# Short Course Example Problem 8

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## Simulation of partitioning tracer transport to detect and quantify NAPLs

**Abstract:*** In this example, the equilibrium behavior of conservative and partitioning tracers in the presence of a DNAPL is simulated. First, a 1-D experiment described by Jin et al. (1995) will be simulated with the water-oil mode. After completing the 1D simulation, the user is asked to design an input file for a 2D tracer experiment based on a conceptual model and description.*

### Problem Description

DNAPLs occur in the subsurface at numerous contaminated sites and are usually considered to be long-term sources of groundwater contamination. The development and application of new remediation technologies require an understanding of flow and transport of DNAPLs in the subsurface. Knowledge of DNAPL distribution is important for implementation of source control strategies. Appropriate risk based decisions can not be made for a contaminated site without knowing if DNAPL is present at the site.

Current methods used for characterizing potential DNAPL sites include soil gas analysis, core sampling, cone penetrometer testing, and monitoring well sampling. These methods provide data for relatively small volumes of the subsurface and require the use of a dense sampling network and application of geostatistics to determine the overall contaminant distribution. The partitioning tracer test is an alternative, larger-scale method for locating and quantifying DNAPL saturation in the subsurface. This method involves the use of partitioning tracers, which distribute into DNAPLs, and are thus retarded and separated from non-partitioning tracers during transport.

The procedure for estimating DNAPL saturation, s_{n}, involves calculation of a retardation factor (R) for the partitioning tracer, which is done by a comparative moment analysis with the nonreactive tracer. The retardation factor is defined as the velocity of water (nonreactive tracer) divided by the velocity of the partitioning tracer. With knowledge of R, K_{ln} (water-DNAPL partition coefficient), K_{d} (sorption coefficient), ρ_{b} (dry soil bulk density), and s_{l} (aqueous saturation), s_{n} can be calculated from:

The terms on the right-hand side of the equation describe retention of the tracer by the aqueous, solid phase, and DNAPL phases, respectively. For a tracer with no sorption to the porous media, the above equation simplifies to:

The experiment described by Jin et al. (1995; Exp. DW2) was conducted in a 30.5-cm stainless steel column with a diameter of 2.21 cm. The column was packed with Ottawa sand. The porosity of the column was 0.362 and the permeability of the sand 15.3 10-12 m2. Residual saturation of tetrachloroethylene (PCE) was established by injecting the organic liquid at a rate of 0.5 ml/min for 1.1 pore volumes in an upward direction, followed by injecting water at the same flow rate for 2.1 pore volumes in a downward direction. Using the methods of weight and volume measurements, the average residual saturation in the column was 0.202 and 0.197, respectively.

Three different tracers were used: Tritium (K_{ln} = 0.00), isopropanol (IPA; K_{ln} = 0.04), and 2,3 dimethyl 2-butanol (DMB; K_{ln} = 2.76). In the experiment, 0.1 pore volumes of water containing the tracers was injected at 0.05 ml/min, followed by injection of clean water at the same rate. Inverse modeling conducted by Jin et al. (1995) yielded a porous medium dispersivity of 0.17 cm. For the molecular diffusion coefficient, a value of 10-10 m2/s was assumed. PCE entrapment was accomplished by assuming a maximum residual saturation of 0.3 in the Saturation Function Card and a constant residual saturation of 0.2 in the Initial Conditions Card. Entrapment was only hysteretic fluid displacement process considered in the simulations. The total simulation period is 2400 minutes of which the first 84.705 minutes were used to inject the tracer cocktail. The flux rate used is computed based on the diameter of column, the injected total volume and the imposed rate. The sign of the Neumann flux is negative because the fluid is injected from the top boundary in a downward direction. For the bottom boundary it is assumed that the fluid outlet was kept level with the top of the column.

**Reference:**

Jin, M. M. Delshad, V. Dwarakanath, D.C. McKinney, G.A. Pope, K. Sepehrnoori, C.E. Tilburg. 1995." Partitioning tracer test for detection, estimation, and assessment of subsurface nonaqueous phase liquids." *Water Resources Research.* 31: 1201-1211.