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- Three common well orientations for crude oil and natural gas production are vertical wells, deviated (or slanted) wells, and horizontal wells. These wells have different applications in field development, but all can be modeled with contemporary well modeling software.
- Tubing hydraulics during crude oil and natural gas production is a very complex physical problem, particularly for multi-phase flow. These parameters that impact tubing hydraulics include:
- the well design: well orientation and tubing size
- the well condition: absolute and relative roughness
- the production rate: dependent on reservoir inflow performance
- number and types of flowing phases: this will change based on:
- the location of the fluids in the well (with respect to the local bubble-point pressure)
- pressure depletion in the reservoir

- the fluid properties: density, viscosity, etc.
- the local flow regimes in the segment tubing:
- laminar or turbulent
- multi-phase flow regimes illustrated in
**Table 6.01**and**Table 6.02**

- Fluids flowing through tubing do not flow as homogeneous fluids but may go through many flow regimes or flow patterns:
- for vertical flow:
- single-phase flow
- bubble flow
- slug flow
- churn flow
- annular flow
- mist flow

- for horizontal flow:
- single-phase flow
- bubble flow
- plug flow
- stratified flow
- wavy flow
- slug flow
- annular flow
- spray flow

- for vertical flow:
- The well does not necessarily need to pass through all of these flow regimes. The flow patterns can be quantified for numerical calculations with flow pattern maps. Flow regime maps are empirically based maps that indicate the flow regime at know pipe/tubing conditions (x-axis and y-axis on the flow pattern map).
- The fundamental relationship for tubing hydraulics is the energy equation developed by Bernoulli.
- The energy balance equation that was specifically adapted from Bernoulli’s equation for pipe/tubing flow is the Darcy-Weisbach Equation. The Darcy-Weisbach Equation can be used for all single-phase flow conditions. Friction losses in well tubing are calculated with Darcy-Weisbach Friction Factor. The Darcy-Weisbach Friction Factor is plotted in the Moody Diagram as a function of the Reynolds Number and the relative roughness of the pipe/tubing.
- Other empirical single- phase flow correlations can be used for tubing hydraulics:
- liquids: the Hazen-Williams Equation for water and light hydrocarbons
- gases: the Weymouth equation, the Panhandle “A” equation, and the Panhandle “B” equation

- There are two main types of tubing hydraulics calculations used by Production Engineers: Pressure Traverse Calculations and Tubing Performance Calculations. Pressure traverse calculations are based on a known flow rate, $q$, and an unknown pressure drop, $\Delta p$. Tubing performance calculations are based on a known flow rate, $q$, a known wellhead pressure, ${p}_{wh}$, and an unknown flowing bottom-hole pressure, ${p}_{wf}$.
- For multi-phase flow, the flow problem is too complex to solve theoretically, and empirical flow correlations based on the flow patterns maps are used. The flow pattern maps have empirical correlations for hold-up, slip, and friction for the different flow regimes observed in laboratory and field experiments. These correlations are used in the energy balance equation to perform tubing hydraulics calculations. The multi-phase correlations currently in use in the oil and gas industry include:
- Verical flow:
- Fancher and Brown
- Hagedorn and Brown
- Beggs and Brill
- Orkiszewski
- Gray
- Duns and Ros

- Horizontal and deviated flow:
- Eaton-Flanigan
- Eaton-Dukler-Flanigan
- Beggs and Brill

- Verical flow: