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

$m = \frac{141.2 B \mu}{khJ_D}$

and Injectivity index is:

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

Hall Plot Application with Wellhead Pressure

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

Given:

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

Rearranging above:

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

See Also

Injectivity index