{"id":226,"date":"2020-11-19T22:06:40","date_gmt":"2020-11-19T22:06:40","guid":{"rendered":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/chapter\/diffusive-exchange-with-aquitards\/"},"modified":"2022-09-20T16:07:32","modified_gmt":"2022-09-20T16:07:32","slug":"diffusive-exchange-with-aquitards","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/chapter\/diffusive-exchange-with-aquitards\/","title":{"raw":"4.2 Diffusive Exchange with Aquitards","rendered":"4.2 Diffusive Exchange with Aquitards"},"content":{"raw":"Geologic systems are often a series of layers of alternating high (aquifers) and low (aquitards) hydraulic conductivity. In such systems, groundwater primarily flows horizontally along the aquifer layers with some vertical leakage into or out of overlying and underlying aquitards. Several studies have shown that leakage through aquitards can affect tracer concentrations in aquifers (e.g., Love et al., 1993). Even when the leakage is hydraulically negligible, diffusive exchange between aquifers and aquitards has the potential to affect tracer concentrations. Water in the aquitards is often older than water in the aquifers, and since concentrations of most tracers decrease with age, concentrations in the aquitard are likely to be lower than those in the aquifer. Diffusive exchange between the aquifer and the aquitard will therefore cause a reduction in the concentration in the aquifer, and hence result in tracer ages within the aquifer that will be older than advective water ages. An analytical solution for a 20 m thick aquifer sandwiched between aquitards showed that the apparent groundwater age in the aquifer estimated using 14<\/sup>C would exceed the hydraulic age by between 50 percent and 180 percent for aquitard diffusion coefficients between 10-<\/sup>2<\/sup> and 10-<\/sup>3<\/sup> m2<\/sup>\/y, but the effect would be less than 20 percent for a 200 m thick aquifer (Sudicky and Frind, 1981; Figure 47). (The reader should be aware that diffusion coefficients can be expressed in two different ways. The above uses the formulation D<\/em> = D<\/em>0<\/sub>\u03b8\u03c4<\/em>, where D<\/em>0<\/sub> is the free solution diffusion coefficient, \u03b8<\/em> is porosity and \u03c4<\/em> is tortuosity. Some other papers use the term diffusion coefficient to refer simply to D<\/em>0<\/sub>\u03c4<\/em>, and so the diffusion coefficient does not specifically include the porosity term.) For radioactive tracers such as 14<\/sup>C, simple approaches are available for correcting for this effect (Sudicky and Frind, 1981; Sanford, 1997).\r\n\r\n[caption id=\"attachment_247\" align=\"alignnone\" width=\"845\"]\"Figure Figure <\/strong>47<\/strong> - The effect of aquitard diffusion on apparent 14<\/sup>C ages in an aquifer for a 20 m thick aquifer sandwiched between two aquitards. Apparent 14<\/sup>C ages are greater than hydraulic ages by 58 percent for an aquitard diffusion coefficient of D<\/em> = 0.001 m2<\/sup>\/y and by 180 percent for D<\/em> = 0.01 m2<\/sup>\/y. The model also assumes an aquifer porosity of 0.35, aquitard porosity of 0.5 and negligible dispersivity. Although the plot assumes a groundwater velocity of 3.65 m\/y, the relative difference between apparent 14<\/sup>C age and hydraulic age is relatively insensitive to the groundwater velocity, and mostly determined by the aquitard diffusion coefficient, aquifer thickness, and the ratio between the aquitard and aquifer porosity. Modified from Sudicky and Frind (1981).[\/caption]\r\n\r\nDiffusive exchange between aquifers and aquitards will have a smaller effect on event marker tracers (such as CFCs, SF6<\/sub>, and 3<\/sup>H) because the extent of tracer diffusion over the timescale that the tracer has been present in groundwater is likely to be relatively small. The distance over which diffusion will occur can be approximated by Equation 14.\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle x=\\sqrt{4Dt}[\/latex]<\/td>\r\n(14)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n
x<\/em><\/td>\r\n=<\/td>\r\ndistance (L)<\/td>\r\n<\/tr>\r\n
D<\/em><\/td>\r\n=<\/td>\r\ndiffusion coefficient of the tracer (L2<\/sup>\/T)<\/td>\r\n<\/tr>\r\n
t<\/em><\/td>\r\n=<\/td>\r\nTime (T)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAssuming D<\/em> = 10-<\/sup>2<\/sup> to 10-<\/sup>3<\/sup> m2<\/sup>\/y and t<\/em> = 70 years gives x<\/em> = 0.5 \u2013 1.7 m. Therefore, diffusive exchange between aquifers and aquitards is only likely to be significant for these tracers if aquifer thicknesses are much less than 10 m.\r\n\r\nHelium differs from most other tracers, in that its concentration increases with age. Thus, diffusive exchange with aquitards usually increases the He concentration in the aquifer, although this still causes an apparent increase in age (like with other tracers). As concentrations of helium increase linearly with time, concentrations within thick aquitards can become very high, and so diffusion of helium from aquitards can have a pronounced effect on ages in confined aquifers.\r\n\r\nThere have been several studies that have obtained core samples through aquitards, and estimated rates of aquitard leakage from isotope concentrations in aquitard pore water (e.g., Hendry et al., 2004; Mazurek et al., 2011). These studies can distinguish between purely diffusive and advective transport through aquitards and hence allow us to better quantify the effect of aquifer-aquitard interaction on environmental tracer concentrations in aquifers.","rendered":"

Geologic systems are often a series of layers of alternating high (aquifers) and low (aquitards) hydraulic conductivity. In such systems, groundwater primarily flows horizontally along the aquifer layers with some vertical leakage into or out of overlying and underlying aquitards. Several studies have shown that leakage through aquitards can affect tracer concentrations in aquifers (e.g., Love et al., 1993). Even when the leakage is hydraulically negligible, diffusive exchange between aquifers and aquitards has the potential to affect tracer concentrations. Water in the aquitards is often older than water in the aquifers, and since concentrations of most tracers decrease with age, concentrations in the aquitard are likely to be lower than those in the aquifer. Diffusive exchange between the aquifer and the aquitard will therefore cause a reduction in the concentration in the aquifer, and hence result in tracer ages within the aquifer that will be older than advective water ages. An analytical solution for a 20 m thick aquifer sandwiched between aquitards showed that the apparent groundwater age in the aquifer estimated using 14<\/sup>C would exceed the hydraulic age by between 50 percent and 180 percent for aquitard diffusion coefficients between 10–<\/sup>2<\/sup> and 10–<\/sup>3<\/sup> m2<\/sup>\/y, but the effect would be less than 20 percent for a 200 m thick aquifer (Sudicky and Frind, 1981; Figure 47). (The reader should be aware that diffusion coefficients can be expressed in two different ways. The above uses the formulation D<\/em> = D<\/em>0<\/sub>\u03b8\u03c4<\/em>, where D<\/em>0<\/sub> is the free solution diffusion coefficient, \u03b8<\/em> is porosity and \u03c4<\/em> is tortuosity. Some other papers use the term diffusion coefficient to refer simply to D<\/em>0<\/sub>\u03c4<\/em>, and so the diffusion coefficient does not specifically include the porosity term.) For radioactive tracers such as 14<\/sup>C, simple approaches are available for correcting for this effect (Sudicky and Frind, 1981; Sanford, 1997).<\/p>\n

\"Figure
Figure <\/strong>47<\/strong> – The effect of aquitard diffusion on apparent 14<\/sup>C ages in an aquifer for a 20 m thick aquifer sandwiched between two aquitards. Apparent 14<\/sup>C ages are greater than hydraulic ages by 58 percent for an aquitard diffusion coefficient of D<\/em> = 0.001 m2<\/sup>\/y and by 180 percent for D<\/em> = 0.01 m2<\/sup>\/y. The model also assumes an aquifer porosity of 0.35, aquitard porosity of 0.5 and negligible dispersivity. Although the plot assumes a groundwater velocity of 3.65 m\/y, the relative difference between apparent 14<\/sup>C age and hydraulic age is relatively insensitive to the groundwater velocity, and mostly determined by the aquitard diffusion coefficient, aquifer thickness, and the ratio between the aquitard and aquifer porosity. Modified from Sudicky and Frind (1981).<\/figcaption><\/figure>\n

Diffusive exchange between aquifers and aquitards will have a smaller effect on event marker tracers (such as CFCs, SF6<\/sub>, and 3<\/sup>H) because the extent of tracer diffusion over the timescale that the tracer has been present in groundwater is likely to be relatively small. The distance over which diffusion will occur can be approximated by Equation 14.<\/p>\n\n\n\n
<\/td>\n\"\displaystyle x=\sqrt{4Dt}\"<\/td>\n(14)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n
x<\/em><\/td>\n=<\/td>\ndistance (L)<\/td>\n<\/tr>\n
D<\/em><\/td>\n=<\/td>\ndiffusion coefficient of the tracer (L2<\/sup>\/T)<\/td>\n<\/tr>\n
t<\/em><\/td>\n=<\/td>\nTime (T)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Assuming D<\/em> = 10–<\/sup>2<\/sup> to 10–<\/sup>3<\/sup> m2<\/sup>\/y and t<\/em> = 70 years gives x<\/em> = 0.5 \u2013 1.7 m. Therefore, diffusive exchange between aquifers and aquitards is only likely to be significant for these tracers if aquifer thicknesses are much less than 10 m.<\/p>\n

Helium differs from most other tracers, in that its concentration increases with age. Thus, diffusive exchange with aquitards usually increases the He concentration in the aquifer, although this still causes an apparent increase in age (like with other tracers). As concentrations of helium increase linearly with time, concentrations within thick aquitards can become very high, and so diffusion of helium from aquitards can have a pronounced effect on ages in confined aquifers.<\/p>\n

There have been several studies that have obtained core samples through aquitards, and estimated rates of aquitard leakage from isotope concentrations in aquitard pore water (e.g., Hendry et al., 2004; Mazurek et al., 2011). These studies can distinguish between purely diffusive and advective transport through aquitards and hence allow us to better quantify the effect of aquifer-aquitard interaction on environmental tracer concentrations in aquifers.<\/p>\n","protected":false},"author":1,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-226","chapter","type-chapter","status-publish","hentry"],"part":229,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":10,"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/226\/revisions"}],"predecessor-version":[{"id":477,"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/226\/revisions\/477"}],"part":[{"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/229"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/226\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/wp\/v2\/media?parent=226"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapter-type?post=226"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=226"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/introduction-to-isotopes-and-environmental-tracers-as-indicators-of-groundwater-flow\/wp-json\/wp\/v2\/license?post=226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}