VISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES

Transcription

1 VISUAL SOLUTE TRANSPORT: A COMPUTER CODE FOR USE IN HYDROGEOLOGY CLASSES Kathryn W. Thorbjarnarson Department of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California 92182, thorbjar@geology.sdsu.edu Julie H. Inami Department of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California Gary H. Girty Department of Geological Sciences, San Diego State University, 5500 Campanile Drive, San Diego, California 92182, ggirty@geology.sdsu.edu ABSTRACT Gaining an understanding of solute transport processes can be a time-consuming process due to useage of Fortran models. Senior undergraduate and beginning graduate students in hydrogeology classes are not always familiar with data file preparation and output graphing procedures. Assignments designed to point out important impacts of various transport processes can turn into many hours of preprocessing and postprocessing data with little time or energy for thought and evaluation. A stand-alone Visual Basic program, Visual Solute Transport, has been created for easy data input and graphing of one-dimensional diffusion and advection-dispersion with equilibrium sorption and decay models. Inquiry-based exercises for evaluation of advection-dispersion, dispersivity and sorption effects are included in the paper. Keywords: Education- geoscience; education- graduate; education-undergraduate; education- computer assisted; hydrogeology and hydrology INTRODUCTION Transport of dissolved contaminants is an important process in groundwater hydrogeology. Many geological science graduates work in the environmental field dealing with the assessment of groundwater contaminant plumes and predictions of the plume s transport. This topic is generally taught in senior-level and graduate-level hydrogeology courses. One-dimensional analytical solutions of the governing equations are typically used to predict solute concentrations and to demonstrate the impact of various transport parameters. Available computer codes are either DOS-based or expensive (ODAST, AT123, CXTFIT, ONE-D described at International Ground Water Modeling Center website: DOS-based programs generally require knowledge of Fortran formatting. The calculated solute concentrations must subsequently be imported into a graphics program for visualization. Students can spend a considerable amount of time in the busywork of data preparation and graphics. This results in less time available for evaluating the impacts and importance of solute transport processes. We have constructed a stand-alone Visual Basic 6 program which allows for data input, calculation and graphing of one-dimensional solute concentrations over time or distance. The program, Visual Solute Transport (VST), also calculates statistical moments (area, mean and variance) of pulse curves which can be used to evalute the impact of each solute transport process. The code can be downloaded from and requires a Windows version 95/98 or higher operating system. We will briefly review solute transport theory and describe the one-dimensional models included in VST. We will then present inquiry-based exercises that delineate the impacts of various solute transport processes. SOLUTE TRANSPORT Advection, dispersion, equilibrium sorption, and transformation can control the transport of solutes. These processes are described in detail in many textbooks (Domenico and Schwartz, 1998; Fetter, 1999). A brief description of the processes, governing equations, analytical solutions and their incorporation in VST follows. In all aqueous environments, diffusion of solutes will occur in the presence of concentration gradients. Fick s second law governs the change in concentration with time (t) and distance (x): C = D t eff 2 C 2 where, C = solute concentration [M/L 3 ], and D eff = effective diffusion coefficient [L 2 /T] The effective diffusion coefficient is generally estimated by: D eff =wd where, D = aqueous molecular diffusion coefficient [L 2 /T], and w = tortuosity factor [unitless] The empirical tortuosity factor accounts for the slower diffusion of solutes through the tortuous pore pathways of a porous medium (w < 1, usually 0.7 for sands). The governing equation for diffusion can be solved given initial and boundary conditions. For a constant Thorbjarnarson, Inami, and Girty - Visual Solute Transport 287

2 Your environmental consulting firm is given the task of selecting sites for prospective landfills. For all the geological materials listed below and given the scenario of the landfill leaking for 10 years at a concentration of 100 mg/l, you must estimate the location, size and maximum concentration of a contaminant plume at 12 years, 25 years and 50 years after the leaking started. Assume the sand aquifer has a hydraulic conductivity of 1,000 m/yr, an effective porosity of 0.35, a hydraulic gradient of 0.001, a longitudinal dispersivity of 1 m and no sorption or transformation. Use the C vs. X graphing option. How does the contaminant plume change with time due to advection and dispersion? Parameter 12 Years 25 Years 50 Years Pore-water velocity (m/d) a Dispersion Coefficient (m 2 /d) a Approximate X distance of Plume Midpoint (m) b Plume Lenght (m) b Maximum Concentration (mg/l) b Table 1. Advection-Dispersion Exercise. a calculated, b Measured off VST graphs or by viewing C vs x data using the View Current Data under the File menu. source concentration, C o, at the x = 0 boundary and initial conditions of zero concentration (Crank, 1956): C( x, t)= C erfc 0 2 x Deff t where, erfc = complementary error function Calculations of C for various values of x and t provide data sets to visualize either: 1) the concentration over time at a distance, x from the source or 2) the concentration over distance at a given time, t. VST provides a Graphical User Interface (GUI) for input of C o,d eff and either 1) distance to be plotted, initial time, final time, number of time steps or 2) time to be plotted, initial and final distance, number of distance steps. A graph can be quickly created and printed from the VST interface. In flowing groundwater, all solutes will be affected by advection and mechanical dispersion. In onedimensional models, the advection of solutes due to water movement is characterized by the mean pore-water velocity: v = Kdh θ dx where, v = mean pore-water velocity [L/T], K = hydraulic conductivity [L/T], q = effective porosity [unitless], and dh/dx = hydraulic gradient [unitless]. Because all solute molecules will not be moving at this mean pore-water velocity, mechanical dispersion will occur due to the slower/faster velocities encountered. The longitudinal dispersion or spreading of the solute in the direction of flow is characterized by the mechanical dispersion coefficient, D m : D m =a x v where, a x = empirical longitudinal dispersivity [L], and v = mean pore-water velocity [L/T] The spreading effects of diffusion and dispersion are usually lumped together into the hydrodynamic dispersion coefficient (D H ): D H =D m +D eff =a x v+wd Some solutes will sorb onto and off of solids during transport. The adsorption onto solids and subsequent desorption off of solids results in a slowing of the solute transport referred to as retardation. Equilibrium sorption assumes instantaneous adsorption and desorption and is characterized by the retardation factor, R: R= 1+ ρ Kd θ where, r b = bulk density [M/L 3 ]=(1-q)r s with r s = aquifer sediment density [M/L 3 ], and K d = sorption distribution or partition coefficient [L 3 /M]. For hydrophobic organic solutes, sorption occurs due to interactions with natural organic carbon on the solids. For sediments with organic carbon fractions greater than 0.01, the sorption partition coefficient has been approximated by (Karickhoff et al., 1979): b K d =f oc K oc where, f oc = fraction of organic carbon on solids [-], K oc = organic carbon partition coefficient [L 3 /M], estimated values for many solutes can be found in reference books (Montgomery and Welkom, 1990). Transformation or decay can influence the solute transport of certain solutes. Many of the transformation 288 Journal of Geoscience Education, v. 50, n. 3, May, 2002, p

3 Figure 1. VST graph produced from Advection-Dispersion Exercise showing impacts of advection and dispersion on solute plume cross-sections (spatial graph) Input parameters for simulations are v = 2.9 m/ry, D = 2.9 m 2 /yr, R = 1, k = 0, Co = 100 mg/l, To = 10 yr and T values are listed on graphs. processes are characterized by an exponential function and a first-order decay rate constant: k = t Where, k = first-order rate constant [1/T], and t 1/2 = half-life of solute [T]. The governing equation for one-dimensional advection-dispersion with equilibrium sorption and first-order decay is: R C t 12 / v C 2 C = + DH 2 krc An approximate analytical solution to this equation given the initial condition of zero concentration and a defined input concentration flux can be found in Javandel et al. (1984) and at the edu/visualsolutetransport web site. The solution is used in VST for the one-dimensional advection-dispersion model. The input concentration can be a constant value, C o, over a time interval, T o,or can exponentially decay from an initial C o value over the time interval, T o, controlled by a source decay factor. The VST interface for this model allows for easy input of the required parameters. A Parameter Help menu aids the student in finding appropriate ranges and/or calculates the parameter. Error trapping in the program prohibits students from entering out-of-range parameters. Figure 2. VST graph produced from Dispersivity Exercise showing impacts of varing longitudinal dispersivity on dispersion coefficients and solute plumes at T=50yrs. D values used are listed in Table 2. All other input parameters are the same as in the Advection-Dispersion Exercise. The graphing of multiple scenarios allows for evalution of impacts of transport processes in inquiry-based exercises. VST currently includes one-dimensional diffusion and advection-dispersion modeling capabilities. Numerous class exercises are possible highlighting diffusion, advection-dispersion, dispersivity, sorption and transformation. For a given scenario, VST can be used to create either a concentration vs. distance graph at a specific time, T, or a concentration vs. time graph at a specific distance downgradient from the contaminant source, X. Concentration vs. distance graphs are representative of cross-sectional slices through the longitudinal centerline of the groundwater plume at that time. Concentration vs. time graphs are representative of the concentration history found by sampling a well at distance X from the contaminant source. We will present example exercises for assessing groundwater plume cross-sections affected by advection-dispersion and/or sorption in this paper. ADVECTION-DISPERSION EXERCISES In this inquiry-based exercise, students calculate model input parameters from given aquifer characteristics and simulate a contaminant plume over time (Table 1). Students are asked to describe changes in the plume with time and can read the plume midpoint, length and maximum concentration off the VST graph (Figure 1). The important impacts of movement of the plume center through advection and increased dispersion with increasing time and distance can be seen qualitatively in the graphs. Another important concept is that no mass Thorbjarnarson, Inami, and Girty - Visual Solute Transport 289

4 Figure 3. VST graph produced from Sorption-Retardation exercise showing impacts of varying retardation factors. Input parameters for simulations are v=10m/yr, D = 100 m 2 /yr,k=0,co = 100 mg/l, To = 10 yr, T=50yrandRvalues are listed on the graph. loss occurs during transport by advection and dispersion. Qualitatively, the area under the curves appears the same. Thus, dispersion is an important process in diluting plume concentrations but due to conservation of mass, this is at the cost of increased plume length. DISPERSIVITY EXERCISE The extent of dispersion is a function of the empirical dispersivity constant. The term constant is a misnomer as dispersivity has been found to be scale dependent. Tracer tests measuring dispersivities using laboratory columns or small-scale field experiments find low values for dispersivity ( to 1 m). Large-scale field experiments find larger values for longitudinal dispersivity (1 m to 100 m) with dispersivities increasing with increased distance travelled to possible asymptotic values (Gelhar, 1986; Fetter, 1999). Further complicating matters is the monitoring well scale with point samplers measuring lower values of dispersivity in comparison to long-screened wells under assumptions of homogeneous conditions (Thorbjarnarson et al., 1997). To illustrate the impacts of dispersivity and the consequences of incorrect estimates, an inquiry-based exercise requires the students to vary dispersivity over 3 orders of magnitude and evaluate changes in the predicted contaminant plume (Table 2). The lower concentrations and longer plume lengths resulting from higher dispersivities can be seen in Figure 2. Utilizing a high dispersivity for predicting solute transport at small scales will drastically underestimate solute concentrations and overestimate transport distance. SORPTION AND RETARDATION EXERCISE Equilibrium sorption slows or retards the advection of a solute. The apparent velocity of a sorbing solute will be lower than the pore-water velocity. In this inquirybased exercise, students calculate retardation factors and apparent velocities of two sorbing compounds (Table 3). Plume midpoints, lengths and maximum concentrations are read off the student s VST simulation graph (Figure 3). Decreased distances traveled over the same time for compounds with higher retardation factors are clearly seen (Figure 3). Lower maximum concentrations The regulators have reviewed your report from the Advection-Dispersion Exercise and question your estimate of the longitudinal dispersivity. You must simulate the contaminant plume produced by the landfill leaking for 10 years at a concentration of 100 mg/l. Estimate the location, size and maximum concentration of a contaminant plume at 50 years after the leaking started. Assume a hydraulic gradient of 0.001, a range of longitudinal dispersivities of 1 m, 10 m and 100 m and no sorption or transformation. Use the C vs x graphing option. What effects do increased dispersivity values have on your contaminant plumes? Parameter Dispersivity of 1 m Dispersivity of 10 m Dispersivity of 100 m Pore-water velocity (m/d) a Dispersion Coefficient (m 2 /d) a Approximate x Distance of Plume Midpoint (m) b Plume Lenght (m) b >500 Maximum Concentration (mg/l) b Table 2. Dispersivity Exercise. a calculated, b Values read off VST graph or from C vs x data viewed using View Current Data option under the File menu. 290 Journal of Geoscience Education, v. 50, n. 3, May, 2002, p

5 Chloride, trichloroethene (TCE) and napthalene have all been released from an industrial source at concentrations of 10 mg/l for 10 years. Your firm has been hired to simulate the solute transport of these 3 chemicals. Aquifer parameters are:v=10m/yr, D = 100 m 2 /yr, porosity = 0.28, fraction organic carbon = 0.005, and quartz sediment density = 2.65 g/cm 3. Physical properties of these three chemical s are listed below. Using this information, characterize each chemical s groundwater plume position, length and maximum concentration at 50 years after the source started leaking. How does sorption affect a plume? Why are aqueous concentrations lower in a sorbing chemical? Parameter Chloride TCE Napthalene Log Koc Kd (cm 3 /g) a Bulk density (g/cm 3 ) a R a Apparent velocity (m/yr) Approximate x Distance of Plume Midpoint (m) b Plume Length (m) b Maximum Concentration (mg/l) b Table 3. Sorption and Retardation Exercise. a calculated, b values read of VST graph or from C vs x data viewed using View Current Data option under the File menu. Bold Log Koc values are given. for higher retardation factors are also apparent (Table 3 and Figure 3). This exercise could be extended to include an examination of the areas under the curve. As equilibrium sorption includes adsorption and subsequent desorption, there is no net mass loss as the solute plume moves through the porous medium. In the spatial graphs of compounds with the same source conditions (T o,c o ), a decrease in the area under the curve with increased retardation can be seen (Figure 3). The decreased areas result from a portion of the mass being sorbed within a plume at any given time. The area under the solute curve in the spatial graphs is a function of the aqueous mass (nonsorbed). The mass fraction in the aqueous phase is 1/R and the mass fraction in the sorbed state is [1 1/R]. This mass is not irreversibly sorbed but will eventually desorb and move downgradient with the plume. Areas under temporal graphs (C vs t) with the same source conditions (C o,t o ) will all be the same irregardless of R value. This result shows that all mass injected eventually passes the monitoring point. For remediation studies, the total mass in existing contaminant plumes is estimated by monitoring well aqueous concentrations and estimated plume volumes (Mass = C x Volume). However, this calculation only accounts for the aqueous mass in sorbing contaminant plumes. If sorption occurs, these estimates must be multiplied by R to obtain the total mass (aqueous and sorbed). To illustrate the ramifications of neglecting sorbed mass in a contaminant plume, half of the mass would not be accounted for in a remediation system with R of 2. CONCLUSIONS Illustration of the impacts of various solute transport processes is made simple by graphing multiple scenarios in the VST program. Students can quickly and easily generate these graphs in the Windows-based graphical interface. Modeling scenarios designed to illustrate the impacts of advection, dispersion, and sorption have been presented. Additional exercises and description of higher level model calculations (moment analysis) are on the model website visualsolutetransport. The compressed 2.8 Mb program files must be uncompressed and installed on systems with Windows 95/98 or higher version operating systems. REFERENCES Crank, J, 1956, The Mathematics of Diffusion, New York, Oxford University Press, 616 p. Domenico, P.A. and F.W. Schwartz, 1998, Physical and Chemical Hydrogeology (2 nd ed.), New York, Wiley, 506 p. Fetter, C.W.,1999, Contaminant Hydrogeology, Upper Saddle River, N.J., Prentice-Hall, 500 p. Gelhar, L.W., 1986, Stochastic subsurface hydrology from theory to application, Water Resources Research, v. 22, p. 135S-145S. Javandel, I., C. Doughty and C.E. Tsang, 1984, Groundwater Transport: Handbook of Mathematical Models, Washington, D.C., American Geophysical Union, 228 p. Karickhoff, S.W., D.S. Brown and T.A. Scott, 1979, Sorption of hydrophobic pollutants on natural sedimen, Water Research, v. 13, p Montgomery, J.H. and L.M. Welkom, 1990, Groundwater Chemicals Desk Reference, Chelsea, MI, Lewis Publ., 640 p. Thorbjarnarson, K.W. and D.M. Mackay, 1997, A field test of tracer transport and organic contaminant elution in a stratified aquifer at the Rocky Mountain Arsenal (Denver, Colorado, U.S.A.), Journal of Contaminant Hydrology, v. 24, p Thorbjarnarson, Inami, and Girty - Visual Solute Transport 291