Steady-State Simulations

Under steady-state conditions, variations with respect to time are eliminated and the steady-state model can now be formulated in terms of the one remaining independent variable, length or distance. In many cases, the model equations now become simultaneous first-order differential equations, for which solution is straightforward. Simulation examples of this type are the steady-state tubular reactor models TUBE and TUBEDIM, TUBTANK, ANHYD, BENZHYD and NITRO. 

Some models, however, take the form of second-order differential equations, which often give rise to problems of the split boundary type. In order to solve this type of problem, an iterative method of solution is required, in which an unknown condition at the starting point is guessed, the differential equation integrated. After comparison with the second boundary condition a new starting point is estimated, followed by re-integration. This procedure is then repeated until convergence is achieved. MADONNA provides such a method. Examples of the steady-state split-boundary type of solution are shown by the simulation examples ROD and ENZSPLIT. 

In order to overcome the problem of split boundaries, it is sometimes preferable to formulate the model dynamically, and to obtain the steady-state solution, as a consequence of the dynamic solution, leading to the eventual steady state. This procedure is demonstrated in simulation example ENZDYN. 

In order to overcome the problem of split boundaries, it is sometimes preferable to formulate the model dynamically, and to obtain the steady-state 

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PLOW 1 RAN was made available in 1974 by Monsanto Co. for steady-state simulation of chemical processes based on sequential modular technology. It requires specification of feed streams and topology of the system. In 1987, an optimization enhancement was added. 

To achieve a steady state, simulation time was set to 60 days which is six times of the SRT. The settling was assumed to ideal settling. A stepwise calibration nethdology was applied to the SBR process and some key parameters in ASM2d were optimized (results not shown). 

Fig. 2. Steady-state simulation result of MeOH excess process.

SPEEDUP Workstations, and Dynamic and steady-state simulation of larger large processes with data base. ... 

Most plant simulations have been steady-state simulations. This is to be expected, since just as a baby must learn to crawl before he can walk, so the simpler steady-state problems must be solved before the unsteady-state ones can be tackled. However, unsteady- state plant simulations are being attempted, and undoubtedly sometime in the future this will be a common tool for plant designers. 

Crowe et al. have written a book entitled Chemical Plant Simulation 2 that gives the details of the steady-state simulation of a contact sulfuric acid plant. It uses an executive program named PACER. This and many other such programs as COPS, Flowsim, GPFS, and PDA are for sale.3... 

Some recent applications have benefited from advances in computing and computational techniques. Steady-state simulation is being used off-line for process analysis, design, and retrofit process simulators can model flow sheets with up to about a million equations by employing nested procedures. Other applications have resulted in great economic benefits these include on-line real-time optimization models for data reconciliation and parameter estimation followed by optimal adjustment of operating conditions. Models of up to 500,000 variables have been used on a refinery-wide basis. 

Figure 6 Moraxen rectal delivery system. Comparative steady-state simulation of morphine plasma levels after single daily rectal administration of Moraxen with 100 mg morphine compared with twice-daily 50 mg morphine (OSRM) in an oral prolonged-release formulation. The simulation is based on the plasma levels from a single-dose study.

Gupta, A.K., Steady State Simulation of Chemical Processes, Ph.D. Thesis, University of Calgary, Alberta (1990). 

Steady State Simulation Results for an Industrial Scale FCC Unit... 

A number of steady-state simulations have been performed with the aim of analyzing the influence of numerical and physicochemical parameters, beginning... 

RGA Method for 2x2 Control Problems To illustrate the use of the RGA method, consider a control problem with two inputs and two outputs. The more general case of NxN control problems is considered elsewhere (McAvoy, Interaction Analysis, ISA, Research Triangle Park, N.C., 1983). As a starting point, it is assumed that a linear, steady-state process model in Eqs. (8-54) and (8-55) is available, where Ui and U2 are steady-state values of the manipulated inputs l7 and Y2 are steady-state values of the controlled outputs and the K values are steady-state gains. The Y and U variables are deviation variables from nominal steady-state values. This process model could be obtained in a variety of ways, such as by linearizing a theoretical model or by calculating steady-state gains from experimental data or a steady-state simulation. 

The ethylbenzene CSTR considered in Chapter 2 (Section 2.8) is used in this section as an example to illustrate how dynamic controllability can be studied using Aspen Dynamics. In the numerical example the 100-m3 reactor operates at 430 K with two feedstreams 0.2 kmol/s of ethylene and 0.4 kmol/s of benzene. The vessel is jacket-cooled with a jacket heat transfer area of 100.5 m2 and a heat transfer rate of 13.46 x 106 W. As we will see in the discussion below, the steady-state simulator Aspen Plus does not consider heat transfer area or heat transfer coefficients, but simply calculates a required UA given the type of heat removal specified. 

To convert a steady-state simulation into a dynamic simulation, the Dynamic button on the top toolbar shown at the top of Figure 3.56 is clicked. If this button is not showing, go to the top toolbar and click View and Toolbars. The window shown at the bottom of Figure 3.56 opens, on which the box in front of Dynamic is clicked. Then the Dynamic item under the reactor block R1 is clicked, which opens the window shown in Figure 3.57. The Heat Transfer page tab lists six possible options that can be used in the dynamic simulation. In our discussion of these alternatives, we will consider the... 

The situation exhibiting five steady states is similar to that for three steady states. Results of the steady state simulation revealed that the third stable steady state is located at the reactor outlet [22]. Calculation of the reactor with an aftersection packed by inert material indicated that five steady states are eliminated. [15]. 

The User Interface. A wide variety of stand alone steady state simulation programs and flowsheet systems are available to the process engineer. These have been reported in a series of articles by Peterson, Chen and Evans in 1978 (j>) and by Chen and Evans in 1979 (6). Some practical advice on the use of the computer Tn design is reported by Weismantel (7 ). A course in the use of several commercially available systems is given in the AIChE Today Series ( ). A report on the use of networks to share chemical engineering programs among educators was recently issued (9 ). ... 

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