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Comparative evaluation of upscaled analytical and numerical models for DNAPL dissolution processes
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Abstract: Mathematical model-based accurate evaluation of the remediation process at organic pollution sites serves as an efficient approach to the management and remediation of contaminant source zones. Numerical and upscaled analytical solution models are effective mathematical methods for reproducing the Dense Nonaqueous Phase Liquid (DNAPL) remediation process. However, in the current design of pollutant removal schemes, effective mass transfer models for characterizing the elution behaviors of contaminants remain lacking. In this study, two mathematical methods integrated with improved mass transfer models were employed to simulate the multi-stage contaminant elution behaviors under two distinct scenarios: A mixed-source region subjected to continuous water flushing and a residual DNAPL source treated with shorter-duration pulse flushing of the ethanol solution. Both the improved numerical model and upscaled analytical solution model demonstrated enhanced accuracy, which was attributed to the incorporation of solubilization mechanisms into mass transfer processes and the adoption of a multi-source region division method. The Mean Absolute Errors (MAE) of the numerical simulation for the two scenarios were 20.68 mg/L and 6.93 mg/L, respectively, whereas those of the upscaled model were 33.29 mg/L and 8.60 mg/L, respectively. Comparing the two improved models, the numerical model exhibited higher accuracy, while the upscaled model was characterized by faster computation speed and fewer input parameters.
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Figure 1. Comparison of DNAPL distributions at different times (PV) in the mixed-source experiment
Figure 2. The initial DNAPL distribution before flushing.
Notes: a-mesh generation for Experiment A; b-mesh generation for Experiment B
Figure 3. The simulated elution concentration (C2) from the upscaled analytical solution model and numerical model, respectively
Notes: a-Experiment A; b-Experiment B
Figure 4. The remaining DNAPL volume (V) in the flow cell varying with the pore volume of injected flushing fluid (PV)
Notes: a-Experiment A; b-Experiment B
Figure 5. DNAPL Nigration Proportion (MP) and average contribution ratio of DNAPL to effluent concentrations in the marked zone (ACR)
Figure 6. Under different initial DNAPL distributions (GTP), the prediction of elution concentration (C2), from the upscaled analytical solution model and the numerical model (multi-source zone mixing model), varying with DNAPL depletion ratio (1−M/M0).
Figure 7. The relationship between the removal ratio of DNAPL in the contaminated region, i.e., (1−M/M0), and the initial proportion of DNAPL ganglia (GF0) when the elution curve enters the second stage
Figure 8. The relationship between the proportion of the flux from DNAPL ganglia (fg) and the initial DNAPL distribution (GTP)
Figure 9. Sensitivity Coefficients (SC) of key parameters for the numerical model predicting the effluent concentration under
Notes: (a) the mixed-source configuration and (b) the pulse flushing of ethanol solutions, for the upscaled analytical solution model predicting the effluent concentration under (c) the mixed-source configuration and (d) the pulse flushing of ethanol solutions
Figure 10. Contaminant fluxes (C2, a) and removal mass (VTCE, b) from the pool- and ganglia-dominated DNAPL source regions predicted by the upscaled analytical solution model and the numerical model in Experiment A
Figure 11. Contaminant fluxes (C2, a) and removal mass (VPCE, b) from the pool- and ganglia-dominated DNAPL source regions predicted by the upscaled analytical solution model and the numerical model in Experiment B
Table 1. List of key parameters used in numerical simulations.
Parameter Classification Value Mixed-source experiment (Experiment A) Pulse flushing experiment (Experiment B) Permeability/(cm/min) 70/100 (or 70/80) mesh 0.10a 0.13d 40/50 mesh 4.00a 12.21h/4.00b Residual saturation Low capillary number DNAPL phase (Sr2) 0.20a 0.12b Aqueous phase (Sr1) 0.10c 0.10c Microemulsion phase (Sr3) - 0.10c High capillary number DNAPL phase (Sr2) 0.00 0.00 Aqueous phase (Sr1) 0.00 0.00 Microemulsion phase (Sr3) - 0.00 Endpoint relative permeability Low capillary number DNAPL phase ($ k_{r2}^o $) 0.37c 0.37c Aqueous phase ($k_{r1}^o $) 1.00c 1.00c Microemulsion phase ($k_{r3}^o $) - 1.00c High capillary number j DNAPL phase ($k_{r2}^o $) 1.00 1.00 Aqueous phase ($k_{r1}^o $) 1.00 1.00 Microemulsion phase ($k_{r3}^o $) - 1.00 Relative permeability exponent Low capillary number DNAPL phase 5.00h 5.00/3.50h Aqueous phase 2.85e 2.85e Microemulsion phase - 2.85e High capillary number j DNAPL phase 1.00 1.00 Aqueous phase 1.00 1.00 Microemulsion phase - 1.00 Capillary pressure endpoint/kPa 2.90d 2.90d Capillary pressure exponent ‒0.50d ‒0.50d Density/(g/mL) DNAPL (TCE/PCE) 1.460f 1.622f Water 0.998f 0.998f Ethanol - 0.787f Interfacial tension of water-oil/(dyn/cm) 35.62g 45.00i Interfacial tension between ethanol solution and PCE phase/(dyn/cm) $ \sigma ={\sigma }_{0}{e}^{-4.1611{{C}_{31}}} $k viscosity of ethanol + water + PCE mixture/(Pa·s) $ {\mu }_{l}={C}_{1l}{\mu }_{1,0}{e}^{1.8132({{C}_{2l}}+{{C}_{3l}})}+{C}_{2l}{\mu }_{2,0}{e}^{0.9646({{C}_{1l}}+{{C}_{3l}})}+{C}_{3l}{\mu }_{3,0}{e}^{(1.5823{{C}_{1l}}-1.5125{{C}_{2l}})} $l Longitudinal dispersion/m 0.015g 0.015g Transverse dispersion/m 0.008g 0.008g a DiFilippo et al., (2010); b Schroth et al., (1996); c Grant, (2005); d Guo et al., (2018); e Liao et al., (2016); f NIST Chemistry WebBook; g Aydin-Sarikurt et al., (2016); h Correction parameters for medium permeability and relative permeability within PCE migration zone (i.e., the region marked by yellow curve in Fig. 2) in pulse flushing experiment; i Demiray et al., (2021); j Agaoglu et al., (2012); k Interfacial tension is a function of ethanol content. the experimental data come from Hayden et al., (1999) and Lunn and Kueper, (1997); l The viscosity of ethanol + water + PCE mixture is calculated in terms of the viscosity of the pure phases. The viscosity data of PCE-C2H5OH, H2O-C2H5OH, and H2O-C2H5OH-PCE systems come from Agarwal and Singh, (2004), Khattab et al., (2012), and Hayden et al., (1999), respectively. 
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Table 2. Calibrated parameters for different mass transfer models.
Experiment Mass transfer model Parameter α S0 K (1/d) τ β Mixed-Source experiment Multi-Source zones mixing model (Equations 2 and 4) 70,000 0.00 - 6.51 0.10 Single-Source zone model (Equation 2) 70,000 0.00 - - Imhoff model (Equation 9) - 1.50 1.00 K - 15.00 - Pulse flushing Single-Source zone model (Equation 2) 630,000 0.49 - - Imhoff model (Equation 9) - - - 2.00 1.19 K - 6.50 -
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Table 3. Root Mean Square Errors (RMSE) and Mean Absolute Errors (MAE) of effluent concentration predictions by different models
Numerical model Upscaled analytical solution model Experiment A Experiment B Experiment A Experiment B RMSE/(mg/L) 36.95 7.92 85.75 10.01 MAE/(mg/L) 20.68 6.93 33.29 8.60
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