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While moving down along hole at depth
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 temperature
will be also varying due to heat exchange with surrounding rocks.
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- tubing head pressure which is set controled by gathering system or injection pump
- wellbore design
pump characterisits(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
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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:
Application
Input & Output
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| Dynamic Input | Dynamic Output |
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| | LaTeX Math Inline |
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| body | Ps, \, T_s, \ \{ q_w, q_o, \, q_o \} |
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| | LaTeX Math Inline |
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| body | \{ s_w, \, s_o, \, s_g \} |
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Application
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| Activity |
| Input | Output |
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| 1 | WPA – Well Performance Analysis | Optimizing the lift performance based on the IPR vs VLP models | | LaTeX Math Inline |
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| body | \{ q_W, \, q_O, \, q_G \} |
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|
as values at separator | | LaTeX Math Inline |
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| body | P_{wf}(l = l_{datum}) |
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as value at formation datum |
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| 2 | DM – Dynamic Modelling | Relating production rates at separator to bottom-hole pressure with VLP | | LaTeX Math Inline |
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| body | \{ q_W, \, q_O, \, q_G \} |
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as values at separator | | LaTeX Math Inline |
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| body | P_{wf}(l = l_{datum}) |
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|
as value at formation datum |
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| 3 | PRT – Pressure Testing | Adjust gauge pressure to formation datum | | LaTeX Math Inline |
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| body | P_{wf}(l = l_{gauge}) |
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as value at downhole gauge | | LaTeX Math Inline |
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| body | P_{wf}(l = l_{datum}) |
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as value at formation datum |
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| 4 | PLT – Production Logging | Interpretation of production logs | | LaTeX Math Inline |
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| body | \{ p(l), \, T(l), \, u_m(l), \, s_w(l), \, s_o(l), \, s_g(l) \} |
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as logs along hole | | LaTeX Math Inline |
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| body | \{ q_w(l), \, q_o(l), \, q_g(l) \} |
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as logs along hole |
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| 5 | RFP – Reservoir Flow Profiling | Interpretation of reservoir flow logs | | LaTeX Math Inline |
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| body | \{ p(l), \, T(l), \, u_m(l), \, s_w(l), \, s_o(l), \, s_g(l) \} |
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as logs along hole | | LaTeX Math Inline |
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| body | \{ q_w(l), \, q_o(l), \, q_g(l) \} |
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|
as logs along hole |
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| 1 | WPA – Well Performance Analysis | Optimizing the lift performance based on the IPR vs VLP models |
|---|
| 2 | Dynamic Modelling | Relating production rates at separator to bottom-hole pressure with VLP |
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| 3 | PRT – Pressure Testing | Adjust gauge pressure to formation datum |
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4 | PLT – Production Logging | Interpretation of pressure-temperature logs and multiphase sensors
Mathematical Model
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The multiphase wellbore flow in hydrodynamic and thermodynamic equilibrium is defined by the following set of 1D equations:
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