1. PRESSURE DROP AND PRESSURE TRANSIENTS IN PIPELINES Darcy-Weisbach and Joukowski
Jón Steinar Gudmundsson
Department of Petroleum Engineering and Applied Geophysics
NTNU
Aker Solutions
October 27, 2009

2. Pipes and Pipelines Production and processing of oil and gas offshore

3. R&D on Pressure Drop and Pressure Transients
Pressure drop in pipelines, Darcy-Weisbach equation. Moody diagram shows relative roughness
Friction factor in pipelines, Haaland equation.
Nikuradse’s sand-grain-roughness and measured roughness (ks and Rq).
Transient pressure in pipelines, Joukowski equation.
Pressure pulse technology, two-phase metering and location and quantification of deposits.
Impulse pumping, new technology, R&D.
Water-hammer in flexible hoses with steel sections.
Subsea compression, jet pump technology

4. Darcy-Weisbach Equation Force balance, steady-state pipe flow

5. Joukowski Equation Transient, mass and momentum balance

6. Frictional Pressure Drop Horizontal Pipeline, Inclined Well

7. Nikuradse’s Sand-Grain Data

8. Blasius, Colebrook-White and Haaland
Haaland n=1 for liquids, same as Coolebrook-White
Haaland n=3 for gases, same as AGA data

9. Haaland Friction Factor Liquids, n=1, Hydraulically smooth and k/d=0
Haaland gives same as Colebrook-White for liquids, less than 1 % difference

10. Haaland Friction Factor Gases, n=3, Hydraulically smooth and k/d=0.001
Haaland for gas based on AGA data, lower than for liquids, transition different

11. Haaland Friction Factor Liquid n=1 and gas n=3, k/d=0.001
Gas 3.8 % lower than liquid at Re=106

12. Nikuradse’s Sand Grain and Real Roughness

13. Sletfjerding Ra = Arithmetic mean roughness
Rq = Root-mean-square roughness
Rz = Mean peak-to-valley roughness

14. Sletfjerding
n=1 for liquids, n=2 for gases

15. Sand-grain roughness ks, Measured roughness Rq , Hurste exponent H
Pipes Used by Sletfjerding
Sand-grain roughness ks, Measured roughness Rq , Hurste exponent H
4.5 < (ks/Rq) < 5.8
21 < ks < 181

16. Equivalent Sand Grain Roughness “Oil country tubular goods”
Materiale
Ruhet
[tomme]
[µm]
Plastbelegg
Polert karbonstål
Elektropolert rustfritt stål
Sementbelegg
Karbonstål
Fiberglassbelegg
Rustfritt stål
0,200∙10-3
0,492∙10-3
1,18∙10-3
1,30∙10-3
1,38∙10-3
1,50∙10-3
2,10∙10-3
5,1
12,5
30,0
33,0
35,1
38,1
53,3

17. Idealized Water-Hammer in 2400 [m] Pipe No wall friction, no attenuation
a=1200 m/s, u=3 m/s, ρ=700 kg/m3, Δp=ρaΔu=25 [bara]

18. Speed of Sound in Pipes
Infinite medium, oil density 870 [kg/m3], oil compressibility 0,62∙10-9 [Pa-1], speed of sound 1360 [m/s].
Finite medium (pipe), Young’s modulus steel 200∙109 [Pa], pipe diametere 0.1 [m], wall thickness 4 [mm], speed of sound
1240 [m/s], 9 % lower. Flexible hose much lower.

19. Speed of Sound in Steel Pipe and Flexible Hose
Most pipes have ratio e/d < 0.05 (d/e > 20)

20. Pressure Waves in Real Pipelines Attenuation with each successive reflection

21. Transient Pulse Friction Added to Steady-State Friction Brunone and Ramos Expressions

22. Numerical Simulation at NTNU
… No Pulse Friction
-.-. Steady Pulse Friction
-x- Transient Pulse Friction
We observe no additional damping (attenuation) when including transient friction, new physics needed. MOC numerical dispersion coincidentally matches attenuation.

23. Statfjord A, December 12, 2007 Pressure wave transmission and reflection depend on acoustic impedance 23

24. Statfjord A Off-Loading Pipeline
Steel and flexible hoses, three cases simulated at NTNU

25. Statfjord A Off-Loading Pipeline Steel and flexible hoses, three cases simulated

26. Impulse Pumping Clavis Impulse Technology AS Patent, Sagov (2004)

27. Impulse Pumping Propagation of pressure waves (pulses)

28. Impulse Pumping Pumping verified by experiments and modelling

29. Modelling of Pressure Wave Propagation

32. Industrial Jet Pump Agir Boosting Technology AS
pipe
mixer
diffuser
nozzle

33. Alphabeta Reservoir Performance

34. Alphabeta Natural Gas Production 4 Wells

35. Alphabeta Inflow Performance

36. Alphabeta Pressures Constant Total Field Rate 240,000 kg/h
Year
WHP
(bara)
PLEM
Difference
(bar)
234
176 2
209
157 19 4
193
145 31 8
159
119 57 16 91 68
108
PLEM = Pipeline End Manifold (75% of WHP)

37. Pump Performance Agir Boosting Technology AS
Industrial jet pump experience and performance data used in calculations
Pressure loss coefficients for LP, HP, M and D sections in series, K=(Δp)/(0.5ρu2)
Performance numbers M, N, R, η, C in terms of flow, pressure, geometry, hydraulic efficiency and density

38. Performance Numbers

39. Performance Equation

41. Alphabeta Drive Fluid Rate
Year
Difference
(bar)
Gas Density
(kg/m3)
Gas Flow Rate
(m3/h) M
(-)
Drive Fluid
139
1719 2 19
124
1927
1.9
1039 4 31
114
2096
1.6
1343 8 57 92
2598
0.90
2962 16
108 50
4780

42. Subsea Gas Boosting Feasibility study

43. Subsea Compression by Agir Boosting Technology
In feasibility study, field and well performance assumed; high quality offshore resource
Performance of traditional jet pumps well known, but not for HP natural gas (K factors need to be determined)
High drive fluid rate and hence large pipe diameter required (dense phase transport)
In feasibility study,14% greater cumulative production first 8 years with pressure boosting

44. Pressure Pulse Technology Markland Technology AS
Technology platform for well and pipe flow/flow condition measurements based on analysis of an induced pressure pulse:
Rate measurements:
Flow rate/phase composition measurements oil/gas producers
Flow Condition profiling:
Pressure/density profile in wells
Deposits in pipes for water, oil and gas, process equipment
Flux changes: Leakages, inflow
One common technology basis for all applications, difference only in procedures and signal processing
Non-invasive, all instrumentation is on the surface, no need to enter the well or pipe with instruments/logs 44

45. Speed of Sound in Two-Phase Mixtures

46. A B
LAB
Pressure
Time A B

47. Pressure Pulse Rate Metering Two equations, two unknowns, u and ρ

48. Flow Condition Profiling
Determine the flow conditions along the path of the tubing/pipe
Pulse travels along pipe with speed of sound and stops the flow
The line packing signal reflects the flow conditions at the front of the pulse
Change in friction (roughness, diameter)
Change in density and acoustic velocity
Change in flux (inflow, outflow)
Flow Condition Profiling to detect wax deposits in pipeline. Principal sketch. 48

49. Measurement Setup
Arrangement of closing valve and pressure transmitters:
Typical setup for producing well:
Close by wing valve
Two transmitters, known spacing
Measure speed of sound
Typical setup for pipeline
If fluid is stable: may choose which side to measure from
Examples:
Oil/condensate pipeline with wax
Oil pipe with sand influx
Producing well with tubing diameter changes 49

50. Pressure Pulse Test of Oil Pipeline
Data from successive measurements on a 100 km oil pipeline with wax deposits at different stages of wax precipitation/cleaning. Measurements on inlet side of pipe. Blue curve on top is what to expect from of a clean pipe. Deviation below blue line is deposits. 50

51. Processed Pressure Pulse Test, Oil Pipeline
Data processed by simulation: adjusting hydraulic diameter in pipe to match measured signal.
Blue and green lines represents period of wax accumulation. Red line shows the result of successive pigging. 51

52. Elements of Pressure Pulse Technology
Equipment:
Pressure transmitters: fast responding, off-the-shelf equipment
Barrier/signal conditioning box.
Data acquisition (pressure with time).
Valve: Use existing valve on site:
Fast pressure buildup time required.
Manual, hydraulic or pneumatic activation.
Operative:
Low flowrate/modest pressure pulse generally an advantage, gives long reach 52

53. NTNU R&D Pressure Drop and Pressure Transients in Pipelines
Concluding Remarks
NTNU R&D Pressure Drop and Pressure Transients in Pipelines
Darcy-Weisbach and Joukowski used in water hammer, impulse pumping, pressure pulse.
Haaland and Colebrook-White same for liquids but different for gases.
Wall roughness key to understanding pressure drop (we know density and viscosity).
Markland Technology AS provides flowrate and deposit monitoring.
Clavis Impulse Technology AS develops new pumping technology.
Agir Boosting Technology AS develops new subsea compression technology.