Process equation-oriented

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. 

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. 

Sarma, P. V. L. N. and G. V. Reklaitis. Optimization of a Complex Chemical Process Using an Equation Oriented Model. Math Prog Study 20 113-160 (1982). 

Process flowsheeting tools can usually be classified within two categories. In the equation-oriented framework, the simulation system creates and... 

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. 

Industrial Applications of Plant-Wide Equation-Oriented Process Modeling—2010... 

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

A. R. M., "Development of a Modularly Organized Equation - Oriented Process Simulator". CACE 79, EFCE, Montreux, April 1979. 

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. 

Simultaneous (also known as equation-oriented) programs in which the entire process is described by a set of equations, and the equations are solved simultaneously, not stepwise as in the sequential approach. Simultaneous programs... 

In the past, most simulation programs available to designers were of the sequential-modular type. They were simpler to develop than the equation-oriented 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, etc., are fixed in time. With the sequential modular approach, computational difficulties can arise due to the iterative methods used to solve recycle problems and obtain convergence. A major limitation of sequential modular simulators is the inability to simulate the dynamic, time-dependent behavior of a process. 

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. 

Two extremes are encountered in flowsheeting software. At one extreme, the entire set of equations (and inequalities) representing the process is employed. This representation is known as the equation-oriented method of flowsheeting. The equations can be solved in a sequential fashion analogous to the modular representation described below or simultaneously by Newton s method, Broyden s method, or by employing sparse matrix techniques to reduce the extent of matrix manipulations. Refer to the review by Evans and Chapter 5. ... 

Both sequential and simultaneous calculational sequences have been proposed for the modular approach as well as the equation-oriented approach. Either the program and/or the user must select the decision variables for recycle and provide estimates of certain stream values to make sure that covergence of the calculations occurs, especially in a process with many recycle streams. Reviews by Evans and Rosen point out many of the problems and practices pertaining to flowsheeting. 

A second solution method is based on an equation-oriented approach, which represents each process unit with a set of equations that are either part of the simulator model library or provided by the user. This method frequently uses an ordered set of equations. Procedures have been developed to automatically determine this information after the simulation flow sheet topology and the complete set of equations have been defined for the process simulation. The equations for all of the process units are solved simultaneously. The equations describing every process in the simulation flow sheet are solved by standard numerical methods that are discussed later. The methods for simulation flow sheet decomposition and equation ordering are covered in the work of Cameron and Hangos and Westerberg et al. ... 

Many other parameters may be involved depending on the method of processing. Such orientation not only occurs when processing from a solution or a melt but may also occur by inducing strain in the material. Glass fiber reinforced polyamide-6 was subjected to such a strain. Heated specimens were extended under controlled strain and cooled under extension. Hencky strain was calculated from the following equation ... 

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... 

Equation-oriented approaches are based on sets of equations that are written for the units in a particalar flowsheet.36 Unlike the sequential-modular systems, which often contain the necemery information for a veriety of process units, equaiion-orianted synthesizers require the pinctirioner to develop the mode] eqon-lions. These are solved through iterative tecbaiques with staadatd numerical methods. 

---