Steady-state results

The principal limitation to using these rules is that the true process parameters are often unknown. Steady-state gain K can be calculated from a process model or determined from the steady-state results of a step test as Ac/Au, as shown in Fig. 8-28. The test will not be viable, however, if the time constant of the process is longer than a few... 

The same experimental procedure used in Fig. 4.15 is followed here. The Pt surface is initially (t < - 1 min) cleaned from Na via application of a positive potential (Uwr=0.2 V) using the reverse of reaction (4.23). The potentiostat is then disconnected (1=0, t=-lmin) andUWR relaxes to 0 V, i.e. to the value imposed by the gaseous composition and corresponding surface coverages of NO and H. Similar to the steady-state results depicted in Fig. 4.18 this decrease in catalyst potential from 0.2 to 0 V causes a sixfold enhancement in the rate, rN2, of N2 production and a 50% increase in the rate of N20 production. Then at t=0 the galvanostat is used to impose a constant current I=-20 pA Na+ is now pumped to the Pt catalyst surface at a... 

Measurements Using Liquid-Phase Reactions. Liquid-phase reactions, and the oxidation of sodium sulfite to sodium sulfate in particular, are sometimes used to determine kiAi. As for the transient method, the system is batch with respect to the liquid phase. Pure oxygen is sparged into the vessel. A pseudo-steady-state results. There is no gas outlet, and the inlet flow rate is adjusted so that the vessel pressure remains constant. Under these circumstances, the inlet flow rate equals the mass transfer rate. Equations (11.5) and (11.12) are combined to give a particularly simple result ... 

Compare the steady-state results with those of ENZSPLIT. 

Figure 5.258. Dissolved oxygen profiles at time T = 1500 for three different floe sizes, all other conditions identical. Note how the larger floe becomes oxygen depleted at its centre. These results were replotted from the steady-state results.

Figure 7. Nonequilibrium Monte Carlo results for the thermal conductivity (To = 2). The circles and squares are the present steady-state results for bulk and inhomogeneous systems, respectively (horizontally offset by 0.015 for clarity), and the triangles are NEMD results [89, 91]. (From Ref. 5.)...

From 320°C on, methane starts being consumed leading directly to C02. The beginning of C02 formation corresponds to the maximum of N02 desorption. Steady-state results (figure not shown) confirm that simultaneously with C02 formation, N2 formation also occurs (deNOx process effectively starts at 320°C). Methane reacts with N02, probably leading to the formation of oxygenated species and NO [18] according to reaction ... 

The steady state result would be considered to hold for time,... 

To define a feature extraction procedure it is necessary to consider that the output signal of a chemical sensor follows the variation of the concentration of gases at which it is exposed with a certain dynamics. The nontrivial handling of gas samples complicates the investigation of the dynamics of the sensor response. Generally, sensor response models based on the assumption of a very rapid concentration transition from two steady states results in exponential behaviour. 

Start the reactor with S>Smax and X=0.1. What is the steady-state result ... 

For continuous processes, checking the steady-state results is very useful. Algebraic equations for this can be added to the program, such that both sides became equal at steady state. For batch systems, all the initial mass must equal all the final mass, not always in mols but in kg. Expressed in mols the stoichiometry must be satisfied. 

FIGURE 5.3 The only physical possible steady-state results along the Hugoniot—the point J and region III. The broken line represents transient conditions. 

In this case the quasi-steady-state result, Eq. (104), is replaced by... 

However, if only the steady-state result is desired, the holdups on the... 

These time-dependent or pseudo-steady-state results are shown in Fig. 1.9. The numerical values correspond to the data in Table 1.1, but the curves have the same qualitative form for any values of the rate constants, etc. b(t) falls exponentially throughout the reaction whilst d(t) builds up to a maximum before decaying. 

Pulsed-current techniques can furnish electrochemical kinetic information and have been used at the RDE. With a pulse duration of 10-4 s and a cycle time of 10-3 s, good agreement was found with steady-state results [144] for the kinetic determination of the ferri-ferrocyanide system [260, 261], Reduction of the pulse duration and cycle time would allow the measurement of larger rate constants. Kinetic parameter extraction has also been discussed for first-order irreversible reactions with two-step cathodic current pulses [262], A generalised theory describing the effect of pulsed current electrolysis on current—potential relations has appeared [263],... 

In this chapter we have studied the dynamic controllability of CSTRs with several types of reactions and with several types of heat removal schemes. The control of a CSTR in a flowsheet with other units is also explored. The predictions made from the steady-state results of Chapter 2 have been quantitatively confirmed ... 

Reactor and Gas Loop Model The number of lumps used is determined by comparing the rigorous steady-state results with models using different numbers of lumps. The rigorous steady-state reactor exit temperature is 500 K with a 460 K inlet reactor temperature. When a 10-lump model is used with the same amount of catalyst, the steady-state exit temperature is 505 K. This occurs because of the numerical diffusion or effective back-mixing that is inherent with a lumped model. A 50-lump reactor model is used in all the simulations. It gives a steady-state reactor exit temperature of 501 K. The differences between the dynamic responses of the 10-lump and 50-lump reactors are shown in the next section. 

Figure 42. Steady-state results of a Wagner-Hebb polarization of Y-doped Z1O2 or TI1O2 with the aid of the cell 0N2, Pt YSZ or YST air, Pt (left, current-voltage curve for Tho.9Yo.1Ch 95 (YST), right partial conductivities for Zro.9Yo.1O1.95 (YSZ)).232 Reprinted from L.D. Burke, H. Rickert, and R. Steiner, Z Phys. Chem. N.F., 74 (1971) 146-167. Copyright 1971 with permission from Oldenbourg Verlagsgruppe.

Figure 42 depicts steady-state results of a Wagner-Hebb polarization of (Y203-doped) Zr02 and Th02 for which the ideal Wagner-Hebb relation is valid.232... 

The steady-state result (Eq. (77)) can be directly used to separate ionic and electronic conductivities the disadvantage of the technique is that it presupposes gas-separation. If not special measures are taken, it becomes unreliable for the ionic transport number less than 1%. Thus, this method well complements the Wagner-Hebb method which is very sensitive to small transference numbers. The partial conductivities of PbO shown in Figure 48 have been de-convoluted by the emf technique just described.3... 

The steady state results are shown in Figure 12. For c2 the single mode gets strongly excited, i.e. the energy is preferentially channeled into this mode (Bose condensation-like excitation). 

The situation exhibiting five steady states is similar to that for three steady states. Results of the steady state simulation revealed that the third stable steady state is located at the reactor outlet [22]. Calculation of the reactor with an aftersection packed by inert material indicated that five steady states are eliminated. [15]. 

A2 is also a known function of T and space velocity since the rate constant K2 is known from the steady state results (eq. 1). The parameters Ai and Af are not known independently however, the ratio Aj/Af equals the adsorption coefficient Kpr of propylene oxide which is a known function of T obtained from the steady state measurements (eq. 1). Since the steady state kinetics indicate that the surface reaction is the rate limiting step it can be concluded that Ai is larger than A2. It was assumed that propylene oxide adsorption is nonactivated and Aj was arbitrarily set equal to be two times larger than A2 at 400°C,for Y =. 002 then Aj was calculated from Af = Ai/Kpro Yp. The numerical simulations indicated that the model predictions are rather insensitive to Aj but are sensitive to the unknown parameters A3 and 0 c Since the Heat of Polymerization of Propylene Oxide is 18 Kcal/mol the parameter 0 was set equal to 0 exp(-18000/RT). 

Empirical Rate Expression and Search for a Reaction Mechanism. Based on the steady state results, the initial rate expression can be represented as ... 

Analogous results can be obtained using stress intensity factors.31,84 For a small center crack in a tensile specimen, Eqns. (30) and (32) give a steady-state result, at large crack lengths,84... 

The steady-state result given in Eqn. (69) will be taken to express the creep behavior controlled by the broken fibers. The volume fraction of broken fibers is... 

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