...
Physical Model
...
...
| Expand |
|---|
|
| LaTeX Math Block |
|---|
| r_{wf} < r \leq r_e |
| LaTeX Math Block |
|---|
| p(t, r ) = p(r) \Leftrightarrow \frac{\partial p}{\partial t} = 0 |
|
| LaTeX Math Block |
|---|
| \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} =0 |
|
| LaTeX Math Block |
|---|
| p(r_e ) = p_i |
|
| LaTeX Math Block |
|---|
| \left[ r\frac{\partial p(r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma} |
|
| LaTeX Math Block |
|---|
| p_{wf}= p(r_w ) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w} |
|
|
...
Equation
| LaTeX Math Block Reference |
|---|
|
shows how the
basic diffusion model parameters impact the relation between
drawdown | LaTeX Math Inline |
|---|
| body | \Delta p = p_i - p_{wf} |
|---|
|
and
total sandface flowrate and plays important methodological role as they are used in many algorithms and express-methods of
Pressure Testing.
It also called Dupuis
| Expand |
|---|
| title | Productivity Index Analysis |
|---|
|
The Total Sandface Productivity Index for low-compressibility fluid and low-compressibility rocks does not depend on formation pressure, bottomhole pressure and the flowrate and can be expressed as: | LaTeX Math Block |
|---|
| J_t = \frac{q_t}{p_i - p_{wf}(t)} =\frac{2 \pi \sigma}{\ln \frac{r_e}{r_w} + S} = {\rm const} |
The Field-average Productivity Index for low-compressibility fluid and low-compressibility rocks does not depend on formation pressure, bottomhole pressure and the flowrate and can be expressed as: | LaTeX Math Block |
|---|
| J_t = \frac{q_t}{p_r(t) - p_{wf}(t)} =\frac{2 \pi \sigma}{\ln \frac{r_e}{r_w} + 0.5 +S} = {\rm const} |
|
See Also
...
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Radial fluid flow / Pressure diffusion / Pressure Diffusion @model / Radial Flow Pressure Diffusion @model
...
