Reaction-diffusion, pore water profile

As we saw with the steady-state water-column application of the one-dimensional advection-diffusion-reaction equation (Eq. 4.14), the basic shapes of the vertical concentration profiles can be predicted from the relative rates of the chemical and physical processes. Figure 4.21 provided examples of profiles that exhibit curvatures whose shapes reflected differences in the direction and relative rates of these processes. Some generalized scenarios for sedimentary pore water profiles are presented in Figure 12.7 for the most commonly observed shapes. 

A two-dimensional transport-reaction model incorporating both radial transport into burrows and vertical diffusion is presented. This model is capable of predicting both the form and magnitude of pore-water profiles extraordinarily well at all stations. A one-dimensional model in which an effective transport coefficient is used to account for the influence of reworking and burrow construction on solute movement is far less satisfactory in predicting the observed profiles. 

Fig. 15.6 Model results of the mutual decomposition of sulfate and methane as a 1 1-reaction in a diffusion controlled pore water profile. Modeling was performed according to the Press-F9-method using the standard software Excel . Details pertaining to the model and the calibration with data from a measured pore-water profile obtained from an upwelling area off Namibia (Niewohner et al. 1998) are discussed in the text.

Some examples of pore water profiles are illustrated in Figure 3, drawn schematically to illustrate the range of behavior that may be observed when different factors are important. Several assumptions have been made in drawing these profiles. One is that they represent steady-state, relative to the sediment-water interface. A second is that the diffusivity is not depth-dependent. A third is that any reactions go to zero at infinite depth. A fourth is that advection has been ignored. The shape of a profile is a clue to interpret what factors are important and their depth... 

The elements deposited within the sediment matrix show that mobilization processes may be occurring in the upper layers. At Station SIN 3, figure 4d for example, the element deposited (pg-cm-2) in the topmost layers decreases, often much more than in the concentration (Mg g 1). This may be due to organic matter decomposition and/or to environmental chemical reactions of solubility and precipitation of the given element. The metal must have been removed rapidly from the water column since the sediment concentration is shown to decrease rapidly with distance from the shipyard (Stations SIN 3 and SIN 2). Lead may not be mobilized significantly after deposition since any diffusion in the pore water would tend to "smooth" the concentration profile with time. 

Reaction rates of nonconservative chemicals in marine sediments can be estimated from porewater concentration profiles using a mathematical model similar to the onedimensional advection-diffusion model for the water column presented in Section 4.3.4. As with the water column, horizontal concentration gradients are assumed to be negligible as compared to the vertical gradients. In contrast to the water column, solute transport in the pore waters is controlled by molecular diffusion and advection, with the effects of turbulent mixing being negligible. 

The profile of Mg2+ in Figure 8.25 indicates downward diffusion of this constituent into the sediments. Mass balance calculations show that sufficient Mg2+ can diffuse into the sediments to account for the mass of organogenic dolomite formed in DSDP sediments (Baker and Bums, 1985 Compton and Siever, 1986). In areas of slow sedimentation rates, the diffusive flux of Mg2+ is high, and the pore waters have long residence times. Dolomites form under these conditions in the zone of sulfate reduction, are depleted in 13c, and have low trace element contents. With more rapid sedimentation rates, shallowly-buried sediments have shorter residence times, and dolomites with depleted 13C formed in the sulfate-reduction zone pass quickly into the underlying zone of methanogenesis. In this zone the DIC is enriched in 13C because of the overall reaction... 

Many such studies of sedimentary phosphorus profiles, also incorporating pore water measurement of soluble reactive phosphate, have demonstrated that redox-controlled dissolution of iron (hydr)oxides under reducing conditions at depth releases orthophosphate to solution. This then diffuses upwards (and downwards) from the pore water maximum to be re-adsorbed or co-precipitated with oxidized Fe in near-surface oxic sections. The downwards decrease in solid phase organic phosphorus indicates increasing release of phosphorus from deposited organic matter with depth, some of which will become associated with hydrous iron and other metal oxides, added to the pool of mobile phosphorus in pore water or contribute to soluble unreactive phosphorus . The characteristic reactions involving inorganic phosphorus in the sediments of Toolik Lake, Alaska, are shown in... 

Sedimentary denitrification rates have been estimated from measured pore-water solute profiles using diagenetic models, determined direcdy via sediment incubation both on deck and in situ, and determined from N-incubation techniques. Sedimentary diagenetic process can be thought of as a simple reaction—diffusion-transport system (Berner, 1980 Boudreau, 1997). In a simple fine-grained sediment system, transport is via molecular diffusion and the diagenetic equation describing this system can be expressed as ... 

The amount of sedimentary denitrification occurring in the ocean today is one of the most poorly quantified terms in the marine combined nitrogen budget. Most modem measurements of denitrification rate have utilized pore-water N03 profiles (estimated from diffusion calculations—reaction models) whole-sediment incubations, either on deck or in situ, or by the isotope paring technique. It appears that shelf and upper slope sediments are quantitatively the most important sites of sedimentary denitrification (Christensen, et al., 1996 Christensen et al., 1987 Devol, 1991 Devol and Christensen, 1993 Gruber and Sarmiento, 1997 Kristensen, et al., 1999 Middelburg et al., 1996). Typical denitrification rates in these areas... 

The redissolution or burial of organic matter in sediments is a decision that is made jointly by the physics of diffusion, chemistry of organic matter oxidation, and the biology which mediates the chemical reactions. The concentration profile of a solute in sediment pore water is governed by the diffusion equation, which can be written most simply as... 

The coincidence of maxima in the methane oxidation rate and the sulfate reduction rate in Saanich Inlet strongly suggests that the methane oxidizing agent was sulfate, either via direct reaction, or coupled indirectly through reactions with other substrates (Devol, 1983). A methane-sulfate coupled reaction diffusion model was developed to describe the inverse relationship commonly observed between methane and sulfate concentrations in the pore waters of anoxic marine sediments. When fit to data from Saanich Inlet (B.C., Canada) and Skan Bay (Alaska), the model not only reproduces the observed methane and sulfate pore water concentration profiles but also accurately predicts the methane oxidation and sulfate reduction rates. In Saanich Inlet sediments, from 23 to 40% of the downward sulfate flux is consumed in methane oxidation while in Skan Bay this value is only about 12%. 

If there are no or very few irrigated burrows present in the sediment, lateral diffusion is not significant and the r dependence of Eq. (6.12) can be ignored. In that case, the equation becomes the more traditional onedimensional transport-reaction equation used to model pore-water solute profiles where advection is relatively unimportant (Berner, 1971 1980 Lerman, 1979). Both the cylindrical microenvironment model and the onedimensional Cartesian coordinate model will be used here to quantify the Mn distributions at NWC and DEEP. 

Calvert, S. E., and Price, N. B. (1972). Diffusion and reaction profiles of dissolved manganese in the pore waters of marine sediments. Earth Planet. Sci. Lett. 16, 245-249. 

Fig. 3.1 Concentration profiles in the pore water fractions of sediments obtained off the estuary of the River Congo, at a depth of approximately 4000 m. The sediments contain a relatively high amount of TOC. Values ranging from 1 to 3.5 wt. % indicate that this sediment is characterized by the high reaction rates of various early diagenesis processes. These processes are reflected by diffusion fluxes over gradients and by reaction rates determined by gradient changes (after Schulz et al. 1994).

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