Reaction number, dimensionless

We do this for isothermal constant-density conditions first in a BR or PFR, and then in a CSTR. The reaction conditions are normalized by means of a dimensionless reaction number MAn defined by... 

Determine the fractional conversion /A of A for a zero-order reaction (A - products) in a laminar flow reactor, where c o = 0.25 mol L 1, jfcA = 0.0015 mol L-1 s-1, and t = 150 s. Compare the result with the fractional conversion for a PFR and for a CSTR 16-4 Using equation 16.2-18, develop a graph which shows the fractional conversion /A as a function of the dimensionless reaction number MAo for a zero-order reaction, where Mao = kt/cAo< equation 4.3-4. what are the real limits on Mao ( e > values f°r which reasonable values of /A are obtained) Explain. 

In Table 17.2, fA (for the reaction A products) is compared for each of the three flow reactor models PFR, LFR, and CSTR. The reaction is assumed to take place at constant density and temperature. Four values of reaction order are given in the first column n = 0,1/2,1, and 2 ( normal kinetics). For each value of n, there are six values of the dimensionless reaction number MAn = 0, 0.5, 1, 2, 4, and °°, where MAn = equation 4.3-4. The fractional conversion fA is a function only of MAn, and values are given for three models in the last three columns. The values for a PFR are also valid for a BR for the conditions stated, with reaction time t = t and no down-time (a = 0), as described in Section 17.1.2. 

The dimensionless second-order reaction number, from equation 4.34, with T = t (constant density), is... 

Grewer, T., DECHEMA Monograph, 1980, 88(1818-1835), 21-30 One of the principal causes of batch chemical processes becoming unstable is the combination of a high reaction exotherm and a low reaction rate (or rates if there is more than one component reaction in the overall process). A secondary cause of reaction delay leading to instability is too little mass transfer. To permit safe operation of such reaction systems, the reaction energy (which may be expressed as a dimensionless reaction number) and the reaction rate(s) must be known. The possibility of there being a lower safe limit as well an upper safe limit to reaction temperature is discussed. 

At any specified extent of reaction />, the dimensionless number density of molecules with N monomers is n p, A), defined as the number of A-mers divided by the total number of monomers. This number density is proportional to the probability that a randomly selected polymer has A... 

Overall reaction order Nusseit Number (dimensionless)... 

Vi Change in number of moles upon reaction for reaction I Dimensionless 7.47... 

In this expression, n is the charge number (dimensionless), F is the Faraday constant (96 485 C mol ) and is the reversible potential of the cell reaction. 

Hatta number, dimensionless height equivalent to a theoretical plate or stage, m height of a transfer unif, m elecfrical currenf, A wafer flux, m /m s fhermal conducfivify, J/m s K k ky, ky mass fransfer coeffidenf, various unifs elimination rafe consfanf, s reaction rafe consfanf, s partition coefficienf, various unifs permeabilify, m/s or m ... 

Damkoehler number—system residence time/characteristic reaction time (dimensionless) diameter of microcarrier beads (p,m) energy dissipation/circulation fnnetion P/(kD total force imparted by the impeller, radial and axial (eq. 18-64) (Nm-2)... 

In this equation n is the charge number (dimensionless), which indicates the number of electrons exchanged in the dissolution reaction, and F is the Faraday constant, F = 96,485 C/mol. In the absence of an external polarization a metal in contact with an oxidizing electrolytic environment acquires spontaneously a certain potential, called the corrosion potential, The partial anodic current density at the corrosion potential is equal to the corrosion current density / Equation (4) thus becomes ... 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

Asymptotic Solution Rate equations for the various mass-transfer mechanisms are written in dimensionless form in Table 16-13 in terms of a number of transfer units, N = L/HTU, for particle-scale mass-transfer resistances, a number of reaction units for the reaction kinetics mechanism, and a number of dispersion units, Np, for axial dispersion. For pore and sohd diffusion, q = / // p is a dimensionless radial coordinate, where / p is the radius of the particle, if a particle is bidisperse, then / p can be replaced by the radius of a suoparticle. For prehminary calculations. Fig. 16-13 can be used to estimate N for use with the LDF approximation when more than one resistance is important. 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Damkdhler (1936) studied the above subjects with the help of dimensional analysis. He concluded from the differential equations, describing chemical reactions in a flow system, that four dimensionless numbers can be derived as criteria for similarity. These four and the Reynolds number are needed to characterize reacting flow systems. He realized that scale-up on this basis can only be achieved by giving up complete similarity. The recognition that these basic dimensionless numbers have general and wider applicability came only in the 1960s. The Damkdhler numbers will be used for the basis of discussion of the subject presented here as follows ... 

Equations 8-148 and 8-149 give the fraction unreacted C /C o for a first order reaction in a closed axial dispersion system. The solution contains the two dimensionless parameters, Np and kf. The Peclet number controls the level of mixing in the system. If Np —> 0 (either small u or large [), diffusion becomes so important that the system acts as a perfect mixer. Therefore,... 

In section 11.3 we saw how a classical reaction engineering approach45 can been used to model both electrochemical promotion and metal support interactions. The analysis shows that the magnitude of the effect depends on three dimensionless numbers, II, J and Op (Table 11.3) which dictate the actual value of the promotional effectiveness factor. 

The Lotka-Volterra reaction described in Section 2.5.4 has three initial conditions—one each for grass, rabbits, and lynx—all of which must be positive. There are three rate constants assuming the supply of grass is not depleted. Use dimensionless variables to reduce the number of independent parameters to four. Pick values for these that lead to a sustained oscillation. Then, vary the parameter governing the grass supply and determine how this affects the period and amplitude of the solution. 

This dimensionless number measures the breadth of the molecular weight distribution. It is 1 for a monodisperse population (e.g., for monomers before reaction) and is 2 for several common polymerization mechanisms. 

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