You are viewing an old version of this page. View the current version.
Compare with Current
View Page History
« Previous
Version 11
Next »
Motivation
Reservoir pressure dynamics away from wellbore and boundaries is representative of two very important complex reservoir properties: transmissibility
\sigma and pressure diffusivity
\chi.
These can be roughly estimated with a homogeneous reservoir model where wellbore and boundaries effects can be neglected.
Physical Model
Mathematical Model
(1) |
\frac{\partial p}{\partial t} = \chi \, \left[ \frac{\partial^2 p}{\partial t^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right] |
| | |
(4) |
\left[ r \frac{\partial p}{\partial r} \right]_{r=0} = - \frac{q_t}{2 \pi \sigma} |
|
Computational Model
(5) |
p(t,r) = p_i - \frac{q_t}{4 \pi \sigma} {\rm Ei} \left(-\frac{r^2}{4 \chi t} \right) |
|
Approximations
Late-time response |
---|
(6) |
p(t,r) = p_i - \frac{q_t}{4 \pi \sigma} \left[
\gamma + \ln \left(\frac{r^2}{4 \chi t} \right) \right]
= p_i - \frac{q_t}{4 \pi \sigma} \ln \left(\frac{2.24585 \, t}{r^2} \right)
|
|
See also
Physics / Fluid Dynamics / Radial fluid flow / Line Source Solution
[ Radial Flow Pressure @model ] [ 1DR pressure diffusion of low-compressibility fluid ]