Dimensionless transient water flux response from aquifer to unit step change in net pay pressure:
| LaTeX Math Block |
|---|
|
W_{eD}(t, r_{aD}) = \int_0^{t}
\frac{\partial p_1( t_D, r_D)}{\partial r_D} \Bigg|_{r_D=1} dt_D |
where
| aquifer pressure diffusivity |
| net pay area |
| solution of unit-pressure radial composite reservoir transient flow | LaTeX Math Block Reference |
|---|
|
– | LaTeX Math Block Reference |
|---|
|
|
| LaTeX Math Block |
|---|
| \frac{\partial p_1}{\partial t_D} = \frac{\partial^2 p_1}{\partial r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_1}{\partial r_D} |
|
| LaTeX Math Block |
|---|
| p_1(t_D = 0, r_D)= 0 |
|
| LaTeX Math Block |
|---|
| p_1(t_D, r_D=1) = 1 |
|
| LaTeX Math Block |
|---|
| \frac{\partial p_1(t_D, r_D)}{\partial r_D}
\Bigg|_{r_D=r_{aD}} = 0 |
or | LaTeX Math Block |
|---|
| p_1(t_D, r_D = \infty) = 0 |
|
The Dimensionless Water Influx
is a unique function of time
for each dimensionless value of
which represents the ratio of external aquifer size
to net pay size
:
| LaTeX Math Block |
|---|
|
r_{aD} = \frac{r_a}{r_e} |
This function is readily tabulated for a wide range of
variations.
There are also polynomial approximations.
See Also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling
[ Depletion ] [ Aquifer ] [ Aquifer Drive @model ]
