Sequential Steady State

Figure 11.4. Single Pass Sequential Steady State (SPSSS) operation. [Mujtaba, 1997]c...

Single Pass Sequential Steady State Operation (SPSSS)... 

PLOW 1 RAN was made available in 1974 by Monsanto Co. for steady-state simulation of chemical processes based on sequential modular technology. It requires specification of feed streams and topology of the system. In 1987, an optimization enhancement was added. 

Steady state and non steady state kinetic measurements suggest that methane carbon dioxide reforming proceeds in sequential steps combining dissociation and surface reaction of methane and CO2 During admission of pulses of methane on the supported Pt catalysts and on the oxide supports, methane decomposes into hydrogen and surface carbon The amount of CH, converted per pulse decreases drastically after the third pulse (this corresponds to about 2-3 molecules of CH< converted per Pt atom) indicating that the reaction stops when Pt is covered with (reactive) carbon CO2 is also concluded to dissociate under reaction conditions generating CO and adsorbed... 

According to the preceding results we cannot determine the steady state of the system using the sequential approach suggested by Woodley [27]. This method involves sequential study of two phenomena reactant transfer in biphasic medium and enzyme kinetics in the aqueous medium. In the steady state, substrate transfer rate is equal to the reaction rate. 

Chapter 5 deals with steady-state data reconciliation problem, from both a linear and a nonlinear point of view. Special consideration is given, in Chapter 6, to the problem of sequential processing of information. This has several advantages when compared with classical batch processing. 

A procedure used to assist in identifying sequential mechanisms when the double-reciprocal plots exhibit parallel lines ". In some cases, bireactant mechanism can have various collections of rate constants that result in so-called parallel line kinetics, even though the mechanism is not ping pong. However, if the concentrations of A and B are kept in constant ratio with respect to each other, a sequential mechanism in a 1/v v. 1/[A] plot would be nonlinear (since in the denominator the last term of the double-reciprocal form of the rate expression contains [A] for example, for the steady-state ordered Bi Bi reaction scheme in which [B] = a[A], the double-reciprocal rate expression becomes 1/v =... 

Easterby proposed a generalized theory of the transition time for sequential enzyme reactions where the steady-state production of product is preceded by a lag period or transition time during which the intermediates of the sequence are accumulating. He found that if a steady state is eventually reached, the magnitude of this lag may be calculated, even when the differentiation equations describing the process have no analytical solution. The calculation may be made for simple systems in which the enzymes obey Michaehs-Menten kinetics or for more complex pathways in which intermediates act as modifiers of the enzymes. The transition time associated with each intermediate in the sequence is given by the ratio of the appropriate steady-state intermediate concentration to the steady-state flux. The theory is also applicable to the transition between steady states produced by flux changes. Apphcation of the theory to coupled enzyme assays makes it possible to define the minimum requirements for successful operation of a coupled assay. The theory can be extended to deal with sequences in which the enzyme concentration exceeds substrate concentration. 

A procedure that assists in the characterization of binding mechanisms for sequential (/.e., non-ping pong) reactions . The same general initial rate expression applies to the steady-state ordered Bi Bi reaction, the rapid-equilibrium random Bi Bi reaction, and the Theorell-... 

Kinetics of O-Methylaiion. The steady state kinetic analysis of these enzymes (41,42) was consistent with a sequential ordered reaction mechanism, in which 5-adenosyl-L-methionine and 5-adenosyl-L-homocysteine were leading reaction partners and included an abortive EQB complex. Furthermore, all the methyltransferases studied exhibited competitive patterns between 5-adenosyl-L-methionine and its product, whereas the other patterns were either noncompetitive or uncompetitive. Whereas the 6-methylating enzyme was severely inhibited by its respective flavonoid substrate at concentrations close to Km, the other enzymes were less affected. The low inhibition constants of 5-adenosyl-L-homocysteine (Table I) suggests that earlier enzymes of the pathway may regulate the rate of synthesis of the final products. 

We have implemented the principle of multiple selective excitation (pulse sequence II in fig. 1) thereby replacing the low-power CW irradiation in the preparation period of the basic ID experiment by a series of selective 180° pulses. The whole series of selective pulses at frequencies /i, /2, , / is applied for several times in the NOE build-up period to achieve sequential saturation of the selected protons. Compared with the basic heteronuclear ID experiment, in this new variant the sensitivity is improved by the combined application of sequential, selective pulses and the more efficient data accumulation scheme. Quantitation of NOEs is no longer straightforward since neither pure steady-state nor pure transient effects are measured and since cross-relaxation in a multi-spin system after perturbation of a single proton (as in the basic experiment) or of several protons (as in the proposed variant) differs. These attributes make this modified experiment most suitable for the qualitative recognition of heteronuclear dipole-dipole interactions rather than for a quantitative evaluation of the corresponding effects. 

As pointed out earlier, CVD is a steady-state, but rarely equilibrium, process. It can thus be rate-limited by either mass transport (steps 2, 4, and 7) or chemical kinetics (steps 1 and 5 also steps 3 and 6, which can be described with kinetic-like expressions). What we seek from this model is an expression for the deposition rate, or growth rate of the thin film, on the substrate. The ideal deposition expression would be derived via analysis of all possible sequential and competing reactions in the reaction mechanism. This is typically not possible, however, due to the lack of activation or adsorption energies and preexponential factors. The most practical approach is to obtain deposition rate data as a function of deposition conditions such as temperature, concentration, and flow rate and fit these to suspected rate-limiting reactions. 

Thus put, details of the individual reactions—which are, in any event, certain to be complex—remain as undetermined and debatable as before. What becomes clear (and consistent with experiment) is that (a) product gases such as carbon dioxide can form via two fundamentally unrelated paths (b) humic acids can be abstracted by secondary degradation or by stripping reactions such as decarboxylation (i.e. by reactions respectively characterized by kn> fe, etc. and by k) (c) in a sequential reaction series such as Reaction 2, a zero rate of humic acid formation denotes establishment of a steady state condition rather than formation of a simple equilibrium of the type coal humic acids. 

The value of Vmax, cat, or any rate constant for a series of sequential reactions may be derived by considering the time taken for each step, as follows. The dimensions of v are moles per second. The dimensions of 1/v are seconds per mole, and 1/v is the time taken for 1 mol of reagents to give products. Similarly, the reciprocal of kc,M (i.e., [Elo/V ) has the dimensions of seconds and is the time taken for one molecule of reagent to travel the whole reaction pathway in the steady state at saturating [S]. The reciprocal rate constant may be considered a transit time. 

The non-dimensionalization used in this work is perhaps the simplest, but it suffers from the defect that important physical bifurcation parameters are not isolated. The simple cuspoid diagrams are probably not those that would be obtained from experiments, where the residence time is a convenient parameter. Balakotaiah and Luss (1983) considered such a formulation for two parallel or simultaneous reactions the diagrams for the case of sequential reactions are similar, at least when the activation energies are equal. The maximum multiplicity question, however, is independent of the formulation and we conjecture that diagrams with seven steady states could be found in a small region of parameter space, though we have not looked for them. 

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