Allocating Remedial Costs at Superfund Sites with Commingled Groundwater Contaminant Plumes

Remedial efforts at Superfund sites across the country focus on groundwater contaminant plumes that have been produced by contributions from multiple parties. Allocating cleanup costs between the parties in a fair and equitable manner can be a problem of substantial complexity. Considerable time and money may be spent determining the amount of contamination attributable to each party in order to apportion liability. Contaminant plumes that have evolved over long periods of time may affect large volumes of groundwater and require extensive remediation. Pump and treat remedial costs are driven by both the volume of water extracted and the mass of contaminants removed. Allocation methods based solely on the mass of contaminants contributed by each party are inadequate in this setting since they do not account for both components of the remedial costs. This paper presents an approach for equitably allocating remedial costs when addressing overlapping or commingled groundwater plumes. The method accounts for the major elements driving the costs of remediating dispersed contaminant plumes.     

MTBE Transport Screening Analysis in Vadose Zone Risk and Liability Apportionment Assessment

The problem of allocating liability cleanup costs is an arduous task when more than one potentially responsible party has contributed to the groundwater plume. This problem is most likely to be encountered when dealing with methyl- tert -butyl-ether (MTBE) contamination, as MTBE is seen to travel large distances in underlying aquifers. There has been a signi®cant effort in the recent past to develop liability allocation methodologies that incorporate fate and transport behavior and toxicological characteristics of the contaminants. The application of such methods often requires estimation of contaminant input from the vadose zone into the underlying aquifer. A screening level analysis is presented here to develop preliminary insights on relative mass contributions arising from different source types. The analysis illustrates how different vadose zone conceptualizations lead to vastly different contaminant loadings. Parametric studies indicate that the contaminant flux into the aquifer is very sensitive to changes in water infiltration rates. Hence, a reliable estimate of this parameter is critical for equitable allocation of remedial costs. Conceptual model formulation, should focus on identifying whether the fuel present in the aquifer can flow as a separate phase. It is also important to obtain reliable estimates for fluid saturations at the site.     

MTBE Transport Screening Analysis in Vadose Zone Risk and Liability Apportionment Assessment

The problem of allocating liability cleanup costs is an arduous task when more than one potentially responsible party has contributed to the groundwater plume. This problem is most likely to be encountered when dealing with methyl-tert -butyl-ether (MTBE) contamination, as MTBE is seen to travel large distances in underlying aquifers. There has been a significant effort in the recent past to develop liability allocation methodologies that incorporate fate and transport behavior and toxicological characteristics of the contaminants. The application of such methods often requires estimation of contaminant input from the vadose zone into the underlying aquifer. A screening level analysis is presented here to develop preliminary insights on relative mass contributions arising from different source types. The analysis illustrates how different vadose zone conceptualizations lead to vastly different contaminant loadings. Parametric studies indicate that the contaminant flux into the aquifer is very sensitive to changes in water infiltration rates. Hence, a reliable estimate of this parameter is critical for equitable allocation of remedial costs. Conceptual model formulation, should focus on identifying whether the fuel present in the aquifer can flow as a separate phase. It is also important to obtain reliable estimates for fluid saturations at the site.     

Simulation of the effect of remediation on EDB and 1,2-DCA plumes at sites contaminated by leaded gasoline

An analytical model is used to simulate the effects of partial source removal and plume remediation on ethylene dibromide (EDB) and 1,2-dichloroethane (1,2-DCA) plumes at contaminated underground storage tank (UST) sites. The risk posed by EDB, 1,2-DCA, and commingled gasoline hydrocarbons varies throughout the plume over time. Dissolution from the light nonaqueous phase liquid (LNAPL) determines the concentration of each contaminant near the source, but biological decay in the plume has a greater influence as distance downgradient from the source increases. For this reason, compounds that exceed regulatory standards near the source may not in downgradient plume zones. At UST sites, partial removal of a residual LNAPL source mass may serve as a stand alone remedial technique if dissolved concentrations in the source zone are within several orders of magnitude of the applicable government or remedial standards. This may be the case with 1,2-DCA; however, EDB is likely to be found at concentrations that are orders of magnitude higher than its low Maximum Contaminant Level (MCL) of 0.05 μg/L (micrograms per liter). For sites with significant EDB contamination, even when plume remediation is combined with source depletion, significant timeframes may be required to mitigate the impact of this compound. Benzene and MTBE are commonly the focus of remedial efforts at UST sites, but simulations presented here suggest that EDB, and to a lesser extent 1,2-DCA, could be the critical contaminants to consider in the remediation design process at many sites.     

Influence of temporally variable groundwater flow conditions on point measurements and contaminant mass flux estimations

Monitoring of contaminant concentrations, e.g., for the estimation of mass discharge or contaminant degradation rates, often is based on point measurements at observation wells. In addition to the problem, that point measurements may not be spatially representative, a further complication may arise due to the temporal dynamics of groundwater flow, which may cause a concentration measurement to be not temporally representative. This paper presents results from a numerical modeling study focusing on temporal variations of the groundwater flow direction. “Measurements” are obtained from point information representing observation wells installed along control planes using different well frequencies and configurations. Results of the scenario simulations show that temporally variable flow conditions can lead to significant temporal fluctuations of the concentration and thus are a substantial source of uncertainty for point measurements. Temporal variation of point concentration measurements may be as high as the average concentration determined, especially near the plume fringe, even when assuming a homogeneous distribution of the hydraulic conductivity. If a heterogeneous hydraulic conductivity field is present, the concentration variability due to a fluctuating groundwater flow direction varies significantly within the control plane and between the different realizations. Determination of contaminant mass fluxes is also influenced by the temporal variability of the concentration measurement, especially for large spacings of the observation wells. Passive dosimeter sampling is found to be appropriate for evaluating the stationarity of contaminant plumes as well as for estimating average concentrations over time when the plume has fully developed. Representative sampling has to be performed over several periods of groundwater flow fluctuation. For the determination of mass fluxes at heterogeneous sites, however, local fluxes, which may vary considerably along a control plane, have to be accounted for. Here, dosimeter sampling in combination with time integrated local water flux measurements can improve mass flux estimates under dynamic flow conditions.     

Liability Theories in Contaminated Groundwater Litigation

Disputes regarding contaminated sites have given rise to an explosion of federal and state court litigation. Congress enacted the Resource Conservation and Recovery Act of 1976 ("RCRA"), 42 U.S.C. §§6901 et seq. , as a contemplated "cradle to grave" regulatory scheme for solid waste, and passed the Comprehensive Environmental Response, Compensation, and Liability Act ("CERCLA"), 42 U.S.C. §§9601 et seq. , to address the investigation and remediation of contaminated sites. RCRA and CERCLA each contemplate a strict, joint and several regulatory liability scheme to address sites that have required billions of dollars to investigate and remediate, and which will require additional billions in order to complete the job. Federal and state law cases involving groundwater contamination cases have presented special challenges to litigants and the Courts. Determining the source of groundwater contamination is often a matter of technical dispute, particularly in the case of commingled plumes or older plumes where original point source locations can no longer be located or where there has been a significant amount of contaminant degradation over time. Contaminated plumes derived in whole or in part from potential continuing sources can present difficult remedy selection issues and uncertainty regarding future cost obligations. While a variety of federal and state law theories of liability are available to address groundwater contamination, each presents certain benefits and limitations. For example, CERCLA claims can cover a wide spectrum of potentially responsible parties and are based on strict liability; however, CERCLA excludes petroleum from the scope of its liability scheme and limits recovery to necessary response costs consistent with the National Contingency Plan. RCRA claims can include petroleum contamination, but cannot seek recovery of past costs. Common law theories such as nuisance, trespass and negligence can permit recovery of a broader scope of potential damages and provide for joint and several liability, but they are not based on notions of strict liability and sometimes present difficult statute of limitations problems. This article identifies federal and California state law liability theories addressing responsibility for groundwater contamination, and reviews the elements of liability, potential limitations on available relief, and recent case law developments under these theories.     

Transport of reactive colloids and contaminants in groundwater: effect of nonlinear kinetic interactions

Transport of reactive colloids in groundwater may enhance the transport of contaminants in groundwater. Often, the interpretation of results of transport experiments is not a simple task as both reactions of colloids with the solid matrix and reactions of contaminants with the solid matrix and mobile and immobile colloids may be time dependent and nonlinear. Further colloid transport properties may differ from solute transport properties. In this paper, a one-dimensional model for coupled and contaminant in a porous medium (COLTRAP) is presented together with simulation results. Calculated breakthrough curves (BTC's) during contamination and decontamination show systematically the effect of nonlinear and kinetic interactions on contaminant transport in the presence of reactive colloids, and the effect of colloid transport properties that differ from solute transport properties. It is shown that in case of linear kinetic reactions, the rate of exchange of mobile and immobile colloids have a large impact on the shape of BTC's even if the solid matrix is saturated with respect to colloids. BTC's during the contamination and decontamination phase have identical shapes in this case. Moreover, the slow reactions of contaminants and colloids may lead to unretarded breakthrough of contaminants. Independent of reaction rates, nonlinear reactions lead to BTC's that are steeper during contamination than in the linear case. A characteristic aspect of nonlinear sorption is that shapes of BTC's differ during the contamination and decontamination phase. It has been observed that shapes of some of the simulated adsorption and desorption curves are similar as shapes found in experiments reported in literature. This stresses the importance of incorporating both kinetics and nonlinearity in models for coupled colloid and contaminant transport and the capability of COLTRAP to interpret experimental results. Finally, to figure out whether nonlinear processes play a role, it is very important to consider both contamination and decontamination in transport experiments.     

Quantification of groundwater contamination in an urban area using integral pumping tests

In this paper, the integral groundwater investigation method is used for the quantification of PCE and TCE mass flow rates at an industrialized urban area in Linz, Austria. In this approach, pumping wells positioned along control planes perpendicular to the groundwater flow direction are operated for a time period on the order of days and sampled for contaminants. The concentration time series of the contaminants measured during operation of the pumping wells are then used to determine contaminant mass flow rates, mean concentrations and the plume shapes and positions at the control planes. The three control planes used in Linz were positioned downstream of a number of potential source zones, which are distributed over the field site. By use of the integral investigation method, it was possible to identify active contaminant sources, quantify the individual source strength in terms of mass flow rates at the control planes and estimate the contaminant plume position relative to the control planes. The source zones emitting the highest PCE and TCE mass flow rates could be determined, representing the areas where additional investigation and remediation activities will be needed. Additionally, large parts of the area investigated could be excluded from further investigation and remediation activities.     

Assessing the natural attenuation of organic contaminants in aquifers using plume-scale electron and carbon balances: model development with analysis of uncertainty and parameter sensitivity

A quantitative methodology is described for the field-scale performance assessment of natural attenuation using plume-scale electron and carbon balances. This provides a practical framework for the calculation of global mass balances for contaminant plumes, using mass inputs from the plume source, background groundwater and plume residuals in a simplified box model. Biodegradation processes and reactions included in the analysis are identified from electron acceptors, electron donors and degradation products present in these inputs. Parameter values used in the model are obtained from data acquired during typical site investigation and groundwater monitoring studies for natural attenuation schemes. The approach is evaluated for a UK Permo-Triassic Sandstone aquifer contaminated with a plume of phenolic compounds. Uncertainty in the model predictions and sensitivity to parameter values was assessed by probabilistic modelling using Monte Carlo methods. Sensitivity analyses were compared for different input parameter probability distributions and a base case using fixed parameter values, using an identical conceptual model and data set. Results show that consumption of oxidants by biodegradation is approximately balanced by the production of CH4 and total dissolved inorganic carbon (TDIC) which is conserved in the plume. Under this condition, either the plume electron or carbon balance can be used to determine contaminant mass loss, which is equivalent to only 4% of the estimated source term. This corresponds to a first order, plume-averaged, half-life of > 800 years. The electron balance is particularly sensitive to uncertainty in the source term and dispersive inputs. Reliable historical information on contaminant spillages and detailed site investigation are necessary to accurately characterise the source term. The dispersive influx is sensitive to variability in the plume mixing zone width. Consumption of aqueous oxidants greatly exceeds that of mineral oxidants in the plume, but electron acceptor supply is insufficient to meet the electron donor demand and the plume will grow. The aquifer potential for degradation of these contaminants is limited by high contaminant concentrations and the supply of bioavailable electron acceptors. Natural attenuation will increase only after increased transport and dilution.     

A regional flux-based risk assessment approach for multiple contaminated sites on groundwater bodies

In the context of the Water Framework Directive (EP and CEU, 2000), management plans have to be set up to monitor and to maintain water quality in groundwater bodies in the EU. In heavily industrialized and urbanized areas, the cumulative effect of multiple contaminant sources is likely and has to be evaluated. In order to propose adequate measures, the calculated risk should be based on criteria reflecting the risk of groundwater quality deterioration, in a cumulative manner and at the scale of the entire groundwater body. An integrated GIS- and flux-based risk assessment approach for groundwater bodies is described, with a regional scale indicator for evaluating the quality status of the groundwater body. It is based on the SEQ-ESO currently used in the Walloon Region of Belgium which defines, for different water uses and for a detailed list of groundwater contaminants, a set of threshold values reflecting the levels of water quality and degradation with respect to each contaminant. The methodology is illustrated with first results at a regional scale on a groundwater body-scale application to a contaminated alluvial aquifer which has been classified to be at risk of not reaching a good quality status by 2015. These first results show that contaminants resulting from old industrial activities in that area are likely to contribute significantly to the degradation of groundwater quality. However, further investigations are required on the evaluation of the actual polluting pressures before any definitive conclusion be established.     

Modelling of sequential groundwater treatment with zero valent iron and granular activated carbon

Multiple contaminant mixtures in groundwater may not efficiently be treated by a single technology if contaminants possess rather different properties with respect to sorptivity, solubility, and degradation potential. An obvious choice is to use sequenced units of the generally accepted treatment materials zero valent iron (ZVI) and granular activated carbon (GAC). However, as the results of this modelling study suggest, the required dimensions of both reactor units may strongly differ from those expected on the grounds of a contaminant-specific design. This is revealed by performing an analysis for a broad spectrum of design alternatives through numerical experiments for selected patterns of contaminant mixtures consisting of monochlorobenzene, tetrachloroethylene, trichloroethylene (TCE), cis-1,2-dichloroethylene (cis-DCE), and vinyl chloride (VC). It is shown that efficient treatment can be achieved only if competitive sorption effects in the GAC unit as well as the formation of intermediate products in the ZVI unit are carefully taken into account. Cost-optimal designs turned out to vary extremely depending on the prevailing conditions concerning contaminant concentrations, branching ratios, and unit costs of both reactor materials. Where VC is the critical contaminant, due to high initial concentration or extensive production as an intermediate, two options are cost-effective: an oversized ZVI unit with an oversized GAC unit or a pure GAC reactor.     

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.     

New methodology to investigate potential contaminant mass fluxes at the stream-aquifer interface by combining integral pumping tests and streambed temperatures

The spatial pattern and magnitude of mass fluxes at the stream-aquifer interface have important implications for the fate and transport of contaminants in river basins. Integral pumping tests were performed to quantify average concentrations of chlorinated benzenes in an unconfined aquifer partially penetrated by a stream. Four pumping wells were operated simultaneously for a time period of 5 days and sampled for contaminant concentrations. Streambed temperatures were mapped at multiple depths along a 60m long stream reach to identify the spatial patterns of groundwater discharge and to quantify water fluxes at the stream-aquifer interface. The combined interpretation of the results showed average potential contaminant mass fluxes from the aquifer to the stream of 272microgm(-2)d(-1) MCB and 71microgm(-2)d(-1) DCB, respectively. This methodology combines a large-scale assessment of aquifer contamination with a high-resolution survey of groundwater discharge zones to estimate contaminant mass fluxes between aquifer and stream.     

Assessing performance and closure for soil vapor extraction: integrating vapor discharge and impact to groundwater quality

Soil vapor extraction (SVE) is typically effective for removal of volatile contaminants from higher-permeability portions of the vadose zone. However, contamination in lower-permeability zones can persist due to mass transfer processes that limit the removal effectiveness. After SVE has been operated for a period of time and the remaining contamination is primarily located in lower-permeability zones, the remedy performance needs to be evaluated to determine whether the SVE system should be optimized, terminated, or transitioned to another technology to replace or augment SVE. Numerical modeling of vapor-phase contaminant transport was used to investigate the correlation between measured vapor-phase mass discharge, MF(r), from a persistent, vadose-zone contaminant source and the resulting groundwater contaminant concentrations. This relationship was shown to be linear, and was used to directly assess SVE remediation progress over time and to determine the level of remediation in the vadose zone necessary to protect groundwater. Although site properties and source characteristics must be specified to establish a unique relation between MF(r) and the groundwater contaminant concentration, this correlation provides insight into SVE performance and support for decisions to optimize or terminate the SVE operation or to transition to another type of treatment.     

Use of principal component analysis to profile temporal and spatial variations of chlorinated solvent concentration in groundwater

This work aims at evaluating spatial distribution patterns of concentration variations for chlorinated solvents in groundwater, based on principal component analysis and geographic information system (GIS) tools. The study investigates long-time series of chlorinated solvent concentrations in groundwater measured for 18 contaminated industrial sites. The characterization of contaminant plumes and delineation of pollutant sources are essential for choosing appropriate monitoring and remediation strategies, as contaminated groundwaters are characterized by complex patterns of spatial and temporal concentration variability, with wide unpredictable fluctuations over time. The present work describes the results of a new exploratory statistical method called the Variability Index Method (VIM) applied to environmental data to assess the performance of using concentration variations as molecular tracers to reveal aquifer dynamics, industrial impacts, and point sources for contamination plumes. The application of this method provides a useful assessment of controls over contaminant concentration variations as well as support for remediation techniques.     

Remedial Options for Leaking Underground Storage Tanks

Remedial options for leaking underground storage tanks were investigated in a joint project of the Electric Power Research Institute and the Underground Storage Tank Committee of the Utility Solid Waste Activities Group. Both existing and emerging technologies were examined. Thirteen remedial techniques were identified and initially characterized as in situ or non-in situ. In situ methods include volatilization, biodegradation, leaching and chemical reaction, vitrification, passive remediation, and isolation or containment. Non-in situ techniques include land treatment, thermal treatment, asphalt incorporation, solidification and stabilization, groundwater extraction and treatment, chemical extraction, and excavation. Soil and groundwater remediation problems have many site-specific considerations which must be considered in choosing an appropriate remedial option; these include cleanup goals, site and contaminant characteristics, cost, exposure pathways, and others. Appropriate remedial techniques are chosen by assessing technical, implementational, environmental and economic considerations of each available option to achieve the desired cleanup goal at the specified site.     

Comment on “Analysis of groundwater contamination using concentration-time series recorded during an integral pumping test: Bias introduced by strong concentration gradients within the plume” by Allelign Zeru and Gerhard Schäfer

We consider the results of a recent paper in this journal [Zeru, A. and Schäfer, G., 2005. Analysis of groundwater contamination using concentration–time series recorded during an integral pumping test: Bias introduced by strong concentration gradients within the plume. Journal of Contaminant Hydrology 81 (2005) 106–124], which addresses the field-scale characterisation of contaminant plumes in groundwater. There, it is concluded that contaminant concentration gradients can bias Integral Pumping Test (IPT) interpretations considerably, in particular if IPTs are conducted in advective fronts of contaminant plumes. We discuss implications of this setting and also argue that the longitudinal and transverse dispersivities used in the examples of Zeru and Schäfer (2005) of up to 30 m and 3 m, respectively, are generally very high for the here relevant capture zone scale (< 20 m). However, regardless of both longitudinal and transverse concentration gradients, we further show through a counter-example that IPT results are unbiased as long as the concentration attenuation along the flow direction is linear over the capture zone extent.     

A pragmatic approach for estimation of source-zone emissions at LNAPL contaminated sites

When considering natural attenuation as a remediation strategy at a site contaminated by a light non-aqueous phase liquid (LNAPL), it is important to consider the emission of contaminants from the source zone. A quantification of source-zone emissions is essential both for comparison with down-gradient mass fluxes to provide an estimate of fractional mass flux reduction, as well as for estimating the source lifetime. Because the spatial distribution of LNAPL at a field site is strongly dependent on both the spill circumstances and the heterogeneity of the geologic materials, which can be problematic for in-situ determination, alternative methods for estimating source-zone emissions are needed. In this work, a three-dimensional multiphase flow and transport modelling approach is used to investigate the relationship between the lateral extent of an LNAPL body and the emission of contaminants to groundwater at a contaminated site. For simulations involving an LNAPL release in an aquifer comprised of heterogeneous porosity and permeability distributions that were generated geostatistically, it is shown that a simple linear relationship exists between the lateral extent of the LNAPL body in the capillary fringe and the emission to the aqueous phase. The parameters describing the relationship are found to be linear functions of the groundwater flow velocity and the vertical infiltration rate. This site-specific relationship provides a simple method to estimate contaminant emissions to groundwater at LNAPL contaminated sites.     

Forensic Analysis of Chlorinated Hydrocarbon Plumes in Groundwater: a Multi-Site Perspective

Forensic analyses of chlorinated hydrocarbon plumes typically entail reviews of site records, flow and transport modeling, and analysis of indicator compounds to gain insights into the behavior of a contaminant plume in the subsurface. Such approaches are directed toward unraveling the specific circumstances associated with the disposal history and hydrogeology of a site. A complimentary approach is to compare the behavior of a particular plume with a population of plumes from other sites that may be influenced by similar mechanisms (e.g. transformation processes such as reductive dehalogenation). In other words, hypotheses pertaining to plume behavior can be tested against a knowledge base of what is typical behavior and what is not. To address this proposed methodology, three example applications of statistical techniques to a multi-site data set are presented to provide background for problems that may be pertinent to forensic analyses. These examples include measuring the frequency of association between selected chlorinated hydrocarbon compounds, assessing the effects of transformation processes on temporal concentration trends in populations of groundwater monitoring wells, and dating plumes, in a relative sense, by concentration correlation analyses. In each case, the results of the statistical analyses are consistent with expectation, indicating that meaningful trends in chlorinated hydrocarbon plume behavior may be discerned from a diverse multi-site data set.     

Comment on "Analysis of groundwater contamination using concentration-time series recorded during an integral pumping test: Bias introduced by strong concentration gradients within the plume" by Allelign Zeru and Gerhard Schäfer

We consider the results of a recent paper in this journal [Zeru, A. and Sch?fer, G., 2005. Analysis of groundwater contamination using concentration-time series recorded during an integral pumping test: Bias introduced by strong concentration gradients within the plume. Journal of Contaminant Hydrology 81 (2005) 106-124], which addresses the field-scale characterisation of contaminant plumes in groundwater. There, it is concluded that contaminant concentration gradients can bias Integral Pumping Test (IPT) interpretations considerably, in particular if IPTs are conducted in advective fronts of contaminant plumes. We discuss implications of this setting and also argue that the longitudinal and transverse dispersivities used in the examples of Zeru and Sch?fer (2005) of up to 30 m and 3 m, respectively, are generally very high for the here relevant capture zone scale (<20 m). However, regardless of both longitudinal and transverse concentration gradients, we further show through a counter-example that IPT results are unbiased as long as the concentration attenuation along the flow direction is linear over the capture zone extent.