Sequential modular calculations

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. 

In a sequential-modular program the executive program sets up the flow-sheet sequence, identifies the recycle loops, and controls the unit operation calculations interacting with the unit operations library, physical property data bank and the other sub-routines. It will also contain procedures for the optimum ordering the calculations and routines to promote... 

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. 

Sequential Modular. By far the most experience with flowsheeting systems has been with the sequential modular architecture (59- 3). It is this architecture that is most easily understood by the process engineer. Each module calculates all output streams from input streams subject to module parameters. Generally, the stream variables consist of component flows, temperature (or enthalpy) and pressure as the independent variables. Other dependent variables such as total flow, fraction vapor and total enthalpy (or temperature) are often carried in the stream. 

Partitioning and the Cycle Matrix. Sequential modular systems require an order of calculation (precedence order) be given to the modules. There are generally four steps taken to determine this ordering. 

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. 

A number of variations are possible with such two tiered sytems. Tearing can take place in the conventional way and the torn streams can be estimated. Each module in turn can be calculated as in the sequential modular systems. A linearized model of each module can then be generated which in turn can be used in the linearized flowsheet model. From Equation (1)... 

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. 

For convergence calculations ASPEN employs some advanced features with the well-proven sequential modular architecture. 

Chemical processes more often than not contain recycle, a feature that complicates their analysis. Recycle often occurs, as in the styrene process where unreacted ethylbenzene is recovered and recycled back to the reactor as a physical mass flow. Recycle also occurs in the form of heat exchange (again in the styrene process) and sometimes as information, e.g., a specification that two variable temperatures must equal each other. The sequential-modular solution strategy is based upon knowing all inputs to a module and using these to calculate all outputs. When an input stream to a module is the output of a downstream module (i.e., there is recycle), calculations cannot be performed for the upstream module because one of its inputs is not yet known. This is illustrated in Fig. 4.7 unit 1 cannot be calculated because input stream 4 is the output of unit 2 nor can unit 2 be calculated because input stream 2 is an output of unit 1. This same problem of circular reasoning was encountered in Example 1. This dilemma in the sequential modular solution scheme can be... 

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. 

Now that the problem is formulated we turn our attention to solving the equations. One solution method that we could use is the sequential modular method. For this method, select one of the process units as the starting point for the calculation. Then, assume values for some of variables to reduce the degrees of freedom to zero for that rniit. Next, precede unit-by-unit through the flow sheet... 

As we noted at the beginning of this chapter, there are two broad approaches to the automated solution of the balance equations for a process system the sequential modular approach and the equation-based approach. This section outlines the first of these methods. The balance equations (and any other equations that may arise from physical considerations or process specifications) for each unit are written and solved. If there are no recycle streams, the calculation moves from one unit to another, until all units have been covered. If there is a cycle (the conventional term for a recycle loop in a process flowchart), a trial-and-error procedure is required values of one or more stream variables in the cycle are assumed the balance equations for units in the cycle are solved, one unit at a time, until the values of the assumed variables are recalculated new variable values are assumed and the procedure is repeated until the assumed and calculated values agree. 

If the calculations were to be done by hand, overall system and subsystem balances would eventually yield n equations in unknowns, and the equations could then in principle be solved for all the desired process variables. It would be difficult to write a sequential modular program to implement this method for an arbitrary process, however. Instead, the following iterative approach is used. 

The sequential modular method of flowsheeting, as mentioned previously, is the one most commonly encountered in computer packages. A module exists for each process unit in the information flowsheet. Given the values of each input stream composition, flow rate, temperature, pressure, enthalpy, and the equipment parameters, the module calculates the properties of its outlet streams. The output stream for a module can become the input stream for another module for which the calculations proceed until the material and energy balances are resolved for the entire process. 

The two basic flowsheet software architectures are sequential modular and equation-based. In sequential modular, we write each unit model so that it calculates output(s), given feed(s), and unit parameters. This is the most commonly used flowsheeting architecture at present, and examples include Aspen+ plus Hysys (AspenTech), ChemCAD, and PROll (SimSci). In equation-based (or open-system) architectures, all equations are written describing material and energy balances as algebraic equations in the form/(x) = 0. This is the preferred architecture for new simulators and optimization, and examples include Speedup (AspenTech) and gPROMS (PSE pic). Each is discussed in turn. 

In Sequential-Modular approach, the calculation sequence plays an important role in obtaining overall convergence. Transmission of information techniques may be used to untie the nested loops and simplify the calculation sequence. 

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. 

In an acyclic system, the sequential modular approach is ideal from a computational viewpoint. However, most of the process plants involve recycles, particularly those highly integrated, in that case the problem cannot be solved directly and an iterative process must be used. Consider, for example, the simple flowsheet in Figure 8.8a. All the degrees of freedom are satisfied however, to calculate the mixer, we need to completely know both the feed stream and the recycle stream, but we only know the feed. To calculate the recycle stream, we should solve the compressor ... 

The sequential modular approach can be formulated in a way suitable for interval methods. Modules are connected in the same way but must be modified to handle interval arithmetic. A generic module requires point values or intervals for all the input streams and unit parameters and calculates the conditions for the output streams as respectively values or intervals. 

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. 

---