Equation (5.17) was used to model the removal of DOC by MIEX resin in a CMFR with resin recycle and partial resin regeneration. Inputs to the model included: numerical conditions (e.g., number of cubic elements), CMFR operating conditions (see Table 5.1), resin properties (see Table 5.3), and DOC properties (see Table 5.5 and Figure 5.4). As mentioned previously, the key process parameters used to control the performance of the CMFR were the hydraulic residence time, resin regeneration ratio, and volume fraction of MIEX resin. Since the model was developed in non-steady-state form, it can handle transients, such as changes in the influent solute concentration and changes to the regeneration ratio, although these aspects were not explored in this work. The model was used to predict the time-varying, effluent concentration of total DOC (i.e., C'/C0').
The validity of the model was evaluated by comparing model predictions to experimental data for the nine test conditions shown in Table 5.1. All simulations were run for six solids residence times, and the RTD was approximated using 80 particle age-classes. Figure 5.6 illustrates modeling results corresponding to Run 5 in Table 5.1 (the theoretical solids residence time was 100 min). Figure 5.6a shows the time-varying, relative effluent DOC concentration and its approach to steady-state. The shape of the concentration profile over the first few hundred minutes is a result of resin conditioning. At time equal to zero, all of the resin was fresh resin. As time progresses, a majority of the resin (i.e., 90%) remained in the system sorbing DOC, while the remaining fraction of resin (i.e., 10%) was removed and an equivalent amount of fresh resin was added. Therefore, DOC removal was greatest at start-up and then decreased to its steady-state value, which was achieved after approximately
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300 minutes (i.e., three solids residence times). The average, steady-state, relative effluent concentration of total DOC was 0.39 ± 0.002. The small perturbations in the effluent concentration profile were due to the Monte Carlo approximation of the age distribution. Figure 5.6b shows the steady-state age distribution of resin particles in the contactor at the end of the simulation (histogram) and the fit of Equation (5.14) to the resin age data (solid line). It is clear that the age distribution of resin particles exhibits the expected exponential behavior of a CMFR, e.g., the best-fit solids residence time using Equation (5.14) of 102 min is in excellent agreement with the theoretical solids residence time of 100 min.
Figure 5.7 illustrates the relatively good agreement between the model predictions and the observed pilot plant results. Due to the nature of the Monte Carlo simulation, the predicted, steady-state, effluent DOC concentration was calculated as the average concentration from three solids residence times to the end of the simulation. The corresponding coefficient of variation for the effluent DOC concentration was less than 0.6% for all simulations. The observed DOC concentrations were the average reported values, with error bars representing one standard deviation. As expected for extended pilot plant trials, the DOC concentration of the raw water varied over the course of the study, adding to experimental variability. In most cases, the model tends to show slightly better removal of DOC than was observed (although model predictions were usually within one standard deviation). Possible explanations include incomplete regeneration of the resin and competition by inorganic anions. The model correctly captures the impact of changes in the regeneration ratio and the volume fraction of MIEX resin in the contactor on DOC removal, as demonstrated in previous work by the authors (Boyer and Singer, 2006). For example, Figure 5.7 shows that the effluent DOC concentration increases (i.e., removal decreases) as
the regeneration ratio decreases (Runs 7–9). No data were available to compare the model predictions to the pilot plant performance during start-up conditions.
FIGURE 5.6 Illustrative model simulation for NBA water: (a) time-varying, total concentration of DOC and (b) age distribution of resin particles in the contactor.
107 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 9 Operating conditions DO C ( m g /L ), C' /C0 '
Pilot plant data Model predictions
FIGURE 5.7 North Bay Aqueduct: comparison of steady-state model predictions and observed pilot plant data for various operating conditions (see Table 5.1).
5.5.2.2 Durham
In the previous section for North Bay Aqueduct water, it was shown that by using equilibrium and kinetic parameters estimated from batch laboratory experiments, Equation (5.17) could be used to predict the effluent DOC concentration from the CMFR. In the absence of batch kinetic data for Durham water, Dp,e was estimated by fitting Equation (5.17)
to data from one of the continuous-flow pilot plant runs. As discussed previously, Dp,e was
fitted to the removable fraction of DOC. Table 5.2 lists the test conditions used to fit Dp,e (see
row marked with an asterisk). The model was run for six solids residence times, and the RTD was approximated using 80 particle age-classes. The results of this fitting exercise are illustrated in Figure 5.8. The figure shows good agreement between model predictions and experimental data, excluding the first data point at a solids residence time of 0.4. The less satisfactory agreement between the model and the first grab sample was most likely attributable to the resin being partially loaded with DOC at start-up (a result of maintaining a
constant resin inventory and switching between operating conditions for the different pilot plant runs). The best-fit Dp,e and Dl values are shown in Table 5.5. As discussed earlier, the
free-liquid diffusivity for DOC in Durham water is in good agreement with reported values for aquatic NOM.
Using the best-fit Dp,e value, Equation (5.17) was used to predict the relative effluent
concentration of total DOC at four distinct operating conditions (see Table 5.2). Simulations were run for six solids residence times, and the RTD was approximated using 80 particle age- classes. Figure 5.9 shows a comparison between the model predictions and observed data. The predicted steady-state effluent DOC concentration was calculated as the average concentration from three solids residence times to the end of the simulation. The observed DOC concentrations for the pilot plant runs were the average reported values, with the error bars representing one standard deviation. The Durham pilot plant study exhibited less variability in effluent DOC measurements, and achieved greater removal of DOC than the North Bay Aqueduct study, consistent with the higher KD value and lower fN value for
Durham water. As was shown for North Bay Aqueduct water in the previous section, Figure 5.9 shows reasonably good agreement between model predictions and observed data for Durham water. A paired student’s t-test was conducted to determine whether the model predictions, for both North Bay Aqueduct and Durham waters, were statistically different from the observed pilot plant data. The null hypothesis was that there was no difference between the observed data and model predictions. A P-value of 0.2867 and a 95% confidence interval of (-0.0209, 0.0647) were calculated using the hypothesis testing function in MATLAB; thus, the null hypothesis that there was no difference between pilot plant data and model predictions cannot be rejected. The preceding statistical analysis affirms the accuracy
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of the two-scale model for predicting the effluent DOC concentration for a range of process operating conditions in two distinct raw waters.
FIGURE 5.8 Continuous-flow model fit to Durham pilot plant data.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 Operating conditions DO C ( m g /L ), C' /C0 '
Pilot plant data Model predictions
FIGURE 5.9 Durham: model predictions versus observed pilot plant data for various operating conditions (see Table 5.2).
5.6 CONCLUSIONS
The objectives of this research were to formulate and apply a mathematical model to describe DOC removal by ion exchange in a CMFR with resin recycle and partial resin regeneration. The composite two-scale model consisted of a microscale model that described DOC transport via intraparticle pore diffusion and a macroscale model that described the continuous-flow, recycle reactor. Equilibrium and kinetic parameters were estimated from batch laboratory experiments conducted using MIEX resin and three raw drinking waters. A Monte Carlo approach was used to model multiple particle size- and particle age-classes of MIEX resin in the CMFR. Linear isotherms were fit to the equilibrium data, and the kinetics of DOC uptake were accurately described by intraparticle pore diffusion. The two-scale model was used to predict the time-varying effluent DOC concentration from the reactor and was validated by comparing model predictions with the results of two pilot-scale continuous- flow studies. The model was found to successfully predict the effluent DOC concentration for multiple process operating conditions and two distinct raw waters.
CHAPTER 6: REMOVAL OF DISSOLVED ORGANIC CARBON BY ANION