\backslash frac\{\backslash partial\; s\}\{\backslash partial\; t\}\; +\; q\; \backslash cdot\; \backslash frac\{\backslash partial\; \}\{\backslash partial\; x\}\; \backslash left(\; \backslash frac\{f\}\{\backslash phi\; \backslash ,\; A\; \}\; \backslash right)\; =\; 0s(t=0,x)\; =\; 0s(t,0)\; =\; 1@wikipediawikipedia
Ideally balanced water + dead oil 1D waterflood model without gravity and capillary effects.
...
In many practical applications (for example, laboratory SCAL tests and reservoir proxy-modeling) one can assume constant porosity and reservoir width:
| LaTeX Math Block |
|---|
| anchor | ProxyBL |
|---|
| alignment | left |
|---|
| \frac{\partial s}{\partial t_D} +\frac{\partial f}{\partial x_D} = 0 |
| | LaTeX Math Block |
|---|
| anchor | ProxyIC |
|---|
| alignment | left |
|---|
| s(t=0,x) = 0 |
| | LaTeX Math Block |
|---|
| anchor | ProxyBC |
|---|
| alignment | left |
|---|
| s(t,0) = 1 |
|
where
| LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle t_D = \frac%7BV_\phi \, t%7D%7Bq%7D |
|---|
|
| dimensionless time |
| LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle x_D = \frac%7Bx%7D%7BL%7D |
|---|
|
| dimensionless distance |
| reservoir length along -axis |
| LaTeX Math Inline |
|---|
| body | V_\phi= \phi \cdot h \cdot D \cdot L |
|---|
|
| reservoir pore volume |
See Also
...
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Dynamic Flow Model / Reservoir Flow Model (RFM)
...
