Subsaturation conditions

Scale control can be achieved through operation of the cooling system at subsaturated conditions or through the use of chemical additives. The most direct method of inhibiting formation of scale deposits is operation at subsaturation conditions, where scale-forming salts are soluble. For some salts, it is sufficient to operate at low cycles of concentration and/or control pH. However, in most cases, high blowdown rates and low pH are required so that solubihties are not exceeded at the heat transfer surface. In addition, it is necessary to maintain precise control of pH and concentration cycles. Minor variations in water chemistry or heat load can result in scaling (Fig. 12). 

Onken, B. M., and Adriano, D. C. (1997). Arsenic availability in soil with time under saturated and subsaturated conditions. Soil Sci. Soc. Am. J. 61, 746-752. 

There are two main reasons for the similarity in dehydrochlorination behavior among different PVC samples. First, vinyl chloride is most often polymerized in a rather narrow temperature interval, 40-75oC, because of the high tendency to chain transfer to monomer which determines the molecular weight (25). Second, the monomer concentration at the reaction site is constant during the major part of the polymerization because PVC is insoluble in vinyl chloride and the propagation mainly occurs in the polymeric phase (26). At 50°C, the gel contains 30 g vinyl chloride per 100 g PVC (27. 28) as long as a separate liquid monomer exists. In practice, the "pressure drop" occurs at about 70% conversion and thereafter the monomer concentration decreases in the gel. However, only a minor part of the batch is formed under subsaturation conditions. 

At the beginning of the consumption of the electron acceptor by the biodegradation of DOC the dissolved component A q can be expected in low concentration far away from equilibrium (subsaturation condition). By a continuous release of dissolved A(jq) during DOC biodegradation equilibrimn and supersaturation of the solid B g can... 

The polymerization of VCM is highly exothermic (i.e., 100 kj mol ). Thus, the efficient removal of the reaction heat is very critical for the operation of large-scale reactors [44]. When all of the free liquid monomer has been consumed, the pressure in the reactor starts to fall as a result of the monomer mass transfer from the vapor phase to the polymer phase due to subsaturation conditions. In industrial PVC production, the reaction is usually stopped when a certain pressure drop has been recorded. Because the polymer is effectively insoluble in its own monomer, once the polymer chains are first generated, they precipitate immediately to form a separate phase in the polymerizing mixture. Thus, from a kinetic point of view, the polymerization of VCM is considered to take place in three stages [45]. 

The same group [114] has also reported that M increases with increasing [M].q. From experimental results, the following dependence was obtained M oc [M]°4 . This relationship is ascribed to variation of the chain transfer to monomer (Cm). The chain transfer constant to monomer, Cm is constant at saturation pressures and decreases with decreasing pressure at subsaturation conditions. 

Emulsion polymerization of vinyl chloride was also carried out at subsaturation conditions by Butucea et al. [127] who followed the effect of monomer, emulsifier and initiator on the polymerization behavior. Some results from these investigations are summarized in Table 9. This table shows that the rate of polymerization increases with increasing concentration of all these reaction components. From these results the following semiempirical equation for the dependence of the rate on the initiator, monomer (in water) and emulsifier concentrations was suggested. 

Under subsaturation conditions, variation of monomer concentration also influences other parameters such as the volume fraction of polymer in particles, rate constants and saturation of reaction media. Kinetic studies are more complicated and call for knowledge of the relations between different parameters or constants and the monomer concentration. 

At subsaturation conditions, the rate is proportional to the 0.4th power of the initiator concentration which agrees well with the micellar predictions. This behavior indicates that the monomolecular termination is more suppressed while the bimolecular termination is more favoured. Thus, the reaction order 0.4 should result from a strong contribution of primary radical termination and/or desorption of radicals. 

The presence of radical byproducts such as Cl radicals and the formation of unsaturated and defect structures in PVC point to a complex polymerization mechanism. The partitioning of the volatible radicals (monomeric. Cl,..) between vapor, water and polymer particles may vary the radical concentration in particles and the aqueous phase. Exit of radicals from the particles and the aqueous phase to the vapor phase probably negatively influences the growth events in the system. The low concentration of monomer in the vapor phase favors more termination. The decrease of the chain transfer to monomer with decreasing reactor pressure (at subsaturation pressures) favors the hypothesis that the volatile radicals exit to the vapor phase. The chain transfer is constant at saturation pressure and decreases with increasing pressure at subsaturation conditions. 

For substances that do not partition into a phase (e.g., ionic species into air), the Z value is zero and a division by zero issue can arise when solving the mass balance equations. This can be circumvented by using aquivalence (essentially f/H) as the equilibrium criterion or activity (concentration in water/solubility in water or equivalently fugacity/vapor pressure). Indeed, when examining fugacities, it is desirable to calculate the activity to ensure that subsaturation conditions prevail, that is, all fugacities are less than the liquid or subcooled liquid vapor pressure. 

Figure 12.3 Where to utilize some extra binding energy AGR when [S] < KM1 The Gibbs free energy changes are for the reaction condition of subsaturating [S], so that v = (fccat/ATM)[E]0[S3. The activation energy is lowered by AGR on the stabilization of only ES1, or of ES and ES (in the latter case, as long as [S] remains below KM otherwise, there is a transition to Figure 12.2). Stabilization of ES only does not affect A Gy.

During high discharge, many areas of the Genesee basin are subsaturated with respect to calclte, while during summer baseflow periods calcite saturation or supersaturation is widespread. Under these conditions calcite could mediate phosphorus mineral formation. 

The minimum in degradation rate found for subsaturation PVC obtained around 55°C becomes less obvious if the monomer concentration at the reaction site is used as variable instead of the relative monomer pressure, P/PQ. The observed behavior is mainly due to the influence of the polymerization conditions on the formation of thermally labile chlorine, i.e. tertiary chlorine and internal allylic chlorine. Tertiary chlorine is associated with ethyl, butyl and long chain branches. The labile structures are formed after different inter-and intramolecular transfer reactions. Generally, the content increases with decreasing monomer concentration and increasing temperature in accordance with the proposed mechanisms. The content of internal double bonds instead decreases with increasing temperatures. 

The solubility chart divides the field of the solution into two regions the subsaturated region where the solution will dissolve more of the solute at fhe existing conditions, and file supersaturated region. 

An understanding of these principles allows one to enhance isotope effects by proper choice of conditions. Thus, in equilibrium perturbation studies of liver alcohol dehydrogenase with the nucleotides as perturbants, the use of subsaturating levels of alcohol and ketone permitted the commitments to be those of the nonsticky alcohol and ketone, rather than those of the nucleotides (104, 119). 

Direct measurements of ambient supersaturations in clouds have been extremely challenging. Not only does one try to measure a small deviation from saturation, but clouds are frequently patchy with supersaturated regions next to subsaturated ones corresponding to dry entrained masses. Previous measurements have indicated that ambient supersaturations are usually less than 1% and almost never exceed 2% (Warner 1968). A median value of 0.1% was reported in these measurements. Most of our knowledge of these supersaturations is based on theoretical calculations using measurements of atmospheric conditions and are rather similar to that presented here as an example. Ranges of supersaturations expected in various cloud types are given in Table 17.3. 

Sorvik et al. [81, 82] carried out the emulsion polymerization of VC at subsaturated pressures. They reported that the reaction order with respect to monomer concentration is ca. 1.0. The polymerization proceeds under monomer-starved conditions in which the rate of polymerization is proportional to the monomer concentration at the reaction loci. The rate of polymerization linearly decreases with decreasing pressure (without any maximum). The dependence of polymerization rate on the equilibrium monomer concentration, Rp oc [M]cq can be expressed as the dependence on the monomer concentration in water because this dependence is a function of the saturation degree X and, therefore, we can write Rp oc [M]e,w or Rp oc [8.8X], respectively. 

The molecular weights of PVC under monomer saturation conditions are nearly independent of conversion whereas under subsaturation pressures increases with conversion up to the total consumption of monomer. Under monomer saturated conditions the concentration of monomer at reaction loci is constant up to ca. 80% conversion. Here, the growth and termination events proceed under stable conditions (the constant monomer concentration and the chain transfer effect) at which the molecular weights are independent of conversion. As the polymerization proceeds at subsaturation pressures, the concentration of monomer decreases and the weight ratio monomer/polymer decreases and so does the growth of polymer chain. 

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