...
Assume the well is producing
of water,
of oil
, and of gas as measured
daily at separator with pressure
and temperature
.
While moving down along hole at to depth
along the
hole the wellbore pressure
will be growing due to gravity of fluid column and friction losses emerging from fluid contact with inner pipe walls .
Wellbore temperature
will be also varying due to heat exchange with surrounding rocks
.The volume shares
| LaTeX Math Inline |
|---|
| body | \{ s_w(l), \, s_o(l), \, s_g(l) \} |
|---|
|
, occupied by different phases will be varying along hole due to along-hole pressure-temperature variation, phase segregation and phase slippage.
Definition
...
Mathematical model of multiphase wellbore flow Multiphase Wellbore Flow predicts the temperature, pressure and flow speed distribution along the wellbore trajectory with account for:
- 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 via complex well design
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:
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The 3-phase water-oil-gas model is usually built as a superposition of gas-liquid model and then oil-water model:
Input & Output
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| Dynamic Input | Dynamic Output |
|---|
| LaTeX Math Inline |
|---|
| body | Ps, \, T_s, \ \{ q_w, q_o, \, q_o \} |
|---|
|
| | LaTeX Math Inline |
|---|
| body | P(l), \, T(l), \, \{ s_w, \, s_o, \, s_g \} |
|---|
|
|
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