Hall Plot

Brief

Hall Plot is the engineering technique to analyze performance of injection wells published in 1963 by Howard Hall .

Hall Plot is applied to determine the change in the Injectivity index of the wells.

Hall Plot uses readily available Well flowing data: injection rate and wellhead pressures.

The interpretation technique is fitting the data points with the straight lines to estimate injectivity change.

Hall Plot in the E&P Portal

Math & Physics

From Darcy's law for an unfractured injection well located in the center of a circular drainage area, the injection rate in pseudo-steady state is:

${q_{inj}} = \frac{kh}{141.2 B \mu} \times J_D \times (P_{wf} - \bar{P})$

Hall integrated both sides with respect to time :

$\sum q_{inj} \Delta t = \frac{kh}{141.2 B \mu} \times J_D \times \sum (P_{wf} - \bar{P}) \Delta t$

The Cartesian graph of cumulative injection versus cumulative $(P_{wf} - \bar{P})$ yields a straight line with slope:

$m = \frac{kh}{141.2 B \mu} \times J_D$

and Injectivity index is:

$I = \frac{1}{m}$

Hall Plot Application with Wellhead Pressure

Since bottomhole pressure and reservoir pressure are not readily available, the Hall Plot can be used with tubing head pressure.

Application with Tubing Head Pressure

[your derivation here]

Rearranging:

$\sum P_{wf} \Delta t = \frac{141.2 B \mu}{kh J_D} \times \sum q_{inj} \Delta t + \sum \bar{P} \Delta t$

Given:

$P_{wf} = P_{wh} + \Delta P_{friction} + \Delta P_{gravity}$

See Also

Injectivity index