An underground hazardous waste storage tank is leaking. The contaminant concentration directly beneath the site is 0.5 mg/L. The contaminant is travelling at an effective rate of 0.4 m per day towards a water well which is 2 km away.
Assume that the degradation of the contaminant follows a first order reaction, and the initial concentration of the contaminant becomes half in 10 years.
In this case, the contaminant concentration expected at the well under steady state conditions is ________ mg/L (rounded off to two decimal places).
This question asks for the steady-state contaminant concentration at a water well located downstream from a leaking hazardous waste tank.
Given Information Summary
- Initial Contaminant Concentration ($C_0$): 0.5 mg/L
- Contaminant Travel Rate ($v$): 0.4 m/day
- Distance to Well ($L$): 2 km = 2000 m
- Degradation Type: First-order reaction
- Half-life ($t_{1/2}$): 10 years
Calculate Degradation Rate Constant (k)
First, convert the half-life to days:
$t_{1/2} = 10 \text{ years} \times 365 \text{ days/year} = 3650 \text{ days}$
Use the first-order reaction half-life formula to find k:
$k = \frac{\ln(2)}{t_{1/2}}$
$k = \frac{\ln(2)}{3650 \text{ days}} \approx \frac{0.6931}{3650} \approx 0.00018988 \text{ day}^{-1}$
Calculate Steady-State Concentration at the Well (CL)
The steady-state concentration C(x) at a distance x, considering advection and first-order degradation, is given by:
$C(x) = C_0 \exp\left(-\frac{k}{v} x\right)$
Substitute the known values for the well location (x = L = 2000 m):
$C_L = 0.5 \text{ mg/L} \times \exp\left(-\frac{0.00018988 \text{ day}^{-1}}{0.4 \text{ m/day}} \times 2000 \text{ m}\right)$
First, calculate the exponent term:
$\frac{k}{v} L = \left(\frac{0.00018988}{0.4}\right) \times 2000 \approx 0.0004747 \times 2000 \approx 0.9494$
Now, calculate the final concentration:
$C_L = 0.5 \text{ mg/L} \times \exp(-0.9494)$
$C_L \approx 0.5 \text{ mg/L} \times 0.3869 \approx 0.19345 \text{ mg/L}$
Final Concentration
Rounding the result to two decimal places, the concentration at the well is approximately 0.19 mg/L.
This value falls within the range provided (0.18 to 0.2).
Important Questions from Groundwater Occurrence
An unconfined aquifer of areal extent $20 \text{ km} \times 20 \text{ km}$ has hydraulic conductivity of $4 \text{ m/day}$, porosity of $0.32$, and storage coefficient (specific yield) of $0.18$. If the initial saturated thickness of the aquifer is $30 \text{ m}$, and $4\times10^8 \text{ m}^3$ of water is extracted from the aquifer, then the decline in the saturated thickness is _____________ (rounded off to two decimal places) m.
An unconfined aquifer extends over an area of $1 \text{ km}^2$ and has hydraulic conductivity, total porosity and specific retention of $20 \text{ m per day}, 30\%$ and $10\%$, respectively. After pumping some groundwater from this aquifer, the water table dropped to a depth of $20 \text{ m}$ from the ground level. If the water table was initially at $14.5 \text{ m}$ below the ground level, the change in groundwater storage in million cubic meters would be_______
Match the following items between Column I and Column II with the most appropriate combinations:
Column I Column II P Properties of confined and semi- confined aquifers 1 Perched aquifer Q Property of an unconfined aquifer 2 Coefficient of storage R Property of semi-confined aquifer 3 Specific yield S A special case of an unconfined aquifer 4 Leakage factor A fully penetrating well is installed in a homogenous and isotropic confined aquifer. The aquifer has uniform thickness of 16 m and hydraulic conductivity of 25 m/d. Water is being pumped out from the well at a constant rate of $0.1 \text{ } m^3/s$ till steady state condition is reached. If a drawdown of 3.5 m is observed at a distance of 75 m from the well then the drawdown at a distance of 150 m from the well will be________ (in m, rounded off to two decimal places).
- One of the key assumptions made by Dupuit-Forchheimer about the flow behavior in the porous medium towards subsurface drains is
