Effect of Dimensionless Groupings on Process Performance

Sensitivity analyses were conducted to determine the relative effect of the dimensionless groupings on process performance, where process performance was assessed by evaluating the steady-state DOC concentration. Each dimensionless group was varied over the range shown in Table 6.2, while the remaining dimensionless groups were set equal to their default value. A total of 384 simulations were conducted.

The effect of the inverse of the resin regeneration ratio, θ, on process performance is illustrated in Figure 6.3. The resin regeneration ratio (fR), by definition, is bound between 0

and 1, meaning that θ varies between 1 and infinity. For example, at fR = 0 (θ = infinity),

there is no resin regeneration and the resin is continuously recycled. Eventually, the resin capacity is exhausted and the effluent solute concentration is equal to the influent solute concentration (i.e., C/C0 approaches unity as θ approaches infinity). At fR = 1 (θ = 1), there is

will be at a minimum. Figure 6.3 shows that the dimensionless, steady-state effluent solute concentration increases exponentially as θ increases, i.e., DOC removal decreases as the resin regeneration ratio decreases, which is expected based on the above discussion. For the standard slurry reactor, fR typically varies from 0.01 to 0.2 (i.e., θ = 5–100), which

corresponds to 38–92% DOC removal at the default simulation conditions for γ, 2 R

σ , and λ. Hence, the resin regeneration ratio, as expected, has a substantial impact on DOC removal. The effects of γ, 2

R

σ , and λ on process performance are also illustrated in Figure 6.3. For example, at θ = 50, a two-fold increase in γ decreases C/C0 by a factor of 0.65, whereas a

two-fold increase in λ increases C/C0 by a factor of 1.3. The response of C/C0 to the

macroscale and microscale mass transfer moduli suggests that their impact on process performance is similar in magnitude but opposite in direction. Assuming an anion exchange resin of uniform size results in a slight increase in the dimensionless solute concentration compared to an anion exchange resin of variable size (i.e., 2

R

σ = 0.5).

The impact of the macroscale mass transfer modulus, γ, on process performance is illustrated in Figure 6.4, in a similar manner as Figure 6.3. The solute concentration is shown to decrease exponentially as γ increases. The macroscale mass transfer modulus increases under the following conditions: increasing concentration of anion exchange resin, increasing solids residence time, decreasing resin radius, and increasing rate of diffusive mass transfer. However, because θ and λ have been kept constant at the default simulation conditions shown in Figure 6.4, the solids residence time, resin radius, and pore diffusion coefficient cannot be adjusted to increase γ without impacting other model parameters. Therefore, in the mathematical model and in practice, γ is increased by increasing the anion exchange resin concentration in the reactor. For anion exchange treatment in a standard slurry reactor, XR

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varies from 10 to 40 mL/L (i.e., γ = 4.5–18), which corresponds to 38–71% DOC removal at the default simulation conditions. Figure 6.4 also shows that at constant γ, increasing θ or λ by a factor of 2 results in a similar increase in the solute concentration, and assuming an anion exchange resin of uniform size results in a slight increase in the solute concentration. This is expected based on the results presented in Figure 6.3.

The effect of the variability of the resin size distribution, 2 R

σ , on process performance is illustrated in Figure 6.5. The expected value (i.e., arithmetic mean) of the resin radius was kept constant for all simulations. Figure 6.5 shows that the solute concentration decreases as the variance of the lognormal resin size distribution increases, i.e., for a constant REV,

neglecting the variance in resin size results in a lower predicted DOC removal than the actual DOC removal achieved. Figure 6.5 also shows that at constant 2

R

σ , increasing θ or λ by a factor of 2 results in a similar increase in the solute concentration, whereas increasing γ by a factor of 2 results in a decrease of similar magnitude in the solute concentration.

The impact of the microscale mass transfer modulus, λ, on process performance is illustrated in Figure 6.6, and shows that the solute concentration increases (DOC removal decreases) exponentially as λ increases. The microscale mass transfer modulus increases as the solids residence time increases, the resin radius decreases, the rate of diffusive mass transfer increases, and the retardation factor decreases. Similar to the macroscale mass transfer modulus, the microscale mass transfer modulus cannot be changed by adjusting τS,

REV, or Dp,e without causing a change in the other model parameters. Instead, in both the

model and in practice, the microscale mass transfer modulus is predominantly influenced by the retardation factor, which in turn is a function of the linear distribution coefficient, KD. For DOC removal from the three raw drinking waters analyzed by Boyer et al. (2008), KD was

found to vary from 11.9 to 66.3 L/g (i.e., λ = 0.010–0.057), which corresponds to 40–69% DOC removal at the default simulation conditions. Figure 6.6 also shows that increasing θ and γ by a factor of 2 had opposing effects of similar magnitude on process performance. There was little difference in the solute concentration for changes in 2

R

σ from 0 and 0.5. The relative effect of the dimensionless groupings on the time-varying solute concentration was also evaluated (results not shown), and it was determined that the transient results follow the same trends as the steady-state results. In summary, the resin regeneration ratio, resin concentration, and linear distribution coefficient were shown to have a substantial impact on the removal of DOC by anion exchange treatment in a CMFR with resin recycle and partial resin regeneration.

FIGURE 6.3 Influence of the inverse of the resin regeneration ratio on steady-state process performance.

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FIGURE 6.4 Influence of the macroscale mass transfer modulus on steady-state process performance.

FIGURE 6.6 Influence of the microscale mass transfer modulus on steady-state process performance.