Simulation problem

The computer effort required to get a solution to a simulation problem is important because, ia the cases of optimization of desiga and dynamic simulation for control, many simulator mns must be made. At times the models of process units are simplified and often linearized to speed up the convergence. 

Clearly, however, the flow simplification would be invalid on a small site with episodic projects, or in contexts with significant downtime due to changeover and setup activities for project-specific assays. Such simulation problems covering multiple projects and multiple assays, with use of a mix of shared and dedicated resources, can rapidly become intractable, and an early, com-monsense selection of the focus area for simulation is essential. 

Simulation methods are embedded in simulation tools supporting to model simulation problems and partly supporting comprehensive visualization of simulation results (Fu 2002 Mason 2002). 

To illustrate this criterion, consider a simulation problem chosen to be similar to the catalytic reduction of nitric oxide (A3, K11) ... 

We first considered applications of this approach within process engineering. Steady-state flowsheeting or simulation tools are the workhorse for most process design studies the application of simultaneous optimization strategies has allowed optimization of these designs to be performed within an order of magnitude of the effort required for the simulation problem. An application of this strategy to an ammonia synthesis process was presented. Currently, flowsheet optimization is widely available commercially and has also been installed on the FLOWTRAN simulator for academic use. 

Fast switching circuits like this one can cause simulation problems. Discontinuities can create time step too small errors. In order to aid in convergence, the following statement was added to each of the simulators. 

The present problem is a design problem, since the required conversion rate of 0.75 is given and we want to find the value of Da that achieves this. But for educational purposes, before we present the solution of this design problem, we first present the simulation problem where Da is given and the conversion is unknown. 

Here we assume that Da = 1.4 and that the reaction is first-order. The solution of the simulation problem is as follows. 

Fixed point iteration scheme for the simulation problem Figure 6.23... 

Here is our MATLAB routine absorbtoweriterXe.m that finds the output liquid concentration Xe for the simulation problem (a) according to Figure 6.23. 

A close look at the intermediate output values of Xenew in a call of absorbtoweriterXe reveals that convergence is almost instantaneous. This is so because the role of Xe in the IVP (6.130) is linear, indicating that one linear interpolation will give the exact self-replicating value of Xe for the simulation problem in case of a linear equilibrium relation. For a quadratic equilibrium relation, refer to problem 3 in the Chapter exercise section. 

Differing from the previous simulation problem in which the apparatus and system parameters, as well as the feed rates were given to us and we needed to find the exit liquid concentration Xe, we now consider the task of designing an absorption tower with a specified cross-sectional area Ac, the given system parameter values L, V, and Ka = TO Kg, and the known feed rates X/ and Yj for a linear equilibrium relation Y = aX + b. 

A call of absorbtoweriterHt(2.5,68,.72,0.01,720,7000,0.001,1.8404,1.4) with the same data used in Figure 6.24 and that computed Xe = 1.8404 for a given height of 20 m in the simulation problem now finds Ht = 19.999 m in the design problem when we specify the simulated output value Xe = 1.8404 instead. This validates our algorithms. 

We advise our students to use these two absorption tower programs in tandem for best results with both design and simulation problems. Special care needs to be taken if we compute data such as the above, where the height varies from 57 to 78 to, or by 37% as Xe varies only in its 5th significant digit, or by approximately 0.02%. 

For all of the above configurations and situations, we have presented both the simulation problem, where the number of trays is given in the multitray case, or the height is given for the packed column, and the design problem, where the number of trays in the multitray case is not known, or the height is unknown for the packed column. 

As pointed out earlier, in it would be utopia if we each had a 50,000 computer software simulator continually at our fingertips with which we could solve most every simulation problem. Hey, who s kidding It would just be nice to have a state-of-the-art computer continually at our fingertips, wouldn t it Well, we really should at least have a good... 

The solution of a chemical process simulation problem using the sequential modular technique is represented in Fig. 2. Here, the modeling equations can be written such that the outlet stream from each unit is a function of the inlet streams to each unit ... 

Table I shows the flexibility of the computational system. Six types of frequently encountered problems are classified according to their respective boundary conditions. In each classification, one or more run options can be selected. For example, Class 1 are typical simulation problems where the reactor outlet pressure and feed conversion are specified and the inlet pressure and radiant temperature are calculated. Alternatively, the effect of fouling can be determined by calculating a coking factor from a known pressure drop. The following examples illustrate applications of the system in problems under Classes 1, 5 and 6 respectively.

Look for this logo in the chapter and go to OrganicChemistryNow at http //now.brookscole.com/hornback2 for tutorials, simulations, problems, and molecular models. 

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