In linear formation approхimation the pressure response to the varying rates in the offset wells is subject to convolution equation:
LaTeX Math Block |
---|
|
p_n(t)
= p_{0,n} + \sum_{k = 1}^N \int_0^t p^u_{nk}(t - \tau) \, \dot q_k \, d\tau
\approx p_{i,n} + \sum_{k = 1}^N \sum_{\alpha = 1}^{N_k} \big( q^{(\alpha)}_k - q^{(\alpha-1)}_k \big) \ p^u_{nk}(t - t_{\alpha k}) |
...
|
|
|
---|
1 | | pressure at -th well at arbitrary moment of time |
2 | LaTeX Math Inline |
---|
body | --uriencoded--p_%7B0n%7D = p_{i,n}n(0) |
---|
|
| initial pressure at -the well |
3 | | rate value of -th transient at -th well |
4 | | pressure transient response in -th wel to unit-rate production from -th well |
5 | | starting point of the -th transient in -th well |
6 | | number of wells in the test |
7 | | number of transients in -th well |
...
The weight coefficients
and
control contributions from corresponding components and should be calibrated to the reference transients (manuualy or automatically).
The
Hint |
---|
0 | MDCV |
---|
1 | Multiwell Deconvolution |
---|
|
XDCV methodology constitute a big area of practical knowledge and not all the tricks and solutions are currenlty automated and require a practical skill.
See also
...
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Production Analysis (PA) / Pressure Deconvolution / Multiwell deconvolution (MDCV) / XDCV