Lumped Parameter Models
A Single-cell, Lumped Parameter Model A lumped parameter water balance model is used to simulate the temporal trends of spatially-averaged condition of the entire area of interest. This area of interest can be a groundwater basin, a watershed, or a contaminated site. Develop an equation that describes the water and solute mass balance for a watershed. Solve (i) the water balance equation for the aquifer head and outflow rate; and (ii) solute mass balance equation for the mean solute concentration as a function of time and outflow rate of solute mass. Finally, calculate the residence times for water and solute and comment on their relative magnitude and the factors controlling their magnitude. (Lumped Parameter Models- 8)  
Groundwater Contamination due to septic tanks Domestic waste water is currently discharged into individual septic tanks which drain to groundwater system. The discharge of waste water into the aquifer has produced an increase in nitrate concentration in the aquifer and in the sloug. A sewer construction program has been proposed as one way of controlling aquifer and slough pollution. Develop a water quality balance analysis to evaluate the effectiveness of the sewer construction program. (Lumped Parameter Models- 8)  
Lake / Aquifer Eutrophication and the Sewer Project Intermediate to Advanced - Contaminant mass balance in mixed systems; groundwater-lake coupling. Background: A sewer construction program has been proposed as a method of controlling eutrophication in a small lake which is surrounded by suburban community. The lake receives practically all of its water from a phreatic groundwater system which surrounds the lake. Evaporation from the lake surface is equal to precipitation. Suburban development is distributed throughout the groundwater basin. Domestic waste water is currently discharged into individual septic tanks which drain to the groundwater system. Water supply is also obtained from the ground and consumptive use is small. (Lumped Parameter Models- 8)  
Accidental Pesticide Spill - I As a result of a labeling error, a banned water-soluble pesticide was accidentally applied over an agricultural area. The area is drained by a small creek which sustains the flow entirely as a result of subsurface drainage from the agricultural area. Inhabiting the creek is the largest known population of a rare and endangered species of minnow which is particularly sensitive to environmental contamination. Concentrations of the pesticide greater than 50 ppb are known to be toxic to this species of minnow. The state environmental agency proposed to do a 9 mo., $500,000 sampling and modeling study before recommending any action. Environmentalists propose that a soil-treatment process applied to the upper 20 cm of the soil be initiated immediately. This will cost several million dollars and involved tilling of the soil which would destroy the crops. The farmers have suggested that the problem be solved by capturing the minnows and holding in a fish hatchery for a few months until the creek contamination has cleared. You are hired to develop a quantitative analysis of these proposals. (Lumped Parameter Models- 8)  
A Multi-Cell Lumped Parameter Model A multi-cell, lumped parameter model is also known as Tank model for regional groundwater flows. It has the advantage of being computationally very efficient, and is particularly useful / needed when data available is limited. Consider a four-cell aquifer model of specified dimensions and natural replenishment. Find the steady-state head in each cell relative to the river elevation using an analytical approach. Solve the problem using MAGNET and compare the results. (Lumped Parameter Models- 8)  
Capping of a Landfill Water levels in the St. Johns landfill is well above the water level in the surrounding surface water bodies due to infiltration of precipitation. This provides a driving force for leachate loading into the surface waters as well as the deep aquifer below the landfill. Metro recently capped the landfill to prevent further infiltration of precipitation. You are asked to evaluate to evaluate the effectiveness of landfill capping by developing an analysis which describes the dissipation of the leachate mound inside the landfill (Lumped Parameter Models- 8)  
Containment of a Contaminated Site using a Slurry Wall A contaminated waste disposal site is contained by constructing a slurry wall keyed into an aquitard. A contaminated waste disposal site is contained by constructing a slurry wall keyed into an aquitard as shown below. The contained area is roughly circular with radius R and is covered with a clay cap which prevents infiltration of precipitation. For the given parameters, find: (1) the steady-state water level inside the wall; (2) the total steady flow leaking through the slurry wall; and (3) the time required for the average concentration of a nonreactive solute inside the contained area to be reduced to 5% of its original value. (Lumped Parameter Models- 8)