One of the Productivity Diagnostics methods based on correlation between weighted average pressure drawdown:

\overline {\delta p} (t) = \frac{1}{Q} \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) q_t d\tau

and weighted-average total sandface flowrate cumulatives:

\bar q_t(t) = \frac{1}{Q} \int_0^t q^2_t(\tau) d\tau

where

	production/injection time
	total sandface flowrate as function of time
	drain-area formation pressure as function of time
	bottomhole pressure as function of time

It shows unit slope on log-log plot for stabilized reservoir flow:

\overline {\delta p}(t) = J^{-1} \bar q_t(t)

where

constant productivity index

In case pressure data is available for a fair interpolation it is recommended to plot sandface cumulatives rather than surface which provides better linearity for stabilized reservoir flow.

The average pressure drawdown is usually calculated over interpolated values of formation pressure and bottomhole pressure :

\overline {\delta p} (t) = \frac{1}{Q} \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) q_t(\tau) \, d\tau = \frac{1}{Q}  \sum_k \left( p_{wf}(\tau_k) - p_e(\tau_k) \right) q_t (\tau_k) \, \delta \tau_k

The main difference between weighted-average and Normalized Hall Plot is the averaging methodology.

The Normalized Hall Plot gives equal weight to all data points , while q-weighted J-plot gives more weight to higher flowrate data points, lower weight to lower flowrate data points and zero weight to no-flow data points (): .

When flowrate is constant both methods are equivalent because .

See Also