Operating Parameter Profiling

Optimization of the pressure levels and the duration of inert and product sweeps in pressure swing adsorptive reactors was referred to in Section 7.4.3. One can, 

Keft - Film mass transfer coefficient - Convective velocity in reactor 

Deft - Effective diffusion coefficient k - Reaction rate constant 

---

After the genetic algorithm computations a new operational parameter profile has been... 

Equation (8) provides a general relationship between the reactor temperature profile and the operating parameters. In relating the system heat transfer to the conversion-molecular weights relationship for a reactor of fixed size, the heat transfer coefficient emerges as the correlating parameter. 

Figure 1.8. Schematic frequency distributions for some independent (reaction input or control) resp. dependent (reaction output) variables to show how non-Gaussian distributions can obtain for a large population of reactions (i.e., all batches of one product in 5 years), while approximate normal distributions are found for repeat measurements on one single batch. For example, the gray areas correspond to the process parameters for a given run, while the histograms give the distribution of repeat determinations on one (several) sample(s) from this run. Because of the huge costs associated with individual production batches, the number of data points measured under closely controlled conditions, i.e., validation runs, is miniscule. Distributions must be estimated from historical data, which typically suffers from ever-changing parameter combinations, such as reagent batches, operators, impurity profiles, etc.

First we tuned the simulation model using existing operation conditions. Product properties as well as conversion and temperature profile along the reactor axis closely coincided with the actual data after properly choosing the kinetic constants and other operation parameters. 

The column start up is from an initial arbitrarily chosen composition profile. The steady state composition profile obtained from the first run can then be used as the starting profile for subsequent runs. With the MADONNA version for Windows, changes in operating parameters, such as feed rate, can be made with the CONTINUE feature. This can be programmed easily with IF-THEN-ELSE statements. In this way realistic dynamics can be obtained for the column conditions moving from one steady state to another. 

Key operating parameters that may change (or be optimized) throughout a product s development and approval cycle are dissolution sampling time points and dissolution limits or specifications by which the dissolution results should be evaluated. The results generated from the dissolution test need to be evaluated and interpreted based on the intended purpose of the test. If the test is used for batch-to-batch control, the results should be evaluated in regard to the established limits or specification value. If the test is being utilized as a characterization test (i.e., biopharmaceutical evaluations, formulation development studies, etc.) the results are usually evaluated by profile comparisons. 

By and large the theoretical framework for evaluating profile shapes is well established and has led to a better understanding of the choice of operating parameters. It has been particularly helpful in generating proximity effect algorithms in order to specify exposure requirements for complex geometries (see ref. 39 for a review of proximity correction procedures). 

The initial profile is computed by the Saeman model (Eq. (1)). The inlet flow rate and/or the operating parameters can be modified during the resolution of the dynamic equation. Spurting et al. [7] give a similar equation, but the computed variable is not the local height of the bed, but the maximum half angle subtended by the bed at the cylinder axis. 

Figure 1.7 shows typical composition profiles. Notice that there is a peak in the CB at some point in time. The higher the value of feB relative to fee, the higher the peak in CB and the earlier in the batch the peak occurs. The batch should be stopped when the peak occurs if we wish to maximize selectivity. Thus batch time is an important operating parameter for series reactions. This is not the case for parallel reactions. Reactor temperature should be adjusted to favor feB. 

Table 9.8 shows the results of base case (case 1) optimisation with nominal values of operating parameters and those obtained by using worst-case design algorithm (case 2). The profit in Case 2 is based on weighted average of 20.5 nominal and 13.5 worst-case scenarios. Figure 9.17 shows nominal (optimum) and worst-case (optimum) temperature profile. 

In this case study we will model, simulate and design an industrial-scale BioDeNOx process. Rigorous rate-based models of the absorption and reaction units will be presented, taking into account the kinetics of chemical and biochemical reactions, as well as the rate of gas-liquid mass transfer. After transformation in dimensionless form, the mathematical model will be solved numerically. Because of the steep profiles around the gas/liquid interface and of the relatively large number of chemical species involved, the numerical solution is computationally expensive. For this reason we will derive a simplified model, which will be used to size the units. Critical design and operating parameters will be identified... 

Figure 5.9. Temperature profiles for the columns in Example 5.15. Table 5.3 Operating parameters of designs 1 and 2 for column 1...

In order to calculate Ug(r) and Ud r) from the specified operating parameters Ug and Gs, it is necessary to know the dominant factor defining radial heterogeneity. Extending the energy minimization method to overall hydrodynamics, a stable radial profile calls for not only Model LR for local hydrodynamics at every point, but also the minimization of the cross-sectional average Nst for overall stability, which is defined by... 

Multiple Steady States. Not only can the nonlinearity of our dynamic model equations produce limit cycle responses, it can give rise to multiple steady state conditions in which the same set of operating parameters can produce different reactor profiles. By accident, three of these multiple steady state responses were obtained and they are suimnarized in Table XIV. 

Changing the exit gas pressure also gave three multiple steady state responses in which the same set of operating parameters produced different reactor profiles. Finally, a rough estimate for the location of the bifurcation points was given for the coal moisture, steam feed rate, and exit gas pressure transient response runs. 

The basic principle of one-column process is identical to four-zone SMB. The performance of the process for the amino acids separation was compared with four-zone SMB by computer simulation using Aspen Chromatography. The system and operating parameters are listed in Table 1. It was set that T2, T3 and T4 are initially filled with desorbent and T1 is empty in the simulation. Liquid in each tank is ideally mixed. Liquid of the average solute concentration in a tank is introduced into the column. The simulated concentration profile of two amino acids in the one-column process is presented in Figure 3. 

---