Flowsheeting convergence

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

When simulating this flowsheet convergence problems appear. These may be attributed to the following reasons ... 

Stream report (material and heat balance), including flowsheet convergence report. 

The analysis of the computational sequence is recommended, even if this is found automatically. Selecting tear streams before key units, as reactors and separators, avoid severe failure and accelerate the flowsheet convergence. 

Some software performs a degrees of freedom analysis and offers a selection of specifications from a menu. Note that the specification mode of individual units should be consistent with the overall flowsheet convergence, as it will be explained later. 

Feedback controller may be placed inside or outside of a flowsheet convergence loop. There are cases when the manual definition of the computation sequence is useful. As typical applications we cite ... 

Some specifications perfectly feasible for stand-alone units might become infeasible when simulating the whole flowsheet. Most of the troubles in getting flowsheet convergence have as origin inconsistencies in the overall input/output material balance, as for example specifying all the outputs as absolute flow rates, or when no exit points are available for some components. 

The flowsheet convergence deserves a comment. Closing the recycle has to cope with the accumulation of different components. Make-up of the recycled component is always necessary to get convergence. For example, a splitter may remove completely the toluene, while an external feed gets it back. A controller could manipulate the external flow such the difference between exit and make-up toluene goes to zero. 

After placing the recycle block, two more unit operations are required. First, it is necessary to have a makeup solvent input to make up for solvent losses in the product streams. Without it, the solvent loop would dry up (and steady-state flowsheet convergence would not be possible in the simulator). To do this, use a Make-Up/Blow-Down block (it is in the ProMax Auxiliary Objects section) and corresponding... 

When the modules are connected to one another as represented in a flowsheet, a long train of units may become coupled together for calculations. Thus, a set of modules may require a fixed precedence order of solution so that convergence of the calculations may be slower than in equation-based codes. 

A computational sequence for modular flowsheeting. Initial values of both recycles are guessed, then the modules are solved in the order 1, 2, 3, 4, 5, and 6. Calculated values for recycle streams S9 and S10 are compared with guessed values in a convergence block, and unless the difference is less than some prescribed tolerance, another iteration takes place with the calculated values, or estimates based on them, forming the new initial guessed values of the recycle streams. 

Finally, a great advantage to SQP is that it does not require convergence of the equality constraints, h(x) = 0, at intermediate points. Consequently, the process model (or at least the part directly incorporated into the optimization problem) can be solved simultaneously with the optimization problem. In the next section we discuss the application of the SQP algorithm to flowsheet optimization. Here, if the number of variables in the optimization problem is small, application is straightforward. On the other hand, when the number of variables, n, becomes large (n > 100, say), special-purpose extensions to SQP are required. These are discussed in the remainder of this section. 

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. 

Modular simulators are frequently constructed on three levels. The lowest level consists of thermodynamics and other physical property relations that are accessed frequently for a large number of flowsheeting utilities (flash calculations, enthalpy balances, etc.). The next level consists of unit operations models as described above. The highest level then deals with the sequencing and convergence of the flowsheet models. Here, simultaneous... 

To gain the maximum benefit from the use of a flowsheet program, the operator/designer must be adequately trained. A suitable program will have 20-30 standard units available, numerous equation-solving procedures, control facilities and probably optimization facilities. The unit-equipment subroutine must adequately represent the process equipment, recycle streams need to be specified, and suitable solution convergence is required. For the effective use of CAD packages, it... 

At this point all the units in the flowsheet are installed and converged. The last issue is to converge the recycle stream. The initial guessed values are adjusted to be close to the calculated values of flow and composition leaving the split S1. When these two streams are fairly close, the source of the recycle stream is defined as the split SI and the recycle stream is defined as a Tear stream. The flowsheet did not converge when the default convergence method... 

Cf si Properties (fl si flowsheet FJ a Streams. Q Utflifes Itl di Blocks Fl Gfl Reactions f l a Convergence El Qj Fbwsheebng Options 1=1 a Design Spec... 

Wegstein) was used. Switching to the Broyden method successfully converged to flowsheet. Figure 6.97 gives the temperature and composition profiles in the two reactors. 

However, switching to the FS2 flowsheet with the presence of the furnace preventing the quench, the simulation was rather easily converged to a steady state. These startup experiences indicate that the FS2 flowsheet is much more robust than the FS1 flowsheet. 

There are two sources of complexity in this flowsheet. The first is the split of the feed between the bypass stream and the stream going through the heat exchanger. The second is the recycle stream from the reactor back to the heat exchanger. The final flowsheet is shown in Figure 7.15, but to get to this converged flowsheet, these issues must be handled. 

Kluzik, H. A., "A Study of the Simultaneous Modular Convergence of Chemical Process Flowsheets",... 

With all it features, the PROSIM program needs further improvements, especially in the convergence procedures for both single-and multiple-stage calculations. Work is proceeding on this at the present time. Another logical extension of the program is to flowsheet simulation, as well as reduced crude properties prediction. 

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