On the equivalence of nonlocal and radial-diffusion models for porewater irrigation

Aller (1977, 1978, 1980) and Aller and Yingst (1978) have demonstrated that the presence of well-irrigated worm-tubes and other animal burrows in sediments can significantly alter the rate of exchange of solutes between porewater and the overlying waters. Specifically, the burrows modify the geometry of the porewater system such that solutes can diffuse toward or away from either the sediment-water interface or the burrow. The burrow constitutes an additional boundary source or sink..

An experimental and modeling study of pH and related solutes in an irrigated anoxic coastal sediment

Macrofaunal irrigation is an important process in nearshore sediments, facilitating greater exchange between sediments and seawater and imparting significant lateral heterogeneity to the porewater profiles of many constituents. Like many macrofaunal activities, irrigation is a transient behavior, i.e. tubes and burrows are flushed periodically, at frequencies that generally are species-specific. As a result, transient concentrations within the dwelling arise, potentially impacting gradients, fluxes and reaction rates in the vicinity of the dwelling. We investigated the impact of periodic burrow irrigation on the distribution of several diagenetically important porewater constituents. Laboratory experiments evaluated irrigation periodicity using artificially irrigated tubes embedded in nearshore organic-rich sediments, and microdistributions of oxygen and pH in laboratory experiments were measured with microelectrodes. To help interpret our results, we also constructed a simplified time and space-dependent transport-reaction model for oxygen, pH and sulfide in irrigated sediments. Laboratory results show substantial differences in the pH field of sediments surrounding an irrigated tube as a function of irrigation frequency. Higher pH values, indicative of an overlying water signature, were observed in the vicinity of the tube wall with increasing duration of irrigation. Conversely, oxygen concentrations did not vary significantly with the amount of irrigation, most likely a result of extremely high sediment oxygen demand. Model results are consistent with laboratory findings in predicting differences in the measured variables as a function of irrigation frequency. However, the nature and extent of the model-predicted differences are often at variance with the experimental data. Overall, experimental and modeling results both suggest irrigation periodicity can substantially influence porewater distributions and diagenetic processes in sediments. Future studies should examine the influence of irrigation periodicity on the types and rates of reactions, and the attendant biological features, in the environment encompassing the tube or burrow wall

A provisional diagenetic model for pH in anoxic porewaters: Application to the FOAM Site

This paper presents a diffusion-advection-reaction model for the pH of anoxic porewaters in nonirrigated sediments. Because of the couplings demanded by the organic-matter decay reaction, various acid-base interconversions, dissolved-iron generation, and CaCO3 and FeS precipitation, the model does not consider H+ alone, but deals simultaneously with 17 dissolved species. The complex and largely unknown kinetics of some of the processes affecting these species have been approximated by simple ad hoc formulations. For this reason, the model must be considered provisional. We have also made extensive use of the local (partial) equilibrium assumption to circumvent the computational problems generated by rapid association/dissociation reactions. The FOAM Site data are used as a vehicle to display the capabilities of this model. Assuming local equilibrium with FeS, the predicted pH profile is most sensitive to the reaction that liberates iron from the solid phase. The FOAM pH does not conform to a profile expected for anyone iron-source mineral, but appears to reflect a composite source. Based on currently available data, this source might include magnetite and silicate minerals, but is unlikely to involve ferric oxides and hydroxides. The pH of FOAM porewaters is much less sensitive to the precipitation of FeS and CaCO3 than would be suggested by past closed-system models. The overall pH stability of anoxic porewaters is attributable to the fact that the dissolved products of organic-matter decomposition are added in such a way as to form a self-buffering mixture

A modelling study of discontinuous biological irrigation

Irrigation of infaunal dwellings can lead to significant alteration of solute distributions in sediments. As a result, sediment-seawater fluxes of nutrients and dissolved carbon are greatly enhanced, and the biology of benthic communities is affected. The most realistic mathematical representation of irrigation and its effect on sediment geochemistry is Aller\u27s (1980) cylinder model. One critical assumption of this model is that burrows are irrigated continually, and that burrow water solute concentrations are identical to overlying water concentrations at all times. However, the vast majority of infaunal tube- and burrow-dwelling organisms irrigate periodically, i.e. in an on/off cycle. During periodic irrigation, the solute concentration at the tube wall may vary between the limits imposed by the flux from the porewater and the concentration in the overlying water. We introduce modifications to the cylinder model which allow for periodic irrigation. We assess how periodic irrigation affects solute profiles and fluxes of two chemical constituents, silica and ammonium, for different population densities (distance between burrows) and organism sizes (burrow radii). Silica and ammonium follow first and zeroth order reaction kinetics, respectively, and illustrate the behavior of two general reaction classes. Model results show that the effects of periodic irrigation vary with the class of reaction considered. For silica, radially-averaged profiles during discontinuous irrigation varied less than 15% from those with continuous irrigation for nearly all burrow sizes, burrow distances and reaction rate constants considered. However, we observed large temporal changes (as much as a factor of 6) in the areally-averaged silica flux over the irrigation cycle. Despite this time-dependence, the time-averaged silica flux was similar to that calculated for the continuous case. For ammonia, radially-averaged solute profiles were extremely sensitive to the duration of irrigation. In this case, the differences between discontinuous and continuous irrigation were greatest when the duration of irrigation was short (e.g. 5 min), and when the inter-burrow distance was small. As with silica, there was a strong time-dependence in areally-averaged ammonia flux when irrigation was periodic. However, the time-averaged ammonia flux is identical to the flux calculated for continuous irrigation. Our results suggest that irrigation behavior can affect the local burrow environment and this imposes a time dependence on solute fluxes

Simulated fiddler-crab sediment mixing

Using a lattice-automaton model, we simulate the effects of fiddler crabs on the distribution of excess 210Pb in marsh sediments. Three previously-identified modes of bioturbation are investigated: (1) removal-and-fill, where material is excavated to the sediment-water interface and burrows, when abandoned, are subsequently filled by surface material, (2) removal-and-collapse, where the infilling occurs by collapse of the burrow walls, and (3) partial-compaction-and-collapse, where part of the excavated sediment is packed into the burrow wall and abandoned burrows subsequently collapse. These various mixing modes lead to somewhat different laterally-integrated 210Pbex profiles, which are also influenced by burrowing frequency, burrow dimensions, fraction of surface material replaced by new sediment (regeneration), and the fraction of material compacted during burial.Using parameters from a previous study in a South Carolina marsh, we find that data from low-marsh sites are best predicted by the partial-compaction-and-collapse process; this is consistent with the observation that burrow casts indicate far more material is excavated than is deposited as pellets at the sediment-water interface. The profile from the high-marsh site is best simulated by removal-and-fill mixing, with 50% regeneration of material at the sediment-water interface; this is consistent with less frequent flooding at this site.We have also calculated the exchange function for each of these mixing modes and show that they are highly asymmetric, indicating that the mixing is not diffusive. Only in the case of partialcompaction-and-collapse does the exchange function approach a diffusive form when the excavation rate decreases, i.e., the probability of compaction increases

Initial rise of bubbles in cohesive sediments by a process of viscoelastic fracture

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 116 (2011): B04207, doi:10.1029/2010JB008133.An understanding of the mechanics of bubble rise in sediments is essential because of the role of bubbles in releasing methane to the atmosphere and the formation and melting of gas hydrates. Past models to describe and predict the rise of other buoyant geological bodies through a surrounding solid (e.g., magmas and hydrofractures) appear not to be applicable to bubbles in soft sediments, and this paper presents a new model for gas bubble rise in soft, fine-grained, cohesive sediments. Bubbles in such sediments are essentially “dry” (little if any free water) and grow through a process of elastic expansion and fracture that can be described using the principles of linear elastic fracture mechanics, which assume the existence of a spectrum of flaws within the sediment fabric. By extending this theory, we predict that bubbles initially rise by preferential propagation of a fracture in a (sub) vertical direction. We present a criterion for initial bubble rise. Once rise is initiated, the speed of rise is controlled by the viscoelastic response of the sediments to stress. Using this new bubble rise model, we estimate rise velocities to be of the order of centimeters per second. We again show that capillary pressure plays no substantive role in controlling bubble growth or rise.This research was funded by the U.S. Office of Naval research through grants N00014‐08‐0818 and N00014‐05‐1‐0175 (project managers J. Eckman and T. Drake). Support was also provided by the Natural Sciences and Engineering Council of Canada and by the Killam Trust

Comparative diagenesis at three sites on the Canadian continental margin

Diagenesis of carbon, oxygen, nitrogen, and manganese at three sites on the Canadian continental margin is quantitatively compared and contrasted using results from a computer code (CANDI) published by Boudreau (1996a). The data at Station 3 (Cabot Strait) are well explained by the steady state output from CANDI, assuming a porewater balance created by diffusion and reaction only, whereas the data from Stations 4 (Emerald Basin-Scotia Shelf) and 5 (Scotia Slope) are not consistent, in one way or another, with this simple model. The deviations between model and data at Station 4 are best explained by nonsteady-state diagenesis. Model fits to the Station 5 ΣCO2 observations are improved dramatically by adding some irrigation at this site, but the ΣNH3 distribution appears to be subject to an additional anomalous transport to the O2 zone and subsequent oxidation to NO-3. The mechanism for this latter phenomena is unknown and in need of future research. In addition, the O2 and ΣCO2 profiles at all sites require the existence of at least two reactive organic matter types; furthermore, the initial amounts of these OM types at each station is strongly dependent on the intensity of particle bioturbation. Ammonia is preferentially regenerated at Station 3 at a high ratio of about 25 N to 106 C. The net kinetics of the deeper removal of Mn2+ appear to be fractional-order with respect to the concentration of this species, suggesting multiple removal processes. Finally, an oxidant balance, assuming steady state, indicates a considerable difference in the use of oxidants at each station even though the O2 fluxes are similar

The nonlocal model of porewater irrigation: Limits to its equivalence with a cylinder diffusion model

Burrows maintained by animals in aquatic sediments ventilate the sediment and can substantially alter the rates and pathways of biologically-mediated decomposition reactions. A well known and effective way of modeling the impact of such bioirrigation in sediment diagenetic models is to assume that solutes diffuse into an annulus of sediment surrounding the burrow; the reaction diffusion equations are represented in cylindrical polar co-ordinates. More commonly, bioirrigation of sediments is represented by one-dimensional nonlocal irrigation models. Their use is typically justified by the assertion that a nonlocal model is equivalent to a radially-integrated two-dimensional diffusion model in cylindrical-polar co-ordinates. In this paper we highlight limits to this equivalence, drawing on examples from both single-species and multiple-species reaction diffusion models. A modified derivation of the nonlocal model using a higher order Taylor series approximation was tested but found to provide little improvement over the original model. We suggest some approaches for choosing nonlocal coefficients and identify particular limitations to be alert to when applying the nonlocal model

Ongoing transients in carbonate compensation

Uptake of anthropogenic CO2 is acidifying the oceans. Over the next 2000 years, this will modify the dissolution and preservation of sedimentary carbonate. By coupling new formulas for the positions of the calcite saturation horizon, zsat, the compensation depth, zcc, and the snowline, zsnow, to a biogeochemical model of the oceanic carbonate system, we evaluate how these horizons will change with ongoing ocean acidification. Our model is an extended Havardton-Bear-type box model, which includes novel kinetic descriptions for carbonate dissolution above, between, and below these critical depths. In the preindustrial ocean, zsat and zcc are at 3939 and 4750 m, respectively. When forced with the IS92a CO2 emission scenario, the model forecasts (1) that zsat will rise rapidly (“runaway” conditions) so that all deep water becomes undersaturated, (2) that zcc will also rise and over 1000 years will pass before it will be stabilized by the dissolution of previously deposited CaCO3, and (3) that zsnow will respond slowly to acidification, rising by ∼1150 m during a 2000 year timeframe. A further simplified model that equates the compensation and saturation depths produces quantitatively different results. Finally, additional feedbacks due to acidification on calcification and increased atmospheric CO2 on organic matter productivity strongly affect the positions of the compensation horizons and their dynamics.

Release of multiple bubbles from cohesive sediments

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 38 (2011): L08606, doi:10.1029/2011GL046870.Methane is a strong greenhouse gas, and marine and wetland sediments constitute significant sources to the atmosphere. This flux is dominated by the release of bubbles, and quantitative prediction of this bubble flux has been elusive because of the lack of a mechanistic model. Our previous work has shown that sediments behave as elastic fracturing solids during bubble growth and rise. We now further argue that bubbles can open previously formed, partially annealed, rise tracts (fractures) and that this mechanism can account for the observed preferential release at low tides in marine settings. When this mechanical model is applied to data from Cape Lookout Bight, NC (USA), the results indicate that methanogenic bubbles released at this site do indeed follow previously formed rise tracts and that the calculated release rates are entirely consistent with the rise of multiple bubbles on tidal time scales. Our model forms a basis for making predictions of future bubble fluxes from warming sediments under the influence of climate change.This research was funded by the U.S. Office of Naval research through grants N00014‐08‐0818 and N00014‐05‐1‐0175 (project managers J. Eckman and T. Drake), the Natural Sciences and Engineering Council of Canada, and the Killam Trust (Dalhousie University)