Biodegradation of hydrocarbons vapors: Comparison of laboratory studies and field investigations in the vadose zone at the emplaced fuel source experiment, Airbase Vaerløse, Denmark

The natural attenuation of volatile organic compounds (VOCs) in the unsaturated zone can only be predicted when information about microbial biodegradation rates and kinetics are known. This study aimed at determining first-order rate coefficients for the aerobic biodegradation of 13 volatile petroleum hydrocarbons which were artificially emplaced as a liquid mixture during a field experiment in an unsaturated sandy soil. Apparent first-order biodegradation rate coefficients were estimated by comparing the spatial evolution of the resulting vapor plumes to an analytical reactive transport model. Two independent reactive numerical model approaches have been used to simulate the diffusive migration of VOC vapors and to estimate degradation rate coefficients. Supplementary laboratory column and microcosm experiments were performed with the sandy soil at room temperature under aerobic conditions. First-order kinetics adequately matched the lab column profiles for most of the compounds. Consistent compound-specific apparent first-order rate coefficients were obtained by the three models and the lab column experiment, except for benzene. Laboratory microcosm experiments lacked of sensitivity for slowly degrading compounds and underestimated degradation rates by up to a factor of 5. Addition of NH3 vapor was shown to increase the degradation rates for some VOCs in the laboratory microcosms. All field models suggested a significantly higher degradation rate for benzene than the rates measured in the lab, suggesting that the field microbial community was superior in developing benzene degrading activity.     

Natural attenuation of chlorinated ethene compounds: model development and field-scale application at the Dover site

A multi-dimensional and multi-species reactive transport model was developed to aid in the analysis of natural attenuation design at chlorinated solvent sites. The model can simulate several simultaneously occurring attenuation processes including aerobic and anaerobic biological degradation processes. The developed model was applied to analyze field-scale transport and biodegradation processes occurring at the Area-6 site in Dover Air Force Base, Delaware. The model was calibrated to field data collected at this site. The calibrated model reproduced the general groundwater flow patterns, and also, it successfully recreated the observed distribution of tetrachloroethene (PCE), trichloroethene (TCE), dichloroethylene (DCE), vinyl chloride (VC) and chloride plumes. Field-scale decay rates of these contaminant plumes were also estimated. The decay rates are within the range of values that were previously estimated based on lab-scale microcosm and field-scale transect analyses. Model simulation results indicated that the anaerobic degradation rate of TCE, source loading rate, and groundwater transport rate are the important model parameters. Sensitivity analysis of the model indicated that the shape and extent of the predicted TCE plume is most sensitive to transmissivity values. The total mass of the predicted TCE plume is most sensitive to TCE anaerobic degradation rates. The numerical model developed in this study is a useful engineering tool for integrating field-scale natural attenuation data within a rational modeling framework. The model results can be used for quantifying the relative importance of various simultaneously occurring natural attenuation processes.     

Plant aided bioremediation in the vadose zone: model development and applications

Phytoremediation has the potential to enhance clean up of land contaminated by various pollutants. A mathematical model that includes a two-fluid phase flow model of water flow as well as a two-region soil model of contaminant reactions was developed and applied to various bioremediation scenarios in the unsaturated zone, especially to plant-aided bioremediation. To investigate model behavior and determine the main parameters and mechanisms that affect bioremediation in unplanted and planted soils, numerical simulations of theoretical scenarios were conducted before applying the model to field data. It is observed from the results that parameters affecting the contaminant concentration in the water phase, such as aqueous solubility, the octanol-water partition coefficient, and organic carbon content of the soil controlled the contaminant fate in the vadose zone. Simulation using the developed model also characterized the fate and transport of the contaminants both in planted and unplanted soils satisfactorily for field applications. Although phytoremediation has the potential for remediation of contaminated soils, results from both modeling and field studies suggested that plants may not always enhance the remediation efficiency when the soil already has a high microbial concentration, when the contaminant bioavailability is low, or when the overall reaction is mass transfer-limited. Therefore, other steps to increase contaminant bioavailability are needed in phytoremediation applications; natural purification mechanisms such as aging, volatilization, and natural bioremediation should be considered to maximize the plant effect and minimize the cost.     

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.     

Variably saturated flow and multicomponent biogeochemical reactive transport modeling of a uranium bioremediation field experiment

Three-dimensional, coupled variably saturated flow and biogeochemical reactive transport modeling of a 2008 in situ uranium bioremediation field experiment is used to better understand the interplay of transport and biogeochemical reactions controlling uranium behavior under pulsed acetate amendment, seasonal water table variation, spatially variable physical (hydraulic conductivity, porosity) and geochemical (reactive surface area) material properties. While the simulation of the 2008 Big Rusty acetate biostimulation field experiment in Rifle, Colorado was generally consistent with behaviors identified in previous field experiments at the Rifle IFRC site, the additional process and property detail provided several new insights. A principal conclusion from this work is that uranium bioreduction is most effective when acetate, in excess of the sulfate-reducing bacteria demand, is available to the metal-reducing bacteria. The inclusion of an initially small population of slow growing sulfate-reducing bacteria identified in proteomic analyses led to an additional source of Fe(II) from the dissolution of Fe(III) minerals promoted by biogenic sulfide. The falling water table during the experiment significantly reduced the saturated thickness of the aquifer and resulted in reactants and products, as well as unmitigated uranium, in the newly unsaturated vadose zone. High permeability sandy gravel structures resulted in locally high flow rates in the vicinity of injection wells that increased acetate dilution. In downgradient locations, these structures created preferential flow paths for acetate delivery that enhanced local zones of TEAP reactivity and subsidiary reactions. Conversely, smaller transport rates associated with the lower permeability lithofacies (e.g., fine) and vadose zone were shown to limit acetate access and reaction. Once accessed by acetate, however, these same zones limited subsequent acetate dilution and provided longer residence times that resulted in higher concentrations of TEAP reaction products when terminal electron donors and acceptors were not limiting. Finally, facies-based porosity and reactive surface area variations were shown to affect aqueous uranium concentration distributions with localized effects of the fine lithofacies having the largest impact on U(VI) surface complexation. The ability to model the comprehensive biogeochemical reaction network, and spatially and temporally variable processes, properties, and conditions controlling uranium behavior during engineered bioremediation in the naturally complex Rifle IFRC subsurface system required a subsurface simulator that could use the large memory and computational performance of a massively parallel computer. In this case, the eSTOMP simulator, operating on 128 processor cores for 12h, was used to simulate the 110-day field experiment and 50 days of post-biostimulation behavior.     

Microbial siderophores and their potential applications: a review

Siderophores are small organic molecules produced by microorganisms under iron-limiting conditions which enhance the uptake of iron to the microorganisms. In environment, the ferric form of iron is insoluble and inaccessible at physiological pH (7.35–7.40). Under this condition, microorganisms synthesize siderophores which have high affinity for ferric iron. These ferric iron-siderophore complexes are then transported to cytosol. In cytosol, the ferric iron gets reduced into ferrous iron and becomes accessible to microorganism. In recent times, siderophores have drawn much attention due to its potential roles in different fields. Siderophores have application in microbial ecology to enhance the growth of several unculturable microorganisms and can alter the microbial communities. In the field of agriculture, different types of siderophores promote the growth of several plant species and increase their yield by enhancing the Fe uptake to plants. Siderophores acts as a potential biocontrol agent against harmful phyto-pathogens and holds the ability to substitute hazardous pesticides. Heavy-metal-contaminated samples can be detoxified by applying siderophores, which explicate its role in bioremediation. Siderophores can detect the iron content in different environments, exhibiting its role as a biosensor. In the medical field, siderophore uses the “Trojan horse strategy” to form complexes with antibiotics and helps in the selective delivery of antibiotics to the antibiotic-resistant bacteria. Certain iron overload diseases for example sickle cell anemia can be treated with the help of siderophores. Other medical applications of siderophores include antimalarial activity, removal of transuranic elements from the body, and anticancer activity. The aim of this review is to discuss the important roles and applications of siderophores in different sectors including ecology, agriculture, bioremediation, biosensor, and medicine.     

Predicting natural attenuation of xylene in groundwater using a numerical model.

The aquifer beneath an abandoned refinery in the Lower Rhine area, Germany, was contaminated with a number of different mineral oil products. Groundwater sampling in the area around the former xylene plant revealed that a xylene plume had developed in the underlying groundwater, and moreover, that there is strong evidence for in situ microbial xylene degradation with oxygen, nitrate, sulfate and ferric iron as electron acceptors. In order to prevent further xylene spreading, three pumping wells extracting contaminated water were installed downgradient of the spill zone. The numerical reactive transport code Transport Biochemisty Chemistry (TBC) was applied to this situation to quantify the relation of microbial degradation to xylene removal by the pumping wells. It could be shown that the unamended in situ degradation was an appreciable xylene removal process that contributed to about one-third to the total xylene removal (degradation plus extraction). A further objective of the model application was to predict xylene spreading under regional flow conditions, i.e. without operation of the three pumping wells, to consider the possible effects of natural xylene attenuation. To accomplish this, the model calibrated for the situation with operating wells was transferred to the hydraulic situation of regional flow while retaining the parameters of the biochemical model. It turned out that the xylene plume that is expected to develop downgradient of the source area will be limited to an extension of not more than 1000 m. An interesting feature of the simulations results was that xylene degradation under iron-reducing conditions, which was of minor importance for the situation with operating pumping wells, becomes the dominant degradation mechanism under regional flow conditions. Moreover, iron reduction will be the key process in controlling plume evolution. The model application illustrates that multi-species reactive transport models are needed to adequately transfer reactive processes from one hydraulic situation to another, while single species models are not suited for this predictive task.     

Uranium removal from groundwater via in situ biostimulation: Field-scale modeling of transport and biological processes

During 2002 and 2003, bioremediation experiments in the unconfined aquifer of the Old Rifle UMTRA field site in western Colorado provided evidence for the immobilization of hexavalent uranium in groundwater by iron-reducing Geobacter sp. stimulated by acetate amendment. As the bioavailable Fe(III) terminal electron acceptor was depleted in the zone just downgradient of the acetate injection gallery, sulfate-reducing organisms came to dominate the microbial community. In the present study, we use multicomponent reactive transport modeling to analyze data from the 2002 field experiment to identify the dominant transport and biological processes controlling uranium mobility during biostimulation, and determine field-scale parameters for these modeled processes. The coupled process simulation approach was able to establish a quantitative characterization of the principal flow, transport, and reaction processes based on the 2002 field experiment, that could be applied without modification to describe the 2003 field experiment. Insights gained from this analysis include field-scale estimates of the bioavailable Fe(III) mineral threshold for the onset of sulfate reduction, and rates for the Fe(III), U(VI), and sulfate terminal electron accepting processes.     

Identification and reliability of microbial aerobic respiration and denitrification kinetics using a single-well push-pull field test

Methods to derive reaction rates of microbial processes are important since these processes are determining many chemical reactions influencing groundwater quality. Thereby, it is not only important to derive the parameters, but also to have a firm idea about the reliability with which these are determined. Analysis of residuals, sensitivity analyses and analysis of joint confidence intervals provide an interesting tool for this purpose. The method is illustrated in this paper using a push-pull test designed to derive aerobic respiration and denitrification. Therefore, a test solution containing dissolved oxygen and nitrate as reactive tracer and bromide as non-reactive tracer was injected in organic matter rich sediment. Afterwards, this test solution was extracted and water quality was monitored. ReacTrans, a finite-difference, axial-symmetric groundwater flow and solute transport model was developed to simulate the test and derive hydraulic, solute transport and chemical parameters. Aerobic respiration and denitrification were simulated with Michaelis-Menten kinetics. Maximum reaction rates (10.4 and 2.4 mmol/ld for aerobic respiration and denitrification respectively) and Michaelis constants (0.14 and 0.1 mmol/l for aerobic respiration and denitrification respectively) were determined. The reliability with which these parameters are derived is indicated by analysis of residuals, sensitivities and joint confidence intervals. This shows that the Michaelis-Menten parameters can be derived reliable with a push-pull test, whereas the test is insensitive to effective porosity and hydraulic conductivity. Because of the small scale of the test, longitudinal dispersivity was very small and therefore unidentifiable.     

Modeling in-situ uranium(VI) bioreduction by sulfate-reducing bacteria

We present a travel-time based reactive transport model to simulate an in-situ bioremediation experiment for demonstrating enhanced bioreduction of uranium(VI). The model considers aquatic equilibrium chemistry of uranium and other groundwater constituents, uranium sorption and precipitation, and the microbial reduction of nitrate, sulfate and U(VI). Kinetic sorption/desorption of U(VI) is characterized by mass transfer between stagnant micro-pores and mobile flow zones. The model describes the succession of terminal electron accepting processes and the growth and decay of sulfate-reducing bacteria, concurrent with the enzymatic reduction of aqueous U(VI) species. The effective U(VI) reduction rate and sorption site distributions are determined by fitting the model simulation to an in-situ experiment at Oak Ridge, TN. Results show that (1) the presence of nitrate inhibits U(VI) reduction at the site; (2) the fitted effective rate of in-situ U(VI) reduction is much smaller than the values reported for laboratory experiments; (3) U(VI) sorption/desorption, which affects U(VI) bioavailability at the site, is strongly controlled by kinetics; (4) both pH and bicarbonate concentration significantly influence the sorption/desorption of U(VI), which therefore cannot be characterized by empirical isotherms; and (5) calcium-uranyl-carbonate complexes significantly influence the model performance of U(VI) reduction.     

Groundwater flow, multicomponent transport and biogeochemistry: development and application of a coupled process model

A research tool for modeling the reactive flow and transport of groundwater contaminants in multiple dimensions is presented. Arbitrarily complex coupled kinetic–equilibrium heterogeneous reaction networks, automatic code generation, transfer-function based solutions, parameter estimation, high-resolution methods for advection, and robust solvers for the mixed kinetic–equilibrium chemistry are some of the features of reactive flow and transport (RAFT) that make it a versatile research tool in the modeling of a wide variety of laboratory and field experiments. The treatment of reactions is quite general so that RAFT can be used to model biological, adsorption/desorption, complexation, and mineral dissolution/precipitation reactions among others. The integrated framework involving automated code generation and parameter estimation allows for the development, characterization, and evaluation of mechanistic process models. The model is described and used to solve a problem in competitive adsorption that illustrates some of these features. The model is also used to study the development of an in situ Fe(II)-zone by encouraging the growth of an iron-reducing bacterium with lactate as the electron donor. Such redox barriers are effective in sequestering groundwater contaminants such as chromate and TCE.     

Biodegradation during contaminant transport in porous media: 3. Apparent condition-dependency of growth-related coefficients

The biodegradation of organic contaminants in the subsurface has become a major focus of attention, in part, due to the tremendous interest in applying in situ biodegradation and natural attenuation approaches for site remediation. The biodegradation and transport of contaminants is influenced by a combination of microbial and physicochemical properties and processes. The purpose of this paper is to investigate the impact of hydrodynamic residence time, substrate concentration, and growth-related factors on the simulation of contaminant biodegradation and transport, with a specific focus on potentially condition-dependent growth coefficients. Two sets of data from miscible-displacement experiments, performed with different residence times and initial solute concentrations, were simulated using a transport model that includes biodegradation described by the Monod nonlinear equations and which incorporates microbial growth and oxygen limitation. Two variations of the model were used, one wherein metabolic lag and cell transport are explicitly accounted for, and one wherein they are not. The magnitude of the maximum specific growth rates obtained from calibration of the column-experiment results using the simpler model exhibits dependency on pore-water velocity and initial substrate concentration (C0) for most cases. Specifically, the magnitude of micron generally increases with increasing pore-water velocity for a specific C0, and increases with decreasing C0 for a specific pore-water velocity. Conversely, use of the model wherein observed lag and cell elution are explicitly accounted for produces growth coefficients that are similar, both to each other and to the batch-measured value. These results illustrate the potential condition-dependency of calibrated coefficients obtained from the use of models that do not account explicitly for all pertinent processes influencing transport of reactive solutes.     

Interactive effect of Brevibacillus brevis and Glomus mosseae, both isolated from Cd contaminated soil, on plant growth, physiological mycorrhizal fungal characteristics and soil enzymatic activities in Cd polluted soil

The interaction between two autochthonous microorganisms (Brevibacillus brevis and Glomus mosseae) isolated from Cd amended soil increased plant growth, arbuscular mycorrhizal (AM) colonization and physiological characteristics of the AM infection (measured as SDH or ALP activities). The enhanced plant Cd tolerance after coinoculation with native microorganisms seemed to be a consequence of increased P and K acquisition and, simultaneously, of decreased concentration of Cd, Cr, Mn, Cu, Mo, Fe and Ni in plant tissue. Autochthonous microbial strains were more efficient for nutrient uptake, to immobilize metals and decrease their translocation to the shoot than reference G. mosseae (with or without bacteria). Indole acetic acid produced by B. brevis may be related to its ability for improving root growth, nodule production and AM fungal intra and extraradical development. Dehydrogenase, phosphatase and beta-glucosidase activities, indicative of microbial metabolism and soil fertility, were maximized by the coinoculation of autochthonous microorganisms in cadmium polluted conditions. As a consequence, the use of native microorganisms may result very efficient in bioremediation.     

Lattice Boltzmann model for agrochemical transport in soils

Agrochemical transport in soils is complicated and involves physical, chemical and biochemical reactions; its mathematical modelling remains a challenging task. This paper presents a lattice Boltzmann model to simulate the agrochemical movement. The lattice Boltzmann model is a microscopic and process-based model, simulating the transport process by tracking chemical particles. The model presented in this paper is for one-dimensional vertical leaching and assumes that the chemical particles at the microscopic level move in five directions: one stagnant, two in vertical direction and two in an internal horizontal direction bounded by two reactive walls. Reactions at the walls are assumed to take place at two different rates, one in fast rate where the chemicals in the solution and on the wall are in an instant equilibrium, and the other in slow rate where the mass exchange rate between the chemicals in the solution and on the wall is a first-order kinetic. The reactions on both walls are assumed to occur instantly when the chemical particles moving in the internal direction hit the walls. To test the model, we measured the leaching of atrazine through soil columns in the laboratory. The results simulated with the lattice Boltzmann model are compared with the measured breakthrough curves and the non-equilibrium two-site convection-dispersion model; they all show close agreement. The transport parameters needed in the models are obtained from the measurement of adsorption isotherm of atrazine, bromide leaching in the same soil columns and calibration.     

Development of a scalable model for predicting arsenic transport coupled with oxidation and adsorption reactions

Understanding the fundamentals of arsenic adsorption and oxidation reactions is critical for predicting its transport dynamics in groundwater systems. We completed batch experiments to study the interactions of arsenic with a common MnO2(s) mineral, pyrolusite. The reaction kinetics and adsorption isotherm developed from the batch experiments were integrated into a scalable reactive transport model to facilitate column-scale transport predictions. We then completed a set of column experiments to test the predictive capability of the reactive transport model. Our batch results indicated that the commonly used pseudo-first order kinetics for As(III) oxidation reaction neglects the scaling effects with respect to the MnO2(s) concentration. A second order kinetic equation that explicitly includes MnO2(s) concentration dependence is a more appropriate kinetic model to describe arsenic oxidation by MnO2(s) minerals. The arsenic adsorption reaction follows the Langmuir isotherm with the adsorption capacity of 0.053micromol of As(V)/g of MnO2(s) at the tested conditions. The knowledge gained from the batch experiments was used to develop a conceptual model for describing arsenic reactive transport at a column scale. The proposed conceptual model was integrated within a reactive transport code that accurately predicted the breakthrough profiles observed in multiple column experiments. The kinetic and adsorption process details obtained from the batch experiments were valuable data for scaling to predict the column-scale reactive transport of arsenic in MnO2(s)-containing sand columns.     

Mixing-controlled biodegradation in a toluene plume--results from two-dimensional laboratory experiments

Various abiotic and biotic processes such as sorption, dilution, and degradation are known to affect the fate of organic contaminants, such as petroleum hydrocarbons in saturated porous media. Reactive transport modeling of such plumes indicates that the biodegradation of organic pollutants is, in many cases, controlled by mixing and therefore occurs locally at the plume's fringes, where electron donors and electron-acceptors mix. Herein, we aim to test whether this hypothesis can be verified by experimental results obtained from aerobic and anaerobic degradation experiments in two-dimensional sediment microcosms. Toluene was selected as a model compound for oxidizable contaminants. The two-dimensional microcosm was filled with quartz sand and operated under controlled flow conditions simulating a contaminant plume in otherwise uncontaminated groundwater. Aerobic degradation of toluene by Pseudomonas putida mt-2 reduced a continuous 8.7 mg L(-1) toluene concentration by 35% over a transport distance of 78 cm in 15.5 h. In comparison, under similar conditions Aromatoleum aromaticum strain EbN1 degraded 98% of the toluene infiltrated using nitrate (68.5+/-6.2 mg L(-1)) as electron acceptor. A major part of the biodegradation activity was located at the plume fringes and the slope of the electron-acceptor gradient was steeper during periods of active biodegradation. The distribution of toluene and the significant overlap of nitrate at the plume's fringe indicate that biokinetic and/or microscale transport processes may constitute additional limiting factors. Experimental data is corroborated with results from a reactive transport model using double Monod kinetics. The outcome of the study shows that in order to simulate degradation in contaminant plumes, detailed data sets are required to test the applicability of models. These will have to deal with the incorporation of existing parameters coding for substrate conversion kinetics and microbial growth.     

Multicomponent simulation of wastewater-derived nitrogen and carbon in shallow unconfined aquifers. I. Model formulation and performance

One of the most common methods to dispose of domestic wastewater involves the release of septic effluent from drains located in the unsaturated zone. Nitrogen from such systems is currently of concern because of nitrate contamination of drinking water supplies and eutrophication of coastal waters. The objectives of this study are to develop and assess the performance of a mechanistic flow and reactive transport model which couples the most relevant physical, geochemical and biochemical processes involved in wastewater plume evolution in sandy aquifers. The numerical model solves for variably saturated groundwater flow and reactive transport of multiple carbon- and nitrogen-containing species in a three-dimensional porous medium. The reactive transport equations are solved using the Strang splitting method which is shown to be accurate for Monod and first- and second-order kinetic reactions, and two to four times more efficient than sequential iterative splitting. The reaction system is formulated as a fully kinetic chemistry problem, which allows for the use of several special-purpose ordinary differential equation (ODE) solvers. For reaction systems containing both fast and slow kinetic reactions, such as the combined nitrogen-carbon system, it is found that a specialized stiff explicit solver fails to obtain a solution. An implicit solver is more robust and its computational performance is improved by scaling of the fastest reaction rates. The model is used to simulate wastewater migration in a 1-m-long unsaturated column and the results show significant oxidation of dissolved organic carbon (DOC), the generation of nitrate by nitrification, and a slight decrease in pH.     

Modelling of physical and reactive processes during biodegradation of a hydrocarbon plume under transient groundwater flow conditions

Numerical experiments of non-reactive and reactive transport were carried out to quantify the influence of a seasonally varying, transient flow field on transport and natural attenuation at a hydrocarbon-contaminated field site. Different numerical schemes for solving advective transport were compared to assess their capability to model low transversal dispersivities in transient flow fields. For the field site, it is shown that vertical plume spreading is largely inhibited, particularly if sorption is taken into account. For the reactive simulations, a biodegradation reaction module for the geochemical transport model PHT3D was developed. Results of the reactive transport simulations show that under the site-specific conditions the temporal variations in groundwater flow do, to a modest extent, affect average biodegradation rates and average total (dissolved) contaminant mass in the aquifer. The model simulations demonstrate that the seasonal variability in groundwater flow only results in significantly enhanced biodegradation rates when a differential sorption of electron donor (toluene) and electron acceptor (sulfate) is assumed.