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Lesson 9

Gasified Liquid Hydraulics

Read: UDM Chapter 2.7

pages 2.131-2.179

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Gasified Liquid Hydraulics

• Reynolds Number

• Multi-phase flow

• Pressure prediction– HSP– Circulating pressure– Bit pressure drop

• Hole Cleaning

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Reynolds Number

• In practice the flow of gasified liquid is almost always turbulent (Reynolds number > 4000)

• Example water flowing up an 8 1/2” hole with 5” drillpipe.

• AV of 7 ft/min would be turbulent

• AV’s > 100 ft/min are common

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Reynolds Number

• Equation 2.58

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Reynolds Number

• The consequenses of turbulance in the annulus is that the rheology of gasified fluids has little effect on the annular pressure profile.

• This is at least true with un-viscosified base fluid.

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Multi-phase flow

• At least three phases are present in the wellbore– Liquid, gas, and solids

• Liquids could be:– Mud– Oil– Water

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Flow Regimes

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Flow Regimes

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Flow Regimes

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Pressure prediction

• HSP• Annular Friction• Bit pressure drop

– Mud– Gasified mud

• Drillstring pressure drop– Mud– Gasified mud

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HSP

1

2

0144P

PhVdP

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HSP

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HSP

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Gas Volume

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Friction forces

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Fanning Friction Factor

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Reduced Reynolds Number

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Gas volume

• This correlation and equation 2.66 were used to compute the required air injection rate to give a BHP of 2497 psi at 6000’ in an 8 1/2” X 4 1/2” annulus at 350 gpm.

• Required 14.9 scf/bbl

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Gas volume

• Equation 2.63 was used to calculate the volume of air to give the same BHP static.

• Required 13.4 scf/bbl.

• Poettmann and Bergman concluded that the difference is insignificant and a reasonable calculation of air rate for the desired BHP could be done assuming a static fluid column.

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Bit pressure drop

• Mud

• Gasified Mud

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Bit pressure drop - Mud

• Red book

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Bit pressure drop - Gasified Mud

• This relationship neglects any energy loss through the nozzles due to frictional effects and any change in potential energy.

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Bit pressure drop - Gasified Mud

• Substituting equation 2.44 for the density of a lightened fluid this becomes

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Fig. 2.41

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Hole Cleaning

• Settling velocity

• Critical velocity

• Settling Velocity

• Cuttings Transport ratio

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Settling velocity

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Critical velocity

• Guo assumed that the cuttings concentration in the annulus should not exceed some critical value if hole cleaning problems were to be avoided.

• vc = ROP/60Cc

• vc = critical velocity, ft/min

• ROP = Rate of penetration, ft/hr

• Cc = Cuttings concentration, fraction

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Critical velocity

• Taking the critical concentration as 4%, cuttings would need to travel uphole with a velocity 25 times greater than the penetration rate.

• For a penetration rate of 30 ft/hour, this corresponds to a velocity of 12.5 ft/min.

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Settling Velocity

• With a large annulus, the AV may not be such that turbulent flow can be achieved.

• We would then need to alter the viscosity of the fluid.

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Settling Velocity

• For a 0.25” cutting with a density of 21 ppg falling through a fluid of density of 5 ppg.

• Maximum AV = 15 ft/min.

• Settling velocity would have to be restricted to 17.4 ft/min at a penetration rate of 30 ft/hr.

• This would require an effective viscosity of 160 cP.

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Cuttings Transport Ratio

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Cuttings Transport Ratio• The velocity of the system is normally the mean

velocity in the annulus determined by dividing the total flow rate of the various phases of the fluid by the cross-sectional area of the annulus.

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Cuttings Transport Ratio

• The CTR should be calculated throughout the annulus to ensure that adequate hole cleaning takes place at all points and that the cuttings are not packing off in the hole somewhere.

• A CTR of 1.0 implies perfect hole cleaning.

• If CTR>0 cuttings are moving upward.

• CTR should be >0.55

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Example

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ATMPETE 689 UBDATM

ATM ATM

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ATMPETE 689 UBDATM

ATM ATM

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ATM ATM