Drilling Engineering

Июль 28, 2022

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Drilling Engineering

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2. Circulating System
3. For incompressible fluids, the specific weight of the liquid in field unit is given by If
4. Example: Calculate the static mud density required to prevent flow from a permeable stratum at 12,200ft
5. EOS of gas: Hydrostatic Pressure in Gas Column
6. A well contains tubing filled with methane gas (MW = 16) to a vertical depth of
7. The pressure in the annulus (external pressure) at D = 10,000 ft is P2 = 0.052
8. Hydrostatic Pressure in Complex Fluid Column
9. Hydrostatic Pressure in Complex Fluid Column
10. The effective density exerted by a circulating fluid against the formation that takes into account the
11. Example: A 9.5-PPG drilling fluid is circulated through the drill pipe and the annulus. The frictional
12. Buoyancy We , W, Wbo – effective weight, weight of the object in air, and buoyant
13. 10,000 ft of 19.5-lbm/ft drillpipe and 600 ft of 147 lbm/ft drill collars are suspended off
14. Energy balance: ΔPp is heat entering the system ΔPf is heat loss due to friction Flow
15. Applying the energy equation for a flow through a nozzle with neglecting: effects of elevation: D2
16. Flow Through Jet Bits
17. Assuming a constant ΔPb through all the nozzles Pressure drop across the bit ρ – lbm/gal
18. The purpose of the jet nozzles is to improve the cleaning action of the drilling fluid
19. Example: A 12.0 lbm/gal drilling fluid is flowing through a bit containing three 13/32 in nozzles
20. Rheological Model Newtonian fluids: Power law fluids: Bingham fluids: Herschel-Bulkley (Yield power law fluids)
21. Newtonian Model Non-Newtonian Model Bingham-plastic model Power Law model: Yield power law model: Rheological Model
22. Pseudoplastic (Time-independent shear thinning fluids) If the apparent viscosity decreases with increasing shear rate Dilatant (Time-independent
23. Thixotropic (Time-dependent shear thinning fluids): If the apparent viscosity decreases with time after the shear rate
24. Rotational Viscometer
25. A rotational viscometer is used to determine type of the fluid and the rheological model of
26. Rotational Viscometer
27. Rotational Viscometer
28. Rotational Viscometer The data below are obtained from a rotational viscometer. Determine type of fluid and
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Circulating System

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For incompressible fluids, the specific weight of the liquid in field

unit is given by
If P0 = 0 then
The fluid density

Hydrostatic Pressure in Liquid Column

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Example: Calculate the static mud density required to prevent flow from

a permeable stratum at 12,200ft if the pore pressure of the formation fluid is 8500psig.
Solution:
The mud density must be at least 13.4 lbm/gal

Hydrostatic Pressure in Liquid Column

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EOS of gas:
Hydrostatic Pressure in Gas Column

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A well contains tubing filled with methane gas (MW = 16)

to a vertical depth of 10000ft. The annular space is filled with a 9.0 lbm/gal brine. Assuming ideal gas behavior, compute the amount by which the exterior pressure on the tubing exceeds the interior tubing pressure at 10,000ft if the surface tubing pressure is 1000 psia and the mean gas temperature is 140F. If the collapse resistance of the tubing is 8330 psi, will the tubing collapse due to the high external pressure?

Hydrostatic Pressure in Gas Column

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The pressure in the annulus (external pressure) at D = 10,000

ft is
P2 = 0.052 * 9.0 * 10,000 + 14.7 = 4,695 psia
The pressure in the tubing (internal pressure) at D = 10,000ft
Pressure difference = p2 – p = 4695 – 1188 = 3507 < 8330 psia
The tubing will withstand the high external pressure

Hydrostatic Pressure in Gas Column

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Hydrostatic Pressure in Complex Fluid Column

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Hydrostatic Pressure in Complex Fluid Column

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The effective density exerted by a circulating fluid against the formation

that takes into account the pressure drop in the annulus above the point being considered.
The ECD is calculated as:
ρ – mud density, ppg
P – Sum of the hydrostatic pressure and the frictional pressure drop in the annulus between the depth D and surface, Psig
D – the true vertical depth, ft

Equivalent Circulating Density (ECD)

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Example: A 9.5-PPG drilling fluid is circulated through the drill pipe

and the annulus. The frictional pressure losses gradient in the annulus is 0.15. Calculate the equivalent circulating density in PPG.
Solution:
ρ = 9.5 + P/0.052 = 9.5 + 0.15 / 0.052 = 12.4 PPG

Equivalent Circulating Density (ECD)

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Buoyancy
We , W, Wbo – effective weight, weight of the object

in air, and buoyant force.
ρl and ρo - densities of liquid and the object

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10,000 ft of 19.5-lbm/ft drillpipe and 600 ft of 147 lbm/ft

drill collars are suspended off bottom in a 15-lbm/gal mud. Calculate the effective hook load that must be supported by the derrick. Density of steel is 65.5 lbm/gal
Solution:
W = 19.5 * 10000 + 147 * 600 = 283200 lbm
We = W(1 - ρf/ρs) = 283200 * (1 - 15/65.5) = 218300 lbm
(density of steel = 65.5 lbm/gal = 490lbm/cu ft)

Buoyancy

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Energy balance:
ΔPp is heat entering the system
ΔPf is heat loss due

to friction

Flow Through Jet Bits

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Applying the energy equation for a flow through a nozzle with

neglecting:
effects of elevation: D2 - D1 = 0
effects of uptream velocity vo = 0
Heat entering the system ΔPp = 0 and friction loss ΔPf = 0

Flow Through Jet Bits

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Flow Through Jet Bits

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Assuming a constant ΔPb
through all the nozzles
Pressure drop across

the bit
ρ – lbm/gal ; q – gpm ; At - in2

Flow Through Jet Bits

Flow Through Parallel Nozzles

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The purpose of the jet nozzles is to improve the cleaning

action of the drilling fluid at the bottom of the hole. Since the fluid is traveling at a vertical velocity vn , before reaching to the hole and traveling at zero vertical velocity after striking the hole bottom hence all the fluid momentum is transferred to the hole bottom.
Force is time rate of change of momentum, hence:
Substitute vn to the equation above gives
Where Fj is the hydraulic impact force given in pounds.

Flow Through Jet Bits

Hydraulic Impact Force

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Example: A 12.0 lbm/gal drilling fluid is flowing through a bit

containing three 13/32 in nozzles at a rate of 400 gal/min. Calculate the pressure drop across the bit and the impact force developed by the bit.
Solution: Assume Cd = 0.95
Hydraulic impact force:

Flow Through Jet Bits

Flow Through Parallel Nozzles

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Rheological Model

Newtonian fluids:
Power law fluids:
Bingham fluids:
Herschel-Bulkley (Yield power law fluids)

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Newtonian Model
Non-Newtonian Model
Bingham-plastic model
Power Law model:
Yield power law model:
Rheological Model

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Pseudoplastic (Time-independent shear thinning fluids)
If the apparent viscosity decreases with increasing

shear rate
Dilatant (Time-independent shear thickening fluids)
If the apparent viscosity increases with increasing shear rate

Classification of Drilling Fluids

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Thixotropic (Time-dependent shear thinning fluids): If the apparent viscosity decreases with

time after the shear rate is increased to a new constant value
Rheopectic (Time-dependent shear thickening fluids): If the apparent viscosity increases with time after the shear rate is increased to a new constant value
Drilling fluids and cement slurries are generally thixotropic

Classification of Drilling Fluids

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Rotational Viscometer

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A rotational viscometer is used to determine type of the

fluid and the rheological model of the fluid. This can be done by varying the speed of the rotor (varying the shear rate) and reading the dial reading (shear stress). To convert the speed to shear rate and dial reading to shear stress, simply use these corellations:
γ = 1.703 x rpm, 1/s
τ = 1.06 x Dial Reading

Rotational Viscometer

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