Practical Design Calculations for Groundwater and Soil Remediation - Chapter 3

Kuo, Jeff "Plume migration in groundwater and soil" Practical Design Calculations for Groundwater and Soil Remediation Boca Raton: CRC Press LLC,1999 chapter three Plume migration in groundwater and soil In Chapter two we illustrated the necessary calculations for site character-ization and remedial investigation. Generally, from the RI activities the extent of the plume in the vadose zone and/or groundwater is defined. If the contaminants cannot be removed immediately, they will migrate under com-mon field conditions and the extent of the plume will enlarge. In the vadose zone, the contaminants will move downward as a free product or become dissolved in infiltrating water and then move downward by gravity. The downward-moving liquid may come in contact with the underlying aquifer and create a dissolved plume. In addition, the VOCs will volatilize into the air void of the vadose zone and travel under advective forces (with the air flow) or concentration gradients (through diffusion). Migration of the vapor can be in any direction, and the contaminants in the vapor phase, when coming in contact with the groundwater, may also dis-solve into the groundwater. For site remediation or health risk assessment, understanding the fate and transport of contaminants in the subsurface is important. Common questions related to the fate and transport of contami-nants in the subsurface include 1. How long will it take for the plume in the vadose zone to enter the aquifer? 2. How far will the vapor contaminants in the vadose zone travel? In what concentrations? 3. How fast does the groundwater flow? In which direction? 4. How fast will the plume migrate? In which direction? 5. Will the plume migrate at the same speed as the groundwater flow or at a different speed? If different, what are the factors that would ©1999 CRC Press LLC make the plume migrate at a different speed from the groundwater flow? 6. How long has the plume been present in the aquifer? This chapter illustrates the basic calculations needed to answer most of the above questions. The first section presents the calculations for ground-water movement and clarifies some common misconceptions about ground-water velocity and hydraulic conductivity. Procedures to determine the groundwater flow gradient and the flow direction are also given. The second section presents groundwater extraction from confined and unconfined aqui-fers. Since hydraulic conductivity plays a pivotal role in groundwater move-ment, several common methodologies of estimating this parameter are cov-ered, including the aquifer tests. The discussion then moves to the migration of the dissolved plume in the aquifer and in the vadose zone. III.1 III.1.1 Groundwater movement Darcy’s law Darcy’s Law is commonly used to describe laminar flow in porous media. For a given medium the flow rate is proportional to the head loss and inversely proportional to the length of flow path. Flow in typical ground-water aquifers is laminar, and therefore Darcy’s Law is valid. Darcy’s Law can be expressed as v = Q = −K dh [Eq. III.1.1] where v is the Darcy velocity, Q is the volumetric flow rate, A is the cross-sectional area of the porous medium perpendicular to the flow, dh/dl is the hydraulic gradient (a dimensionless quantity), and K is the hydraulic con-ductivity. The hydraulic conductivity tells how permeable the porous medium is to the flowing fluid. The larger the K of a formation, the easier the fluid flows through it. Commonly used units for hydraulic conductivity are either in velocity units such as ft/d, cm/s, or m/d, or in volumetric flow rate per unit area such as gpd/ft2. You may find the unit conversions in Table III.1.A helpful. Example III.1.1 Estimate the rate of fresh groundwater in contact with the plume Leachates from a landfill leaked into the underlying aquifer and created a contaminated plume. Use the information below to estimate the amount of fresh groundwater that enters into the contaminated zone per day. ©1999 CRC Press LLC The maximum cross-sectional area of the plume perpendicular to the groundwater flow = 1600 ft2 Groundwater gradient = 0.005 Hydraulic conductivity = 2500 gpd/ft2 Solution: Another common form of Darcy’s Law (Eq. III.1.1) is Q = KiA [Eq. III.1.2] where i is the hydraulic gradient, dh/dl. The rate of fresh groundwater entering the plume can be found by inserting the appropriate values into the above equation: Q = (2500 gpd/ft2)(0.005)(1600 ft2) = 20,000 gpd Discussion 1. The calculation itself is straightforward and simple. However, we can get valuable and useful information from this exercise. The rate of 20,000 gal/day represents the rate of uncontaminated groundwater that will come in contact with the contaminants. This water would become con-taminated and move downstream or sidestream and, consequently, en-large the size of the plume. To control the spread of the plume, we have to extract this amount of water, 20,000 gpd or ~14 gpm, as a minimum. The actual extraction rate required should be higher than this because the groundwater drawdown from pumping will increase the flow gra-dient. This increased gradient will, in turn, increase the rate of ground-water entering the plume zone as indicated by the equation above. 2. Using the maximum cross-sectional area is a legitimate approach that represents the “contact face” between the fresh groundwater and the plume. III.1.2 Darcy’s velocity vs. seepage velocity The velocity term in Eq. III.1.1 is called the Darcy velocity (or the discharge velocity). Does this Darcy velocity represent the groundwater flow velocity? Table III.1.A Common Conversion Factors for Hydraulic Conductivity m/d 1 8.64E + 2 3.05E – 1 4.1E – 2 cm/s 1.16E – 3 1 3.53E – 4 4.73E – 5 ft/d 3.28 2.83E + 3 1 1.34E – 1 gpd/ft2 2.45E + 1 2.12E + 4 7.48 1 ©1999 CRC Press LLC The answer is “no.” The Darcy velocity in that equation assumes the flow occurs through the entire cross-section of the porous medium. In other words, it is the velocity at which water would move through an aquifer if the aquifer were an open conduit. Actually, the flow is limited to the available pore space only (the effective cross-sectional area available for flow is smaller), so the actual fluid velocity through the porous medium would be larger than the Darcy velocity. This flow velocity is often called the seepage velocity or the interstitial velocity. The relationship between the seepage velocity, vs, and the Darcy velocity, v, is as follows: vs = jA = j [Eq. III.1.3] where j is the porosity. For example, for an aquifer with a porosity of 33%, the seepage velocity of groundwater flowing through this aquifer will be three times the Darcy velocity (i.e., vs = 3 v). Example III.1.2 Determine Darcy velocity and seepage velocity There is spill of an inert (or a conservative) substance into the subsurface. The spill infiltrates the unsaturated zone and quickly reaches the underlying water table aquifer. The aquifer consists mainly of sand and gravel with a hydraulic conductivity of 2500 gpd/ft2 and an effective porosity of 0.35. The water level in a well neighboring the spill lies at an altitude of 560 ft, and the level in another well 1 mile directly down gradient is 550 ft. Determine a. The Darcy velocity of the groundwater b. The seepage velocity of the groundwater c. The velocity of plume migration d. How long it will take for the plume to reach the down-gradient well Solution: a. We have to determine the gradient of the aquifer first: i = dh/dl = (560 – 550)/5280 = 1.89 ´ 10–3 ft/ft Darcy velocity = Ki ( 2500 gpd/ft2 )0.134 gpd/ft2 (1.89´10−3 ft/ft) = 0.63 ft/d b. Seepage velocity = v/j 0.63/0.35 = 1.81 ft/d ©1999 CRC Press LLC ... - tailieumienphi.vn