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**Two-Phase Flow in Vertical Wells Notes to Accompany Week 5 Lab—Vertical Two-Phase Flow**

Multi-Phase Flow in Wells (see also PPS Ch. 7, pp 184 onward)

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**Multiphase Flow in Wells**

The simultaneous flow of 2 or more phases will occur in Almost all oil wells Whenever the pressure drops below the bubble point, gas will evolve, and from that point to the surface, 2-phase flow will occur In many gas wells Condensation may occur as a result of the reduction of pressure and temperature as fluids flow up the well

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**Two-Phase Flow Is More Complicated Than Single-Phase Flow**

The phases tend to separate because of differences in density Shear stresses at the pipe wall are different for each phase - different density and viscosity Expansion of the highly compressible gas phase with decreasing pressure increases the in situ volumetric flow rate of the gas

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**Two-Phase Flow—More Complicated**

For upward flow, the less dense, more compressible, less viscous gas phase tends to flow at a higher velocity than the liquid phase causing a phenomenon known as slippage Consider the 2-phase example to the right where both α and β are flowing upwards α is less dense than β and will move faster than β This phenomenon is called “holdup” – that is, the denser phase is “held-up” in the pipe relative to the lighter phase So, the volume of the denser phase in the pipe is disproportionately greater than the volumetric flow rate of the denser phase feeding into the pipe

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**Two-Phase Flow Regimes**

The flow regime or flow pattern is a qualitative description of the phase distribution For gas-liquid, upward flow, 4 flow regimes are generally agreed upon in the two-phase literature Bubble, Slug, Churn, and Annular These occur as a progression with increasing gas rate for a given liquid rate Slug and churn flow are sometimes combined in a flow pattern called intermittent flow Some investigators have named annular flow as mist or annular-mist flow

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Flow Regimes in Vertical, Upward Multiphase Flowing Wells is a Qualitative description of the Phase Distribution Gas in the center and liquid “hugging” or “climbing” the walls Increasing Gas-Liquid Ratio Mist Flow Intermittent Flow

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The flow regime in gas-liquid, vertical flow can be predicted with a flow regime map – a plot relating flow regime to flow rates of each phase, fluid properties, and pipe size The chart to the right is from Govier and Azis and shows these flow patterns and the approximate regions in which they occur as functions of gas and liquid velocities

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**Taitel-Dukler Flow Regime Map (from PPS Fig. 7-11)**

A theoretical flow regime map was developed by Taitel, Barnea, and Dukler in 1980 This map identifies 5 flow regions, again based on gas and liquid velocities Taitel-Dukler Flow Regime Map (from PPS Fig. 7-11)

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Bubble Flow Dispersed bubbles of gas in a continuous liquid phase

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Slug Flow At higher gas rates, the bubbles coalesce into larger bubbles, called Taylor bubbles, that eventually fill the entire pipe cross section Between the large gas bubbles are slugs of liquid that contain smaller bubbles of gas entrained in the liquid

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Churn Flow With a further increase in gas rate, the larger gas bubbles become unstable and collapse, resulting in churn flow, Churn flow is a chaotic flow of gas and liquid in which the shape of both the Taylor bubbles and the liquid slugs are distorted It is a highly turbulent flow pattern Churn flow is characterized by oscillatory, up-and-down motions of the liquid

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Annular Flow At higher rates, gas becomes the continuous phase, with liquid flowing in an annulus coating the surface of the pipe and with liquid droplets entrained in the gas phase

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**Note Differences in Flow Regimes**

in Horizontal Pipes—gravity effects are important (we will look at horizontal two-phase flow in Week 6 Lab)

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Two-Phase Flow Models There are many different correlations that have been developed to calculate gas-liquid pressure gradients, most of which are empirically derived Each correlation was likely derived for a specific set of conditions, so no single correlation will apply to all real-world cases Become familiar with the assumptions inherent to each correlation and which correlation is best to use

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Two-Phase Flow Models The table at the right compares the relative errors of 8 different 2-phase flow correlations for different flow conditions VW = vertical wells DW = deviated wells VNH = vertical well cases w/o Hagedorn and Brown data Etc. In this table, the smaller the relative performance factor, the more accurate is the correlations The different flow correlation models are in the left column

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**Multiple Flow Regimes May Exist in a Well**

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**Multiphase Flow Concepts**

Flow Regimes Velocities: Superficial Slip In-situ Holdup vs. input volume fraction

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**Flow Regimes: Vertical Flow**

Four flow regimes: Bubble Slug Churn Annular Change based on gas and liquid rate

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**Flow Regime Map: Vertical Flow**

Govier and Aziz

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**Flow Regime Map: Vertical Flow**

Taitel-Dukler Flow Regime Map (from PPS)

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**Flow Regimes in Horizontal Pipe Good animation:**

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Velocity Concepts

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Velocity Differences

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**Holdup Vs. Input Fraction**

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**Holdup Vs. Input Fraction**

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**Two-Phase Flow Pressure Drop Calculation**

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**Two-Phase Flow Models Several different empirical correlations:**

Separated flow models: Hagedorn-Brown (1965): only for vertical wells Beggs-Brill (1973): any wellbore inclination and flow direction Homogenous flow models: Poettmann-Carpenter (1952) Guo-Ghalambor (2005)

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**Two-Phase Gradient Curves**

Based on given water/oil ratio (liquid density) and varying gas-liquid-ratio Includes friction and potential pressure drops For a fixed size Affected by GLR

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**Example of Tubing Curve Use (PPS**

wh = wellhead bh = bottom hole

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