...
| LaTeX Math Block |
|---|
|
p(t) = p_i + \int_0^t p_u(t - \tau) dq = p_i + \int_0^t p_u(t - \tau) \cdot q(\tau) d\tau |
In case production history can be approximated by a finite sequence of constant rate production intervals (called Pressure Transients):
| LaTeX Math Block |
|---|
|
p(t) = p_i + \sum_{\alpha = 1}^{N} \left[ q^{(\alpha)} - q^{(\alpha-1)} \right] \cdot p_u(t - t^{\alpha}) |
...
| pressure at -th well at arbitrary moment of time |
| initial pressure at -the well |
| index number of a a pressure transient (period of time where rate was constant) |
| total number of transientstransients |
| LaTeX Math Inline |
|---|
| body | --uriencoded--t%5e%7B\alpha%7D |
|---|
|
| starting point of the -th transient |
| LaTeX Math Inline |
|---|
| body | --uriencoded--q%5e%7B(\alpha)%7D |
|---|
|
| rate value of - th transient which th transient which starts at the time moment | LaTeX Math Inline |
|---|
| body | --uriencoded--t%5e%7B(\alpha)%7D |
|---|
|
|
| pressure transient response to response to the unit-rate production (DTR) |
with assumption:
| LaTeX Math Inline |
|---|
| body | --uriencoded--q%5e%7B(-1)%7D = 0 |
|---|
|
, which means that well was shut-in before it started the first transient
- at which means pressure drop is zero before the well starts unit-rate production
...
