A proxy model of watercut in producing well with reservoir saturation
LaTeX Math Inline |
---|
body | s=\{ s_w, \, s_o, \, s_g \} |
---|
|
and reservoir pressure
:
LaTeX Math Block |
---|
|
{\rm Y_{wm}} = \frac{1 - \epsilon_g}{1 - \frac{M_{ro}}{M_{rw}} \cdot \frac{B_w}{B_o} }, \quad \epsilon_g = \frac{A}{q_t} \cdot M_{ro} \cdot \left[ \frac{\partial P_c}{\partial r} + (\rho_w-\rho_o) \cdot g \cdot \sin \alpha \right] |
where
If capillary effects are not high
or saturation does not vary along the streamline substantially
LaTeX Math Inline |
---|
body | \displaystyle \frac{\partial s_w}{\partial r} \rightarrow 0 |
---|
|
, then
LaTeX Math Inline |
---|
body | \displaystyle \frac{\partial P_c}{\partial r} = \dot P_c \cdot \frac{\partial s_w}{\partial r} \approx 0 |
---|
|
.
If flow is close to horizontal
LaTeX Math Inline |
---|
body | \sin \alpha \rightarrow 0 |
---|
|
then gravity effects are vanishing too:
LaTeX Math Inline |
---|
body | (\rho_w-\rho_o) \cdot g \cdot \sin \alpha \approx 0 |
---|
|
.
In these cases
LaTeX Math Block Reference |
---|
|
simplifies to:
LaTeX Math Block |
---|
anchor | Ywsimple |
---|
alignment | left |
---|
|
{\rm Y_{wm}} = \frac{1}{1 - \frac{M_{ro}}{M_{rw}} \cdot \frac{B_w}{B_o} } |
The models
LaTeX Math Block Reference |
---|
|
and
LaTeX Math Block Reference |
---|
|
can also be used in
production analysis assuming homogeneous reservoir
water saturation :
LaTeX Math Block |
---|
|
s_w(t) = s_{wi} + (1-s_{wi}-s_{or}) \cdot \rm RFO(t)/E_S |
where
See also
Water cut (Yw)