Reactor-fractionator simulation

Figure 3.35 Presentation page of a block-oriented simulator for the analysis of a coupled FCC reactor-fractionator (Hysim 1995).

Two-fluid or multifluid models can be extended to simulate not only gas-liquid flows but also any combinations of different phases present in stirred reactors. To simulate gas-liquid-solid, slurry reactors, liquid and solid phases are often lumped together and treated as a slurry phase with effective properties. This approximation is reasonable as long as the solid volume fraction is low ( 1 %). For higher solid loading. 

The studies were conducted in stainless steel tubular reactors approximately 3.8 cm in diameter and about 1200 cm3 in volume. The reactors were immersed in electrically heated fluidized solids baths. A naphtha fraction to be reformed was vaporized and heated to reaction temperature before contacting the catalyst. The reactor effluent was separated into liquid and gaseous fractions. A portion of the hydrogen-rich gaseous fraction was recycled through the reactor to simulate commercial reforming practice. The recycle gas was combined with the vaporized naphtha fraction prior to the reactor inlet. The mole ratio of recycle gas to naphtha at the reactor inlet was approximately 7 in all of the runs to be discussed here. 

Workshop 6.4- Connect Reactor Model to Fractionator Simulation I 46S... 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

Consider Equations (6-10) that represent the CVD reactor problem. This is a boundary value problem in which the dependent variables are velocities (u,V,W), temperature T, and mass fractions Y. The mathematical software is a stand-alone boundary value solver whose first application was to compute the structure of premixed flames.Subsequently, we have applied it to the simulation of well stirred reactors,and now chemical vapor deposition reactors. The user interface to the mathematical software requires that, given an estimate of the dependent variable vector, the user can return the residuals of the governing equations. That is, for arbitrary values of velocity, temperature, and mass fraction, by how much do the left hand sides of Equations (6-10) differ from zero ... 

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. 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

Thus, the reactor will be perfectly mixed if and only if = at every spatial location in the reactor. As noted earlier, unless we conduct a DNS, we will not compute the instantaneous mixture fraction in the CFD simulation. Instead, if we use a RANS model, we will compute the ensemble- or Reynolds-average mixture fraction, denoted by ( ). Thus, the first state variable needed to describe macromixing in this system is ( ). If the system is perfectly macromixed, ( ) = < at every point in the reactor. The second state variable will be used to describe the degree of local micromixing, and is the mixture-fraction variance (maximum value of the variance at any point in the reactor is ( )(1 — ( )), and varies from zero in the feed streams to a maximum of 1/4 when ( ) = 1/2. 

Figure 21 shows the simulated dynamic behavior of the gas temperatures at various axial locations in the bed using both the linear and nonlinear models for a step change in the inlet CO concentration from a mole fraction of 0.06 to 0.07 and in the inlet gas temperature from 573 to 593 K. Figure 22 shows the corresponding dynamic behavior of the CO and C02 concentrations at the reactor exit and at a point early in the reactor bed. The axial concentration profiles at the initial conditions and at the final steady state using both the linear and nonlinear simulations are shown in Fig. 23. The temporal behavior of the profiles shows that the discrepancies between the linear and nonlinear results increase as the final steady state is approached. Even so, there are only slight differences (less than 2% in concentrations and less than 0.5% in temperatures) in the profiles throughout the dynamic responses and at the final steady state even for this relatively major step-input change.

Fig. 15.9 Steady-state solutions for the benzene mole fraction from the simulation of benzene oxidation near a turning point in a perfectly stirred reactor. Depending on the starting estimates, a number of spurious (nonphysical) solultions may be encountered. The true solution is indicated by the filled circles, while the shaded diamonds indicate (sometimes spurious) solutions that are computed through various continuation sequences.

The mole fractions of air have been simulated as 0.21 and 0.79 for 02 and N2 respectively. The two parameters, S/C, O/C (oxygen to carbon) ratios have been used to analyze the reforming reactors effectively. These two relationships can be written as follows ... 

Equation 6-74 is a first order differential equation substituting Equations 6-70 and 6-78 for the temperature, it is possible to simulate the temperature and time for various conversions at AXa = 0.05. Table 6-4 gives the computer results of the program BATCH63, and Figure 6-7 shows profiles of both fractional conversion and temperature against time. The results show that for the endothermic reaction of (+AHR/a) = 15.0 kcal/gmol, the reactor temperature decreases as conversion increases with time. 

Fig. 21. The diffusion constant on a neutral network D0 is plotted versus the mutation rate pm. The simulations ( ) are for RNA sequence length N = 76 and population size M = 1000 and are allowed to equilibirate before the statistics are taken. The solid line is the theoretical D0 and ( ) are flow-reactor simulations for a flat landscape. The dotted line is calculated for D0X, where A = 0.3 is the estimated fraction of neutral mutants. Reprinted from Huynen etal. (1996) with permission. Copyright (1996) National Academy of Sciences, USA.

At a first glance, this controller is sufficient for maintaining the product purity. However, simulation results indicate that, in order to maintain x-q at the desired level when the system is subjected to a small (5%) increase in the mole fraction yi o, the recycle flow rate R would need to rise to 501.3mol/ min (a fivefold increase from the nominal value). Thus, due to its inhibitive effect on the reaction rate, the accumulation of the impurity I is highly detrimental to the operation of the process. Consequently, the control of the impurity levels in the reactor is of critical importance and directly linked to the main objective of product-purity control. 

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