Kinetic rate expression for

Therefore, the overall kinetic rate expression for ethyl lactate conversion from lactic acid and ethanol can be given by ... 

Write a simulation program to integrate the kinetic rate expressions for Go and Oco in time, starting with initial coverages 0q1 and 0co- What is the maximum value of T0R(C02) (in s-1) At what elapsed time does this occur What are the coverages Go and Oco at the maximum T0R(C02) ... 

Let s define a system as an individual cell or multiple cells. The system does not contain any of the abiotic phase of culture. Instead, it is the biotic2 phase only, which possesses mass m on a dry basis and specific volume v. Let s assume that there are c components in the cell and the mass of the /th component per unit volume of system is (Cx ). It is also assumed that there exist kinetic rate expressions for p reactions occurring in the system and the rate of /th component formed from the fth reaction per unit volume of system is rx... 

In the reactive case, r is not equal to zero. Then, Eq. (3) represents a nonhmoge-neous system of first-order quasilinear partial differential equations and the theory is becoming more involved. However, the chemical reactions are often rather fast, so that chemical equilibrium in addition to phase equilibrium can be assumed. The chemical equilibrium conditions represent Nr algebraic constraints which reduce the dynamic degrees of freedom of the system in Eq. (3) to N - Nr. In the limit of reaction equilibrium the kinetic rate expressions for the reaction rates become indeterminate and must be eliminated from the balance equations (Eq. (3)). Since the model Eqs. (3) are linear in the reaction rates, this is always possible. Following the ideas in Ref. [41], this is achieved by choosing the first Nr equations of Eq. (3) as reference. The reference equations are solved for the unknown reaction rates and afterwards substituted into the remaining N - Nr equations. 

There is significant support for this mechanism, both from kinetic and spectroscopic data. For example, the oxidation of CO adsorbed on a precious metal by oxygen from the ceria has been observed to occur below 400 K in temperature programmed-desorption (TPD) measurements [27]. Indeed, recent spectroscopic data has shown that Pd particles are oxidized by their ceria zirconia support, beginning at -470 K [28]. Evidence for the other important step in the reaction, the oxidation of reduced ceria by steam, has also been presented [29]. Finally, the kinetic rate expression for the WGS reaction over ceria-supported precious metals, in which the reaction is zeroth order in CO, agrees with expected rate expression for the mechanism shown above [29]. 

The kinetic rate expression for hydrolysis is derived by assuming steady-state for all reaction Intermediates. Assiimlng further that the rate of hydrolysis Is first-order In ether, the following equations are obtained ... 

Using the experimentally determined values of the rate constants, WGS calculated to be 25.4 by equation 11. The actual value of the equilibrium constant at 637 K is 17.6, and this agreement is acceptable. The second check was performed by predicting both the rate and the kinetic rate expression for WGS and comparing these predictions to reported values. 

The problem of the kinetics of coke formation is a very Important especially with the Increasing demand for the use of low steam to methane ratios [ 10]. Kinetic rate expressions for the coke formation need to be developed. These rate equations should give the rate of coke formation 1n terms of the partial pressure of the various components and not only 1n terms of the carbon deposition and time it should also take Into consideration pore blockage as well as active site coverage by coke. 

There exist kinetic rate expressions for p reactions occurring in the system and the rate of the 7th component formed from the ith reaction per unit volume of the system is. ... 

Almost aU metals corrode, but many metals corrode very slowly under normal environmental conditions, due in part to kinetic limitations of the metal dissolution reaction. Thus, the rate of metal corrosion can be anticipated and controlled by developing kinetic rate expressions for metal oxidation reactions. There is a major difference, however, between classical electrochemical metal dissolution kinetics and metal dissolution in a corrosion system, that difference being the occurrence of one or more oxidation and reduction reactions on the same metal. 

Given the form of this expression and the reaction barrier discussed above, it is not surprising that the experimentally derived kinetic rate expression for many processes is ... 

The previous analysis although simple and idealized, is the basis for the development of most of the rigorous kinetic rate expressions for gas-solid catalytic reactions with the exception of the partial oxidation reactions for which the Redox kinetic models (section 3.2.5) are still competing with the CSD kinetic models. 

Internal system divided into arterial and venous blood compartments, a brain compartment, two separate compartments for the poorly perfused and well perfused tissues. The latter two compartments are subdivided into intracellular bicarbonate and total extracellular C02 (plus intracellular dissolved C02) pools. Kinetic rate expressions for the C02 hydration in these pools are included as well as balance equations for the ions. 

Extensions of the simple network of consecutive irreversible reactions can easily be expanded to include multiple steps and products, formed by reversible and irreversible elementary reactions. In all complex processes the writing of a reaction network produces the most general description of the kinetic process. Fortunately, in many cases the network is such that the steady state assumptions can be invoked. When this is possible, the kinetic rate expressions for the elementary processes of the reaction mechanism can often be solved analytically, as in the example above, to yield a simpler rate expression for the overall process. The identification of such a mechanistic rate expression, using experimental rate data from a kinetic study, can serve to identify the likely mechanism of that reaction. 

Steady state solutions have been invoked in developing rate expressions from this mechanism for each of the observed products. This allows the use of mechanistic kinetic rate expressions for the formation of the products rather than having to deal with the full twenty-reaction network of elementary reactions. A twenty-reaction network would require at least forty parameters to be fitted in correlating data from this system. As we will, see this number is considerably reduced by solving the mechanism at steady state and fitting the resultant steady state rate expressions. 

The next task was to model the reformer itself to understand design issues and be able to predict performance of various reactor/catalyst types and transient behavior. However, upon trying to obtain kinetic rate expressions for the reforming reactions, it was found that very little information existed in the public domain. This led to the decision/need to develop reaction kinetics for catalytic partial oxidation and steam reforming at National Energy Technology Laboratory s (NETL s) onsite research facility. 

Table 3 lists the kinetic rate expressions for each of the hydrolysis and fermentation reaction rates shown in Fig. 5 and in the mass balance equations of Tables 1 and 2. Each of the reaction rates were found to fit the data through trial and error, starting with the simplest model. For the hydrolysis reaction rates (rs,arch and / maltose), the simplest form was the Michaelis-Menten model without inhibition. For all other reaction rates which described fermentation kinetics, the simplest form was the Monod model without inhibition. More descriptive models were found in the literature and tested one by one until the set of kinetic rate equations with the best fit to the experimental data were determined. This was completed with the hydrolysis datasets first, then the complete SSF datasets. 

The implications of the work presented in this paper, are that now it should be possible to move away from lumped component and gas phase power law kinetic rate expressions for FCC to a situation where the major components are accounted for individually. In future work when the reactivity of the adsobed species has been more clearly quantified, a fundamental description of which species will poison an FCC catalyst as well as which are most likely to act as coke precursors should be possible. Thus, prediction of FCC riser and stripper kinetics without excess parameter retuning will be conceivable. 

As a prelude to the development of kinetic rate expressions for heterogeneous chemical reactions, if A reacts with B, for example, then the next step in the mechanism is ha + Ba, forming an activated complex on the snrface. Each reversible step in the seqnence above is characterized by a forward rate constant adsoiption for adsoiption, with units of mol/area time atm, and a backward rate constant A ,desoiption for desorption, with units of mol/area time. The ratio of these rate constants adsorption/ h, desoiption defines the adsorption/desorption equi-... 

In a recently published reactor design textbook, a problem begins as follows The heterogeneous gas-phase catalytic chemical reaction, A - - B C, is carried out in an isothermal isobaric flow reactor. If Q represents the molar density of species i, then the volume-based kinetic rate expression for the reaction is... 

TABLE 9.8 Macro Kinetic Rate Expressions for WGSR [25, 51, 52, 56, 73-78]... 

Monnery WD, Hawboldt KA, Pollock A, Svrcek WY (2000) New experimental data and kinetic rate expression for H2S pyrolysis and re-association. <2hem Eng Sci 55 957-966... 

Sabatier-type volcano plots have been constructed for a number of different commercially relevant systemsl l. A simple kinetic expression that simulates the Sabatier result is found when one realizes that the decomposition of molecules requires a vacant site for molecular fragments to adsorb on. For instance, in the N2O decomposition reaction, the dominant surface species (most abundant reaction intermediate) is atomic oxygen (O), which is in equilibrium with the gas phase. When the slow step in the reaction is dissociative adsorption of N2O, the mean-field kinetic rate expression for N2O decomposition, normalized per unit surface area of catalyst, becomes ... 

Using these design equations, one can calculate the volume V of the reactor required to achieve a specified fractional conversion Xa/(Xa/ = 1 - (Q//Cao)) of reactant A in the reactor. Here, q is the volumetric feed flow rate and -rJC ) is the kinetic rate expression for the rate of disappearance of reactant A. 

Annaland TV, Kuipers JAM, van Swaaij WPM A kinetic rate expression for the time-dependent coke formation rate during propane dehydrogenation over a platinum alumina monolithic catalyst, Catal Today 66(2—4) 427—436, 2001. 

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