Sequential iterative procedure

Based on the best conqiosition of promoters, the conqiosation of main components was optimized. The contents of V, Sb, W, Sn and supporter were taken as five influences, and Xp, Sacn also as the outcomes. 20 Original sample points were distributed, at wdiich the catalysts were prepared and evaluated. The ranges of the results were, Xp 11.6% 88.2%, Sacn 15.0% 44.4% and Yacn 2.4% 28.9%. Accordingly, A 5-20-12-2 network was adopted in the sequential iterative procedure. The results of the optimization and evaluation in the first and second iteration are listed in Table 1 and 2. 

A sequential iterative procedure was used to obtain the optimal design flowsheet with the procedure summarized in Figure 8.15. The optimization method is intuitive however, it is rather time-consuming when the numbers of design variables becomes large in a plantwide optimization. Figure 8.16 shows some of the TAG plots within the... 

The above integral screening is even more advantageous if the Fock matrix is formed incrementally. Consider two sequential density and Fock matrices in the iterative procedure (eq. (3.52)). 

The older modular simulation mode, on the other hand, is more common in commerical applications. Here process equations are organized within their particular unit operation. Solution methods that apply to a particular unit operation solve the unit model and pass the resulting stream information to the next unit. Thus, the unit operation represents a procedure or module in the overall flowsheet calculation. These calculations continue from unit to unit, with recycle streams in the process updated and converged with new unit information. Consequently, the flow of information in the simulation systems is often analogous to the flow of material in the actual process. Unlike equation-oriented simulators, modular simulators solve smaller sets of equations, and the solution procedure can be tailored for the particular unit operation. However, because the equations are embedded within procedures, it becomes difficult to provide problem specifications where the information flow does not parallel that of the flowsheet. The earliest modular simulators (the sequential modular type) accommodated these specifications, as well as complex recycle loops, through inefficient iterative procedures. The more recent simultaneous modular simulators now have efficient convergence capabilities for handling multiple recycles and nonconventional problem specifications in a coordinated manner. 

One drawback of the sequential procedure is that by adopting a two-step procedure, the MM part is uncoupled from the QM part. The mutual polarization between the solute and the solvent is thus precluded. To include the solute polarization by the solvent we have used an iterative procedure that brings the solute to the electrostatic equilibrium with the solvent. Using this scheme we have obtained some in-solution dipole moments of the solute that are in very good agreement with other theoretical results. Using these polarized solutes has improved the accuracy of the solvent... 

This methodology has been developed by Matteson and coworkers, with particular emphasis on chiral boronic esters derived from pinanediol. Sequential chiral centers can be assembled by an iterative procedure with excellent enantiomeric excess at each step. The two chiral centers in eldanolide (37), for example, were assembled in this manner (Scheme 36). ... 

Furthermore, the expression mechatronic approach is common in product development. That is, that the traditional sequential design procedure (mechanics —> electronics control/ communication), which results in partly optimized products and time- and cost-intensive iterations, is overcome and replaced by an interdisciplinary cooperation of the development teams in the sense of concurrent engineering (van Brussel 1996). Thus, optimal products can be developed at reduced costs. 

While SHAKE/RATTLE is a robust procedure the sequential, iterative character of nonlinear solvers needed for its implementation can lead inefficiencies when it is implemented on a parallel computer. Therefore, a number of the alternative methods avoid iteration. We briefly summarize a few of the popular alternative schemes here. 

Figure 8.15 Sequential iterative optimization procedure for this system.

A common feature in the models reviewed above was to calculate pressure and temperature distributions in a sequential procedure so that the interactions between temperature and other variables were ignored. It is therefore desirable to develop a numerical model that couples the solutions of pressure and temperature. The absence of such a model is mainly due to the excessive work required by the coupling computations and the difficulties in handling the numerical convergence problem. Wang et al. [27] combined the isothermal model proposed by Hu and Zhu [16,17] with the method proposed by Lai et al. for thermal analysis and presented a transient thermal mixed lubrication model. Pressure and temperature distributions are solved iteratively in a iterative loop so that the interactions between pressure and temperature can be examined. 

A well-known class of techniques for reducing the number of iterates is the use of tearing (L4). We shall illustrate this procedure by way of an example taken from Carnahan and Christensen (C3). Let us consider the two-loop network shown in Fig. 5 and assume that formulation A is used. To abbreviate the notation let us denote the material balance around vertex i [Eq. (35)] by fi = 0 and the model of the element [Eq. (36)] by fu — 0. Then assuming all external flows and one vertex pressure, p, say, are specified, we have a set of 12 equations that must be solved simultaneously. But if we now assume a value for ql2, the remaining equations may be solved sequentially one at a time to yield the variables in the following... 

A more subjective approach to the multiresponse optimization of conventional experimental designs was outlined by Derringer and Suich (22). This sequential generation technique weights the responses by means of desirability factors to reduce the multivariate problem to a univariate one which could then be solved by iterative optimization techniques. The use of desirability factors permits the formulator to input the range of property values considered acceptable for each response. The optimization procedure then attempts to determine an optimal point within the acceptable limits of all responses. 

For a sequential-modular simulation program to be able to solve a flowsheet with a recycle, the design engineer needs to provide an initial estimate of a stream somewhere in the recycle loop. This is known as a tear stream, as the loop is torn at that point. The program can then solve and update the tear stream values with a new estimate. The procedure is repeated until the difference between values at each iteration becomes less than a specified tolerance, at which point the flowsheet is said to be converged to a solution. 

The key to improve the method of developing catalysts is to set up some quantitative catalytic relationships, with which one can make the developmental procedme become a combinational one of qualitative analyses, quantitative predictions and experiments. For some simple catalytic systems, without any pre-determined experiment, quantum chemistry can be used to estimate catalytic properties quantitatively. Unfortunately, up to now it is difficult to apply this method to the multicomponent catalytic systems. A certain amount of experiments is necessary to develop the multicomponent catalysts. But, how to decrease the amoimt of experiments noticeably is a matter to which researchers have paid great attention, it is also the problem to be solved in this paper. Hence, we proposed a novel computer-aided technique, by which the procedure of developing catalysts is transferred to an iterative or sequential one. 

---