Radius Of Influence When Interference Among Well Is Present Calculator

Radius Of Influence When Interference Among Well Is Present Formula:

\[ r_i = \sqrt{(r' \times B) \times \exp\left(\frac{2\pi k b_p (H_i - h_w)}{Q}\right)} \]

Radius of Well in Environ. Engin. (r'):

Distance Between Well (B):

Coefficient of Permeability (k):

m/s

Aquifer Thickness During Pumping (bₚ):

Initial Aquifer Thickness (Hᵢ):

Depth of Water (h_w):

Discharge (Q):

m³/s

Radius of Influence in Environ. Engin. (rᵢ):

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1. What is Radius of Influence When Interference Among Well is Present?

The radius of influence in environmental engineering is measured from the center of the well to the point where the drawdown curve meets the original water table. When interference among wells is present, this calculation becomes crucial for understanding how multiple wells affect each other's drawdown zones.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_i = \sqrt{(r' \times B) \times \exp\left(\frac{2\pi k b_p (H_i - h_w)}{Q}\right)} \]

Where:

\( r_i \) — Radius of Influence (m)
\( r' \) — Radius of Well (m)
\( B \) — Distance Between Wells (m)
\( k \) — Coefficient of Permeability (m/s)
\( b_p \) — Aquifer Thickness During Pumping (m)
\( H_i \) — Initial Aquifer Thickness (m)
\( h_w \) — Depth of Water (m)
\( Q \) — Discharge (m³/s)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula accounts for the interference effects between wells by incorporating the distance between wells and the exponential relationship between various aquifer properties and pumping parameters.

3. Importance of Radius of Influence Calculation

Details: Accurate calculation of radius of influence is essential for designing well fields, preventing interference between adjacent wells, optimizing pumping rates, and ensuring sustainable groundwater extraction without causing excessive drawdown or environmental impacts.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, m/s for permeability, m³/s for discharge). All values must be positive and valid. Ensure consistent units throughout the calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is well interference?
A: Well interference occurs when the drawdown cones of multiple pumping wells overlap, affecting each other's performance and the overall aquifer response.

Q2: How does distance between wells affect radius of influence?
A: Closer well spacing increases interference effects, potentially reducing individual well yields and increasing overall drawdown in the aquifer.

Q3: What factors influence the radius of influence?
A: Pumping rate, aquifer properties (permeability, thickness), duration of pumping, and well configuration all affect the radius of influence.

Q4: When is this calculation most important?
A: This calculation is crucial when designing well fields for municipal water supply, irrigation systems, or dewatering projects where multiple wells operate simultaneously.

Q5: Are there limitations to this equation?
A: This equation assumes homogeneous aquifer conditions and steady-state flow. It may be less accurate in heterogeneous aquifers or under transient conditions.