...
Assume the well is producing
of water,
of oil,
of gas as measured at separator with pressure
and temperature
.
...
- tubing head pressure which is controled by gathering system or injection pump
- wellbore design (pipe diameters, pipe materials and inter-pipe annular fillings)
- fluid friction with tubing /casing walls
- interfacial phase slippage
- heat exchange between wellbore fluid and surrounding rocks
Consider a 3-phase water-oil-gas flow:
| LaTeX Math Inline |
|---|
| body | \alpha = \{ w, \, o, \, g \} |
|---|
|
.
The
-phase
flow fraction ( also called
phase cut or
input hold-up or
no-slip hold-up ) is defined as:
...
| LaTeX Math Block |
|---|
|
q_t = \sum_\alpha q_\alpha = q_w + q_o + g_g |
The multiphase wellbore flow assumes that every phase occupies its own area area
of the total cross-sectional
area area of the lifting pipe.
This area can be connected into a single piece of cross-sectional area (like in case of slug or annular flow) or disconnected dispersed into a number of connected spots (like in case of bubbly flow).
A share of total pipe cross-section area occupied by moving
-phase is called an
-phase
in-situ hold-up and defined as:
| LaTeX Math Block |
|---|
|
s_\alpha = \frac{A_\alpha}{A} |
so that a sum of all in-situ hold-ups is is subject to natural constraint:
| LaTeX Math Block |
|---|
| anchor | s_norm |
|---|
| alignment | left |
|---|
|
\sum_\alpha s_\alpha = s_w + s_o + s_g = 1 |
When word hold-up is used alone it usually means in-situ hold-up.
The actual average cross-sectional velocity of moving
-phase is called
in-situ velocity and defined as:
...
