State quasi-steady

For reactions where product formation is a limiting step, the difference between product formation (k and complex dissociation rates is small. With a steady-state assumption, the rate of the formation of substrate complex and the buildup concentration rate (fcj) is assumed to be equal to that of its dissociation (fe, ), suggesting that [E5] does not change during the course of the reaction. Derivation of reaction rates based on a steady-state assumption is similar to that of an equilibrium assumption. The key difference is in the method of expressing [ 5]. The steady-state condition is shown in Equation 4.13, and the derivations are given in Equations 4.14 to 4.19. 

When k2 = k, K can be simplified to which is identical to derived from an eqnilibrinm assumption.  

The derivation of the reversible rate equation is similar to that of the irreversible eqnation. However, the difference is in both the forward and reverse reaction rates for the prodnct. See Eqnation 4.20. It can be converted to an irreversible reaction by considering [P] as equal to zero. 

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A] = b/a (equation (A3.4.145)) is stationary and not [A ] itself This suggests d[A ]/dt < d[A]/dt as a more appropriate fomuilation of quasi-stationarity. Furthemiore, the general stationary state solution (equation (A3.4.144)) for the Lindemaim mechanism contams cases that are not usually retained in the Bodenstein quasi-steady-state solution. 

The effects of ultrasound-enlianced mass transport have been investigated by several authors [73, 74, 75 and 76]. Empirically, it was found that, in the presence of ultrasound, the limiting current for a simple reversible electrode reaction exhibits quasi-steady-state characteristics with intensities considerably higher in magnitude compared to the peak current of the response obtained under silent conditions. The current density can be... 

Amorphous Silicon. Amorphous alloys made of thin films of hydrogenated siUcon (a-Si H) are an alternative to crystalline siUcon devices. Amorphous siUcon ahoy devices have demonstrated smah-area laboratory device efficiencies above 13%, but a-Si H materials exhibit an inherent dynamic effect cahed the Staebler-Wronski effect in which electron—hole recombination, via photogeneration or junction currents, creates electricahy active defects that reduce the light-to-electricity efficiency of a-Si H devices. Quasi-steady-state efficiencies are typicahy reached outdoors after a few weeks of exposure as photoinduced defect generation is balanced by thermally activated defect annihilation. Commercial single-junction devices have initial efficiencies of ca 7.5%, photoinduced losses of ca 20 rel %, and stabilized efficiencies of ca 6%. These stabilized efficiencies are approximately half those of commercial crystalline shicon PV modules. In the future, initial module efficiencies up to 12.5% and photoinduced losses of ca 10 rel % are projected, suggesting stabilized module aperture-area efficiencies above 11%. 

A quasi-steady state proeess is a fed-bateh fermenter where dC /dt = 0 and p = u/V. Beeause V inereases, p therefore deereases, and thus the reaetor moves through a series of ehanging steady states for whieh p = D, during whieh C, and p deerease and C, remains eonstant. 

Under steady-state conditions, the temperature distribution in the wall is only spatial and not time dependent. This is the case, e.g., if the boundary conditions on both sides of the wall are kept constant over a longer time period. The time to achieve such a steady-state condition is dependent on the thickness, conductivity, and specific heat of the material. If this time is much shorter than the change in time of the boundary conditions on the wall surface, then this is termed a quasi-steady-state condition. On the contrary, if this time is longer, the temperature distribution and the heat fluxes in the wall are not constant in time, and therefore the dynamic heat transfer must be analyzed (Fig. 11.32). 

Many HVAC system engineering problems focus on the operation and the control of the system. In many cases, the optimization of the system s control and operation is the objective of the simulation. Therefore, the appropriate modeling of the controllers and the selected control strategies are of crucial importance in the simulation. Once the system is correctly set up, the use of simulation tools is very helpful when dealing with such problems. Dynamic system operation is often approximated by series of quasi-steady-state operating conditions, provided that the time step of the simulation is large compared to the dynamic response time of the HVAC equipment. However, for dynamic systems and plant simulation and, most important, for the realistic simulation... 

This procedure constitutes an application of the steady-state approximation [also called the quasi-steady-state approximation, the Bodenstein approximation, or the stationary-state hypothesis]. It is a powerful method for the simplification of complicated rate equations, but because it is an approximation, it is not always valid. Sometimes the inapplicability of the steady-state approximation is easily detected for example, Eq. (3-143) predicts simple first-order behavior, and significant deviation from this behavior is evidence that the approximation cannot be applied. In more complex systems the validity of the steady-state approximation may be difficult to assess. Because it is an approximation in wide use, much critical attention has been directed to the steady-state hypothesis. 

One way to examine the validity of the steady-state approximation is to compare concentration—time curves calculated with exact solutions and with steady-state solutions. Figure 3-10 shows such a comparison for Scheme XIV and the parameters, ki = 0.01 s , k i = 1 s , 2 = 2 s . The period during which the concentration of the intermediate builds up from its initial value of zero to the quasi-steady-state when dcfjdt is vei small is called the pre-steady-state or transient stage in Fig. 3-10 this lasts for about 2 s. For the remainder of the reaction (over 500 s) the steady-state and exact solutions are in excellent agreement. Because the concen-... 

In a short time period, the dynamic model shown in Equation (3.13.1.1) at quasi-steady-state condition, OTR to microbial cells would be equal to oxygen molar flow transfer to the liquid phase.4... 

For quasi-steady state, the specific growth rate reaches the media dilution rate, /l D. If Fm>Fspecific growth rate may decrease. 

Develop a suitable rate expression using the Michaelis-Menten rate equation and the quasi-steady-state approximations for the intermediate complexes formed. 

The respiratory quotient (RQ) is often used to estimate metabolic stoichiometry. Using quasi-steady-state and by definition of RQ, develop a system of two linear equations with two unknowns by solving a matrix under the following conditions the coefficient of the matrix with yeast growth (y = 4.14), ammonia (yN = 0) and glucose (ys = 4.0), where the evolution of C02 and biosynthesis are very small (o- = 0.095). Calculate the stoichiometric coefficient for RQ =1.0 for the above biological processes ... 

The quasi-steady-state analysis approach to the dryout problem... 

The important reason for the quasi-steady-state approach arises from the difficulty in obtaining a solution to the transient convection problem for two-phase situations. 

This equation has been discussed by Nelson and Pasamehmetoglu (1992) relative to the application of the quasi-steady-state model for the convection problem. 

Frequently function R can be written as a single term having the simple form of equation 1. For Instance, with the aid of the long chain approximation (LCA) and the quasi-steady state approximation ((JSSA), the rate of monomer conversion, I.e., the rate of polymerization, for many chain-addition polymerizations can be written as... 

A quasi steady-state radical population exists. 

The quasi-steady hypothesis is used when short-lived intermediates are formed as part of a relatively slow overall reaction. The short-lived molecules are hypothesized to achieve an approximate steady state in which they are created at nearly the same rate that they are consumed. Their concentration in this quasi-steady state is necessarily small. A typical use of the quasi-steady... 

The assumption of a quasi-steady state is applied to the CHs and CHs CO radicals by setting their time derivatives to zero ... 

The free-radical concentrations will be small—and the quasi-steady state hypothesis will be justified— whenever the initiation reaction is slow compared with the termination reaction, kj /f[CH3CHO]. 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

Hie quasi steady state approximation can be conveniently applied to equations 19 to 21, without any significant loss of accuracy, due to tlie high reactivity of tlie reacting species in aqueous solution. Hms, the system of ordinary differential equations is readily reduced to a system of algebraic non linear equations. 

The rates of the elementary steps can be formulated in a conventional manner, and the quasi-steady state hypothesis is applied to the adsorbed substrate (A ). The... 

For gas absorption, this problem can often be circumvented by the assumption of a quasi-steady-state condition for the gas phase. In this, the dynamics of the gas phase are effectively neglected and the steady state, rather than the dynamic form of component balance is used to describe the variation in gas phase concentration. 

Assuming equilibrium conditions and a linear equilibrium relationship, where Y] = m Xi, and a quasi-steady-state conditions in the gas with dYj/dt = 0 to be achieved, a component balance for the entire two phase system of Fig. 3.56, gives... 

Again one way of dealing with this is to replace those differential rate equations, having low time constants (i.e., high K values) and fast rates of response, by quasi-steady-state algebraic equations, obtained by setting... 

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