Sequential Modular Simulation

PLOW 1 RAN was made available in 1974 by Monsanto Co. for steady-state simulation of chemical processes based on sequential modular technology. It requires specification of feed streams and topology of the system. In 1987, an optimization enhancement was added. 

Equations-Oriented Simulators. In contrast to the sequential-modular simulators that handle the calculations of each unit operation as an iaput—output module, the equations-oriented simulators treat all the material and energy balance equations that arise ia all the unit operations of the process dow sheet as one set of simultaneous equations. In some cases, the physical properties estimation equations also are iacluded as additional equations ia this set of simultaneous equations. 

The essential differences between sequential-modular and equation-oriented simulators are ia the stmcture of the computer programs (5) and ia the computer time that is required ia getting the solution to a problem. In sequential-modular simulators, at the top level, the executive program accepts iaput data, determines the dow-sheet topology, and derives and controls the calculation sequence for the unit operations ia the dow sheet. The executive then passes control to the unit operations level for the execution of each module. Here, specialized procedures for the unit operations Hbrary calculate mass and energy balances for a particular unit. FiaaHy, the executive and the unit operations level make frequent calls to the physical properties Hbrary level for the routine tasks, enthalpy calculations, and calculations of phase equiHbria and other stream properties. The bottom layer is usually transparent to the user, although it may take 60 to 80% of the calculation efforts. 

The computer effort required for convergence depends on the number and complexity of the recycles ia the dowsheet, the nonlinearities ia the physical properties, and the nonlinearities ia the calculation of phase or chemical equiHbria. In sequential-modular simulators these calculations are converged one at a time, sequentially, and ia a nested manner. In equation-oriented simulators they are converged as a group and, ia the case of complex dow sheets involving nonideal mixtures, there could be significant reduction ia computer effort. 

Historically, sequential-modular simulators were developed first. They were also developed primarily ia iadustry. They coatiaue to be widely used. la terms of unit operatioas, each module can be made as simple or complex as needed. New modules can be added as needed. Equation-oriented simulators, on the other hand, are able to handle arbitrary specifications and limitations for the entire process dow sheet more dexibly and conveniendy than sequential-modular simulators, and process optimization can also be carried out with less computer effort. 

Algorithmic stmcture of simulator EO, equation oriented HS, hybrid system SM, sequential modular and SMD, sequential modular, suitable for design. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

In the past, most simulation programs available to designers were of the sequential-modular type. They were simpler to develop than the equation based programs, and required only moderate computing power. The modules are processed sequentially, so essentially only the equations for a particular unit are in the computer memory at one time. Also, the process conditions, temperature, pressure, flow-rate, are fixed in time. 

Sequential modular. Refers to the process simulator being based on modules, and the modules solved in a sequential precedence order imposed by the flowsheet information flow. 

Commercial process simulators mainly use a form of SQP. To use LP, you must balance the nonlinearity of the plant model (constraints) and the objective function with the error in approximation of the plant by linear models. Infeasible path, sequential modular SQP has proven particularly effective. 

Biegler, L. T. Improved Infeasible Path Optimization for Sequential Modular Simulators—I The Interface. Comput Chem Eng 9 245-256 (1985). 

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. 

Biegler. L. T., and Cuthrell, 1. E., Improved infeasible path optimization for sequential modular simulators — II The optimization algorithm, Comp, and Chem. Eng. 9(3), 257-267 (1985). 

The solution of a chemical process simulation problem using the sequential modular technique is represented in Fig. 2. Here, the modeling equations can be written such that the outlet stream from each unit is a function of the inlet streams to each unit ... 

A major academic effort has been mounted to reevaluate system architectures. This has been motivated by the limitations of the sequential modular method for design and optimization (21). This in turn has led to a strong research effort in equation solving methods tailored to meet the needs of process simulation. 

The computational architecture is a sequential modular approach with advanced features. To model a process, each equipment module is simulated by a program module. The overall process is simulated by connecting the models together in the same way as the equipment in the flow sheet. When the input streams are known then the outputs can be calculated. The entire flowsheet can be calculated "sequentially" in this manner. Advanced features are discussed below in connection with an example. 

Implementation of dynamic simulators has led to interesting research issues. For example, many have been implemented in a sequential modular format. To carry out the integration correctly from the point of view of correctly assessing integration errors, each unit model can receive as input a current estimate for the state variables (variables x), the unit input stream variables, and any independent input variables specified versus time... 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

Process design for continuous processes is carried out mostly using steady-state simulators. In steady-state process simulation, individual process units or entire floivsheets are calculated, such that there are no time deviations of variables and parameters. Most of the steady-state floivsheet simulators use a sequential modular approach in which the flowsheet is broken into small units. Since each unit is solved separately, the flowsheet is worked through sequentially and iteration is continued until the entire flowsheet is converged. Another way to solve the flowsheet is to use the equation oriented approach, where the flowsheet is handled as a large set of equations, which are solved simultaneously. 

Clearly define, in your own words, the terms design variables and state variables, sequential modular flowsheet simulation, equation-based flowsheet simulation, tear stream, convergence block, and design specification. 

The next example illustrates the structuring of a sequential modular process simulation using blocks of the types just described. 

Choose a tear stream variable and convert the flowchart into a block diagram for a sequential modular simulation, using blocks MIX. REACT. SEP. and a convergence block CONVC. 

An example of a sequential modular simulation of a relatively large process is given in Example 10.3-3, following a discussion of the second broad approach to process simulation. 

The sequential modular approach to process simulation solves system equations in blocks corresponding to the unit operations that make up the process. The block diagram for the process looks very much like the traditional process flowchart. Since engineers are accustomed to viewing chemical processes as sequences of unit operations, they lend to feel comfortable with this approach. 

In the equation-based approach, the equations for all units are collected and solved simultaneously. The natural decomposition of the system into its constituent unit operations is therefore lost. Moreover, the simultaneous solution of large numbers of equations, some of which may be nonlinear, can be a cumbersome and time-consuming problem, even for a powerful computer. For all these reasons, most commercial simulation programs were still based on the sequential modular approach when this text was written. 

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.)... 

Set up a sequential modular simulation of the process, using the following blocks ... 

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