MASS TRANSFER PROCESS IN THE SATURATED SUBSURFACE WITH A GROUNDWATER CIRCULATION FLOW FIELD

 

O. WEBER, U. MOHRLOK, G.H. JIRKA

Institute for Hydromechanics (IfH), University of Karlsruhe,

D-76128 Karlsruhe, Germany

E-mail: weber@ifh-hp6.bau-verm.uni-karlsruhe.de

 

 

Abstract

Vertical circulation flow systems induced by groundwater circulation wells are an established in-situ groundwater pollution remediation technique. For a effective remediation of a groundwater pollution with a groundwater circulation well it was necessary to unterstand the influence of a circulation flow field on the mass transfer process. Therefore one-dimensional soil column experiments and two-dimensional tank experiments with a circulation flow field have been carried out to systematically investigate the mass transfer process between the residual NAPL and the aqueous phase. A dissolution model to describe the mass transfer process has been developed. This model assumes that the each residual NAPL phase has a spherical shape and is homogeneously distributed in the porous medium. With this model it was possible to determine the mass removed during the experiments and to estimate from experimental data the initial NAPL mass in the contamination source.

 

Keywords: mass transfer process, groundwater circulation well, groundwater remediation.

 

1. Introduction

The groundwater circulation well is an in-situ remediation technique for the removal of groundwater contamination. In the theoretical work by Stamm (1997), the controlling parameters for an effective circulation well operation have been identified. The results of Stamm (1997) could be confirmed by large scale laboratory (Scholz, 1998a) and field experiments (Scholz, 1998b). To unterstand the influence of a circulation flow on the mass transfer processes one- and two-dimensional experiments dissolving a residual NAPL phase have been carried out at the Institute for Hydromechanics (IfH). The mass transfer processes are depending on the lumped mass transfer coefficient and the concentration gradient between die NAPL phase and the aqueous phase. Many studies to determine the lumped mass transfer coefficient can be found in the literature (e.g. Powers et.al., 1992; Imhoff et.al., 1993). In these works correlation functions for the lumped mass transfer coefficient were developed. For a contamination source in a natural aquifer it is difficult or impossible to determine the lumped mass transfer coefficient by applying these correlation functions because the necessary parameters cannot be evaluated with sufficient accuracy. The purpose of the present work is the development of a dissolution model to predict the removed mass and to estimate the initial NAPL mass without knowledge of the lumped mass transfer coefficient. First, one-dimensional experiments were carried out to validate the model. In a next step, the model was applied to the remediation of a contamination source with a circulation flow field in a two-dimensional tank experiment.

 

2. Model Development

The mass transfer process between the NAPL and the aqueous phase is controlled by the kinetics of interphase mass exchange at pore-scale, by the flow as well as by the amount and the distribution of the non-aqueous phase in the pore space. The specific dissolution flux J from the NAPL to the aqueous phase is given by a diffusion approach (Miller et.al., 1990):

(1)

where A_n is the interfacial area between the NAPL phase and aqueous phase, b is the mass transfer cofficient, C_s is the water solubility of the NAPL and C is the dissolved NAPL concentration in water. Furthermore D is the molecular diffusion coefficient in the aqueous phase and d is the diffusion thickness in the boundary layer. Dividing eq. 1 by the volume of porous media V, and rearranging yields:

(2)

where A_n/V is the specific surface area (total surface to volume ratio). Because the surface area cannot be measured, the lumped mass transfer coefficient G, which is the product of the mass transfer coefficient and specific surface area, is introduced. For one-dimensional groundwater flow with Darcy velocity q through a region of residual NAPL phase, neglecting dispersion and assuming quasi steady state condition, the NAPL concentration dissolved in the aqueous phase is given by (Powers et.al., 1992):

(3)

Considering the contact length L between the NAPL and the aqueous phase in flow direction, the integration of eq. 3, with the boundary condition C = 0 at x = 0, gives the effluent concentration. This yields to the following expression for the lumped mass transfer coefficient:

(4)

In many studies (e.g. Powers et.al., 1994) it was observed that the effluent concentration during the dissolution experiments reduces over time. Therefore the lumped mass transfer coefficient G decreases with time (eq. 4). This result can be explained by the reduction of the NAPL mass within the porous medium and the corresponding decrease of total surface area. To describe this situation of decreasing concentration, the following dissolution model was developed, which is able to determine the removed NAPL mass from the contamination source.

 

For the dissolution model it is assumed that each residual NAPL phase in the porous medium have a spherical shape and the aqueous phase is in contact with the overall surface of each sphere. All spheres have the same initial radius r₀ and are homogeneously distributed in the contamination source. Assuming that the contact length L is proportional to the sphere radius r and the NAPL density is constant, the following relationship between the contact lengths L and the NAPL masses m_n in the contamination source at different times can be given by:

(5)

With the assumption of constant mass transfer coefficient b and the porous medium volume V (eq. 2) during each experiment, the relationship between the lumped mass transfer coefficient G and the NAPL masses m_n at different times is given by:

(6)

By multiplying eq. 5 and 6 the parameter g can be defined as the mass ratio at different times m_n(t)/m_n,0. Using eq. 4 yields the expression:

(7)

where the measured effluent concentration C₀ at the beginning of the experiments and C(t) at time t have to be less then the saturation concentration C_s. The Darcy velocity q is assumed to be constant during the individual experiments.

 

Since the NAPL mass is retained only in dead-end pores, the assumption, that the specific surface area A_n/V decreases proportional to the NAPL mass (eq. 6), is not valid. In this case the thickness d of the boundary layer and therefore the mass transfer coefficient b changes.

 

Eq. 7 can be simplified for C₀/C_s<<1 and using the mass balance for the removed mass m(t) = m_n,0 - m_n(t) to:

(8)

Otherwise, the removed mass m(t) can be calculated from the measured concentration C(t) by the general definition:

(9)

where the flow rate Q is constant during the experiments. Rearranging eq. 8 for C(t), substituting into eq. 9 and integrating, subject to the boundary condition m(t) = 0 at t = 0, yields the following expression for the mass removed from the contamination source:

(10)

This equation enables the calculation of the time-dependent removed NAPL mass m(t) from the known initial parameters C₀, Q and m_n,0.

 

Furthermore it is possible to determine the initial NAPL mass m_n,0 in the contamination source at t = 0. By integrating eq. 9 and introducing the parameter g in the mass balance equation for the removed mass m(t) we obtain:

(11)

To calculate the initial NAPL mass m_n,0 with eq. 11 we need at least two measured concentration values C₀ at the beginning of the experiment and C(t) a given time later.

 

3. Experimental results

This dissolution model was applied to one-dimensional column experiments and two-dimensional experiments with a circulation flow field. All experiments were carried out with TCE as a contamination source that has been emplaced in residual saturation.

 

3.1 Column experiments (one-dimensional)

The columns are constucted of stainless steel, 0,5 m in length and 0,1 m in diameter and filled up with fine gravel material (hydraulic conductivity 3.3×10^-4 m/s). The contamination source with an installed TCE mass m_n,0* = 2.044 g has been placed in the column in a small layer (Fig. 1). The TCE mass removed during the column experiment was determined with water samples at the sample point A. Figure 2 shows the calculated removed mass (eq. 9) from one of the TCE dissolution experiments in the column. The removed mass from the experiment was also calculated with eq. 10 using the initial parameters C₀, Q and m_n,0. A good matching between the calculated by (eq. 9) removed mass and the calculated removed mass (eq. 10) could be found.

 

 

Fig. 1: Column experiment with four sample points and the emplaced contamination source.

 

The initial mass m_n,0 can be estimated using eq. 11 from at least two measured concentration value at the beginning of the experiment. Figure 2 shows the calculated initial mass normalized with the known m_n,0*. In the first 40 minutes there are large fluctuations in the estimated values caused by concentration fluctuations at the beginning of the experiments. For later time the calculated initial mass m_n,0 converges to the installed TCE mass m_n,0*.

 

 

Fig. 2: Measured and calculated removed mass during the one-dimensional column experiment and calculated normalized initial TCE mass m_n,0.

 

3.2 Tank experiments (two-dimensional)

Also a series of two-dimensional experiments were carried out to simulate a groundwater circulation well. Figure 3 shows the design and the dimensions of the groundwater simulation tank. The tank was homogeneously filled with fine gravel material, of the hydraulic conductivity of 3.3×10^-4 m/s. For all experiments a contamination source with m_n,0* = 292 g TCE was emplaced in the aquifer as a cubic volume (0.25 m ´ 0.25 m ´ 0.25 m) in residual saturation. The aqueous phase samples are analysed to determine the spatial TCE concentration distribution and the remediation process. For the experiments the circulation flux was set to Q = 0.047 m³/h. Figure 4 shows the calculated mass (eq. 10) removed during the experiment which agrees well with the calculated removed mass (eq. 9). The calculation of the removed mass using eq. 10 was done in an identical manner for the one-dimensional and two-dimensional experiments with the very different flow fields. Figure 4 shows the calculated initial TCE mass (eq. 11) normalized with m_n,0* of the contamination source.

 

 

Fig. 3.: Groundwater simulation tank (tank width = 0.25 m) with 54 sampling points and the circulation well flow field.

 

 

Fig. 4: Measured and calculated mass removed during the two-dimensional experiment with a circulation flow field and calculated normalized initial TCE mass m_n,0.

 

4. Conclusions

Several one-dimensional column and two-dimensional experiments have been carried out to investigate the influence of a circulation flow to the mass transfer processes. The mass removed during the experiment and the initial NAPL mass could be determined by the developed dissolution model describing the mass transfer process. This model could be applied successfully to both kind of experiments with the very different flow fields. These results must be still examined in large scale field experiments.

 

Acknowledgements

The authors would like to thank the German Ministry for Research (BMBF) and the Stiftung Industrieforschung, Köln, for financial support.

 

References

Imhoff, P.T., Jaffé, P.R., Pinder, G.F. (1993): An experimental study of complete dissolution of a nonaqueous phase liquid in saturated porous media, Water Resources Research, Vol. 30, No.2, 307-320.

Miller, C.T., Poirier-McNeill, M.M., Mayer, A:S. (1990): Dissolution of Trapped Nonaqueous Phase Liquids: Mass Transfer Characteristics, Water Resources Research, Vol. 26, No.11, 2783-2796.

Powers, S.E., Abriola, L.M., Walter, J., Weber, J. (1992): An Experimental Investigation of Nonaqueous Phase Liquid Dissolution in Saturated Subsurface System: Steady State Mass Transfer Rates, Water Resources Research, Vol. 28, No. 10, 2691-2705.

Powers, S.E., Abriola, L.M., Walter, J., Weber, J. (1994) An Experimental Investigation of Nonaqueous Phase Liquid Dissolution in Saturated Subsurface System: Transient mass transfer rates, Water Resources Research, Vol. 30, No. 2, 321-332.

Scholz, M., Weber, O., Mohrlok, U. (1998a): Large scale experiments for in situ flushing using groundwater circulation wells: identification of processes and limiting parameters, in Groundwater Quality: Remediation and Protection (Ed. By P. Grathwohl, G. Teutsch, K. Kovar, J. Krasny and D. Lerner), IAHS Publ. No.250, Wallingford, UK ISBN 1-901502-55-4, pp. 185-189.

Scholz, M., Mohrlok, U. (1998b): Detailed three-dimensional field experiment with a groundwater circulation well for in situ flushing, in Groundwater Quality: Remediation and Protection,(Ed. By P. Grathwohl, G. Teutsch, K. Kovar, J. Krasny and D. Lerner), IAHS Publ. No.250, Wallingford, UK ISBN 1-901502-55-4, pp. 133 -140.

Stamm, J., (1997): Numerische Berechnung dreidimensionaler Strömungsvorgänge um Grundwasser-Zirkulations-Brunnen zur In-situ-Grundwassersanierung, VDI-Report, Serie 15, No. 169, Düsseldorf