Simulation modules, iterative

S //Asa mediator between CFD calculations and macro-scale process simulations, the reactor geometry is represented by a relatively small number of cells which are assumed to be ideally mixed. The basic equations for mass, impulse and energy balance are calculated for these cells. Mass transport between the cells is considered in a network-of-cells model by coupling equations which account for convection and dispersion. The software is capable of optimizing a process in iterative simulation cycles in a short time on a standard PC, but it also requires experimentally-based data to calibrate the software modules to a specific micro reactor. 

The designer usually wants to specify stream flow rates or parameters in the process, but these may not be directly accessible. For example, the desired separation may be known for a distiUation tower, but the simulation program requires the specification of the number of trays. It is left up to the designer to choose the number of trays that lead to the desired separation. In the example of the purge stream/ reactor impurity, a controller module may be used to adjust the purge rate to achieve the desired reactor impurity. This further complicates the iteration process. 

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. 

The third module is the simulator itself. As stated earlier, each of simulators from the different software vendors uses the core code from Berkeley to iterate solutions of the circuit using mesh equations. 

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. 

Once the instantaneous velocity is obtained, particle trajectories can be simulated. To introduce two-way coupling, it is necessary to calculate the source terms in the balance equations of mass, momentum and energy for the continuous phase. With such source terms, the continuous phase flow field needs to be solved again, which is later used to calculate new trajectories. The number of iterations between turbulence and particulate modules to obtain convergence is typically three. However, in strongly coupled flows, convergence may be difficult to reach (Kohnen et ai, 1994). 

Many process simulators use this procedure because it is quite easy to implement. You only need to have a module or subroutine for a mixer, a reactor, and a separator, and the equations for each of these are quite simple. One problem that arises, though, is that the procedure takes many iterations to converge if the conversion is low. And, if there are interlocking recycle streams, convergence may not occur at all. However, it is quite a good scheme, and you can apply it using a spreadsheet. 

Abstract. High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving observational modulation equations or correlated modulation equations iteratively under physical constraints. Simulations and experiments show that wide field and high resolution images of space hard X-rays and soft 7-rays can be obtained by scan observation of a collimated non-position-sensitive detector. 

The boundary conditions that may be simulated with the flow-compaction module are autoclave pressure, impermeability or permeability with prescribed bag pressure, no displacement or no normal displacement (tangent sliding condition). The governing equations (Eqs [13.3] and [13.4]) are coupled during individual time-steps of the transient solution. A Newton-Raphson iterative procedure is used to solve the resulting nonlinear system of equations. Details in the solution of the flow-compaction for autoclave processing can be found in reference 17. 

The most computationally intense procedure is a solution of the 2D Poisson equation (5.142). The algorithm of stack simulation can thus be effectively parallelized each stack module cell - - BP can be solved on a separate processor. Upon completion of an iteration step, adjacent modules exchange with the information (the cell currents and BP potentials) required for the next iteration. 

The simulation program comprises a number of modules, grouped in overlay phases. To save computation time the calculation of the matrix of total exchange areas was kept out of the inner iteration loop. This did not significantly affect the speed of convergence of the outer iteratioii cycle. With realistic starting estimates for Q. and T only 5 to 10 iterations were required. The CTP.U. time per iteration amounted to 50 sec on a Siemens 4004-150, a machine which is 14 times faster than the IBM 360-30 e.g. 

For equipment requiring iterative solutions, there will be user-selectable convergence and tolerance criteria in the equipment module. There will also be convergence criteria for the whole flowsheet simulation, which can be adjusted by the user. 

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