Steady-state simulation programs

Stockman et al. (1997) provide details on the practical problems and limitations of lattice gas and lattice Boltzmann methods in flow and transport simulation. In particular, they focus on errors associated with boundary conditions, the accuracy required for useful comparison with experimental data, programming, and problem size and run-time issues. For lattice gas methods, they find that averaging over a large number of time steps is sometimes needed to resolve the flow velocity field. This limits the applicability of lattice gas methods to flow simulation under steady state or slowly varying conditions. In contrast, dispersive processes alone can be adequately simulated with lattice gasses by averaging a much smaller number of time steps. Lattice Boltzmann methods do not require averaging. 

Write a general implicit program for transient compressible liquids and gases, taking constant spatial meshes for simplicity. For both flows, assume an initially hydrostatic reservoir, with the sandface suddenly exposed to a prescribed pressure level different from hydrostatic. Run the simulations to steady-state and monitor the flow rate history at the well. Show that the asymptotic results agree with the three complementary steady flow formulations amd solutions given in this chapter. 

FIGURE 5.18 Simulation of steady-state diffusion-limited current at an embedded microdisk electrode by COMSOL 4.0a. (A) The mesh generated by the program. (B) The concentration profile of redox species. (C) The flux distribution over the disk surface. 

This program helps calculate the rate of methanol formation in mol/m s at any specified temperature, and at different hydrogen, carbon monoxide and methanol concentrations. This simulates the working of a perfectly mixed CSTR specified at discharge condition, which is the same as these conditions are inside the reactor at steady-state operation. Corresponding feed compositions and volumetric rates can be calculated from simple material balances. 

The eomplex FCC system involves not only turbomaehinery, but also related proeess eomponents. All of these must be properly designed and sized to operate within system parameters from startup to steady state design point, and through shutdown. System response to emergeney eonditions is also mandatory. Computer simulation is, therefore, an integral part of the design proeess. A eomputer program eapable of this simulation is deseribed below. 

The relative fluctuations in Monte Carlo simulations are of the order of magnitude where N is the total number of molecules in the simulation. The observed error in kinetic simulations is about 1-2% when lO molecules are used. In the computer calculations described by Schaad, the grids of the technique shown here are replaced by computer memory, so the capacity of the memory is one limit on the maximum number of molecules. Other programs for stochastic simulation make use of different routes of calculation, and the number of molecules is not a limitation. Enzyme kinetics and very complex oscillatory reactions have been modeled. These simulations are valuable for establishing whether a postulated kinetic scheme is reasonable, for examining the appearance of extrema or induction periods, applicability of the steady-state approximation, and so on. Even the manual method is useful for such purposes. 

N umerical simulations of reactor start-up were programmed, predicting monomer and initiator concentrations, total polymer concentration, weight and number average molecular weights, viscosity and population density distribution dynamics. The following two relationships obtained from steady state observations were utilized in the simulation. 

Distillation is a well-known process and scale-up methods have been well established. Many computer programs for the simulation of continuous distillation columns that are operated at steady state are available. In fine chemicals manufacture, this concerns separations of products in the production of bulk fine chemicals and for solvent recovery/purification. In the past decade, software for modelling of distillation columns operated at non-steady state, including batch distillation, has been developed. In the fine chemicals business, usually batch distillation is applied. 

The dimensionless model equations are programmed into the ISIM simulation program HOMPOLY, where the variables, M, I, X and TEMP are zero. The values of the dimensionless constant terms in the program are realistic values chosen for this type of polymerisation reaction. The program starts off at steady state, but can then be subjected to fractional changes in the reactor inlet conditions, Mq, Iq, Tq and F of between 2 and 5 per cent, using the ISIM interactive facility. The value of T in the program, of course, refers to dimensionless time. 

This program is designed to simulate tracer experiments for residence time distributions based on a cascade of 1 to 8 tanks-in-series. An nth-order reaction can be run, and the steady-state conversion can be obtained. The important parameters to change are as follows for the tracer experiments k, CAINIT, and CAO ( = 0 for E curve, = 1 for F curve). For reaction studies, the parameters to change are n, k, CAO, and CAINIT. 

The simulation starts with the initial axial concentration profiles set to zero. The program is rather slow to run and therefore after the first run, the program should perhaps be modified so that the steady-state values from the first run are used as starting values for subsequent simulations. 

In the program, the column starts up assuming an initial zero concentration profile of the more volatile component. Use the results of 1) to 4) to establish an initial steady-state concentration profile through the column and using this as the starting point, then carry out further simulations to study the effects of step changes in R, F, q and Xp. 

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... 

I start program DAV07 at 1 year of simulation time and run it to 10 years of simulation time. A time step of less than a day is necessary initially, as the system adjusts rapidly from its starting values. The time step increases as the system approaches steady state. I tune the simulation by adjusting the value of diffc, the transport parameter, and solcon, the solar constant, to... 

The steady-state, annual average temperature profile is not a very exciting application of a model that is intrinsically able to calculate changes with time. In this section I apply the simulation to a calculation of the seasonal variation of temperature as a function of latitude. The program is listed as DAV09. 

Note that the program is written such that the number of stages in the cascade, Nstage, can be varied as an additional parameter in the simulation. The stage numbers can be plotted versus the final values by choosing [i] as the X-axis. In this way the steady state concentration profiles can be graphed. A part of the program is shown below. 

The program is written in array form, with Nclll )., the parameter representing the desired number of compartments in the column. The simulation starts with a uniform holdup distribution throughout the column and with the column operating at steady-state. At time, Tswitch, the organic solvent flow is suddenly increased, as effected by the use of a MADONNA IF-THEN-ELSE command. 

Note that the total number of plates, the feed plate location and reflux ratio can all be varied during simulation. The array form of the program also allows graphing the axial steady state tray-by-tray concentration profile. Part of the program is shown below. 

A reaction simulation program, REACTION, which will run on a personal computer, and which is specifically adapted for the non-steady states prevailing in batch reactions, is described and illustrated by a typical reaction model. Among... 

Table 5.5 gives values of parameters and steady state conditions. The variables with overscores or bars over them are steadystate values. Note that the time basis used in this problem is hours. Table 5.6 gives a FORTRAN program that simulates this system using Euler integration. The right-hand sides of the... 

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