total sandface flowrate as function of time
drain-area formation pressure as function of time
bottomhole pressure as function of time
One of the Productivity Diagnostics methods based on correlation between rate-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 rate-weighted average total sandface flowrate:
\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 |
|
Fig. 1. q-weighted J-plot |
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 |
It is highly recommended to plot sandface flowrates rather than surface flowrates to achieve better linearity in correlation 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
.
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Productivity Diagnostics
