Numbers of Transfer Units

The fractional extraction schemes described above are typical of those practiced in industry. A related kind of process employs a second solvent in a separate extraction operation to wash the raffinate 

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NTU p is the "exterior apparent" overall gas-phase number of transfer units calculated neglecting axial dispersion simply on the basis of equation 56, whereas NTU stands for the higher real number of transfer units (Nq ) which is actually required under the influence of axial dispersion. The correction factor ratio can be represented as a function of those parameters that are actually known at the outset of the calculation... 

In these equations S denotes the stripping factor, Equation 77 is only vaUd for a sufftciendy high number of transfer units so that the correction... 

To estimate the number of transfer units for design, the following empirical correlations which were derived from efficiency measurements employing a variety of trays and operating conditions under the aforementioned assumptions are recommended (111) ... 

This term is a measure of the unit s length. Sometimes it is referred to as the number of transfer units. This simply says that the optimum pressure drop increases as the heat exchanger gets longer, ie, has more transfer units. The forms of F, and F both foUow from the fact that in turbulent flow the... 

In order to determine the packed height it is necessary to obtain a value of the overall number of transfer units methods for doing this are available for binary systems in any standard text covering distillation (73) and, in a more complex way, for multicomponent systems (81). However, it is simpler to calculate the number of required theoretical stages and make the conversion ... 

NTU Number of transfer units (general) Dimensionless Dimensionless... 

NTU (Number of Transfer Units) The NTU required for a given separation is closely related to the number of theoretical stages or plates required to cariy out the same separation in a stagewise or plate-type apparatus. For equimolal counterdiffusion, such as in a binary distillatiou, the number of overall gas-phase transfer units Nqg required for changing the composition of the vapor stream from yi to yo is... 

The number of transfer units in any direct dryer is given by... 

The second (integral) terms represent the numbers of transfer units for an infinitely dilute gas. The first terms, frequently amounting to only small corrections, give the effect of a finite level of gas concen-t rati on. 

In these equations, the first term is a correction for finite liqiiid-phase concentrations, and the integral term represents the numbers of transfer units required for dilute solutions. It would be very unusual in practice to find an example in which the first (logarithmic) term is of any significance in a stripper design. 

The number of transfer units can be calculated from the adiabatic design equation, Eq. (14-46) ... 

The response of solute concentration in the raffinate to the sol-vent-to-feed ratio S /F can be calculated by Eqs. (15-26) and (15-27) for a constant number of transfer units based on the overall raffinate phase N r-... 

Fxample 5 Number of Transfer Units Let us calculate the numher of transfer units required to achieve the separation in Example 3. The solution to the problem is the same as in Example 3 except that the denominator is changed in the final equation [Eq. (15-25)] ... 

A similar term of number of transfer units per actual stage could also be envisioned. 

Likewise, the height of a transfer unit based on raffinate-phase compositions is the height of tower divided by the number of transfer units [Eq. (15-30)]. 

Two dimensionless variables play key roles in the analysis of single transition systems (and some multiple transition systems). These are the throughput parameter [see Eq. (16-129)] and the number of transfer units (see Table 16-13). The former is time made dimensionless so that it is equal to unity at the stoichiometric center of a breakthrough cui ve. The latter is, as in packed tower calculations, a measure of mass-transfer 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. 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

Since the term (1 -i- k i)/k approaches unity for large /c -value, the number of plates is equal to one half the number of transfer units for a strongly retained component. For these conditions, when Np = N/2, Eq. (16-174) and Eq. (16-161) produce the same peak retention time, peak spreading, ana predict essentially the same peak profile. 

The local equilibrium curve is in approximate agreement with the numerically calculated profiles except at very low concentrations when the isotherm becomes linear and near the peak apex. This occurs because band-spreading, in this case, is dominated by adsorption equilibrium, even if the number of transfer units is not very high. A similar treatment based on local eqnihbrinm for a two-component mixture is given by Golshau-Shirazi and Gniochou [J. Phys. Chem., 93, 4143(1989)]. 

Alternatively, the number of transfer units (NTU) in the foam based on, say, the ascending stream can be found from Eq. (22-48) ... 

Number of Transfer Units. For dilute solutions the number of transfer units Nqg is obtained by... 

Equation 3 Is quite accurate for calculating the number of transfer units for the example cooling tower... 

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