The capability of the first-order, dual-porosity model, which explicitly accounts for non-ideal transport caused by the presence of ‘immobile’ water, to predict the non-ideal transport of non-sorbing solute in a constructed aggregated soil has been investigated. Miscible-displacement experiments performed with a well-characterized aggregated soil and a non-reactive tracer (pentafluorobenzoate) served as the source of the data. Values for the input parameters associated with physical non-equilibrium were determined independently and compared with values obtained by curve fitting of the experimental measurements. The calculated and optimized values compared well, suggesting that the non-equilibrium parameters represent actual physical phenomen

Augustijn, D.

Brusseau, M.L.

Gersti, Z.

Rao, P.S.C.

English

Augustijn, Dionysius C.M.

University of Twente Research Information

Journal of Hydrology ELSEVIER [3] Journal of Hydrology 163 (1994) 187-193 Technical Note  Simulating solute transport in an aggregated soil with the dual-porosity model: measured and optimized parameter values M.L. Brusseau a'*, Z. Gerstl u, D. Augustijn c, P.S.C. R a o  c a429 Shantz Bldg., 38 Soil and Water Science Department, University of Arizona, Tucson, AZ  85721, USA blnstitute of Soil and Water, 50250, Bet Dagan, Israel CSoil and Water Science Department, University of Florida Gainesville, FL 32611, USA Received 6 December 1993; revision accepted 19 March 1994 Abstract The capability of the first-order, dual-porosity model, which explicitly accounts for non-ideal transport caused by the presence of 'immobile' water, to predict the non-ideal transport of non- sorbing solute in a constructed aggregated soil has been investigated. Miscible-displacement experiments performed with a well-characterized aggregated soil and a non-reactive tracer (pentafluorobenzoate) served as the source of the data. Values for the input parameters associated with physical non-equilibrium were determined independently and compared with values obtained by curve fitting of the experimental measurements. The calculated and optimized values compared well, suggesting that the non-equilibrium parameters represent actual physical phenomena. 1. Introduction The impact of  structured soils on the transport of  dissolved chemicals has been studied by many researchers (see Brusseau and Rao, 1989, 1990, for recent reviews). These investigations have shown that the presence of  macroscopic-scale low- permeability domains (e.g. aggregates, macropores) can cause non-ideal transport of  solutes, as exemplified by asymmetrical breakthrough curves and 'preferential' transport. Several mathematical models have been developed to simulate solute transport in structured systems, the most widely used being the first-order, dual- porosity model developed by Deans (1963) and Coats and Smith (1964), and extended to sorbing solute by Van Genuchten and Wierenga (1976). * Corresponding author. 0022-1694/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0022-1694(94)02502-3 188 M.L. Brusseau et al. / Journal of Hydrology 163 (1994) 187-193 The approach typically taken in using any mathematical model is to fit the model to a data set, whereby the values for one or more parameters are optimized. Given the uncertainties associated with solving the inverse problem, especially for multiple- parameter optimizations, there is concern that such optimized parameters may not represent actual physical phenomena. To address these concerns, a preferred method of evaluating a model's performance is to compare simulations produced with independently measured parameters to measured data. Despite its widespread use, the performance of the first-order, dual-porosity model has rarely been tested by use of the preferred method. One such test was reported by Rao et al. (1980), who used measured data to predict transport of non-sorbing solutes in columns packed with synthetic porous ceramic spheres. Such an evaluation has apparently not been done for solute transport in aggregated soil. The purpose of the present work was to evaluate the ability of the first-order, dual-porosity model to simulate solute transport in a well-characterized aggregated soil. Specifically, the optimized parameter values obtained by fitting the dual-porosity model to the breakthrough curves are compared with values measured independently. 2. Materials and methods 2.1. Materials  Spherical aggregates were prepared by placing a loam soil (Yolo loam), amended with a 0.5% polyacrylicamide solution, in plaster-of-paris moulds (see Rao et al., 1980). The moulded, moist aggregates were dried overnight at 50°C. This procedure produced well-characterized, stable soil aggregates having a large intraparticle porosity. These aggregates were packed into a column and dispersed in 125 #m glass beads. The use of  the glass beads results in an interaggregate domain similar to that of  a non-aggregated sandy medium. The properties of  the aggregates and of the packed column are presented in Table 1. Pentafluorobenzoate (PFBA) was used as the non-sorbing tracer. 2.2. Miscible-displacement method The approach and apparatus used in the miscible displacement experiments were Table 1 Properties of aggregates and packed column Aggregate diameter 1.1 cm Total water content (0) 0.42 lnteraggregate water content (am) 0.21 Intra-aggregate water content (0ira) 0.21 Bulk density (p) 1.66 g cm -3 Column length 10 cm Column diameter 2.5 crn Peclet number (P) 40 M.L. Brusseau et al. / Journal of Hydrology 163 (1994) 187-193 189 identical to those described by Brusseau et al. (1990). Briefly, two single-piston HPLC pumps (Gilson Medical Electronics, Model 302) were connected to the glass column (packed with the soil) by a Rheodyne switching valve (Model 7060) placed in-line to facilitate switching between solutions which did or did not contain the solute of interest. After completion of packing, electrolyte solution (0.01 M CaCI2) was pumped through the column to ensure complete water saturation and to condition the porous medium to the electrolyte. Solutions containing 100 mg 1-1 of PFBA were then pumped into the column at three flow rates, equivalent to pore-water velocities of 1.4, 14.5, and 87.3 cm h -1. A flow-through, variable-wavelength UV detector (Gilson Holochrome) was used to monitor continuously the concentration of PFBA in the column effluent, with output recorded on a strip chart recorder (Fisher, Recordall Series 5000). 2.3. Mathematical model The results of the miscible displacement experiments were analysed with the dual- porosity model of Van Genuchten and Wierenga (1976): 3ROC~ IOT + (1 - 3)ROC~IOT = (1/P)OZC~ /OX 2 - OC~ IOX (1) (1 - 3)ROC~/OT = w(C~ - C~) (2) where C~ = Cm/ Co (3a) P = qL/DOm (3b) C~ = Cim/C 0 (3c)  R = 1 + (p/O)Kp (3d) T = v t /L  (3e) fl  : (0  m + f p K p ) / ( O  + pKp) (3f) X = x / L  (3g) a) = aZ/vmO m (3h) where C m and Cim are the aqueous-phase concentrations for the mobile and immobile domains, respectively [M L-3], Co is the input concentration, v is the average pore- water velocity [L T -l] (with Vm = q/Om, the velocity in the mobile domain), q is Darcy flux [L T-l], t is time, x is distance, L is column length, D is the local-scale dispersion coefficient for the mobile domain [L 2 T-l],  p is soil bulk density [M L-3], /9 is fractional volumetric water content (with subscripts m and im representing mobile and immobile domains, respectively), f is the fraction of sorbent associated with the mobile domain, Kp is the equilibrium sorption constant [L 3 M-l], and a is the 190 M.L. Brusseau et aL / Journal of Hydrology 163 (1994) 187-193 first-order mass transfer coefficient [T-l]. A non-linear, least-squares optimization program (Van Genuchten, 1981) was used under flux-type boundary conditions to determine values for the unknowns: P, R,/3, and to. 2.4. Predic t ing/3  and  w parameters  When R tends to 1, as was the case herein, the fraction of instantaneous retarda- tion,/3, is equivalent to 0m/0. Thus, values for/3 can be calculated from measured values of 0m and 0. The values for 0 m and 0 reported in Table 1 were measured by a gravimetrical mass balance of the column (i.e. individual measurements for amount of water associated with each domain). The Damkohler Number, to, contains the first-order mass transfer coefficient (a) and represents the mass transfer of solute between the intra-aggregate and interag- gregate domains. The coefficient associated with the first-order model can be related to a diffusion coefficient, based on a Ficks' Law approach, by employing an equation of the following form (cf. Parker and Valocchi, 1986; Brusseau et al., 1989) = aDoOim/'rl 2 (4) where a is a shape factor, D O is the aqueous diffusion coefficient [L 2 T-l],  r is the tortuosity factor, and I is, for the present case, the radius of the aggregates. With measured values for 0ira and l (see Table 1), and known values for Do (0.026 cm h -1) and the shape factor (15 for the present case-spherical geometry), values for a can be calculated by using a value of 2 for r, which is based on data reported in the literature (cf. Brusseau, 1993). 3. Results and discussion Breakthrough curves for pentafluorobenzoate, obtained for three pore-water velo- cities (1.4, 14.5, and 87.3 cm h-l), are presented in Fig. I(A). These data exhibit behaviour typical of transport in structured soil systems, wherein the breakthrough curve is shifted leftward and the amount of tailing increases with increasing velocity. For all cases, the optimized simulations produced with the first-order, dual-porosity model provide very good fits to the data. The simulations produced with the inde- pendently determined values for/3 and to reported in Table I provide good predictions of the experimental data (see Fig. 1 (B)). The optimized values for/3 and w are reported in Table 2. The calculated values for these two parameters are also listed in Table 2. The 95% confidence intervals for two of the three optimized/3 values capture the calculated/3 value (0.5). This suggests that the optimized/3 term does, in fact, represent a real physical entity, i.e. the internal porosity of the aggregates. The/3 value obtained for the experiment performed at the fastest velocity is smaller than the measured value. Possibly, at relatively large velocities, the effective 'immobile' domain includes some interaggregate regions in addition to the intra-aggregate domain. A similar velocity dependence of/3 was reported by Nkedi-Kizza et al. (1983). M.L. Brusseau et al. / Journal of  Hydrology 163 (1994) 187-193 191 1 0 . 8  0 . 6  ~111 . v . 1 . 4  I H t  • v . , ~  o4 F I i /  • v . . 7 ~  , on ~ 0.2 ~ o 2 4 0 ¢~ 0 6 8 0 1 [ ~ ~  -- - -  f ~.1 0 ,8  0 ,6  ~ 1 /  . v . 1 4  / F ' /  • V "  14.5 7 ~ Predicted Simulation 0 ~ 0 2 4 6 8 0 PORE VOLUMES Fig. 1. Breakthrough curves for transport of pentafluorobenzoate in a column packed with 1.1 cm diameter aggregates: (A) experimental data and optimized simulations produced with the first-order, dual-porosity model; (B) experimental data and predicted simulations produced with the first-order, dual-porosity model. Pore-water velocities are in centimetres per hour. 192 M.L. Brusseau et al. / Journal of  Hydrology 163 (1994) 187-193 Table 2 Calculated and optimized non-equilibrium parameter values Experiment fl w Calculated Optimized Calculated Optimized PFBA, v = 1.4 0.5 0.50 (0.49-0.52) 2.2 1.11 (1.04-1.18) PFBA, v = 14.5 0.5 0.56 (0.49-0.64) 0.2 0.24 (0.18-0.31) PFBA, v = 87.3 0.5 0.40 (0.39-0.41) 0.04 0.02 (0.01-0.03) 95% confidence intervals are in parentheses; pore-water velocities (v) are in centimetres per hour; PFBA = pentafluorobenzoate. The optimized and calculated ~ values differ by a factor of  2 or less. There is some uncertainty associated with the calculated values because of  the use of  an literature- based value for r ,  the intra-aggregate tortuosity. However, the predicted w values remain reasonably close to the optimized values for the range of tortuosity values typically reported in the literature (1.5-3). 4. Conclusion The analyses presented above provide evidence that non-ideal t ransport  caused by diffusive mass transfer between intra- and interaggregate pore-water domains is present in an aggregated-soil system. They also show that the first-order, dual- porosity model provides a valid and consistent description of  the physical-non- equilibrium phenomenon. The non-equilibrium-associated parameters included in the model, values for which are typically obtained by fitting, appear to represent actual physical phenomena, at least for well-characterized systems. Thus, the dual-porosity model can be used to analyse experimental data with some degree of confidence. Of  course, the use of  this model and the physical meaning of the parameters should be evaluated carefully for each system to which the model is applied. The structure associated with soils found in the field will rarely be as well defined as that of  our model system. Hence, it must be recognized that the application of  the dual-porosity model to many field systems will be an approximation of reality, albeit a useful one. Acknowledgement A portion of this work was supported by a grant provided by the US Depar tment  of  Agriculture CSRS Water  Quality Program. References Brusseau, M.L., 1993. The influence of solute size, pore-water velocity, and intraparti¢le porosity on solute dispersion and transport in soil. Water Resour. Res., 29(4)" 1071-1080. M.L. Brusseau et al. / Journal of Hydrology 163 (1994) 187-193 193 Brusseau, M.L. and Rao, P.S.C., 1989. Sorption nonideality during organic contaminant transport in porous media. CRC Crit. Rev. Environ. Control., 19: 33-99. Brusseau, M.L. and Rao, P.S.C., 1990. Modeling solute transport in structured soils: A review. Geoderma, 46: 169-192. Brusseau, M.L., Jessup, R.E. and Rao, P.S.C., 1989. Modeling the transport of solutes influenced by multi- process nonequilibrium. Water Resour. Res., 25: 1971-1988. Brusseau, M.L., Jessup, R.E. and Rao, P.S.C., 1990. Sorption kinetics of organic chemicals: Evaluation of gas-purge and miscible displacement techniques. Environ. Sci. Technol., 24: 727-735. Coats, K.H. and Smith, B.D., 1964. Dead-end pore volume and dispersion in porous media. Soc. Pet. Eng. J., 4: 73-84. Deans, H.A., 1963. A mathematical model for dispersion in the direction of flow in porous media. Trans. AIME, 228: 70-80. Nkedi-Kizza, P., Biggar, J.W., van Genuchten, M.Th., Wierenga, P.J., Selim, H.M., Davidson, J.M. and Nielsen, D.R., 1983. Modeling tritium and chloride 36 transport through an aggregated oxisol. Water Resour. Res., 19: 691-700. Parker, J.C. and Valocchi, A.J., 1986. Constraints on validity of equilibrium and first-order kinetic trans- port models in structural soils. Water Resour. Res., 22: 399-407. Rao, P.S.C., Rolston, D.E., Jessup, R.E. and Davidson, J.M., 1980. Solute transport in aggregated porous media: Theoretical and experimental evaluation. Soil Sci. Soc. Am. J., 44:1139-1146. Van Genuchten, M.Th., 1981. Non-equilibrium transport parameters from miscible displacement experi- ments. Res. Rep. 119, US Salinity Laboratory, US Department of Agriculture, Washington, DC. Van Genuchten, M.Th. and Wierenga, P.J., 1976. Mass transfer studies in sorbing porous media: Analytical solutions. Soil Sci. Soc. Am. J., 40: 473-479. 

Simulating solute transport in an aggregated soil with the dual-porosity model: measured and optimized parameter values

NARCIS 

A mathematical model for dispersion in the direction of flow in porous media.

Constraints on validity of equilibrium and first-order kinetic transport models in structural soils.

Dead-end pore volume and dispersion in porous media.

Mass transfer studies in sorbing porous media: Analytical solutions.

Modeling solute transport in structured soils: A review.

Modeling the transport of solutes influenced by multiprocess nonequilibrium.

Modeling tritium and chloride 36 transport through an aggregated oxisol.

Non-equilibrium transport parameters from miscible displacement experiments.

Solute transport in aggregated porous media: Theoretical and experimental evaluation.

Sorption kinetics of organic chemicals: Evaluation of gas-purge and miscible displacement techniques.

The influence of solute size, pore-water velocity, and intraparti¢le porosity on solute dispersion and transport in soil.

Simulating solute transport in an aggregated soil with the dual-porosity model: measured and optimized parameter values

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