Simultaneous modular

Simultaneous modular. The process simulator is composed of modules, but simplified, approximate, or partial representation of the modules enables solution techniques used in equation-based methods to be employed. 

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... 

Comparison of the results of equation-based and simultaneous modular-based optimization for two connected distillation columns... 

Chen, H. S. and M. A. Stadtherr. A Simultaneous-Modular Approach to Process Flowsheeting and Optimization I. Theory and Implementation. AIChE J 30 1843-1856 (1984). 

Mahalec, V. H. Kluzik and L. B. Evans. Simultaneous Modular Algorithm for Steady State Flowsheet Simulation and Design. Paper presented at the 12th European Symposium on Computers in Chemical Engineering. Montreaux, Switzerland (1979). 

Kisala, T. P. R. A. Trevino-Lozano J. F. Boston H. I. Britt et al. Sequential Modular and Simultaneous Modular Strategies for Process Flowsheet Optimization. Comput Chem Eng 11 567-579 (1987). 

Sequential Modular Methods / 15.3.2 Simultaneous Modular Methods / 15.3.3 Calculation of Derivatives... 

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. 

Dynamic simulation, process control, real-time optimization Process synthesis, flowsheet convergence, simultaneous modular vs. equation-oriented... 

Simultaneous Modular. There has been an almost continuum of architectures suggested to take advantage of the better features of sequential modular, linear and simultaneous architectures. Most of these suggestions seek to retain the calculation modules (since millions of dollars have been invested in sequential modular software) and thus the name simultaneous modular has been applied. FLOWPACK II (93) apparently has some simultaneous modular features. 

Simultaneous modular architecture can probably be further broken down into two categories. 

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. 

Kluzik, H. A., "A Study of the Simultaneous Modular Convergence of Chemical Process Flowsheets",... 

Mahalec, V. Kluzik, H. Evans, L. B., "Simultaneous Modular Algorithm for Steady State Flowsheet Simulation and Design", CACE 79, EFCE Montreux, April 8-11, 1979. 

Lin, T. D., "A Simultaneous Modular Simulator and A Sequential Block - Modular Simulator for Process Design or Simulations", Paper presented at AlChe Meeting, Houston, April 1979. 

Another potential advancement is permitted in the ASPEN system. Tear streams can be designated as desired, so that a user might define blocks or series of blocks and simulate these sets as quasi-linear blocks. The convergence method could utilize this information and solve the material (and energy) balances explicitly. In this way, a simultaneous modular architecture could be utilized. Implementation of these programs will be for later enhancements of ASPEN, not the initial version. 

Ihese difficulties vanish if the system equations are simply collected and solved for all unknown variables. Several powerful equation-solving algorithms are available in commercial programs like Maple , Mathematica , Matlab , Mathcad , and E-Z Solve that make the equation-based approach competitive with the sequential modular approach. Many researchers in the field believe that as this trend continues, the former approach will replace the latter one as the standard method for flowsheet simulation. (Engineers are also working on simultaneous modular methods, which combine features of both sequential modular and equation-based approaches. We will not deal with these refinements here, however.)... 

Jirapongphan, S., J. F. Boston, H. I. Britt, and L. B. Evans, A nonlinear simultaneous modular algorithm for process flowsheet optimization, Paper presented at AIChE 73rd Annual Meeting, Chicago, November 1980. 

More recant efforts to develop computer-aided process synthesis methodologies can be cbeincterized as either sequential modular, simultaneous modular, or equation oriented, Sequeatial-modular approaches are ben for steady-state simulation where process inputs are defined and process para met ara ate available. The best feature of sequential-modular approaches is that they are flowsheet oriented, bot they are not as flexible as the other methodologies in parfonuing design and optimization tasks.39... 

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 ... 

L. T. Biegler, Simultaneous Modular Simulation and Optimimtion. in Proceedings of the Second... 

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. 

Jirapongphan, S., Simultaneous Modular Convergence Concept in Process Flowsheet Optimization, Sc.D. Thesis, M.I.T., Cambridge, Massachusetts (1980). 

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. 

First, we define the objective function (see Figure 8.22b) such as energy consumption, the number of trays of a column, and the conversion of a reactor. We have up to three optimization algorithms for this case SQR, general reduced gradient, and simultaneous modular SQP. The particularities of the methods can be found elsewhere [44,45]. We define the independent variables and the constraints over variables from the streams or the equipment just by selecting the unit or the stream and the variable and the range of values of operation and an initial value. 

The simultaneous modular approach along with equation-based methods have been used to optimise three case studies. The modular approach has advantages but when optimising there is a price to pay for this. More bounding steps are required resulting in higher computation times although in the case of the water network problem, the most nonlinear of the problems, the price was small. 

The simultaneous modular approach has been applied. This corresponds to using a recycle module where the parameters are independent variables in the optimisation and the residuals are the residuals of the constraints X-rXc = 0. In this case, the recycle is converged as the optimisation converges. 

---