Equation-oriented simulation

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. 

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. 

In an equation-oriented simulator, the executive program sets up the flowsheet and the set of equations that describe the unit operations and then solves the equations using data from the unit operations library and the physical property data bank and calling on the file of thermodynamics subroutines. 

Figure 2.9 Software architecture of an Equation-Oriented simulator...

The development of trade software such as Aspen Dynamics or ProsimBatch proves the interest of manufacturers in the use of dynamic simulation for process design and operation. However, some specific process cases may lead end user to develop dedicated simulator of his own. In this context, a library of common building blocks which allows a modular modeling and an equation-oriented simulation of processes seems to be relevant and useful. Providing these software components is the main objective of PrODHyS. Developed in our research department, it results from the unification of works performed since several years in this domain (Jourda et al., 1996 Sargousse, 1999 Moyse, 2000 Hetreux et al., 2002 Ferret et al., 2002). 

Examples of equation-oriented simulators include ACSL, gPROMS, and Aspen Custom Modeler (Luyben, 2002). 

In the equation-oriented approach, the executive organizes the equations and controls a general-purpose equation solver. The equations for material and energy balances may be grouped separately from those for the calculation of physical properties or phase equiHbria, or as ia the design of some simulators, the distinction between these groups of equations may disappear completely. 

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

Pantelides, C. C., and Barton, P. I., Equation-oriented dynamic simulation. Current status and future perspectives. Comput. Chem. Eng. 17. S263 (1993). 

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

Hutchison, H. P., Jackson, D. J., and Morton, W., The development of an equation-oriented flowsheet simulation and optimization package—II. Examples and results, Comp, and Chem Eng. 10(1), 31 (1986). 

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. 

The modelling tools in current commercial simulators may roughly be classified into two groups depending on their approach block-oriented (or modular) and equation-oriented. 

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. 

Hutchinson, H. P., D. J. Jackson, and W. Morton, Equation Oriented Flowsheet Simulation, Design and Optimization, Proc. Eur. Fed. Chem. Eng, Conf. Comput. Appl. Chem. Eng., Paris, April 1983 The Development of an Equation-Oriented Flowsheet Simulation and Optimization Package, Comput. Chem. Eng., v. 10, p. 19 (1986). 

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. ... 

Both the equation-oriented and the modular simulation approaches are implemented in CHEOPS for steady-state and for dynamic models. 

Pantelides, C.C., Barton, P.L Equation-oriented dynamic simulation Current status und future perspectives. Computers Chemical Engineering 17, 26.3 285 (1993)... 

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... 

In Equation-Oriented (EO) approach all the modelling equations are assembled in a large sparse system producing Non-linear Algebraic Equations (NAE) in steady state simulation, and stiff Differential Algebraic Equations (DAE) in dynamic simulation. Thus, the solution is obtained by solving simultaneously all the modelling equations. 

It may be concluded that Sequential-Modular approach keeps a dominant position in steady state simulation. The Equation-Oriented approach has proved its potential in dynamic simulation, and real time optimisation. The solution for the future generations of flowsheeting software seems to be a fusion of these strategies. The release 11.1 of Aspen Plus (2002) incorporates for the first time EO features in the environment of a SM simulator. 

In Equation-Oriented (EO) approach the software architecture is close to a solver of equations. EO is more suited for dynamic simulation since this can be modelled by a system of differential-algebraic equations (DAE) of the form ... 

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