Journal of Environmental Engineering

A model, incorporating Darcy's law, is developed for single‐species gas flow inside a nonisotropic porous medium, within which gas is continuously generated. A linear parabolic equation is derived to express the internal pressure variations in terms of the permeability, gas production rate, and boundary conditions of a site when a series of extraction wells are present. The model is used to determine the gas fluxes within a site of rectangular cross section, into which an arbitrary number of horizontal extraction pipes have been installed. This solution is used to predict the consequences of cumulative failures within a complex pumping system, and hence estimate the circumstances under which gas is first able to escape from a site. Using the results of the model some brief guidelines are offered for designing such installations. The analytical solution technique is contrasted with purely numerical methods for similar problems, and the speed and accuracy of each are compared. An efficient computer implementation for preliminary design studies is suggested.

Methane production from the decomposition of municipal refuse is well documented. However, there is little information on the extent to which the chemical constituents of refuse degrade. Decomposition of shredded municipal refuse was studied under laboratory conditions with leachate recycle and neutralization. Containers were destructively sampled weekly for solids analysis. Cellulose and hemicellulose accounted for 91% of the methane potential of municipal refuse. Mineralization of 71% of the cellulose and 77% of the hemicellulose was measured in a container sampled after 111 days. The average carbon recovery obtained from mass balances on the decomposed refuse was 88.4% with a range of 64–111%. The measured methane yield was between 77 L and $107L{\mathrm{CH}}_4\mathrm{per}\mathrm{dry}\mathrm{kg}$ of refuse. Mass balances suggested that the yield may be as high as $152L{\mathrm{CH}}_4\mathrm{per}\mathrm{dry}\mathrm{kg}$ of refuse. Mass balances also showed an imbalance between the soluble sugar concentration of fresh refuse and the mass of terminal electron acceptors (oxygen and nitrate) available for sugar oxidation to carbon dioxide. This imbalance explained an observed decrease in refuse pH and the accumulation of carboxylic acids shortly after the initial incubation.

The paper presents a simple model for estimating leakage through a compacted clay barrier for a single inflow event. This algebraic model yields estimates of leakage fraction that compare closely with those obtained by solving the governing partial differential equation numerically. The algebraic model exhibits negligible bias and a standard error of estimate of less than 20% over its range of applicability. In most practical cases, the leakage fraction for a single inflow event is largely determined by the value of a single dimensionless parameter termed the leakage number. This parameter accounts for the hydraulic conductivities of the drainage layer and barrier, the lateral drainage distance, the barrier slope, the drainage‐layer porosity, and the inflow volume. The effects of inflow duration and barrier thickness on leakage tend to be relatively minor. The practical application of the leakage model is illustrated in a design example.

To design a drainage system for a landfill cover or bottom liner properly, the engineer must be able to estimate the maximum saturated depth over the barrier for any proposed configuration. This paper presents an analytical solution for steady drainage on a sloping impervious barrier with no flow across the upstream boundary. Based on the Dupuit approximation, this solution defines all possible phreatic‐surface profiles. The shape of the phreatic‐surface profile depends on the values of three dimensionless parameters: the barrier slope, the ratio of the vertical inflow rate to the hydraulic conductivity of the drainage layer, and the ratio of the saturated depth at the downstream boundary to the maximum drainage distance. Several distinctly different types of profiles are possible. A graph is provided for determining the maximum saturated depth directly.

The diffusion effects occuring in a biofilm in which a consecutive bioreaction takes place are studied theoretically, and effectiveness factors $\left(\mathrm{Ef}\right)\text{,}$ which evaluate the effect of the diffusion rates on substrate decomposition rates, are represented by a simple algebraic relation expressed in terms of normalized substrate bulk concentrations (B) and normalized characteristic biofilm parameters. On the other hand, the overall decomposition rates of the substrates can be expressed by a Monod‐type equation for the substrate bulk concentration. The apparent half velocity constants in the Monod‐type rate equation are affected by the diffusion and biochemical reaction rates of the substrates. The ratio of the apparent half velocity constants to the corresponding specific half velocity constants (λ) is related to $\mathrm{Ef}\text{.}$ The relationship is expressed in the following equation: $\mathrm{Ef}=(1+B)/(\lambda +B)\text{.}$ The applicability of these theoretical relations is experimentally demonstrated in volatile fatty acids decomposition. This equation may be rationally used for the design and/or performance of biofilm reactors.

This study was undertaken to evaluate the laboratory performance of the anaerobic fluidized bed digesting secondary biological sludge at 35 °C with four hydraulic‐retention times (HRTs): 1, 2.5, 5, and 10 days. In addition, the effects of both operating temperature (15 °C, 25 °C and 35 °C) and the initial sludge solubilization on the digester performance were also examined. It was found that at 35 °C, an adequate degree of sludge digestion was obtainable with an HRT of only 1–2 days if the influent biological sludge was presolubilized by treatment with 17.5 meq/L of sodium hydroxide. If no presolubilization was used, the necessary HRT was increased to 10 days. When the temperature was decreased to 25 °C and the sludge was presolubilized, the required HRT was 2.5–3 days. However, as the temperature was further decreased to 15 °C, the system was unable to achieve adequate digestion in as long as 10 days, even with presolubilization. It was also observed that the fluidized‐bed system was able to accept abrupt increases of loading without a corresponding buildup of excessive organic acids.

A model has been developed to describe the gas production and soluble‐COD variations from the digestion of waste‐activated sludge in the anaerobic fluidized‐bed reactor. It indicates that a substantial rate increase can be attained by prehydrolysis of the biological sludge, external to the reactor. The model indicates that the rate‐limiting step is in the sludge hydrolysis. The model is developed from an assumption of first‐order kinetics in a set of series and parallel, irreversible reactions. That is, the formation of soluble substrate is first order with respect to the particulate biomass present, and that the production of methane is first order with respect to the soluble substrate present. The amount of particulate biomass can be approximated by the sludge‐suspended solids and that the amount of soluble substrate can be approximated by the soluble COD present in the reactor. The model correlates well with the laboratory data observed in the study.

A linear programming, diameter discretization, heuristic approach is presented for the optimum design of large gravity sewer networks. The mathematical model contains a nonlinear convex function relating pipeline diameter and slope, which is approximated by piecewise linear segments. This approach uses a modified Hazen‐Williams hydraulic model at part‐full flow conditions, along with a newly developed universal expression to determine the coefficient of roughness. Moreover, the hydraulic formulation contains a regression equation to determine Darcy's friction factor based on the depth of flow in the pipe. The developed model has been extensively and successfully used to design several large sewer networks.

The design of class‐I (discrete particles) settling tanks would be more rational and economical if designed for overall particle removal rather than for an overflow rate based on the smallest particle to be removed. The overall percentage removals of discrete particles corresponding to different overflow rates were evaluated for several sets of samples having different sieve‐analysis parameters (different combinations of the effective size and the nonuniformity coefficients). A predictive model has been developed for evaluating the overall percentage removal from sieve‐analysis parameters, such as the effective size and the nonuniformity coefficient of the discrete particles present in the influent. Such a model can be used for a rational fixing of the design overflow rate to provide the desired overall percentage removal of the particles of a given size distribution. The experimentally observed data of several other researchers are found to be in total agreement with the values predicted from the writer's model. This justifies the robustness of the presented model.

Batch equilibrium studies are conducted under controlled laboratory conditions to determine the volatilization rate for perchloroethylene (PCE) from water and soil. The PCE is observed to volatilize rapidly from water. The rate of volatilization and the rate constant of PCE from water are found to increase with an increase in area to volume ratio but are independent of aqueous PCE concentration. Rate constants determined in this study indicate that aqueous PCE volatilizes faster from soil than from water. However, volatilization from soil depends not only on area to volume ratio but also on the presence of organic carbon and concentration of aqueous PCE applied to the soil. The greater the organic carbon of soil media content, the slower is the rate of volatilization. The rate of volatilization of pure PCE from soil is comparatively low and is greatly retarded by organic carbon content of the soil. A flux experiment is also carried out with pure PCE. The results indicate a low flux rate of submerged PCE into a stagnant water column.

The seasonal and long‐term variations of dissolved solids in lakes and reservoirs are analyzed in accordance with the hydrologic‐ and mass‐balance equations. The volume and surface area are expressed as power functions of depth that yield analytical solutions for the long‐term analysis. The equation defining the water elevation and volume may be approximated by exponential functions that simplify the solution of the mass‐balance equation of the dissolved solids. For the intermediate and seasonal time scales, periodic and exponential functions define the hydrologic components, providing the forcing functions for the dissolved solids equations. For both cases, an exponential residence time transforms the mass‐balance equation, leading to analytical solutions. Given the mass and volume, the concentration follows. The temporal variations of dissolved solids, calculated by the associated mass and volumetric equations, are compared to the observed change in salinity in lakes and reservoirs of various geophysical and hydrological characteristics.

A predictive mathematical model that describes the adsorption and biodegradation phenomena in recycle fluidized‐bed (RFB) adsorbers was developed. The model incorporated liquid film transfer, biodegradation and diffusion in the biofilm, adsorption onto activated carbon, and biofilm growth. The model equations were solved by a combinatorial technique involving the methods of orthogonal collocation and finite differences. Computer simulations of the model were used for adsorber performance predictions from parameters obtained from adsorption equilibrium and kinetic studies, biokinetic experiments, and correlation techniques. Sensitivity tests were also performed to determine the effect of physical and biological parameters on model profiles. Recycle fluidized adsorber experiments were conducted to test the predictive capability of the model. Two ideally biodegradable compounds, glucose and sucrose, as well as two actual wastewaters, a dairy waste and a landfill leachate, were used to compare the predicted model profiles with experimental data for nonbioactive and bioactive RFB adsorbers. The performance predictions obtained from modeling were in satisfactory agreement with the experimental data.

The ammonia-volatilization efficiencies of sprinklers (9/32-in.- and 5/16-in.-nozzle sizes), fan nozzles, and gated pipe are studied. Median ammonia-volatilization efficiencies over that occurring with gated pipe of 11.6%, 7.74%, and 2.8% are found for 9/32-in. (0.7cm) and 5/16-in. (0.80cm) sprinklers and for fan nozzles, respectively. The difference in volatilized efficiency between all application devices is significant. Sprinklers volatilize significantly more ammonia than do fan nozzles, which, in turn, volatilize more ammonia than does gated pipe (p = 0.025). Sufficient data are not available to determine the effects of water or air temperature or pH on volatilization. The amount of ammonia volatilization is not sufficiently large to be of design significance.

In aqueous solutions, un-ionized ammonia exists in equilibrium with the ammonium and hydroxide ions. The toxicity of these solutions has been primarily attributed to the un-ionized species although both forms are toxic at certain concentrations. The concentration of un-ionized ammonia in water is a function of the total ammonia concentration, pH, temperature, and ionic strength; and a number of these variables are functions of the time of day. In this paper, a technique for reducing estimates of un-ionized ammonia made at arbitrary time of day to a daily average value is presented. As an example, this technique is applied to Las Vegas Bay, an arm of Lake Mead.

A field test is performed to determine the upwelling flow from a 20-m deep air diffuser operating in Upper Bear Creek reservoir in northern Alabama. Dye is injected at a constant rate from a 6-m long diffuser pipe directly above the 12-m long air diffuser. Dye concentrations and velocities are measured in the flow-away current to estimate the total upwelling flow. The field estimate is compared to equations from the literature. The measured Upper Bear Creek diffuser upwelling flow is consistent with these equations for the normal air flow rate of 0.012 m³/sec. The dye and velocity measurements indicate an upwelling flow of 12 m³/sec and 10 m³/sec, respectively. A second test with an air flow rate of 0.024 m³/sec indicates an upwelling flow of 18 m³/sec from the dye dilution and 13 m³/sec from the velocities.