Equilibrium contact time

Figure 1. Operational definition of equilibrium contact time (ECT) in the FFT Process fabric (65/36 polyester/cotton sheeting, 3.7 oz/yd2) speed of fabric (100 ft/min) nozzle gap width (0.5 in.) machine contact time (MCT) (0.025 sec) foam (0.15 g/cc density, 46% solids content).

High mass-transfer rates in both vapor and hquid phases. Close approach to eqiiilihriiim. Adiabatic contact assures phase eqiiilihriiim, Only moderate mass-transfer rate in liquid phase, zero in sohd. Slow approach to equilibrium achieved in brief contact time. Included impurities cannot diffuse out of solid. Sohd phase must be remelted and refrozen to allow phase equilibrium. 

The discussion above assumes that equilibrium contact between liquid adhesive and rough substrate is achieved. However, adhesives set in what may be quite a short time, and so may never reach equilibrium contact. It is therefore relevant to consider the kinetics of penetration of the adhesive into a pore. 

Adsorption for gas purification comes under the category of dynamic adsorption. Where a high separation efficiency is required, the adsorption would be stopped when the breakthrough point is reached. The relationship between adsorbate concentration in the gas stream and the solid may be determined experimentally and plotted in the form of isotherms. These are usually determined under static equilibrium conditions but dynamic adsorption conditions operating in gas purification bear little relationship to these results. Isotherms indicate the affinity of the adsorbent for the adsorbate but do not relate the contact time or the amount of adsorbent required to reduce the adsorbate from one concentration to another. Factors which influence the service time of an adsorbent bed include the grain size of the adsorbent depth of adsorbent bed gas velocity temperature of gas and adsorbent pressure of the gas stream concentration of the adsorbates concentration of other gas constituents which may be adsorbed at the same time moisture content of the gas and adsorbent concentration of substances which may polymerize or react with the adsorbent adsorptive capacity of the adsorbent for the adsorbate over the concentration range applicable over the filter or carbon bed efficiency of adsorbate removal required. 

If contact time is not enough for each stage to reach equilibrium, one may calculate the number of actual plates NAP by incorporating contacting efficiency. Two principal types of efficiency may be employed overall and stage. The overall exchanger efficiency, rj , can be used to relate NAP tind NTP as follows... 

It may be concluded that during the contact time in the competing process for the energy in the various spin systems, the carbon atoms are trying to reach thermal equilibrium with the proton polarization, which is in itself decreasing with a time constant, (Tig, H). In fact the protons undergo spin diffusion and can be treated together, whereas the carbon atoms behave individually. Therefore one implication is that we can also expect to obtain a C-13 spin polarization proportional to the proton polarization. 

Let us consider a circular puddle of liquid, L, on solid, S, in the presence of liquid vapor, V. The puddle is of radius Rq and small initial thickness Bq. We assume that holes nucleate spontaneously in the puddle and grow with radius r(t) as time t passes because the equilibrium contact angle. Go, is nonzero. The liquid is unstable as a wetting film. Equilibrium thickness of a film, < is given by [27,28]... 

A notable aspect of this equation is that L appears within it as prominently as the rate constant k+ or the groundwater velocity vx, indicating the balance between the effects of reaction and transport depends on the scale at which it is observed. Transport might control fluid composition where unreacted water enters the aquifer, in the immediate vicinity of the inlet. The small scale of observation L would lead to a small Damkohler number, reflecting the lack of contact time there between fluid and aquifer. Observed in its entirety, on the other hand, the aquifer might be reaction controlled, if the fluid within it has sufficient time to react toward equilibrium. In this case, L and hence Da take on larger values than they do near the inlet. 

Figure 7.10 The effect of increasing the flow rate and decreasing the contact time for WGS reaction over G-66 A, Cu0.2Ceo 02 y, and Cu01Ce09O2 catalysts. Empty symbols illustrate low flow rate, SV = 5000 h 1 and filled symbols high flow rate, SV = 30.000 h 1. The dotted line represents the equilibrium curve for a feed gas composition of 0.5% CO and 1.5% H2 in He. The solid lines are model fits assuming first-order reversible kinetics. (Reprinted from [51]. With permission from Elsevier.)...

Studies of the pyrolysis of these three alkyls may conveniently be discussed in a combined section. The decompositions were carried out in a conventional toluene carrier flow system using contact times of 1-2 sec120,122,123. The conditions used satisfy both plug flow and thermal equilibrium requirements68,69. Toluene to alkyl ratios greater than 50 in the trimethyl gallium system and greater than 200 in the trimethyl indium and thallium studies were required to obtain first-order dependence in terms of the alkyl concentration. Under these conditions methane and ethane are produced by the reactions... 

When a recovery well is located within a contaminant plume and the pump is started, the initial concentration of contaminant removed is close to the maximum level during preliminary testing. As the pump continues to operate, cleaner water is drawn from the plume perimeter through the aquifer pores toward the recovery well. Some of the contaminant is released from the soil into the water in proportion to the equilibrium coefficient. For example, if the Kd is 1000, at equilibrium, 1 part is in the water and 1000 parts are retained in the soil. If the water-soil contact time is sufficient, complete equilibrium will be established. After the first pore volume flush (theoretically), the concentration in the water will be 0.9 and that on the soil will be 999. With each succeeding flush, the 1000 1 ratio will remain the same. If the time of water-soil contact is not sufficient to establish equilibrium, the recovered water will contain a lesser concentration. A typical decline curve is shown on Figure 9.2. Note the asymptotic shape of the curve where the decline rate is significantly reduced. 

The rate at which pollutants sorb to sediments has frequently been assumed to occur rapidly and consequently equilibration studies have often been conducted by mixing sample for 24 hours. Karickhoff (I, 66) has reported that sorption may require up to two months to reach an apparent equilibrium. Similarly, desorption has also been observed to require on the order of months to reach completion (67, 68). McCall and Agin (67) observed that the desorption rate of picloram was inversely related to the contact time. 

When the resin is incompletely ionised, its effective capacity will be less than the maximum. If equilibrium between resin and liquid is not achieved, a dynamic capacity may be quoted which will depend on the contact time. When equipment is designed to contain the resin, it is convenient to use unit volume of water-swollen resin as the basis for expressing the capacity. For fixed-bed equipment, the capacity at breakpoint is sometimes quoted. This is the capacity per unit mass of bed, averaged over the whole bed, including the ion exchange zone, when the breakpoint is reached. 

Various adsorption parameters for the effective removal of Pb + and ions by using new synthesized resin as an adsorbent from aqueous solutions were studied and optimized. Time-dependent behavior of Pb + and ions adsorption was measured by varying the equilibrium time between in the range of 30-300 min. The percentage adsorption of Pb + plotted in Fig. 26.2 as a function of contact time... 

Time-depended behavior of Cu + ion adsorption was measured by varying the equilibrium time between in the range of 0.5-72 h. The percentage adsorption of Cu + ions plotted in Fig. 28.2 as a function of contact time. The percentage adsorption of Cu + indicates that the equilibrium between the Cu + ions and sumac leaves was attained 4 h. Therefore, 4 h stirring time was found to be appropriate for maximum adsorption and was used in all subsequent measurement. The effect of temperature and pH the adsorption equilibrium of Cu + on sumac leaves was investigated by varying the solution temperature from 283 to 303 and pH from 6 to 10. The results are presented in Fig. 28.3. The results indicated that the best adsorption results were obtained at pH 8 at 293 K. 

Ion exchange involves the formation and breakage of bonds between ions in solution and exchange sites in a zeolitic adsorbent. The reaction equilibrium of the ion exchange process depends most significantly on contact time, operating temperature and ionic concentration. 

The time required for a system to reach equilibrium can be determined by shake-out tests, as described in earlier sections. Contact times are varied between about 0.5 and 15 min, at suitable intervals, and the extraction coefficient for each contact time plotted as a function of time. With this method, there is a lower practical limit on the contact time of about 0.25 min. These data will not be directly applicable to a continuous process because the rate of metal extraction is a function, in part, of the type and degree of agitation. However, a good idea of whether the extraction rate is sufficiently fast for the system to be suitable for use in a large contactor can be obtained. For example, if equilibrium is attained in less than 1 min, almost any type of contactor may be used. 

In addition to the presence of these elements in ores, they are also available from recycled feeds, such as catalyst wastes, and as an intermediate bulk palladium platinum product from some refineries. The processes that have been devised to separate these elements rely on two general routes selective extraction with different reagents or coextraction of the elements followed by selective stripping. To understand these alternatives, it is necessary to consider the basic solution chemistry of these elements. The two common oxidation states and stereochemistries are square planar palladium(II) and octahedral platinum(IV). Of these, palladium(II) has the faster substitution kinetics, with platinum(IV) virtually inert. However even for palladium, substitution is much slower than for the base metals so long as contact times are required to achieve extraction equilibrium. 

The reaction to form the palladium complex is similar to that reported for amine salts, although here, because a bidentate chelating ligand is used, no chlorine atoms are retained in the complex, and the system is easy to strip. Also, as both reactions involve initial ion pair extraction, fast kinetics are observed with 3-5 min contact time to reach equilibrium at ambient temperature. The extraction conditions can be easily adjusted in terms of acidity to suit any relative metal concentrations and, because the reagent is used in the protonated form, good selectivity over base metals, such as iron and copper,... 

Note that Eq. 10.5 is written to allow the velocity to vary as a function of location typical application of the advection-dispersion equation assumes the velocity and the hydrodynamic coefficients to be constant. Moreover, the time dependence of these parameters arises when flow (infiltration) is unsteady or transient in these cases, the contact time between contaminants and the solid matrix (and any immobile water within it) is too short to allow an equilibrium to be reached. 

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