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

Pipes and Pipelines Production and processing of oil and gas offshore

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

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

Joukowski Equation Transient, mass and momentum balance

Frictional Pressure Drop Horizontal Pipeline, Inclined Well

Nikuradse’s Sand-Grain Data

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

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

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

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

Nikuradse’s Sand Grain and Real Roughness

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

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

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

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

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]

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.

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

Pressure Waves in Real Pipelines Attenuation with each successive reflection

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

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.

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

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

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

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

Impulse Pumping Propagation of pressure waves (pulses)

Impulse Pumping Pumping verified by experiments and modelling

Modelling of Pressure Wave Propagation

Industrial Jet Pump Agir Boosting Technology AS pipe mixer diffuser nozzle

Alphabeta Reservoir Performance

Alphabeta Natural Gas Production 4 Wells

Alphabeta Inflow Performance

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)

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

Performance Numbers

Performance Equation

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

Subsea Gas Boosting Feasibility study

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

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

Speed of Sound in Two-Phase Mixtures

A B LAB Pressure Time A B

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

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

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

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

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

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

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.