Steady-state Mass Balance Model Research Articles

Application of a Mass Balance Model To Assess In-Place Arsenic Pollution

A simple, steady-state mass balance model based on aquivalence as an equilibrium criterion is used to estimate chemical behavior in a lake and, together with the linear additivity principle (LAP), to quantify chemical contributions, especially that of in-place pollution. Since the model is linear, it is argued that chemical contributions from particular sources that vary spatially or temporally can be quantified and their effect isolated from total chemical dynamics. This is demonstrated by considering three loading scenarios for Moira Lake in eastern Ontario that has received elevated arsenic (As) inputs since 1866. Steady-state estimates of precontamination and high contamination conditions are generated by linearly scaling model results obtained with a unit inflow of 0.001 mg/L (unit profile)

Field Application of a Steady-State Mass Balance Model for Hydrophobic Organic Chemicals in an Estuarine System

A one-dimensional, steady-state mass balance model was applied to describe instream and sediment concentrations of four hydrophobic organic chemicals in a discharge canal and receiving water bayou. The chemicals examined were hexachlorobenzene, hexachlorobutadiene, hexachloroethane, and 1,2,4-trichlorobenzene. The objective of the study was to test a mass balance modeling approach for relating point source effluents to resulting sediment concentration, in support of future implementation of national sediment quality criteria (SQC). The modeling effort relied upon ambient monitoring data that were collected for purposes other than supporting a modeling effort. Given data uncertainties and assumptions in the modeling framework, model results were reasonably consistent with observations in the receiving water bayou. There were large discrepancies between model results and observed sediment concentrations in the discharge canal. These discrepancies are likely caused by an undocumented source of chemicals to the canal sediments, due to historical landfilling of wastes; and/or canal sediment concentrations being in temporal disequilibrium, due to historically higher chemical loading. The merits of steady-state versus time-variable models for describing sediment quality are compared. Steady-state models are most appropriate for effluent permitting purposes, where the objective is to determine the long-term relationship jbetween wastewater loads and resulting sediment concentrations. A time-variable model framework will be required to establish model credibility for situations where the steady-state assumption is violated, although the required information on historical chemical loads is often unavailable.

Critical loads of sulfur and nitrogen for lakes II: Regional extent and variability in Finland

The concept of critical loads has been developed to assist in the design of environmentally sound abatement strategies for the emissions of acidifying compounds. In this paper the critical loads of S and N for lakes in Finland are computed and mapped, based on methods presented in an accompanying paper. The employed steady-state mass balance model allows the simultaneous evaluation of the reductions required of S and N deposition exceeding these critical loads. Special emphasis has been put on the presentation of the spatial variability and the uncertainty of the critical loads and their exceedances. The derived critical loads of S and N for lakes in Finland show a substantial spatial variability. The highest exceedance of critical loads is presently estimated in the south-east of the country, where up to 80% of the lakes show an exceedance of the critical loads of S. The evaluation of two emission scenarios shows that only “maximum feasible reductions” would be sufficient for protecting most Finnish lakes from the impacts of acidic deposition. The results of this study form a basis for setting national targets for emission reductions in Finland.

Critical loads of sulfur and nitrogen for lakes I: Model description and estimation of uncertainty

Presently considerable effort is devoted to the development of methods for estimating critical loads of acidic deposition. In this paper a steady-state mass balance model for lakes is presented, allowing the simultaneous calculation of critical loads of acidifying S and N deposition and their exceedance. Special emphasis is given to the derivation of model inputs and parameters and the quantification of their uncertainties. The inclusion of rate-limited processes in the model leads to the dependence of the critical loads not only on catchment properties but also on the loading to the ecosystem. As a consequence, critical load values have to be re-calculated whenever deposition patterns change. The methods presented in this study are used in an accompanying paper to derive regional distributions of critical loads of S and N for lakes in Finland and to quantify their uncertainties.

Physico-Chemical Model of Toxic Substances in the Great Lakes

A physico-chemical model of the fate of toxic substances in the Great Lakes is constructed from mass balance principles, incorporating principal mechanisms of paniculate sorption-desorption, sediment-water and atmosphere-water interactions, and chemical and biochemical decay. The steady state mass balance model of the suspended solids in the open lake water yields net solids loss rates from 0.02 mjdfor Saginaw Bay to 1.22 m/dfor Lake Ontario. Calibration of the toxic model is through comparison to plutonium-239 data collected in the 1970s using a 23-year time variable calculation. The results indicate that, in general, the sediments are interactive with the water column in the Great Lakes through resuspension and horizontal transport. Fifty percent response times of 239Pu following a cessation of load extend beyond 10 years with sediment resuspension. The calibrated model was also applied to polychlorinated biphenyl (PCB) using a high and low estimate of contemporary external load and with and without volatilization. The lower load level (lake range 640 to 1,390 kg/yr) with volatilization (at an exchange rate of 0.1 m/d) appears to be more representative of observed surface sediment data for the open lake waters. Calculated water column concentrations for the lower load level with and without volatilization ranged from 0.25 to 0.90 ng/Lfor open lake waters. Fifty percent response times for PCB following cessation of load varied from less than 5 years when volatilization was included to 10 to 20 years without volatilization. Comparison of these response times to decline of concentrations of PCB in Lake Michigan bloaters indicates that, at least for that lake, volatilization is occurring at an exchange rate of about 0.1 m/d.

Comment on “A Model for Total Phosphorus in Saginaw Bay”

The subject paper (Canale and Squire 1976) presents the results of the application of a steady-state mass balance model to chloride and total phosphorus data for Saginaw Bay in 1974. Richardson (1974, 1976) has modeled chloride in Saginaw Bay on both a steady-state and a time variable basis. In this work, the steady-state model was shown to be inadequate for this system, except during stable periods in summer and fall. Since most of the loading of pollutants to the bay does not occur at these times, the time variable model was developed. The purpose of this comment is to compare similar aspects of these projects and to contrast the steady-state and time variable approaches with respect to their ability to simulate observed phenomena and the utility of their results.