Hyperfiltration‐induced fractionation of lithium isotopes: Ramifications relating to representativeness of aquifer sampling

Abstract

A 10‐mM LiCl solution was hydraulically forced through a 0.3‐cm‐thick smectite membrane at a constant solution flux in order to depict the chemical and isotopic evolution of analogous hyper filtration cells in the subsurface. At steady state (∼19 days) there was, relative to the input solution, a measured 12% buildup of solute within the entire cell and a calculated 248% solute increase at the clay/solution interface. The maximum depletion of 7Li (about 13‰ relative to the input solution) was calculated to occur about 1 cm away from the membrane out into the high‐pressure reservoir. When scaled to realistic solution fluxes in natural systems, the position of maximum fractionation would occur meters away from a shale/aquifer contact. A steady state hyperfiltration model indicates that a solute's heavy isotopic species will always be depleted on the high‐pressure side of a clay membrane, a prediction corroborated not only by the Li experiment but also by previous hyperfiltration studies involving stable isotopes of C and Cl. The extent of fractionation increases with higher values of the membrane's reflection coefficient, σ. In the experiment a σ of 0.55 for the 90% porosity clay membrane yielded these results. Because shales have substantially lower porosities with attendant higher values of σ, we conclude that the hyperfiltration phenomenon in the subsurface may result in sampling of waters that are not chemically and isotopically representative of the formation penetrated by the well.

Permselective Membrane Fouling During Azo Dye Wastewater Treatment

“…(3) can be ignored if length of the solution column is large relative to the ratio (D/Jv) [4]. Equation (4a) is still continuous over a finite interval.…”

“…Solving Eq. (2a) for the following boundary conditions C(0, t) = C(0,t) for t F 0; C(x, 0) = 0 for x F 0; C(v, t) = 0 for t F0, and assuming steady state Jv yields [4,10]:…”

“…www.clean-journal.com brane, solute builds up at the high-pressure interface, so that the concentration change with time is a function of the advective flux (J v ), the diffusion coefficient of the solute (D), and the position of interest (x) within the high-pressure interface where x = 0 [4,10]. Solving Eq.…”

“…For porous media having no permselective properties (like highly porous sandstones), r = 0 and x has the maximal value of c s J v À J s ð Þ =Dp. The parameters r, LP, and x, also referred to as phenomenological coefficients, control the kinetic responses of the membrane in different ways [4]. From this geometry the mass balance equation within the boundary layer for an imperfect membrane and a closed system (solute-fixed or membrane-fixed frame of reference) yields the following advectivediffusive differential equations [4,10,12]:…”

Modified Reverse Osmosis System for Treatment of Produced Waters

“…Many studies have experimentally confirmed the ability of clays to act as semi-permeable membranes (Marshall, 1948;Wyllie, 1948Wyllie, , 1949Kemper, 1960Kemper, , 1961Berstein, 1960;McKelvey and Milne, 1963;Milne et al, 1963;Milne et al, 1964;Olsen, 1969Olsen, ,1972Kemper and Rollins, 1966;Kharaka and Berry, 1973;Coplen and Hanshaw, 1973;Srivastava and Jain, 1975;Kharaka and Smalley, 1976;Fritz and Marine, 1983;Benzel and Graf, 1984;Fritz and Eady, 1985;Campbell, 1985;Haydon and Graf, 1986;Demir, 1988;Fritz et al, 1987;Fritz and Whitworth, 1994;. Ishiguro, et al (1995) tested a bentonite membrane formed by smearing some bentonite clay between two pieces of filter paper in a simple cross-flow configuration and achieved NaCl rejections as high as 90.3%.…”