welltest_pta.bourdet_derivative

welltest_pta.bourdet_derivative(dt, dp, L=0.2, use_smooth=True)[source]

Compute the Bourdet logarithmic pressure derivative.

Uses the three-point window formulation:

\[\left.\frac{d\,\Delta p}{d\,\ln \Delta t}\right|_i \approx \frac{\Delta p_{j_+} - \Delta p_{j_-}} {\ln\Delta t_{j_+} - \ln\Delta t_{j_-}}\]

where \(j_-\) and \(j_+\) are the nearest indices to \(i\) with \(|\ln \Delta t_j - \ln \Delta t_i| \ge L\). The smoothing parameter \(L\) (typically 0.05–0.4) controls noise rejection.

Parameters:

dt (ndarray) – Elapsed shut-in time (or producing time) in hours, monotonically increasing, starting strictly above zero (use dt[0] = 1e-6 if needed).
dp (ndarray) – Pressure change \(\Delta p = p(t) - p(t=0)\) (psi).
L (float) – Logarithmic smoothing window (default 0.2). Larger = smoother.
use_smooth (bool) – If True (default) returns the absolute value (typical for log–log plots). Set False to keep the signed derivative.

Returns:

Arrays of elapsed time and derivative values where the central- difference formula was evaluable. Length ≤ len(dt) - 2.

Return type:

dt_out, deriv_out