Modeling unsaturated flow and transport in the saprolite of fractured sedimentary rocks: Effects of periodic wetting and drying

Transcription

1 WATER RESOURCES RESEARCH, VOL. 39, NO. 7, 1186, doi: /2002wr001926, 2003 Modeling unsaturated flow and transport in the saprolite of fractured sedimentary rocks: Effects of periodic wetting and drying Stephen J. Van der Hoven Illinois State University, Normal, Illinois, USA D. Kip Solomon University of Utah, Salt Lake City, Utah, USA Gerilynn R. Moline Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA Received 18 December 2002; revised 28 February 2003; accepted 28 March 2003; published 19 July [1] Whereas a number of unsaturated zone modeling studies have been conducted on dual-porosity systems where the matrix has low permeability, few have been conducted on systems where the matrix has relatively high permeability. In humid climates, in situ weathering of bedrock can form saprolite. Saprolite usually has high matrix porosity (and variable permeability) that is a reservoir for solute storage and can have relict fractures that transport solute rapidly. On the basis of a field investigation where natural chemical tracers were monitored at high resolution during storm events, a numerical model was created that simulated variably saturated transport in the saprolite. A series of simulations were performed to explore solute transport during cycles of wetting and drying. Modeling results indicated that the advective flux of solutes from the fractures into the matrix during wetting was greater than from the matrix back into the fractures during drying, resulting in a net storage of solutes in the matrix. We hypothesize that the amount of net solute storage in the matrix may increase as the frequency of wetting/drying cycles increases, up to an optimum frequency. At frequencies higher than the optimum, the amount of solute storage in the matrix may decrease because the system behaves more like a fully saturated system where diffusion is the dominant transport process between fractures and matrix. These conclusions have significant implications for such processes as remedial strategies for contaminants in the unsaturated zone, the application of fertilizers, and quantification of mineral weathering and dissolution rates. INDEX TERMS: 1875 Hydrology: Unsaturated zone; KEYWORDS: unsaturated zone, transport modeling, oxygen isotopes, saprolite, dual porosity, fractures Citation: Van der Hoven, S. J., D. K. Solomon, and G. R. Moline, Modeling unsaturated flow and transport in the saprolite of fractured sedimentary rocks: Effects of periodic wetting and drying, Water Resour. Res., 39(7), 1186, doi: /2002wr001926, Introduction [2] In this paper we investigate unsaturated flow and transport in the widespread setting of a saprolite. Saprolite forms from the in situ chemical weathering of bedrock. Although this process highly alters the rocks, some of the original rock structure is retained. Some of the most important retained structures in terms of groundwater flow and transport are relict fractures. The fractures serve as the primary conduits for groundwater flow in the unweathered rock as well as in the saprolite. Alteration of the matrix properties, however, significantly changes flow and transport in the saprolite when compared to the unweathered bedrock. The weathering process results in an increase in Copyright 2003 by the American Geophysical Union /03/2002WR SBH 6-1 matrix porosity, providing a larger volume for storage of solutes. The permeability of the matrix may also increase, resulting in advection, rather than diffusion, becoming the dominant transport mechanism for exchange of solutes between the fractures and matrix. [3] Saprolites differ from other multiporosity materials such as soils, fractured rocks, or fractured tills. Saprolites retain much of the structure and regularity of the bedrock from which they formed, unlike the chaotic nature of bioturbation in soils. They have higher porosity and permeability than most consolidated rocks, and have generally higher matrix permeability than fractured tills. [4] Modeling of multiporosity geologic systems has proceeded along two tracks: (1) the overlapping continua approach and (2) explicit definition of fractures or other preferential flow pathways. The overlapping continua approach takes a macroscopic view of transport processes,

2 SBH 6-2 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT assuming that the medium can be divided into two regions that occupy the same space (overlapping continua); a mobile region associated with macropores or fractures and an immobile (or low permeability) region associated with soil aggregates or rock matrix blocks [van Genuchten and Wierenga, 1976; Gvirtzman et al., 1988]. A single equation for flow is used to describe the bulk properties of the combined mobile and immobile regions. The advection/dispersion equation is used to describe transport; however, all flow is assumed to occur only in the mobile zone porosity. The concentration of solutes in the mobile and immobile porosity is linked through a first-order transfer coefficient simulating diffusive exchange. [5] Gwo et al. [1995] developed a one-dimensional model for a triple porosity and triple permeability system, and applied it to the conceptual model (discussed in the next section) of flow and transport through the saprolites underlying the Oak Ridge Reservation (ORR), Tennessee. Their model simulates flow and transport in three pores regions and incorporates time dependent transfer coefficients between each of the regions. The transfer coefficients include advection as a function of head differences and diffusion as a function of concentration differences. From simulations using this model they conclude that advective mass transfer might counteract diffusive mass transfer under transient variably saturated conditions by reducing the concentration gradient between pore regions. They suggest that under these conditions, advection may be the dominant mass transfer process. However, a sensitivity analysis indicates that reestablishment of concentration equilibrium is more sensitive to diffusive than advective mass transfer, suggesting a need to carefully quantify diffusive mass transfer during field-scale investigations. [6] Advantages of models using the overlapping continua approach are that they are well suited for soil settings where it is difficult to explicitly define soil structures, are relatively simple to set up, and they are computational efficient. Disadvantages to this approach are that detailed field/ laboratory investigations are necessary to define the flow characteristics of each region and to estimate the transfer coefficient for solute exchange between the pore regions. Further, the overlapping continua approach cannot provide insight into important microscale processes such as flow fingering and fracture coatings [Glass et al., 1995]. Finally, advective flow and transport between high- and low-permeability zones may not be accurately accounted for in models that assume an immobile zone. [7] The second modeling approach is to explicitly construct preferential pathways in the model domain and to solve the flow and transport equations for both highand low-permeability regions. Recent progress in this approach has largely been driven by the need for highlevel nuclear waste storage facilities [Wu et al., 1999] and investigations of fractured clay tills [Therrien and Sudicky, 1996]. Although conceptually more satisfying than the overlapping continua approach, there are numerous problems associated with explicitly including fractures in models. Since subsurface data are usually sparse, there is little justification for placement of a fracture in a particular location, and thus fracture networks are usually generated using a statistical approach based on field observations. Even if the fracture distribution could be reasonably represented, the computational resources necessary for any problem larger than a local scale can be prohibitive. Other limitations include sparse data on the pressure/saturation/relative permeability relationships for fractures and difficulties in quantifying key fracture characteristics such as aperture and asperity. Despite their problems and limitations, both of these two modeling approaches have provided significant insight into our understanding of unsaturated zone flow and transport in multiporosity geologic materials. [8] Our investigation focuses on the variably saturated saprolite that has developed by weathering of sedimentary rocks on the ORR. We use natural tracer data collected during this investigation to refine the conceptual model of this site, and to create a numerical model of transport though the unsaturated zone. While our numerical model incorporates both the overlapping continua and explicit definition approaches in different parts of the model domain, it focuses on the latter approach. Combining the two approaches allows us to capitalize on the strengths of both methods. A series of transient simulations were performed to explore solute transport through the unsaturated zone during repeated cycles of wetting and drying (on the timescale of a precipitation event). Particular attention was paid to the mass exchange of solutes between fractures and the surrounding matrix. [9] This study differs from the other unsaturated zone modeling studies on the ORR in the explicit representation of fractures/preferential pathways and the intensive monitoring of natural tracers at an experimental field site over the period of a storm event. This study also differs from other explicit representation of fractures studies [Wu et al., 1999; Therrien and Sudicky, 1996] in that it explores a geologic setting with a relatively thin unsaturated zone (<4 m) in a humid environment, high matrix porosity (up to 50%), and a relatively permeable matrix (average hydraulic conductivity of cm/s). The results of this study may be applicable to large areas of the eastern United States and many other areas around the world where fractured sedimentary rocks are present in humid climates. 2. Conceptual Model of the Unsaturated Zone [10] The study area is located in the Appalachian Valley and Ridge Province of Tennessee and is characterized by a series of imbricate thrust sheets which results in parallel valleys of less erosion-resistant bedrock (primarily shale) and intervening ridges of more resistant bedrock (sandstone or limestone/dolomite). Locally, bedrock is composed primarily of shale with occasional thin interbeds of limestone and sandstone. The bedding plane dip is 45 to the southeast. Evidence from numerous previous studies indicates that bedding plane fractures are preferential pathways for flow and transport in the unsaturated and saturated zones [Lee et al., 1992; Solomon et al., 1992; Wilson et al., 1993; Moline et al., 1998]. [11] The conceptual model was developed based on previous field and laboratory investigations on the ORR and on observations made during this investigation. This large body of work has recently been summarized [Jardine et al., 2001]. The unsaturated zone can be divided into several units (Figure 1). The zone immediately below the

3 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT SBH 6-3 Figure 1. Local hydrogeologic cross section showing hydrogeologic units, water table fluctuations, and screened intervals of one of the wells and storm flow tubes. surface gains its properties from soil forming processes, while the region beneath that is controlled by intense in situ weathering of bedrock that forms saprolite. The two regions are similar in that both contain multiple pore regions and preferential flow pathways, but the formation and arrangement of pore regions is different. [12] The soils in the study area have been classified as ruptic ultic dystrochrepts and are cm thick [Watkins et al., 1993]. The A horizon has been extensively bioturbated, and has high porosity (ranging from 0.3 to 0.6 with a mean of 0.5) and saturated hydraulic conductivity (ranging from cm/s to 0.03 cm/s with a geometric mean of 0.01 cm/s) [Solomon et al., 1992]. The infiltration rate of the A horizon is high enough to accommodate all but the highest precipitation rates [Wilson and Luxmoore, 1988]. The hydraulic conductivity of the near-surface A horizon is much greater than the Bt horizon and saprolitic C horizon. During periods of intense or prolonged precipitation, the hydraulic conductivity contrast between the A and B horizons can cause intermittent saturation of the A horizon [McKay and Driese, 1999]. Throughout the rest of this paper, the transient perched saturated zone that develops in the upper soil horizons during some precipitation events will be referred to as the storm flow zone. [13] The storm flow zone is characterized by a continuous range of pore sizes. Luxmoore et al. [1990] reviewed the various schemes that have been used to describe the pore size distribution. For conceptual purposes, the micropore, mesopore, and macropore system proposed by Luxmoore [1981], in which macropores are less than 0.01 mm in diameter, mesopores are between 0.01 and 1 mm, and macropores are greater than 1 mm, will be used. The pore regions can also be defined in terms of the soil tension at which they drain. Wilson et al. [1992] reviewed some of the tensions used to distinguish macropores and mesopores. Tensions of 10 cm and 250 cm were found to best distinguish macropores and mesopores, respectively, which are close to the values for the Luxmoore [1981] scheme. The larger pores are created by bioturbation, and therefore their occurrence is chaotic. During nonstorm periods (field capacity), the mesopores and macropores are mostly drained, with only the micropores remaining at or near saturation. During periods of saturation, the majority of water flows through the macropores and mesopores even though they make up only a small percentage of the total porosity [Watson and Luxmoore, 1986]. The dominant process controlling exchange of water and solutes between mesopores and macropores is advection, while the dominant process controlling exchange between micropores and the larger pore regions is diffusion. [14] Underlying the storm flow zone is the saprolite that ranges in thickness from 1 to 7 m. The thickness is greatest beneath the ridge crests and decreases away from them. The porosity in the saprolite ranges from 0.36 to 0.52 with an average of The saturated hydraulic conductivity ranges from cm/s to cm/s with an average of cm/s [Rothschild et al., 1984]. [15] The thickness of the unsaturated zone on the ORR varies. The water table fluctuates ( m) within the saprolite in response to individual storm events and seasonal changes. During extremely wet periods the saprolite may be fully saturated, and during extremely dry periods the saprolite may be completely within the unsaturated zone. [16] The saprolite can also be divided into micropores, mesopores, and macropores. The assignment of pore regions is based on geological features and is less arbitrary than in the storm flow zone [Gwo et al., 1995]. The macropores represent relict fractures in the saprolite. Fracture spacing in unweathered bedrock on the ORR ranges from 0.51 cm to cm [Hatcher et al., 1992]. Dreier et al. [1987] report an average fracture spacing of 2 cm in the saprolite. Neither of these studies indicates the spacing for fractures that are hydraulically active. Although the saprolite has the appearance of relatively unweathered bedrock in outcrop, upon removal it breaks apart into smaller pieces along microfractures in the saprolite matrix. These microfractures represent the mesopores. The unfractured matrix constitutes the micropores. The same soil tension values used to classify pores in the storm flow zone are also used in the saprolite. During nonstorm periods, the fractures are largely unsaturated whereas the matrix remains close to saturation [Solomon et al., 1992; G. Moline, unpublished tensiometer data from the ORR, 1997]. [17] Jardine et al. [2001] provide a summary of flow and transport through the saprolite by way of an example of a precipitation event. Initially, as low-solute precipitation infiltrates, water in the subsurface converges into the microfractures and fractures (mesopores and macropores). As the fractures saturate, a pressure gradient develops that drives advection from the fractures into the matrix (micropores). However, there is a concentration gradient in the opposite direction since the fractures contain low solute water while the matrix contains high solute water. As a result, advective and diffusive transfer act in opposite directions in the early part of a storm event. In addition, most of the flow is occurring in the fractures and bypassing the matrix. [18] After precipitation stops, the amount of infiltration slows, but the fractures are still at or near saturation. Pressure gradients between pore regions are low, and advection into the matrix decreases or even reverses direc-

4 SBH 6-4 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT tion. Since the solute concentrations in the fractures are still relatively low, the concentration gradient is driving diffusive mass transfer from the matrix into the fractures. [19] As the saprolite dries out, the primary fractures desaturate and flow is restricted to secondary fractures and the matrix. The concentration gradient between the microfractures and matrix is small, therefore the diffusive mass transfer is low. The pressure gradient between the two pore regions is low, so advective transfer is also low. Advection through the whole system also decreases because of desaturation of the primary fractures. Eventually, when the microfractures desaturate, advective and diffusive mass transfer between pore regions all but ceases. Diffusion within the matrix will continue until chemical equilibrium is reestablished. Advection will also continue through the matrix until it reaches field capacity. [20] Data from the shallow saturated zone is used to support the model in this paper, so a brief discussion is warranted. Since no direct measurements of water in the unsaturated saprolite were made during this investigation, the processes occurring in this zone can be inferred only by samples collected in the intermittently saturated storm flow zone above it and the saturated saprolite below it. The study area is located in a regional groundwater discharge zone. During nonstorm periods, evidence from hydraulic measurements, major ion chemistry, and dissolved gases indicates that there is an upward vertical flux of water in the saturated zone [Van der Hoven, 2000]. Numerous samples of groundwater at depths of between 10 to 20 m below the water table have a relatively constant d 18 Oof 5.8% to 6.0%. During storm events, the large flux of water through the unsaturated zone (with variable d 18 O content) reverses the hydraulic gradient in the shallow saturated zone. 3. Methods 3.1. Field Methods Monitoring Well Construction [21] Water in the storm flow zone was monitored using storm flow tubes. A separate hole was drilled using a hand auger for each tube. A screened section was placed at the bottom of the hole and blank casing extended above the land surface. The annular space around the screen was backfilled with sand and compacted soil filled the remainder of the annular space to the surface. [22] Groundwater samples from the saturated saprolite were collected from multiport monitoring wells installed in a single 20-cm diameter borehole drilled using the hollow stem auger method. The casing for each port was constructed of 2 cm ID polyethylene tubing. A 10-cm length of wrapped wire mesh screen was attached to the bottom of the casing and approximately 30 cm of the annular space around the screen was filled with sand. A bentonite seal was placed immediately above the screen and the rest of the annular space was filled with compacted backfill Water Sampling [23] Water samples were collected using a peristaltic pump. Each well was purged of approximately one well volume of water at a slow rate prior to sampling. Samples for oxygen isotopic analysis were stored in a glass vial with a Teflon cap at 4 C until analysis Laboratory Methods [24] Oxygen isotopic analyses were performed at the University of Tennessee, Department of Geologic Sciences on a Finnagan Delta Plus gas source mass spectrometer with and a HDO Equilibrator for automated analysis of water samples. The analytical uncertainty of the measurement is 0.1%. 4. Results and Discussion 4.1. Storm Event Sampling Results [25] During the course of the field investigation for this project, four separate storm events were sampled at three different sites. Samples from two of the sites for one storm event are presented as representative of the field data set. The first site (well SW-1D, Figure 1) was located on the gently sloping valley floor. At the time of sampling, the unsaturated zone was approximately 2.5 m thick. The second site (well SW-3D, not shown) is located at the base of a slope, approximately 15 m from the floodplain of the stream. At the time of sampling, the unsaturated zone was approximately 1.5 m thick. [26] During a storm event in April May, 1998, water samples for d 18 O analysis were collected from the storm flow zone and shallow groundwater within the saprolite. Although no water samples were collected from the unsaturated saprolite during this investigation, processes occurring within this zone can be inferred from samples collected in the overlying storm flow zone and the underlying saturated saprolite. [27] During the monitoring period, precipitation fell on a number of days, with slightly less than half (31.8 mm) falling on Julian Day 120 (Figure 2a). The d 18 O of the three precipitation samples collected during this first period ranged from 3.1% to 4.7% with a weighted average of 3.8% (Figure 2a). An additional 40.6 mm of precipitation fell over the next 4 days and had a d 18 O weighted average of 7.9%. [28] The d 18 O of water in the storm flow zone over the period of saturation are shown on Figure 2b. In SF-4C (the shallowest storm flow tube), the d 18 O is the same for both samples, and is isotopically lighter than the precipitation that fell during that period, indicating a mixing between precipitation and water stored in the storm flow zone. In SF-4B, the d 18 O varies only 0.1% over the first few days and then decreases by 0.4% at the end or the period of saturation. The d 18 O from SF-4B also shows mixing between precipitation and stored water, as well as a response to the isotopically light precipitation at the end of the monitoring period. SF-4A (the deepest storm flow tube) shows the largest response to the storm event. Similar to the other two storm flow tubes, the d 18 O of water in the first sample from SF-4A is lighter than precipitation, indicating mixing between precipitation and stored water. Interestingly, the d 18 O decreases in the second sample, despite a slight increase in the d 18 O in precipitation. As the precipitation rate decreased during the period between the first and second samples, advection/ diffusion of water stored in the micropores and mesopores may have contributed a greater percentage of water in the macropores. The d 18 O of the last two samples from SF-4A clearly respond to the isotopically light precipitation that fell during the second half of the monitoring period.

5 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT SBH 6-5 flow zone ( 4.7% and 4.8%, respectively). In both wells, the gradual decrease back to the prestorm d 18 O over the course of the next several days is interpreted to be due to a return to an upward vertical flux of water and recharge of isotopically lighter precipitation that fell during that period. [30] In both locations, the variations in d 18 O indicate that infiltrating precipitation travels along preferential flow paths through the unsaturated saprolite. During the main period of infiltration, the d 18 O at the water table increases to values similar to the d 18 O of water in the storm flow zone. Our interpretation of these data is that the water travels along preferential pathways (relict fractures) through the unsaturated saprolite and that only minor mixing occurs between water in the fracture and water already stored in the saprolite matrix. This interpretation is consistent with the conceptual model of flow and transport in the saprolite on the ORR Numerical Model [31] On the basis of the conceptual model, a two-dimensional numerical model of the unsaturated zone was created using the FRAC3DVS version 3.40 code developed by Therrien and Sudicky [1996]. This code can simulate three-dimensional fluid flow and transport under variably saturated situations in fractured, porous materials. [32] The model domain is 20 cm in the x direction and 250 cm in the z direction (Figure 3). These dimensions were chosen to simulate the geologic setting shown on Figure 1. Boundary conditions on the model were a specified flux across the upper and side boundaries and specified head-on the lower boundary. Since the goal of this study was not to attempt to reproduce the field data, but to explore transport Figure 2. Variations in d 18 O in the storm flow zone and shallow groundwater over the course of a storm event in April May, (a) Precipitation falling during the storm event in mm/hour and the d 18 O of bulk samples of precipitation. (b) The d 18 O composition of water in the storm flow zone mirror the changes in d 18 O in precipitation but are subdued, indicating mixing between newly infiltrated precipitation and water stored in the storm flow zone. (c) The response at the water table is delayed after the start of precipitation. However, the d 18 O increases to a value close to the storm flow zone, indicating that only minor mixing occurs as water flows through the unsaturated saprolite. [29] There is a d 18 O response in the saturated saprolite to the precipitation signal in both wells (Figure 2c). In SW-1, only the port closest to the water table (SW-1D) shows a response to the storm event, and the response is delayed by more than a day after the start of precipitation. However, the d 18 OinSW-1D( 5.1%) is close to the value in the storm flow zone ( 4.7%), suggesting preferential flow through the unsaturated saprolite. In SW-3D, the thinner unsaturated zone results in a d 18 O response in less than a day. The d 18 O in SW-3D begins to increase within a few hours of the start of precipitation and has a d 18 O nearly identical to the storm Figure 3. Physical properties and boundary conditions for the numerical model.

6 SBH 6-6 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT processes in the unsaturated saprolite, some simplifications to the actual field conditions were made. [33] The upper 25 cm were given properties to simulate the storm flow zone. Physical properties, pressure/saturation, and saturation/relative hydraulic conductivity relationships were entered in tabular form from data by Wilson et al. [1992] and Rothschild et al. [1984] and are shown graphically in Figures 3 and 4. These data represent measurements of water retention versus pressure head for core samples tested in the laboratory, field tests of hydraulic conductivity versus pressure head with a tension infiltrometer, and hydraulic conductivity, pressure head, and moisture content measurements from an isolated soil block. The dual-porosity approach was used to simulate flow and transport in the storm flow zone. For this site, the macropores and mesopores, estimated to be between 1% and 5% of the total porosity, are considered to make up the mobile zone. Transfer of solute between the mobile and immobile zones is modeled as a diffusional process. No estimates were available for the first order transfer coefficient of mass between the two zones. To obtain a transfer coefficient, a search of the literature was conducted to ascertain a plausible range of coefficient values and then a number of model runs were made varying the mobile zone porosity and transfer coefficient within the plausible range. The combination of mobile zone porosity (0.03) and transfer coefficient (0.01/day) that best fit the field data was selected for use in all future model runs. [34] The lower 225 cm were assigned properties of the saprolite. Although there is considerable evidence that there are three distinct pore regions in the saprolite, the micropores and mesopores are combined into a single unit in the model that is referred to as the saprolite matrix. Little is known about the spacing and orientation of microfractures, so it would be difficult to represent them realistically in a model. In addition, their representation would have required a considerable increase in computational resources. For these reasons, the matrix in our model represents the two smaller pore regions. [35] The saprolite was modeled as a porous media with a single, 100 mm aperture, vertical fracture running the entire depth of the saprolite (Figure 3). Although the bedding plane dips at 45 at this site, the fracture was assumed to be vertical to simplify the problem. The fracture aperture (100 mm) was chosen based on an estimate of a fracture porosity of 0.1% and a spacing of hydraulically active fractures of 10 cm. [36] From the data sets available for material properties, one set each was chosen to represent the storm flow zone, the saprolite, and the fracture. The pressure/saturation and saturation/relative hydraulic conductivity relationships are shown in Figure 4. The relationships were not actually measured for fractures. However, it is assumed that the fractures dominate the relationships in the saprolite between pressure heads of 0 cm and 10 cm and these values were used for the fractures in this pressure range. At pressures less than 10 cm, a steep linear drop in saturation and relative hydraulic conductivity was assumed down to a minimum relative saturation and hydraulic conductivity of 0.1 and , respectively. The saprolite is assumed to be fully saturated at pressure heads greater than 10 cm and therefore the relative saturation and hydraulic conductivity Figure 4. Relationships between pressure head and percent saturation and percent saturation and relative hydraulic conductivity for the storm flow zone, saprolite, and fractures. (a) The relationship between pressure head and saturation for the storm flow zone, saprolite, and fractures. Note the rapid decrease in saturation in the fracture at pressure heads less than 20 cm. (b) The relationship between saturation and hydraulic conductivity for the storm flow zone, saprolite, and fractures. Note the rapid decrease in hydraulic conductivity in the fracture at a saturation of less than 90%. at a pressure of 10 cm are 1.0. Although it is recognized that unsaturated flow is quite sensitive to changes in the relationships presented in Figure 4, no attempt was made to perform a sensitivity study on these relationships. In addition, the effects of hysteresis are not modeled. The purpose of this modeling was to explore the mechanisms of the transport of solutes between fractures and the surrounding matrix, not to quantify the transport of a specific solute. 5. Observed Versus Model Results [37] A simulation was performed in which the initial and boundary conditions were similar to those of the April May, 1998 storm event described previously. In this simulation, the flux across the upper boundary (precipitation rate) was set at 1.67 mm/h and the other boundary conditions were as described in the previous section. The initial concentration of solute (d 18 O) was set at 6% throughout the domain and the d 18 O of precipitation was 3%. A third type boundary condition was used for solute crossing the upper boundary. After one day of rain, the flux of water

7 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT SBH 6-7 model output were compared in two ways. The first comparison was the timing of observed water level rise and changes in the amount of water crossing the lower boundary (Figures 5c and 5d). Although these quantities cannot be directly compared, the assumption is made that water leaving the bottom of the model would cause a rise in the water table. Water level measurements show that the water table began to rise between 24 and 42 hours after the start of precipitation, while the model shows an increase in the amount of water crossing the lower boundary at 26 hours after the start of precipitation. A second comparison was made between the timing and magnitude of observed d 18 O variations and the modeled d 18 O crossing the lower boundary (Figures 5e and 5f). The field data show that the d 18 O response at the water table begins between 24 and 42 hours after the start of precipitation, while the modeled d 18 O begins to increase at 30 hours after the start of precipitation. At 42 hours, the d 18 O of the sampled groundwater was 5.1% while the modeled d 18 O of the water crossing the lower boundary was 4.7%. Given the simplifications of the model and the differences in amount, timing, and d 18 O of the actual precipitation event compared to the modeled event, we feel that the model s output provides a reasonable match to the field data. Therefore further use of the model to investigate flow and transport in this setting is justified. Figure 5. Observed field data compared to model output. (a) Actual precipitation. (b) Flux of water across the upper boundary (simulated precipitation). (c) Measured rise in water table elevation. (d) Flux of water across the lower boundary. (e) Measured d 18 O near the water table. (f ) Simulated d 18 O of water crossing the lower boundary. across the upper boundary was set to zero and the system was allowed to drain for six days. [38] Figures 5a and 5b illustrate the actual and modeled precipitation rates. Although the actual precipitation rate varied, the modeled precipitation rate was a constant 1.67 mm/h for a period of 1 day. Field observations and 6. Modeling Results and Discussion [39] A series of simulations were performed to evaluate the transport of a solute through the unsaturated zone during wetting and drying cycles. At the beginning of each simulation, the mobile and immobile pores of the storm flow zone were assigned a solute concentration of 3 mg/l. A total of 750 mg of solute was present in the model domain at the beginning of each simulation. The boundary between the storm flow zone and the saprolite shared a set of nodes. As a result, at the beginning of each simulation, about 50 mg of solute was assigned to the uppermost layer of the saprolite and the rest of the solute resided in the storm flow zone. The solute was considered to be conservative. The simulations can be thought of as a range from shorter duration, higher periodicity wetting/drying (Unsat-1) to longer duration, lower periodicity wetting/drying (Unsat-3). Table 1 provides a summary of the wetting and drying frequency for each simulation. In addition to the variably saturated simulations, a saturated steady state flow/transient transport simulation was also performed using the same model domain. Each simulation was run for a total of 28 days and the total flux of water through the domain was the same for all simulations. During the analysis of each simulation, particular attention was paid to the storage of the solute in various components of the unsaturated zone and to solute outflow across the lower boundary. [40] There were only minor differences among the three variably saturated simulations in the mass transported out of the domain, with solute outflow ranging from 8.5% to 10.5% of the initial mass (Figure 6a). During the fully saturated simulation, over 26% of the initial mass flowed across the lower boundary. Despite only small differences in the mass outflow during the variably saturated simulations, there were considerable differences in where the solute mass resided in the two main reservoirs of the unsaturated zone - the immobile pores of the storm flow zone and the matrix pores

8 SBH 6-8 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT Table 1. Summary of Wetting and Drying Cycles for Each Simulation Simulation Name Precipitation Period, days Precipitation Intensity, cm/day Drying Period, days Number of Wetting/Drying Cycles Simulation Length, days Total Flux of Water, cm 3 Unsat Unsat Unsat Sat-1 N/A 0.14 N/A N/A of the saprolite. In the immobile pores of the storm flow zone, the greatest amount of mass remained at the end of the simulation when the frequency of wetting/drying was in the middle of the range that was explored (Unsat-2, Figure 6b). For the saprolite matrix, the largest amount of solute was transported into storage during the simulation that had the highest periodicity of wetting/drying (Unsat-1, Figure 6c). [41] Since the exchange of solute mass between the mobile and immobile pores in the storm flow zone is modeled as a diffusion process, the variations in the removal of mass from the immobile zone pores can be explained in terms of concentration gradients. In the case of the saturated simulation, the mobile pores are constantly being flushed, the concentration gradient is always high, and the greatest amount of mass is removed from the immobile pores over the 28 day period. For the variably saturated simulations, the mobile pores are flushed of solute during periods of precipitation and the concentration gradient between pore regions increases. As the system dries after each period of precipitation, the concentration gradient gradually decreases. For the variably saturated simulations, the greatest amount of solute mass is removed from the immobile pores in the simulation with the most wetting/ drying cycles (Unsat-1, Figure 6b). The rate of mass removal from the immobile zone is fairly constant in Unsat-1, indicating that the concentration gradient remains fairly constant. For the other two variably saturated simulations, the rate of mass removal varies, with the highest rates during and just after precipitation and decreasing to the lowest rate just before the next precipitation event. The least amount of mass is removed from the immobile pores in Unsat-2, the simulation with Figure 6. (opposite) Movement of solute mass through the model domain. (a) The solute mass leaving the domain is much greater for the fully saturated simulations, but there are only minor differences in the mass leaving the domain for the unsaturated simulations. (b) The least amount of solute mass was flushed from the immobile pores of the storm flow zone during the unsaturated simulation that had the intermediate periodicity of wetting/drying cycles, and is a result of having the lowest concentration gradient between the mobile and immobile pores (see text for more detailed explanation). (c) The greatest amount of solute mass enters the saprolite matrix during the simulation that had the highest periodicity of wetting/drying cycles. During any one cycle, more mass enters the matrix from the fracture during wetting than is returned to the fracture during drying.

9 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT SBH 6-9 the lowest periodicity and least amount of time when precipitation is crossing the upper boundary. [42] The amount of mass stored in the saprolite matrix also appears to be a function of the periodicity of precipitation. In the saprolite, advection is the dominant transport process for exchange of mass between the fractures and the matrix. The variations in storage of solute mass in the saprolite matrix can be understood by looking at the direction of flow vectors at various times during a wetting/drying cycle (Figure 7). At the onset of precipitation, water is drawn into the fracture at the boundary with the storm flow zone (Figure 7a). After traveling only a short distance down the fracture, the water encounters a large saturation gradient with the surrounding matrix and is imbibed into the matrix (the wetting front). This process is illustrated by the large horizontal component to the flux vectors in the upper part of the saprolite. Although not shown on Figure 7, the magnitude of the flow vectors is greatest at the wetting front. Through time, the saturation gradient decreases, the flow direction in the fracture and surrounding matrix becomes nearly vertical, and the wetting front migrates further down into the unsaturated zone (Figure 7b). When precipitation stops, the direction of flow reverses and is from the matrix into the fracture throughout the entire domain (Figure 7c). However, the saturation gradient between the matrix and fractures is smaller than during wetting. This difference in saturation gradient results in drying vectors that are up to an order of magnitude smaller than the magnitude of the wetting vectors, and the drying vectors have a much smaller horizontal component. As a result, a greater amount of solute is transported by advection into the matrix during wetting than is transported back into the fracture during drying. As the number of wetting and drying cycles increases for a given time period, the amount of mass stored in the matrix will increase. There is probably some upper limit to the number of cycles for a given time period at which point the storage in the matrix begins to decrease. As the number of cycles increases, the matrix will remain near saturation and advection into the matrix will approach a minimum. This is illustrated by the fully saturated case, where there is little advection into the matrix (Figure 7d) and significantly less solute is stored in the matrix and the solute outflow is greater when compared to the unsaturated simulations (Figures 6a and 6c). [43] The discussion in the preceding two paragraphs points out important differences that could result from modeling the same system with these two modeling approaches on a timescale of hours to days. When using the mobile/immobile approach, the solutes transferred from the mobile pores are assumed to mix with the entire reservoir of immobile pores. The rate of solute transfer between pore regions is dependent on the mass transfer coefficient and the concentration gradient. Since the volume of immobile pores are usually an order of magnitude larger than the mobile pores, the transferred solute will cause only a small decrease in the concentration in the immobile pores and the concentration gradient will remain large. If the preferential pathways are closely spaced and matrix blocks are small enough, for example in some soils, mixing with the entire immobile reservoir may be a valid assumption. However, in most fractured rock settings, the matrix blocks are large enough so that only a fraction of the matrix water Figure 7. Vectors indicating the direction and magnitude of water flux in the unsaturated zone. (a) During initial stages of wetting, water from the storm flow zone is drawn into the fracture and then is strongly imbibed into the matrix as indicated by the flux vectors with a large horizontal component. (b) During the latter stages of wetting, the wetting front has migrated deeper and flux vectors in the matrix above the wetting front become nearly vertical. (c) During drying, the direction of the flux vectors throughout the entire unsaturated zone are from the matrix into the fracture. However, the horizontal component and overall magnitude of the vectors is less than during wetting. (d) The flux vectors for a fully saturated, steady state simulation are vertical in both the fracture and matrix except near the storm flow zone/saprolite boundary where water is drawn into the fracture.

10 SBH 6-10 VAN DER HOVEN ET AL.: MODELING UNSATURATED FLOW AND TRANSPORT actively mixes with water in the fractures over short timescales. When fractures are explicitly defined, solute that is transferred from the fractures to the matrix by advection or diffusion mixes only with the pores immediately surrounding the fracture. For the same transfer of solute as in the mobile/immobile situation, the concentration immediately surrounding the fracture will experience a much greater increase in concentration and there will be a significant drop in concentration gradient. As a result, advective transfer of solute from the fracture to the matrix decreases the concentration gradient (and diffusive transfer) from the fracture to the matrix. This observation is in agreement with the conclusions of Gwo et al. [1995]. 7. Implications for Solute Transport [44] The major implication of this investigation on unsaturated solute transport in geologic materials with preferential pathways is that it is important to evaluate the transient nature of wetting and drying cycles. Given the same total water flux, transport of solutes into different components of the unsaturated zone can vary significantly when the periodicity of precipitation changes. [45] These variations are important when evaluating contaminant transport and remediation strategies. For example, if a radioactive contaminant were released at the surface, its unsaturated transport characteristics would depend on, among other things, the timing and intensity of precipitation thereafter. In a climate with infrequent but intense rainfall, the radioactive contaminant may remain in the shallow subsurface and within the root zone for a long period of time. In a climate with more frequent rain of lower intensity, the radioactive contaminant may be transported below the root zone and stored in the deeper unsaturated zone. In the first instance, the remedial alternative may be to excavate and remove the contaminant as soon as possible. In the second instance, assuming a short half-life, a more reasonable alternative may be to let the contaminant migrate into the deeper subsurface by natural precipitation or irrigation applied at an appropriate frequency and to let radioactive decay reduce contaminant concentrations to acceptable levels. [46] The advection between the matrix and fracture also has implications on contaminants whose transport is retarded by precipitation as a mineral or by adsorption. The transport of these contaminants is controlled primarily by water chemistry. The modeling results and field data indicate that there may be significant temporal chemical variability in the matrix due to advective exchange between the matrix and the fracture. If a contaminant precipitates in the matrix near the fracture, the introduction of water during a storm event, which is chemically undersaturated with respect to this mineral, may cause dissolution. The subsequent reversal of the hydraulic gradient during the drying period after the storm may transport the contaminant into the fracture. The same may be true for adsorbed contaminants. The introduction of water with lower ph or total dissolved solids (TDS) into the matrix during wetting may cause contaminants to desorb and be transported into the fracture during the drying period. [47] There are also implications for the analysis of mineral weathering and dissolution rates. The rate at which minerals weather is dependent on the exposed surface area of the minerals as well as the degree to which the water chemistry is in thermodynamic equilibrium with minerals. The advective exchange between the fracture and matrix affects both the exposed surface area and the thermodynamic equilibrium. By pumping water into and out of the matrix during wetting/drying cycles, the minerals in the matrix come in contact with low TDS and ph waters that promote dissolution. Some of the dissolved ions are flushed into the fractures where transport velocities are high. Calculations of mineral dissolution rates should take into consideration the surface area in the fractures and matrix that are advectively flushed during a wetting/drying cycle, as well as the temporal variations in chemistry. [48] In addition to impacts on contaminant transport and mineral weathering, the results of this investigation can also be applied to agriculture and irrigation. For example, after the application of fertilizer, it is desirable that the fertilizer remain in the root zone for as long as possible. According to these modeling results, fertilizer would remain in the root zone for the longest period of time if a minimum number of wetting and drying cycles are applied by irrigation. More efficient utilization of fertilizers would reduce the amount that needs to be applied to maximize yield and also minimize the potential impact on underlying groundwater. 8. Conclusions [49] The primary conclusions from the simulations relate to the use of explicitly defined fractures in a setting (such as saprolite) where there is high matrix porosity and permeability. During wetting/drying cycles, there is significant advective exchange between the fracture and adjacent matrix. Water and solutes are advectively transported from the fractures into the matrix during wetting, and then back into the fractures as the system dries. This advective flushing of the matrix surrounding a fracture has a number of implications for solute transport in the unsaturated zone. [50] There may be an optimum frequency of wetting/ drying cycles that results in the largest amount of solute storage in the matrix. During wetting, the direction of water flow has a strong horizontal component from a fracture into the matrix and solute is transported a relatively large distance into the matrix. During drying, the flow direction is back into the fracture. However, the flow direction is more vertical than during wetting and the magnitude of the flux is lower. Therefore more solute is transported into the matrix during wetting than is returned during drying. We hypothesize that as the wetting/drying frequency increases past some maximum, advective flow between the fracture and matrix begins to decrease and the system behaves more like the fully saturated simulations where diffusion is the dominant process for transport of solute into the matrix. [51] The relationship of wetting/drying frequency to storage in various components of the unsaturated zone has implications for a number of processes. When evaluating unsaturated zone contaminant transport, it is important to consider natural periodicity of precipitation in order to predict storage within the matrix and exchange between preferential pathways and the matrix. In engineered settings like remediation and agriculture, the periodicity can be adjusted to retain the solute of interest in a particular reservoir for the longest period of time or to flush it from the system as quickly as possible.