Well flow regime with constant rate and constant delta pressure between wellbore and formation does not change in time:
LaTeX Math Block |
---|
|
q_t(t) = \rm const |
LaTeX Math Block |
---|
|
\Delta p(t) = | p_e(t) - p_{wf}(t) | = \Delta p = \rm const |
During the PSS regime the formation pressure declines linearly with time:
.
The exact solution of diffusion equation for PSS:
LaTeX Math Block |
---|
| p_e(t) = p_i + \frac{q_t}{ V_{\phi} \, c_t} \ t |
|
varying formation pressure at the external reservoir boundary
|
LaTeX Math Block |
---|
| p_{wf}(t) = p_e(t) + J^{-1} q_t |
|
varying bottom-hole pressure
|
LaTeX Math Block |
---|
| J = \frac{q_t}{2 \pi \sigma} \left[ \ln \left ( \frac{r_e}{r_w} \right) +S + 0.75 \right] |
|
constant productivity index |
and develops a unit slope on PTA diagnostic plot and Material Balance diagnostic plot:
See also
Steady State (SS) well flow regime