Journal of Environmental Engineering

In situ mobility reduction resulting from the addition of water-soluble polymers to subsurface remedial fluid formulations has the potential to significantly improve the delivery and subsurface distribution of remediation agents within heterogeneous contaminated aquifer systems. However, the increased viscosity, non-Newtonian rheology, competing retention and acceleration mechanisms, and the potential for these fluids to reduce media permeability because of mechanical filtration of these large polymer molecules complicate treatment design calculations and often necessitate numerical simulation for purposeful evaluation and application of this technology. In this paper, laboratory and computational methods are presented that were used to characterize bulk fluid and porous media transport properties of xanthan gum biopolymer-amended fluids for the purpose of facilitating numerical simulation. A detailed discussion of polymerized fluid transport mechanisms and input parameters for simulating polymer transport using the University of Texas Chemical Composition (UTCHEM) simulator is provided. The simulator was used to validate the independently derived input parameters against the results of a five-layer, two-dimensional (2D) sand tank experiment. An overall 74% improvement in sweep efficiency was observed for the polymer-amended fluid within this sand pack, relative to the nonamended case.

The effects of retention time, duration of operation, and the relationship between surface area to depth ratio on nitrogen and phosphorus removal efficiencies were assessed in duckweed-populated flow-through experimental reactors. Reactors were designed so that a group of four reactors had the same surface area but each reactor in a group differed by both depth and detention times, and four sets of reactors had the same volume and detention time but differing surface areas. Removal efficiencies for nitrogen and phosphorus compounds decreased with increasing water depth and increased with increasing surface area to depth ratios. Nitrogen removal efficiency initially increased, reaching maximum removal efficiency after 6–7 days, approached approximately 100% removal efficiency for 9–10 days, and then exhibited a decrease in removal efficiency. Phosphorus removal efficiency reached a maximum after approximately 5 days, followed by reduced removal efficiencies with values approaching 0 after 12–20 days. Maximum productivity occurred at day 5 but was reduced to approximately 25% of maximum productivity by day 8. To maintain optimal productivity, duckweed harvesting should occur at 5-day intervals.

An asphalt cap system physically isolates contaminated soil from surface runoff to reduce contaminant migration from soil to groundwater. It is one of the most frequently selected remedies for managing sites contaminated by hazardous materials. However, despite its wide usage, the apparent permeability of aging caps has rarely been studied. Based on hydraulic calculations for simplified crack models, this study found that the apparent permeability of an aging cap is primarily influenced by the intrinsic permeability of cap materials and the geometry of cracks. The distribution of crack width, a key indicator of cap integrity, was examined for the first time with four asphaltic caps, aged 3, 4, 12, and 15 years, respectively. The apparent permeability of a 15-year-old cap was estimated to range from ${0.87\times 10}^{-5}$ to ${1\times 10}^{-7}\mathrm{cm}/\mathrm{s}$ in various areas. The overall average permeability was calculated to be ${1.3\times 10}^{-6}\pm {0.3\times 10}^{-6}\mathrm{cm}/\mathrm{s}$, representing an increase of nearly one order of magnitude from the permeability of a newly constructed asphalt cap. A spatial analysis indicated that the aged asphalt cap was the most permeable in staging areas or areas with increased traffic load.

The Rhode Island Coastal Resources Management Council (CRMC) has been leading an Ocean Special Area Management Plan (SAMP) aimed at zoning the state’s coastal waters to accommodate offshore wind farm developments. In previous SAMP related work, the authors had considered the wind farm siting issue as an optimization problem between wind resources and technological constraints. In the present analysis, the additional constraints on wind farm siting of ecosystem services “cost”, in particular ecological and social services, are explored in an ecosystem-based management (EBM) conceptual framework. An ecological typology of the coastal area is developed on the basis of ecological variables, using spatial multivariate principal component and cluster analyses. Then, the sensitivity of the resulting ecological subregions to wind farm impact is assessed through the construction of ecological services impact indexes. A fishery service index is used to assess the fisheries services constraints. Ecosystem services constraints are combined with the technological cost and the wind resources to provide a wind farm siting index (WiFSI), which can be used as a tool to identify optimal areas for wind farm siting. In the paper, the authors develop the conceptual approach and present its application to the SAMP area as a case study. The technological cost is based on wind turbines with lattice jacket support structures, as currently proposed in Rhode Island waters, and the WiFSI method is used to identify optimal potential wind farm sites in coastal and offshore Rhode Island waters.

Thermally-enriched stormwater runoff can negatively impact coldwater streams and their associated ecosystem services. The introduction of local and federal guidelines specifically targeting urban runoff temperature in the United States and Canada promulgate the use of practices that reduce thermal pollutant load from a catchment. Several stormwater control measures (SCM) have been shown to buffer thermal impacts to waterways by passing water through cooler subsurface media or by reducing overall discharge volume. Permeable pavement exposes stormwater to these mechanisms, which makes it a promising practice for thermal mitigation. A newly constructed permeable interlocking concrete paver (PICP) parking lot was monitored for 1 year in the mountain region of North Carolina to quantify runoff reduction, temperature buffering, and thermal load export. The effects on hydrology caused by internal water storage (IWS) in the pavement profile were also investigated by dividing the $239\text{-}{\mathrm{m}}^2$ lot into three cells with varying aggregate depths and drainage configurations. Results showed substantial stormwater volume reductions from all permeable pavement configurations, with the most pronounced reductions (99.6 and 100%) experienced in the shallow and deep IWS cells, respectively. Thermal loads from the conventionally drained cell, deep IWS cell, and shallow IWS cell were consequently reduced proportionally to rates of runoff reduction. Median stormwater effluent temperature from the conventionally drained cell (78% runoff reduction) exceeded the critical trout threshold temperature of 21°C; however, outflow only occurred during eight storm events (out of the 54 recorded) and exceeded 21°C for 10.5 h of the stream temperature monitoring period (4.7 h more than ambient stream conditions). Effluent from the two cells with IWS never exceeded trout threshold temperatures because of retention and exfiltration of virtually all incoming stormwater. Temperature differentials between the top and bottom of the PICP profiles suggest that buffering of extreme runoff temperatures can occur. The subsoil interface never reached freezing temperatures during the unseasonably cold winter months, suggesting that frost heaving of permeable pavement systems is not expected in similar climes. These results merit the use of PICP and perhaps other forms of permeable pavement, particularly with the incorporation of IWS, where thermal impact to streams is of concern.

Pressure drop ($\mathrm{\Delta }P$) as a function of air velocity ($V$) is a key parameter controlling air cleaning biofilter cost efficiency. At present the $V–\mathrm{\Delta }P$ relationship in biofilter materials must generally be determined experimentally, as no universal link between the $V–\mathrm{\Delta }P$ relationship and material physical properties have been established. The objective of this study was, therefore, to investigate the link between the $V–\mathrm{\Delta }P$ relationship, material particle size distribution, and wetting conditions for a common biofilter medium, Leca. Measurements of $V–\mathrm{\Delta }P$ was carried out for 36 different Leca particle size fractions with different mean particle diameter ($D_m$) and particle size range ($R$) under both dry and wet conditions. Measurements showed that increasing $D_m$ and decreasing $R$ together with wetted conditions in the filter generally resulted in decreasing $\mathrm{\Delta }P$ for the same $V$. A set of expressions allowing for accurate estimation of the $V–\mathrm{\Delta }P$ relationship based on $D_m$, $R$. and wetting conditions were established, enabling reliable estimation of filter pressure drop (and operation costs) in Leca and similar granular materials.

A model was developed and validated for predicting solubility and diffusion coefficients for contaminants permeating polyethylene (PE) materials used for water pipes and geomembranes. Model development was based on diffusivity and solubility of 13 contaminants and six PE materials that were new and/or aged in chlorinated water. Physical and chemical properties of the contaminants and PEs were included as variables in the model. Tree regression was used to select variables, and multiple linear regression was used to develop predictive equations for contaminant diffusivity and solubility in PE. Organic contaminant properties, especially dipole moment and octanol-water partition coefficient, had greater predictive capability than PE properties. Coefficients of determination $(R^2)>0.8$ were obtained for the multiple linear regressions. Model coefficients changed slightly between new PE materials and chlorine-aged PE, but these changes were not statistically significant. Good agreement was demonstrated between model predictions and measured data from an independent data set. These results provide guidance for material selection for both water pipes and geomembranes and assessing contamination potential.

Iron-coated granular activated carbon (Fe-GAC) was proven to be effective for removing selenite from aqueous solution in batch studies. Design and use of the adsorbent in column settings requires understanding the key mass transfer characteristics for full-scale applications. In this study, rapid small-scale column tests (RSSCTs) were conducted at various empty bed contact times (EBCTs). A pore and surface diffusion model (PSDM) was introduced to predict selenite breakthrough curves of continuous flow packed columns containing Fe-GAC. Effluent Se(IV) breakthrough occurred immediately in the experiment with 0.055-min EBCT. The column reactor was found to treat approximately 780 bed volumes of water containing $1.0\mathrm{mg}/\mathrm{L}$ Se(IV) when EBCT was increased to 0.447 min before breakthrough occurred. The adsorption capacity was estimated to be $3.06\mathrm{mg}/\mathrm{g}$. The adsorption results showed that the PSDM could provide satisfactory predictions for the column performance with the external mass transport coefficient ($k_f$) of $8.55\times {10}^{-3}\mathrm{cm}/\mathrm{s}$. Full-scale column design criteria, such as hydraulic loading rate (HLR), carbon usage rate (CUR), and degree of column utilization (DoCU) were calculated and recommended.

To probe the particle effect on gas-liquid mass transfer in three-phase flow, a series of comparative tests was conducted in a stirred reactor with flat gas-liquid interface in which four kinds of solid particles, i.e., powdered activated carbon (PAC), kieselguhr, barium sulfate (${\mathrm{BaSO}}_4$), and granular activated carbon (GAC) were introduced, respectively. The enhancement factor ($E^p$) for oxygen transfer could be controlled by both the interfacial turbulence and particle species. Either low film mobility or turbulent interphase would limit the particle-induced promotion of mass transfer, which could not be explained by the so-called shuttle effect. The effect of fine particles on $E^p$ follows the order of $\mathrm{PAC}>\text{kieselguhr}>{\mathrm{BaSO}}_4$ opposite to the sequence of particle densities (i.e., ${\rho }_{\mathrm{PAC}}<{\rho }_{\text{kieselguhr}}<{\rho }_{{\text{BaSO}}_4}$), suggesting the key role of particle density on its interfacial performance. The particle impact on mass transfer intensity would militate only when the size was small enough. It was assumed that the collision between particles and the gas-liquid interface and the particle interactions might have played the decisive role on altering the efficiency of oxygen transfer, and an $E^p$ model was developed accordingly to describe this process as a function of particle concentration. Experimental data fit well with the model, which confirms the validity of the assumption for the enhancement effect functioned by particles.

The speciation and distribution of the nutrients nitrogen and phosphorus in riverbed sediment play an important role in river water quality and are the primary product for the river ecosystem. Previous research on river nutrients has not considered the relationship between nitrogen and phosphorus and their mobility effects. To investigate the role of nitrogen and phosphorus in water quality and their interactions between sediments and water, sediment and water samples were taken from 10 sites along the middle main stream of the Huai River in China from Linhuaigang to Fengtai County on December 12, 2008. Nitrogen and phosphorus concentrations in water, organic matter (OM), and different forms and contents of the elements in sediment were investigated. Results showed a positive correlation between total nitrogen in sampled sediments, primarily occupied by organic nitrogen and chlorophyll $a$ concentrations in water ($r^2=0.727$). Total phosphorus in sediments was primarily represented as inorganic phosphorus, accounting for 80.9–96.1% of total phosphorus. The concentrations of non-apatite inorganic phosphorus in sediment ranged from $70.85–231.27\mathrm{mg}/\mathrm{kg}$. Results from statistical correlation analyses showed that the non-apatite inorganic phosphorus content in sediment was obviously negatively correlated with total nitrogen concentration in water ($r^2=-0.875$, $p<0.01$); inorganic nitrogen and non-apatite inorganic phosphorus contents in sediment were positively correlated with total phosphorus and resolvable phosphorus concentrations in water, respectively. Furthermore, data of May 2008 were added and analyzed. The same principles were observed between total nitrogen and non-apatite inorganic phosphorus, total phosphorus and inorganic nitrogen, but a positive correlation was found between (1) total nitrogen in water and (2) exchangeable nitrogen ($p<0.01$) and inorganic nitrogen ($p<0.05$) in sediments.

The inhibition of bromate (${\mathrm{BrO}}_3^{-}$) formation during ozonation with a novel granular molecular sieve catalyst, Ce-MCM-48, was investigated in pilot-scale under simulated practical conditions by varying the initial bromide (${\mathrm{Br}}^{-}$) concentration, total organic carbon (TOC) content, aqueous ozone concentration, water pH, and hydraulic retention time (HRT). The results indicate that the inhibition efficiency of Ce-MCM-48 for ${\mathrm{BrO}}_3^{-}$ formation could reach 82–90% as the initial ${\mathrm{Br}}^{-}$ concentration varied from $200–800\mathrm{\mu g}/\mathrm{L}$ under typical water treatment conditions: aqueous ozone $\text{concentration}=2.0\pm 0.1\mathrm{mg}/\mathrm{L}$, $\mathrm{HRT}=10\min$, initial $\mathrm{pH}=7.7–7.9$, and $T=18\pm 2°\mathrm{C}$. The extension of HRT from 10 to 20 min and pH variation in the range of 6.0–9.0 had insignificant impact on the inhibition efficiency of ${\mathrm{BrO}}_3^{-}$ formation. Compared with ozonation alone, the catalytic ozonation could achieve almost the same efficiencies for TOC removal and Escherichia coli inactivation. A long-term continuous operation experiment for 33 days demonstrated that the granular catalyst Ce-MCM-48 possesses not only a high efficiency, but also a large treatment capacity for minimizing ${\mathrm{BrO}}_3^{-}$ formation during the ozonation process, and thus has potential applications to water treatment.

Computer waste has emerged as a critical issue globally because of the growing quantity of waste and problems arising out of its toxic nature. In India, it is estimated that 480,000 t of electronic waste (e-waste) is generated annually. Computer waste includes plastics and metals that have a good potential for recycling; however, if not managed properly, the additives and chemicals in plastic waste and traces of heavy metals raise concern for human health and the environment. Efficient e-waste management will require a strategy that offers a win-win situation for all the involved stakeholders. This paper uses a game-theoretic approach for analyzing the strategies by identifying the equilibrium points for various scenarios that can help in deciding the incentives and penalties for deriving the self-propelling market-based mechanism for efficient management of e-waste. Results suggest that applying take-back schemes with some incentives to the consumers and penalty to those who do not follow the prescribed procedure for discarding e-waste could be very useful to discourage the land disposal of computer waste. Nash-equilibrium implies that the recycler would prefer to collect the computer waste directly from the consumer only if the incentive return to the consumer is less than 15% of the price of the computer, the recycling fee is less than 5% of the price of the computer, and the price of the recycled material is more than 15% of the price of the computer; otherwise collect it through the producer. Also, for the producer, it would be preferable to take an extra fee from the consumer for end-of-life management of the desktop computer as an advance recovery fee (apparent fee) only up to 4.0% of the cost of the computer. If the producer had to take an extra fee more than 4.0%, it should be taken as an extended producer responsibility fee (hidden fee combined in the cost) so that computer sales are not affected.

A Bayesian chemical mass balance (CMB) source apportionment method is developed using the Markov Chain Monte Carlo (MCMC) approach. Compared with deterministic approaches, the Bayesian method is capable of accounting for the measurement errors and the impact of variability of the source elemental compositions resulting from the heterogeneities and estimate the uncertainties associated with the estimated source contributions. The method estimates the joint probability densities and consequently, the credible intervals and correlation matrices of source contributions of various sources into a receiving water using observed elemental profiles of samples from both potential sources and the receiving surface waters. The model is applied to samples collected from possible sources and runoff and stream flow from two stream crossing sites along Highway 89 in the Lake Tahoe Basin. The contributing sources of total dissolved nitrogen, total dissolved phosphorus concentrations, and microparticles ($<20\mathrm{\mu m}$) from traffic and non-traffic-related sources have been evaluated using the method. The results showed that the model is capable of predicting the source contributions for the dissolved and particulate samples. During both rain events and snowmelt, deicing salt is a major source of dissolved solids whereas vegetation was to be the major source of dissolved nitrogen and phosphorus. Soil was found to be the primary source of microparticles and particulate phosphorus. The method does not definitively show contribution from traffic-related sources; however, in some cases it cannot conclusively rule out a significant contribution from them. The observed credible intervals for dissolved constituents were narrower compared with microparticle samples.

This paper explores methods for analyzing onboard mass emissions data and developing modal models on the basis of case study examples for nine selected nonroad construction vehicles. Data for these vehicles were obtained from the U.S. Environmental Protection Agency (EPA). Several modeling methods were explored, including stratification of the data into operating modes and supplementing the modal models with ordinary least-squares regression and multiple least-squares regression. The modal approach offers the advantages as conceptually the simplest, reducing the influence of autocorrelation in the model and providing substantial explanatory power. The normalized relationship between predicted mode-specific average emissions and exhaust flow is stable, similar, and consistent for all vehicles. For a given engine, the average emission rate can vary by more than a factor of two when comparing highest to lowest rates among different duty cycles. Some engines are common to different types of equipment, such as bulldozers and front-end loaders. For a given type of equipment, such as bulldozers, average ${\mathrm{NO}}_{\mathrm{x}}$ and ${\mathrm{CO}}_2$ mass emission rates can vary by more than 50% depending on the duty cycle. Vehicle category-specific modal models are recommended on the basis of onboard second-by-second in-use activity and emissions data and for use in new modeling tools to estimate emissions produced by nonroad construction vehicles.

Urban development, in addition to causing changes in the hydrological cycle, increases the amount of pollutants as the result of anthropogenic factors such as land use, local activities, and regional traffic. This study aimed to quantify pollutants related to sediments of different sizes on impermeable surfaces. The knowledge that the amount of various pollutants is associated with sediment size is important in the design of treatment facilities capable of removing most of the polluted sediments. The study region is the Cancela Basin, located in Santa Maria, Brazil. Pollutants were quantified in relation to the various sizes of sediments on the impervious surfaces of streets having similar levels of urbanization but different traffic intensities and gradients. Dry sediment samples collected prior to rainfall and surface runoff sediment samples collected during rainfall were separated into four granulometric bands ($\le 63\mathrm{\mu m}$, 63–250 μm, 250–500 μm, and $\ge 500\mathrm{\mu m}$). Organic pollution and nutrient and heavy metal contents were evaluated for each granulometric band. Heavy metals were more concentrated in samples representing granulometry levels $\le 63\mathrm{\mu m}$. In the dry sediment samples, the chemical oxygen demand (COD) and phosphate contents were found in samples representing granulometry levels $\ge 500\mathrm{\mu m}$. Ammonia, nitrates, lead, and zinc were associated with the 63–250 μm granulometric band.

Characterizing the incoming pollution load from contributing watersheds is a basic requirement to assess the functioning of storm water treatment systems. These systems are often built with assumed design performances, but their pollution loads and functioning are seldom checked, making their efficacy questionable. This paper presents a case study of a storm water system built in a 40-ha residential catchment in Gainesville, Florida. Despite its promising performance and assumed low pollution load, a receiving wetland basin overfilled with sediments, and a polishing pond was overgrown with algae. It was hypothesized that the system was not functioning as designed as a response to high sediment loads and poor treatment performance; hence, an investigation was carried out to quantify the suspended sediments through the storm water system during runoff events. Ten events were collected and analyzed for suspended sediment concentration (SSC), sediment mass load, and first flush intensity. In addition, total phosphorus (TP) associated with different particle fractions was analyzed. Results from this study showed that SSC event mean concentration (EMC) was $23.7–194.6\mathrm{mg}/\mathrm{L}$ in untreated runoff, $8.8–65.1\mathrm{mg}/\mathrm{L}$ after a hydrodynamic separator (HDS), and $4.6–107.5\mathrm{mg}/\mathrm{L}$ in the receiving water. A large first flush intensity was found in most events, with 43–86% of the total mass of particulate matter (PM) coming during the first 20% of the storm water volume. Total phosphorus concentration in runoff was typical of similar land uses in Florida, ranging from 0.162 to $0.834\mathrm{mg}/\mathrm{L}$. Event mean concentration and load of PM were not significantly greater than estimates for similar catchments, but the HDS removal efficiency (46–88%) was considerably lower than the design estimates. These findings support the need for proper monitoring and maintenance of storm water treatment units despite their pollution loading intensity.

A major waste stream from antibiotic production is mycelia sludge. This paper explores the use of an aerobic thermophilic bioreactor with solids separation and chemical treatment (acid hydrolysis and oxidation) of excess sludge to treat this waste. This system was evaluated for reduction of total chemical oxygen demand (TCOD) and volatile suspended solids (VSS). The investigation was split into three phases. Phase 1 was the treatment of 5% [weight/volume (w/v)] mycelia waste (with an average TCOD of $92,400\mathrm{mg}/\mathrm{L}$ and VSS of $46,000\mathrm{mg}/\mathrm{L}$). Phase 2 was the treatment of 1% (w/v) mycelia waste in combination with effluent from the antibiotic recovery plant (average TCOD of $36,000\mathrm{mg}/\mathrm{L}$ and VSS of $8,900\mathrm{mg}/\mathrm{L}$), and Phase 3 was as for Phase 2 with chemical treatment. The system was run for 92 days without accumulation of organic or inorganic solids, even though no sludge was wasted from the reactor. The mycelia sludge proved to be readily biodegradable in Phase 1 (average TCOD destruction was 82% and average VSS destruction was 89%). An acclimatization period of 37 days was required when the mixed antibiotic wastewater was introduced in Phase 2. After this period, the average TCOD destruction was 83%. Chemical treatment in Phase 3 improved and stabilized VSS destruction (from 76% in Phase 2 to 87% in Phase 3). This study demonstrates that this system can be used to effectively treat mycelia sludge, both alone and combined with a mixed antibiotic wastewater, with minimal excess sludge formation.

Snow collected from roadways in northern climates is not pristine and may contain sand or gravel, deicing agents, litter, and airborne pollutants. Although fate and transport of contaminants in snowmelt has been studied under laboratory conditions, it is unknown whether the same mechanisms apply to a heterogeneous snow pile. This case study sought to identify and quantify organic species in snow pile meltwater in Edmonton, Canada, and estimate the total potential hydrocarbon loading bound to sediment. Analysis of meltwater and sediment samples revealed that most hydrocarbons were present in sediments, with meltwater containing low concentrations ($<1\mathrm{mg}{\mathrm{L}}^{-1}$) of F2 ($>\mathrm{C}10–\mathrm{C}16$) and F3 ($>\mathrm{C}16–\mathrm{C}34$) fraction hydrocarbons. Sediments showed detectable levels of F2 and F3 hydrocarbons in $\sim 21\%$ of the samples tested, with concentrations ranging from approximately 600 to $7,800\mathrm{mg}·{\mathrm{kg}}^{-1}$, with average F3 concentrations (the main source of hydrocarbons) well below Canadian guidelines for most samples. The estimated total hydrocarbon loading of the snow pile studied was $\sim 5.1\mathrm{t}$ of hydrocarbons. Findings are anticipated to be of value in the establishment of water quality monitoring programs, environmental policy and strategies involving the treatment, disposal, or reuse of residual snow pile sediments.

The effects of temperature, light exposure, and pH on the interconversion of Cr(III) and Cr(VI) in two chlorinated drinking water samples (groundwater and surface water) over a 28-day period were investigated. Six conditions were tested including exposure to a grow lamp (29°C), overhead fluorescent light (20°C), no light (20°C), incandescent light (10°C), no light (4°C), and no light ($-19°\mathrm{C}$). Each condition was tested at pH 7 and 9. No clear interconversion of Cr(VI) and Cr(III) was observed in either the groundwater or surface water under any of the storage conditions except for the surface water samples adjusted to pH 9. These samples provided firm evidence for the conversion of Cr(III) to Cr(VI) at temperatures of 29 and 10°C, with an increase in Cr(VI) concentration from an initial value of 2 ppb ($\mathrm{\mu g}/\mathrm{L}$) to a final value of 10 ppb over 28 days. Further research into whether conversion occurs at low temperatures is recommended to determine whether a hold time of 30 days (used in a standard method) is appropriate.

This paper presents methods for estimating Freundlich isotherm fitting parameters ($K$ and $N$) and their joint uncertainty, which have been implemented into the freeware software platforms R and WinBUGS. These estimates were determined by both Frequentist and Bayesian analyses and subsequently compared with a commonly applied method in which the Freundlich parameter uncertainty is treated independently. By accounting for joint uncertainty in $K$ and $N$, smaller uncertainty regions resulted compared with independent uncertainty estimates, with this effect becoming more pronounced as the degree of nonlinearity increased (i.e., as $N$ decreased from 1). To illustrate the impact when considering uncertainty in adsorption system design, an example is provided in which, at a 95% confidence level, considering joint uncertainty decreased the required sorbent by 57–72% (depending on equilibrium liquid concentration, $C_W$) relative to the commonly applied independent uncertainty treatment of $K$ and $N$.