Difference between revisions of "Hall Plot"

Revision as of 16:30, 27 August 2026

Hall Plot is the engineering technique to analyze performance of injection wells published in 1963 by Howard Hall ^[1].

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

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 ^[2]:

\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

I = \frac{1}{m}

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

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

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

@@ Line 37: / Line 37: @@
 :<math> \sum P_{wf} \Delta t = \frac{141.2 B \mu}{kh J_D} \times \sum q_{inj} \Delta t + \sum \bar{P} \Delta t</math>
 :<math> \sum P_{tub} \Delta t = \frac{141.2 B \mu}{kh J_D} \times \sum q_{inj} \Delta t + \sum \bar{P} \Delta t - \sum \Delta P_{friction} \Delta t - \sum \Delta P_{gravity} \Delta t </math>
+:<math> \sum P_{tub} \Delta t = \frac{141.2 B \mu}{kh J_D} \times \sum q_{inj} \Delta t + \sum \bar{P} \Delta t - \sum (\Delta P_{friction} + \Delta P_{gravity}) \Delta t </math>
 == Nomenclature ==