System modular method

Two approaches exist for solving problems involving systems of columns, the column modular method and the system modular method proposed by Hess.15 In the column modular approach, the equations for each column of a system are solved in succession, and in the system modular approach, the complete set of equations for the system are solved simultaneously. While the system... 

Solution of Systems of Columns by Use of the System Modular Method... 

To demonstrate the application of the column modular method and system modular method (the Almost Band Algorithm for Systems), Examples 6-1 and 6-2 are presented. The statements of Examples 6-1 and 6-2 are presented in Table 6-3, and the solutions are given in Tables 6-4 through 6-6. Example 6-1 is a relatively easy problem to solve while Example 6-2 is more difficult. A flow diagram of the system involved in Examples 6-1 and 6-2 is shown in Fig. 6-11. 

Example 6-1 was also solved by the Almost Band Algorithm for Systems (the system modular method) as well as the column modular method. Results obtained by each of these methods are presented in Tables 6-3 through 6-6. 

Example 6-2 differs from Example 6-1 by the specification of more plates, the temperature of the feed F2, and the flow rate Bx. With the additional stages specified, this problem becomes very sensitive to the value specified for Bt. For Bl = 277 instead of the specified value Bx = 275, Example 6-2 is relatively easy to solve by use of the combination of the column modular method. When Bt was taken equal to 275, Example 6-2 could not be solved by either the column modular or the system modular method. However, Example 6-2 could be solved... 

In order to solve Example 6-2 by the system modular method, the following procedure was used. First, a solution to the following modified form of Example 6-2 was obtained. The recycle stream B2 was replaced by an additional independent feed. This feed was taken to be liquid at 170°F and was assigned the following composition. 

Automatically Controlled Modular System This method employs one large manually controlled transformer-rectifier used in conjunction with a number of modular cabinets located adjacent to each item of plant requiring protection. The main transformer-rectifier feeds d.c. to each of the module units and the modular unit provides the exact amount of current required by the item of plant in question. 

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. 

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.)... 

A column modular method which makes use of the capital 0 method of convergence is presented for solving problems involving systems containing both mass and energy recycle streams. On the basis of an assumed set of values of the variables for the recycle streams, one complete trial is made on each column or unit of the system by use of the most appropriate calculational procedure for the column or unit. Then the capital 0 method is used to place all terminal streams in material and energy balance. The values of the variables so obtained for the recycle streams are used to make the next trial on each column or unit of the system.6, 7... 

A very pedagogical, highly readable introduction to quasi-Newton optimization methods. It includes a modular system of algoritlnns in pseudo-code which should be easy to translate to popular progrannning languages like C or Fortran. 

The innovative features, such as passive, gravity-driven ECCS, simplified RCS, digital I C, optimized plant arrangement, and modular construction methods, characterize the AP600 design. These changes result in fewer systems, equipment, operations, inspections, maintenance, and QA requirements (Table 6.1-7). Features of the AP-6(K) are as follows ... 

Sahlin P. Modeling and simulation methods for modular continuous systems in buildings. Stockholm Royal Institute of Technology, 1996. 

Reduce complexity and design modular systems As far as possible, use proven techniques and combine them in new ways, but let them be independent from each other, e.g., allow different synthesis methods that are independent from your reactor configuration. Furthermore, allow different sequential or parallel analysis methods. This is not a contradiction to the aforementioned integration because workflow integration does not necessarily mean technology integration. 

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. 

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