather than in a sequential modular mode. If the simulation problem allows simultaneous solution of the equation set, this can be attempted. If the process is known to contain many recycles, then the designer should anticipate convergence problems and should select a process simulation program that can be run in a simultaneous mode. 

In this work, we develop an algorithm based on fitting response surfaces -using a kriging metamodel- for the optimization of constrained-noise black box models. Besides, an important characteristic is that we deal with constrained problems in which the metamodel can represent either the objective function or some constraints (or both simultaneously). A typical case is the optimization of process flowsheets using modular simulators in which some units are represented by a metamodel. In these systems it is possible to include external constraints and even the result of some calculations could be constraints to the model. 

So-called plant dispersion" or extra column effects" have to be taken into account by additional mathematical models rather than including them indirectly in the model parameters of the column, e.g. by altering the dispersion coefficient. The combination of peripheral and column models is easily implemented in a modular simulation approach. In a flowsheeting approach the boundary conditions of different models are connected by streams (node balances) and all material balances are solved simultaneously. 

The second component of onr project is the incorporation of nanoscale science experimentation into the introdnctoiy level cnrricula in each science discipline. In doing so, we emphasize topics of cnrrent research interest in nanoscale science and use a common instrament across traditional disciplines. We incorporate a modular approach to facilitate replacement of existing laboratory exercises rather than the replacement of an entire course, or the development of an additional conrse that might be poorly populated as an elective course in a number of majors. Each module is designed aroimd the use of a scanning probe microscope (SPM), operated as either a scanning tuimeling microscope (STM) or as an atomic force microscope (AFM), independent of the scientific discipline involved. We incorporate the SPM because it is commonly used in nanoscale science experiments and because one way to illustrate the field s interdisciplinary nature is to demonstrate the multiple ways one instmment can be used in several traditional fields to obtain results of interest to that field. Thus each module makes use of a SPM and a model for a SPM to instmct the students in a specific science discipline, and simultaneously in the fundamental concepts of nanoscale science. The modules themselves can be found online (15) and will be addressed more completely elsewhere. 

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