This application was originally presented in the User's Manual for the original HBGC code (Yeh et al., 1998). The following problem description was taken directly from that document.
The input file names for this problem (three versions) are "tcbio_1d.in", "tcbio_2d.in", and "tcbio_3d.in". The corresponding superfiles are "hbgc123d.tc1", "hbgc123d.tc2", and "hbgc123d.tc3".
This example is a benchmark problem for the simulation of reactive transport developed by Valocchi and Tebes (1997). It includes kinetic adsorption/desorption, equilibrium aqueous complexation and biodegradation as well as advective-dispersive transport. The problem description is directly from the formulation of Valocchi and Tebes, except as noted.
This problem involves one-dimensional transport of multiple reacting species through a 100 dm long column over a period of 75 hours. The physical parameters describing the system are porosity = 0.4, bulk density = 1.5 kg/dm3, pore water velocity = 10 dm/h, and longitudinal dispersivity = 0.5 dm. Activity corrections were not used. To demonstrate the different input formats for one-dimensional, two-dimensional, and three-dimensional cases, there are three sample files for this problem. All cases use a discretization of 100 elements. The one-dimensional case has 101 nodes, the two-dimensional 202, and the three- dimensional 404. As the velocity is uniform in x-direction, all nodes with the same x-coordinate have the same concentration (minor differences due to numerical effects are possible). A uniform time step size of 0.1 hours was used for all simulations. Aqueous speciation is simulated using 14 equilibrium chemical reactions (Table 1). Two of the aqueous species, Co2+ and CoNTA-, may be removed from solution by adsorption to the media in the column. In addition, there is one kinetic biodegradation reaction affecting the chemical distribution within the column. Initially, the column is free from the biodegradation substrate, HNTA2-, and the adsorbing species. Then for a period of 20 hours a pulse containing Co2+ and NTA- is injected into the column. For the remaining 55 hours, the injection fluid has the same chemical composition as the fluid initially present in the column. Table 2 summarizes the concentrations initially present in the column and in the injected pulse. The adsorption reactions are kinetic and the pH levels in both the pulse and the background solutions are allowed to vary.
Table 1. Tableau for equilibrium reactions.
| H+ | NTA3- | Co2+ | H2CO3* | NH4+ | O2 | Buffer | log Keq | |
| H3NTA | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 14.9 |
| H2NTA- | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 13.3 |
| HNTA2- | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 10.3 |
| CoNTA- | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 11.7 |
| Co(NTA)24- | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 14.5 |
| CoOHNTA2- | -1 | 1 | 1 | 0 | 0 | 0 | 0 | 0.5 |
| CoOH+ | -1 | 0 | 1 | 0 | 0 | 0 | 0 | -9.7 |
| Co(OH)2 | -2 | 0 | 1 | 0 | 0 | 0 | 0 | -22.9 |
| Co(OH)3- | -3 | 0 | 1 | 0 | 0 | 0 | 0 | -31.5 |
| HCO3- | -1 | 0 | 0 | 1 | 0 | 0 | 0 | -6.35 |
| CO32- | -2 | 0 | 0 | 1 | 0 | 0 | 0 | -16.68 |
| OH- | -1 | 0 | 0 | 0 | 0 | 0 | 0 | -14.0 |
| NH3 | -1 | 0 | 0 | 0 | 1 | 0 | 0 | -9.3 |
| HBuffer | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 6.0 |
Table 2. Concentration of component species in the column and in the incoming pulse.
| Component | Type | Background Concentration | Pulse Concentration |
| H+ | Aqueous | pH = 6 | pH = 6 |
| NTA3- | Aqueous | 0.0 | 5.23E-6 mol/L |
| Co2+ | Aqueous | 0.0 | 5.23E-6 mol/L |
| H2CO3* | Aqueous | 4.9E-7 mol/L | 4.9E-7 mol/L |
| NH4+ | Aqueous | 0.0 | 0.0 |
| O2 | Aqueous | 3.125E-5 mol/L | 3.125E-5 mol/L |
| Buffer | Aqueous | 0.0 | 0.0 |
| Biomass | Adsorbed | 5.44E-5 g/dm3 media | N/A |
| CoNTA(ads) | Adsorbed | 0.0 | N/A |
| Co(ads) | Adsorbed | 0.0 | N/A |
Transport of the free cobalt species, Co2+, and CoNTA- through the column is retarded due to adsorption. The availability of adsorbent sites is considered non-limiting and the adsorption process is assumed to be kinetic. Valocchi and Tebes use a linear kinetic model to represent the adsorption process; the reactions and reaction rates have been reformulated to express adsorption in terms of forward and backward rate constants for use in HYDROBIOGEOCHEM123D. The parameters describing adsorption were selected by Valocchi and Tebes to make adsorption a significant kinetic process in the system; they do not necessarily represent realistic adsorption behavior for Co2+ or CoNTA-. The two adsorption reactions simulated are:
(1) CoNTA-(aq) <-> CoNTA(ads) with kf1, kb1
(2) Co2+(aq) <-> Co(ads) with kf2, kb2
where kf1 = 0.26667 /h, kb1 = 0.5003127 /h, and kf2 = 0.26667 /h, kb2 = 0.05259697 /h. Biodegradation of HNTA- removes NTA from the system through the following reaction:
HNTA2- + 1.620 O2 + 1.272 H2O + 2.424 H+ -> 17.307 C5H7O2N + 3.120 H2CO3* + 0.424 NH4+
where KS = 7.64E-7 mol/L, KO = 6.25E-6 mol/L, µmax = 0.0916519 /h, b0 = 5.44E-5 g/dm3 of media, and Kd = 0.00208 /h.
The HYDROBIOGEOCHEM123D results compare well with those supplied by Valocchi and Tebes.
References
Valocchi, A.J. and C. Tebes (1997): Benchmark Problems: A Workshop on Subsurface Reactive Transport Modeling, October 29 - November 1, 1997. Pacific Northwest Laboratory, Richland, WA.
Yeh, G.-T., Salvage, K. M., Gwo, J. P., Zachara, J. M., and Szecsody, J. E. (1998): HydroBioGeoChem: A Coupled Model of Hydrologic Transport and Mixed Biogeochemical Kinetic/Equilibrium Reactions in Saturated-Unsaturated Media. Report ORNL/TM-13668. Oak Ridge National Laboratory, Oak Ridge, TN.