Two-Tier Methods

A more recent approach to the rigorous solution of multistage separation processes 

Another feature of the two-tier method is the use of special iteration variables for improved convergence stability. The equilibrium stage model is formulated as follows, beginning by writing the component material balances and equilibrium relations in terms of component molar flow rates instead of mole fractions  

The nomenclature is the same as before Where double subscripts are used, the first designates the stage and the second the component. Superscript 5 designates a side product. 

The withdrawal factor is equal to 1 when there is no side product from a given phase and stage. Since the internal flow and side product for each phase on a given stage are of identical composition, the withdrawal factors can also be written as 

Incorporate these equations in the above component material balance  

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Several algorithms have been proposed to solve the model equations with chemical reactions (Holland, 1981 Saito et al., 1971 Tierney et al., 1982). Venkataraman et al. (1990) applied the two-tier method for this purpose. 

Separation method selection is governed by a two-tier set of rules for selecting among potential operations. The first tier involves the selection between strategic and opportunistic operations. Strategic separations are favored, as these are known to be required in the flow sheet at some point, as are separations which directly reach a desired product composition. The rules in the first tier state that once all the potential opportunistic and strategic operations have been identified for the current stream, the next step is to determine the order in which these operations should be tried. The foUowing... 

Another characteristic example of analytical strategy is that followed in the United Kingdom for the analysis of tranquilizers and -blockers (78). A total of 180 samples distributed over a whole year (15 samples per month) should be analyzed within a turnaround time of 28 days from receipt of sample. In that case, the expense of developing a two-tier analytical strategy was not justified by the sample throughput. Thus, the selection was direct application of a multiresidue LC/PDA confirmatory method (80). 

Till date, the problem of pelliculization of gelatin products has found major solutions in 1) understanding of the chemistry 2) identification of stabilizers that can be added in formulation fills or films 3) development of rapid test methods for evaluation of possibility of pellicle formation and 4) introduction of two-tier... 

A two-tier approach is often utilized by residue control laboratories whereby samples are first screened to identify the suspected positive (non-compliant) samples, which are subject to further quantitative and confirmatory analysis. Screening methods should be inexpensive and rapid and permit a high sample throughput. The basic criteria that should be met are a detection capability below the RL, a low incidence of false-negative (compliant) results (<5%), and a high degree of repeatability, reproducibility, and robustness. A low incidence of false-positive results is also important to reduce the costs incurred by additional confirmatory analysis. False-positive results in screening analysis can occur for a number of reasons, such as if the test is sensitive to other structurally related compounds naturally present in the matrix or to co-contaminants. 

Until the early 1990s, nearly all products were laid out in what is now referred to as the conventional layout. In this layout, which is still used for most products, individual test plots (ground boards and concrete slabs) are separated in a grid on 1.5-m centers. Each of ten replications contains a mixture of rates, products, test methods and control plots arranged in a randomized block design (Figure 4). Replications are laid out in two tiers of five replications per tier. The conventional layout utilizes about 0.08 ha. 

FIGURE 8.9 The two-tier DC load test method adheres to the lEC 61951-1 2005 standard. The load test is the preferred method for batteries powering DC loads. 

The two-tier DC load test method applies two sequential discharge loads of different currents and time durations. lEC 61951-1 2005 specifies that the battery be first discharged at a low current for 10 sec, followed by a higher current for 3 sec (see Figure 8.9). This test protocol provides lifelike test conditions for many battery applications. The differences between the two load conditions provide additional battery information, but the values are strictly resistive and do not reveal capacity. 

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