Hydruulic gradients modulate non-Fickian transport in heterogeneous porous media

Fluid flow and contaminant transport in heterogeneous porous media is critical in many applications from sustainable groundwater quality management to radioactive waste disposal and water filtration. Accurate contaminant transport modeling is challenged by anomalous (non-Fickian) transport, characterized by early breakthrough, long tailing, non-Gaussian or multipeaked plume shapes, and non-linear scaling of the mean square displacement.

In regional alluvial aquifers, it is unknown how emerging nonpoint source contamination (e.g., salts and nitrates) will interact with aquifer heterogeneity and shitiing hydraulic gradients. Pumping and recharge for irrigation significantly shift the magnitude and direction of regional hydraulic gradients but how variations in the hydraulic gradients, particularly direction, impact non-Fickian transport remains, to our knowledge, unexplored. We investigate the influence of hydraulic gradients on non-Fickian transport with a simple concept, the vertical to horizontal gradient ratio (VHGR).

Large VHGR is predominately vertical flow and flow is increasingly horizontal as VHGR decreases toward 1.

In horizontally stratified clastic sedimentary deposits, horizontal is commonly 100 to 10,000 times greater than vertical . In these systems, groundwater pumping at depth and irrigation recharge from above create very large VHGR (e.g., 100). When pumping and/or recharge is decreased, VHGR values typical of pre-development conditions (e.g., 1 to 10) can prevail. This works shows that the significance of non-Fickian transport processes depends greatly on these differing hydraulic gradient forcings.

We test three hypothetical VHGR scenarios representing intensive to reduced pumping (VHGR = 100, 10, 1) in a highly stratified heterogeneous alluvial aquifer. We find that lower VHGR in our study site results in increased non-Fickian behavior, illustrated by increased spreading in longitudinal and transverse directions, and increased mass holdback and tailing. Thus, regional-scale nonpoint source contaminant management under reduced pumping and recharge may need to account for increased non-Fickian transport (i.e., longer contaminant residence and greater spatial spreading) than previously considered. Conversely, under conditions of strong vertical gradients that drive mass more or less straight through confining beds rather than allowing mass to find preferential flowpaths around them, the ADE may be a very good approximation of the transport physics.

Transcript

1. Figure 4 (BOTTOM): Mean squared displacement, σ2, in the longitudinal (along y’), transverse 1 and 2 (ver�cal and horizontal rela�ve to y’ respec�vely) direc�ons. σ2 in direc�on j is: where is the average over all par�cles. As VHGR decreases: (a) increased spa�al and temporal vari- ance is observed in all direc�ons, and (b) late �me longitudinal and transverse 1 σ2 are more subdiffu- sive and show pre-asympto�c behavior. Sub- and superdiffusion in direc�on j are defined as nonlinear scaling of σ2 with respect to time, and indicate anomalous transport (left). Hydraulic gradients modulate non-Fickian transport in heterogeneous porous media Rich Pauloo * | Graham Fogg | Zhilin Guo | Christopher Henri [1] Univeristy of California, Davis | [2] South University of Science and Technology of China | * corresponding author H21L-1912 AGU Fall Meeting 2019 San Francisco, CA 1. ABSTRACT 2. FLOW & TRANSPORT IN A HETEROGENEOUS ALLUVIAL AQUIFER UNDER VARYING VHGR CORE QUESTION How does varying hydraulic gradient direc�on affect anomalous transport and applicability of the advec�on dispersion equa�on (ADE)? Fluid flow and contaminant transport in heteroge- neous porous media is cri�cal in many applica�ons from sustainable groundwater quality management [1] to radioac�ve waste disposal [2] and water filtra- �on [3]. Accurate contaminant transport modeling is challenged by anomalous (non-Fickian) transport, characterized by early breakthrough, long tailing, non-Gaussian or mul�peaked plume shapes, and non- linear scaling of the mean square displacement [4]. In regional alluvial aquifers, it is unknown how emerg- ing nonpoint source contamina�on (e.g., salts and ni- trates) will interact with aquifer heterogeneity and shi�ing hydraulic gradients. Pumping and recharge for irriga�on significantly shi� the magnitude and direc- �on of regional hydraulic gradients but how varia�ons in the hydraulic gradients, par�cularly direc�on, impact non-Fickian transport remains, to our knowl- edge, unexplored. We inves�gate the influence of hy- draulic gradients on non-Fickian transport with a simple concept, the ver�cal to horizontal gradient ra�o (VHGR): Large VHGR is predominately ver�cal flow and flow is increasingly horizontal as VHGR decreases toward 1. In horizontally stra�fied clas�c sedimentary deposits, horizontal K’ is commonly 100 to 10,000 �mes great- er than ver�cal K’. In these systems, groundwater pumping at depth and irriga�on recharge from above create very large VHGR (e.g., 100). When pumping and/or recharge is decreased, VHGR values typical of pre-development condi�ons (e.g., 1 to 10) can pre- vail. This works shows that the significance of non-Fickian transport processes depends greatly on these differing hydraulic gradient forcings. We test three hypothe�cal VHGR scenarios represent- ing intensive to reduced pumping (VHGR = 100, 10, 1) in a highly stra�fied heterogeneous alluvial aquifer [5]. We find that lower VHGR in our study site results in increased non-Fickian behavior, illustrated by in- creased spreading in longitudinal and transverse di- rec�ons, and increased mass holdback and tailing. Thus, regional-scale nonpoint source contaminant management under reduced pumping and recharge may need to account for increased non-Fickian trans- port (i.e., longer contaminant residence and greater spa�al spreading) than previously considered. Con- versely, under condi�ons of strong ver�cal gradients that drive mass more or less straight through confin- ing beds rather than allowing mass to find preferen- �al flowpaths around them, the ADE may be a very good approxima�on of the transport physics. VHGR varies by orders of magnitude in heavily managed groundwater systems due to pumping and recharge. We show that decreasing VHGR in our study site increases non-Fickian transport, illustrated by increased--and non-Gaussian--mass holdback along the ver�cal di- rec�on (Figure 3), and increased spreading and preasympto�c behavior in the second spa�al moments of the plume (Figure 4) along the mean flow direc�on. At high VHGR (100 and 10), strong advec�on forces par�cle trajectories along nearly ver�cal paths (Figure 1) and straight through high and low-K zones, evidenced by higher early-�me muddy sand and paleosol propor�ons (Figure 2). Significant pumping for irriga�on has depleted global groundwater reserves [8-9], and established strong ver�cal hydraulic gradients due to pumping at depth (i.e., high VHGR). Sustainable groundwater management regimes that reduce pumping and increase recharge will effec�vely decrease VHGR. Thus, regional-scale groundwater quality models will need to account for increased non-Fickian transport (i.e, longer contaminant residence and greater spa�al spreading) under these condi�ons. Conversely, if ver�cal gradients are sufficiently strong, the ADE may be a very good approxima�on of physics because the mass may be driven more or less straight through the aqui- tards. When the ver�cal gradients are weaker, mass can flow around the aquitards, triggering both preferen�al flow through high-K pathways and transverse dispersion and diffusion into and out of the aquitards, augmen�ng early- and late-�me tailing. This work was supported by NSF DGE # 1069333, the Climate Change, Water, and Society IGERT, to UC Davis, and by the U.S./China Clean Energy Research Center for Water-Energy Technologies (CERC-WET). References [1] Weissmann, Gary S., et al. "Dispersion of groundwater age in an alluvial aquifer system." Water resources research 38.10 (2002): 16-1. [2] Berkowitz, Brian, and Harvey Scher. "Theory of anomalous chemical transport in random fracture networks." Physical Review E 57.5 (1998): 5858. [3] Ellio�, M. A., et al. "Reduc�ons of E. coli, echovirus type 12 and bacteriophages in an intermit- tently operated household-scale slow sand filter." Water research 42.10-11 (2008): 2662-2670. [4] Kang, Peter K., et al. "Pore-scale intermi�ent velocity structure underpinning anomalous transport through 3-D porous media." Geophysical Research Le�ers 41.17 (2014): 6184-6190. [5] Weissmann, G.S., S.F. Carle, and G.E. Fogg. 1999. Three dimensional hydrofacies modeling based on soil surveys and transi�on probability geosta�s�cs. Water Resources Research 35, no. 6: 1761–1770. [6] Harbaugh, Arlen W., et al. "MODFLOW-2000, The U. S. Geological Survey Modular Ground-Water Mod- el-User Guide to Modulariza�on Concepts and the Ground-Water Flow Process." Open-file Report. U. S. Geological Survey 92 (2000): 134. [7] Fernàndez-Garcia, Daniel, Tissa H. Illangasekare, and Harihar Rajaram. "Differences in the scale-dependence of dispersivity es�mated from temporal and spa�al moments in chemically and physically heterogeneous porous media." Advances in water resources 28.7 (2005): 745-759. [8] Famiglie�, James S. "The global groundwater crisis." Nature Climate Change 4.11 (2014): 945. [9] Gleeson, Tom, et al. "Water balance of global aquifers revealed by groundwater footprint." Nature 488.7410 (2012): 197. y 90 m 50x ver�cal exaggera�on x y z VHGR = 100 VHGR = 10 VHGR = 1 mean flow direction, y’ z VHGR 3. TRANSPORT IS INCREASINGLY NON-FICKIAN AS VHGR DECREASES VHGR = 100 VHGR = 10 VHGR = 1 no flow on sides Figure 3 (TOP): Mass displacement along the z direc�on at t₂₅, t₅₀ and t₇₅ of the cumula�ve breakthrough curve (right). Ver�cal dashed lines are mean mass loca�ons at �me n predicted by the mean ver�cal velocity via Darcy’s law: . Mass is increasingly held back with de- creasing VHGR, resul�ng in greater spreading along the longitudinal and transverse direc�ons (Figure 4), and increased tailing measured at a control plane at bo�om of the model (Figure 1). �me C/C0 1.00 0.75 0.50 0.25 0.00 t₅₀ t₇₅ t₂₅ rpauloo@ucdavis.edu @RichPauloo richpauloo.com Acknowledgements longitudinal transverse 1 transverse 2 4. DISCUSSION increasing hydraulic conduc�vity Figure 1 (TOP): From le� to right, 3 representa�ve par�cle trajectories for VHGR = 100, 10, and 1. Par�cle trajec- tories are colored by the hydraulic conduc�vity of the hydrofacies they reside in at the �me of the snapshot. The alluvial aquifer T-PROGS domain [5] connects in 3D via sand and gravel lenses. Characteris�c length scales in xy are 2-3 orders of magnitude greater than those in z. Flow and transport are solved with MODFLOW [6] and the random walk code RW3D [7]. Figure 2 (LEFT): Mean Lagrangian hy- drofacies propor�ons converge on the actual propor�ons (black dashed line) over increasing �me scales as VHGR decreases. Rela�vely higher muddy sand and paleosol propor�ons for VHGR = 100 and 10 suggest advec- �on-dominated transport. As VHGR decreases, late �me oscilla�ons in hy- drofacies propor�on--caused by diffu- sion-dominated trajectories that ex- change mass between facies--are in- creasingly common. Time is rescaled by where and are the characteris�c length and mean veloci- ty along mean flow direc�on y’. τ VHGR = 100 VHGR = 10 VHGR = 1 gravel sand muddy sand mud paleosol 10−3 10−2 10−1 100 101 102 103 104 10−3 10−2 10−1 100 101 102 103 104 10−3 10−2 10−1 100 101 102 103 104 0.03 0.06 0.09 0.33 0.36 0.39 0.42 0.18 0.21 0.24 0.27 0.21 0.24 0.27 0.30 0.06 0.09 0.12 time , log(t τ A ) hydrofacies proportion 10−5 10−3 10−1 101 103 105 10−5 10−3 10−1 101 103 105 10−5 10−3 10−1 101 103 105 100 102 104 106 108 1010 1012 1014 1016 time , log(t τ A ) spatial variance , log(σ2) VHGR 1 10 100 0.75 0.97 0.93 0.75 0.98 1.09 0.93 1 1 1 1 1.01 1 1 1 1 1.88 1 1 1.45 instantaneous pulse injec�on of 10,000 par�cles 10 m below water table at t = 0 0 25 50 75 100 0 25 50 75 100 0 25 50 75 100 0.000 0.005 0.010 0.015 0.00 0.01 0.02 0.00 0.01 0.02 0.03 z displacement (m) density t₅₀ t₇₅ t₂₅ d₅₀ d₇₅ d₂₅ t₅₀ t₇₅ t₂₅ t₅₀ t₇₅ t₂₅ d₅₀ d₇₅ d₂₅ d₅₀ d₇₅ d₂₅ increasing hydraulic conduc�vity �me σ2 superdiffusion normal diffusion subdiffusion Fickian non-Fickian C �me 15 km 12.6 km 63 x 75 x 201 cells in xyz 200 m x 200 m x 0.5 m in xyz dispersivity (α) = (xyz discre�za�on) / 100 no flow on sides control plane in xy at z = 0 (model bo�om) specified constant head on top and back faces maintain the VHGR