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Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator

Calculates transient and steady-state drawdown in a semi-confined aquifer with overlying aquitard leakage using the Hantush-Jacob well function W(u, r/B).

Continuous discharge rate from the extraction well.

Product of hydraulic conductivity and main aquifer thickness.

Dimensionless storage coefficient of the confined aquifer.

Vertical hydraulic conductivity of the overlying semi-pervious aquitard.

Saturated thickness of the confining aquitard layer.

Radial distance from pumping well to observation piezometer.

Time elapsed since pumping commenced.

Calculated Result
0.394 m

Transient Drawdown s(r,t)

Steady-State Drawdown

0.807 m

Leakage Factor B

379.5 m

Dimensionless r/B

0.1713

Hantush Function W

1.8555

Aquitard Resistance

320 d

Calculation Breakdown

  1. Aquitard Resistance & Aquifer Leakage FactorResistance c = b'/K' = 320 days; Leakage Factor B = √(T·c) = 379.5 m; r/B = 0.1713
  2. Theis Dimensionless Parameter & Well Functionu = r²·S / (4·T·t) = 0.000313; Hantush Leaky Well Function W(u, r/B) = 1.8555
  3. Transient & Steady-State Drawdown EvaluationTransient s(r,t) = [Q / (4πT)]·W = 0.394 m; Steady Equilibrium s_inf = 0.807 m

Leaky Aquifer Hydrogeology

Interactive visualization based on your current inputs

Value
0.01.93.85.77.6Leakage B / 50 (m)Drawdown (m)Theis Diff (m)Well Function WParameterValue

What Is the Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator?

Calculates transient and steady-state drawdown in a semi-confined aquifer with overlying aquitard leakage using the Hantush-Jacob well function W(u, r/B).

The Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator is an analytical tool in the construction domain designed to evaluate Pumping Rate (Q), Aquifer Transmissivity (T), Aquifer Storativity (S), Aquitard Vertical Hydraulic Conductivity (Kv), Aquitard Layer Thickness (b_aquitard), Observation Distance (r), Pumping Duration (t) using verified mathematical equations. It provides reproducible, deterministic calculations for academic, professional, and practical applications.

How Does the Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator Work?

This calculator computes results by taking input values for Pumping Rate (Q), Aquifer Transmissivity (T), Aquifer Storativity (S), Aquitard Vertical Hydraulic Conductivity (Kv), Aquitard Layer Thickness (b_aquitard), Observation Distance (r), Pumping Duration (t) and applying the governing equation: Evaluates Hantush-Jacob well function W(u, r/B) integrating exponential Bessel decay to calculate drawdown s as a function of radial distance and leakage factor B.. Values are checked for dimensional consistency and processed through standard arithmetic routines.

Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

s=Q4πTW(u,r/B),u=r2S4Tt,B=T⋅baquitardKvs = \frac{Q}{4 \pi T} W(u, r/B), \quad u = \frac{r^2 S}{4 T t}, \quad B = \sqrt{\frac{T \cdot b_{aquitard}}{K_v}}

Evaluates Hantush-Jacob well function W(u, r/B) integrating exponential Bessel decay to calculate drawdown s as a function of radial distance and leakage factor B.

How to Use the Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator

  1. Enter your value for Pumping Rate (Q) in m³/day.
  2. Enter your value for Aquifer Transmissivity (T) in m²/day.
  3. Enter your value for Aquifer Storativity (S).
  4. Enter your value for Aquitard Vertical Hydraulic Conductivity (Kv) in m/day.
  5. Enter your value for Aquitard Layer Thickness (b_aquitard) in m.
  6. Enter your value for Observation Distance (r) in m.
  7. Enter your value for Pumping Duration (t) in days.
  8. Verify your input parameters to ensure they match your design or problem specifications.
  9. Review the calculated results, intermediate mathematical steps, and graphical visualization below.

Step-by-Step Example Calculation

Industrial Wellfield in Leaky Alluvial Aquifer

Input Values:

pumpingRate:1200
transmissivity:450
storativity:0.0004
aquitardConductivity:0.025
aquitardThickness:8
radialDistance:65
pumpingDuration:3
Worked Steps: Computes leakage factor B, well function value, drawdown, and comparison against non-leaky Theis cone.

Understanding Your Result

The calculated output gives the primary solution for Hantush-Jacob Leaky Confined Aquifer Drawdown under the specified conditions. Use this value to compare against standard design tolerances, benchmarks, or reference ranges in construction.

Factors That Affect the Result

  • Input precision and measurement accuracy of Pumping Rate (Q), Aquifer Transmissivity (T), Aquifer Storativity (S), Aquitard Vertical Hydraulic Conductivity (Kv), Aquitard Layer Thickness (b_aquitard), Observation Distance (r), Pumping Duration (t).
  • Operating conditions, environmental parameters, and specific construction tolerances.
  • Boundary constraints and deviations from nominal theoretical model assumptions.

When Should You Use This Calculator?

  • When performing technical analysis or dimensioning related to Hantush-Jacob Leaky Confined Aquifer Drawdown.
  • To cross-verify manual calculations or theoretical models in construction.
  • For preliminary estimates before conducting detailed field measurements or laboratory testing.

Assumptions & Limitations

  • Assumes no storage change within the aquitard itself (incompressible aquitard assumption). For thick clays with aquitard storage, Hantush (1960) modified theory applies.
  • As r/B approaches zero, the Hantush-Jacob solution simplifies to the classic Theis non-leaky confined equation.

Frequently Asked Questions

What is the physical meaning of the leakage factor B?+
The leakage factor B has dimensions of length (m). High B values indicate low aquitard leakage (near-confined behavior), while small B values indicate intense vertical leakage recharging the aquifer rapidly.
Does the drawdown reach a steady state?+
Yes. In leaky aquifers, once vertical leakage through the aquitard equals the pumping extraction rate Q, the cone of depression stabilizes completely into steady state: s = (Q / 2πT) · K0(r/B).

Calculation Accuracy & Reference Note

This calculator implements verified mathematical formulas for Hantush-Jacob Leaky Confined Aquifer Drawdown Calculator. Always verify critical results against official domain standards and manufacturer documentation.

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