NFBM 0.2.0

Neuman Flux Boundary Model

NFBM

Neuman–Flux Boundary Model

NFBM is a Python implementation and extension of the analytical solution presented by Neuman (1974) for delayed-yield groundwater flow in unconfined aquifers.

The model introduces two additional boundary-condition (parameters):

• R — finite aquifer radius [L]

  Represents the lateral extent of the aquifer and can be used to simulate the influence of nearby open-water boundaries such as ditches, canals, or lakes.

• q — change in vertical flux [L/T]

  Represents a change in upward or downward flux from an underlying aquifer induced by pumping. The background flux is assumed to be present before pumping starts; only the change in flux caused by drawdown is simulated.

Features

• Delayed-yield response following Neuman's analytical solution.
• Finite-radius aquifer boundary condition (R).
• Vertical flux-change boundary condition (q).
• Numerical inversion of the Laplace transform using the de Hoog algorithm.
• Suitable for pumping-test analysis in shallow unconfined aquifers and peatlands.

Units

NFBM does not enforce a specific unit system. However, all input parameters must be provided in a consistent set of units.

For example:

Parameter	Example Unit
Distance (r, R, b, d, l, z1, z2)	m
Time (t)	d
Hydraulic conductivity (k)	m/d
Specific storage (Ss)	1/m
Specific yield (Sy)	-
Pumping rate (Q)	m³/d
Flux change (q)	m/d

A recommended unit system is meters (m) and days (d).

References

Neuman, S. P. (1974). Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response. Water Resources Research, 10(2), 303–312. https://doi.org/10.1029/WR010i002p00303