...
LaTeX Math Block |
---|
| \frac{d Q^{\downarrow}_{AQ}}{dt_D} = \frac{ B \cdot (p_i - p(t_D)) - Q^{\downarrow}_{AQ} \cdot p'_D(t_D)}{p_D(t) - t_D \cdot p'_D(t_D)} |
| LaTeX Math Block |
---|
| p_D= \frac{370.529 \, \sqrt{t_D} +137.528 \, t_D + 5.69549 \, t_D^{1.5}}
{328.834 +265.488 \, \sqrt{t_D} + 45.2157 \, t_D + t_D^{1.5} } |
|
LaTeX Math Block |
---|
| q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt} |
| LaTeX Math Block |
---|
| p'_D= \frac
{716.441 + 46.7984 \, \sqrt{t_D} + 270.038 \, t_D + 71.0098 \, t_D^{1.5} }
{ 1296.86 \, \sqrt{t_D} + 1204.73 \, t_D + 618.618 \, t_D^{1.5} + 538.072 \, t_D^2 + 142.41 \, t_D^{2.5} } |
|
| LaTeX Math Block |
---|
| t_D= \frac{\pi \, \chi \, t}{A_e} |
|
Expand |
---|
| Equation LaTeX Math Block Reference |
---|
| is not a solution of diffusion equation but an approximation of VEH model which does not involve convolution integral. |
|
Computational Model
...
LaTeX Math Block |
---|
| Q^{\downarrow}_{AQ}(t_{D,n}) = Q^{\downarrow}_{AQ}(t_{D, \, n-1}) + (t_{D,n}-t_{D,\, n-1}) \cdot
\frac{ B \cdot (p_i - p(t_{D,n})) - Q^{\downarrow}_{AQ}(t_{D, \, n-1}) \cdot p'_D(t_D)}{p_D(t_{D,n}) - t_{D,n} \cdot p'_D(t_{D, n})} |
|
See Also
...
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Aquifer Drive / Aquifer Drive Models
...