## 3 Results
### Modeling Results  
All modeling results presented herein were completed using a single component, such as one of the four BTEX compounds, with the particle diameter serving as the independent parameter for each model run. The first results presented below are specifically for xylene, based on the equations and parameters presented in Section 2.2. The typical batch curves generated by the model for total mass \(M_{Sx}\) (grams) and dissolved concentration \(C_{Sx}\) (grams/m\({}^{3}\)) of xylene, for three dispersed phase particle sizes of 5000 \(\upmu\)m, 2000 \(\upmu\)m, and 200 \(\upmu\)m, are shown in Figures 10-12, respectively. In all cases, the model predicts a steady decline in the xylene mass \(M\), and a rise and later fall in the dissolved xylene concentration, with different character depicted for the concentration curve, depending on the particle size. Large NAPL phase particles result in a lower dissolved phase concentration (Figure 10) over time, due to the limited amount of surface area for  
A summary graph of the time required to attain 99% biodegradation versus particle size for xylene, over the range of particle sizes of 6000 \(\upmu\)m to 100 \(\upmu\)m, is depicted in Figure 13. The data in this graph were developed using model runs with the mass transport from dispersed particles to the dissolved phase occurring only by diffusion. Below a particle size of 500 \(\upmu\)m, the time period needed to reach 99% biodegradation levels is in the range of 500 to 1000 h. These biodegradation time periods are roughly consistent with the experimental biodegradation results presented in Figure 8 and Tables 1 and 2 above. The qualitative agreement in biodegradation times between the experimental and modeling results suggests that perhaps the portion of WTCO dispersed and biodegraded in these experiments is predominantly lighter hydrocarbons of similar biodegradability (half-life values) as the xylene employed in the modeling. Figure 11: Mass and concentration of xylene particles with \(\mathrm{D_{P}}=2000\)\(\upmu\)m.  
Figure 12: Mass and concentration of particles of xylene with \(\mathrm{D_{P}}=200\)\(\upmu\)m.  
The sensitivity of the results for the time period used to reach 99% biodegradation as a function of variation in the biodegradation constant for xylene is shown in Figure 14. The first and last values shown in the figure represent the high end (168 h) and low end (672 h) of the range of biodegradation half-life values for xylene [16]. Over this range of biodegradation rate constants, the time to 99% biodegradation varies from 1200 h to 300 h.  
Additional model runs for xylene were completed using advective transport (Equations (13)-(16)) as compared to diffusive transport (Equation (12)) only. The results presented in Figure 15 depict the time to 99% biodegradation as a function of advection velocity over the range from 0 to 5 m/s, for the two different particle sizes of 150 and 500 m. The results indicate that the positive effect of advection mass transport is greater at the larger particle size of 500 m (biodegradation time decreases from 940 h to 490 h), and much less for the smaller particle size of 150 m (biodegradation time decreases only from 840 h to 740 h). Figure 14: \(K_{r}\) vs. Time for xylene to reach 99% biodegradation (D\({}_{\text{P}}\) = 500 m). Figure 13: Particle size vs. time for xylene to reach 99% biodegradation. Finally, the variation in time to attain 99% biodegradation as a function of the range of reported biodegradation rate constants for all four BTEX compounds is presented in Figure 16 (xylene data only presented previously in Figure 14). The graph suggests that the biodegradation times are quite insensitive to the range of biodegradation rate constants for benzene and toluene, while the trend for ethylbenzene is quite similar to that for xylene. The difference between the BT versus EX compounds is expected to be related to their aqueous solubility values.