Oil and Gas Pipeline Design, Maintenance and Repair

Transcription

1 Oil and Gas Pipeline Design, Maintenance and Repair Dr. Abdel-Alim Hashem Professor of Petroleum Engineering Mining, Petroleum & Metallurgical Eng. Dept. Faculty of Engineering Cairo University Part 2: Steady-State Flow of Gas through Pipes ١

2 INTRODUCTION Pipes provide an economic means of producing and transporting fluids in large volumes over great distances The flow of gases through piping systems involves flow in horizontal, inclined, and vertical orientations, and through constrictions such as chokes for flow control ٢

3 ENERGY OF FLOW OF A FLUID ٣

4 BERNOULLI'S EQUATION Z P V H Z P V h γ 2g γ 2g A + A + = + B + B + A p B f P = the pressure V = the velocity Z = the height H p = the equivalent head added to the fluid by a compressor at A h f = represents the total frictional pressure loss between points A and B. ٤

5 VELOCITY OF GAS IN A PIPELINE Q=VA M=q ρ = M 2 = q2ρ2 V ρ = V ρ M = qρ = q 2ρ2 = q bρb q = V A ρ b q = q b ρ P =Z RT ρ ρ = P ZRT ρ = b P b ZRT b b Pb T Z q = q b Tb P Zb ٥

6 VELOCITY OF GAS IN A PIPELINE P b T q = qb Z since Zb =.0 Tb P q Z P b T b 4x44q Z P b T b V = = 2 A Tb P πd Tb P V q Pb ZT = b ( ) 2 USCS d Tb P V = upstream gas velocity, ft/s q b = gas flow rate, measured at standard conditions, ft 3 /day (SCFD) d = pipe inside diameter, in. P b = base pressure, psia T b = base temperature, R (460 + F) P = upstream pressure, psia T = upstream gas temperature, R(460 + F) ٦

7 VELOCITY OF GAS IN A PIPELINE Gas velocity at section 2 is given by V q Pb ZT = b 2 d Tb P2 Gas velocity at any point in a pipeline is given by V = q Pb ZT b ( USCS) 2 d Tb P V = q Pb ZT b ( SI) 2 d Tb P ٧

8 EROSIONAL VELOCITY 00 V max = ρ V max = maximum or erosional velocity, ft/s ρ = gas density at flowing temperature, lb/ft 3 V max = 00 ZRT 29 γ g P Z = compressibility factor of gas, dimensionless R = gas constant = 0.73 ft 3 psia/lb-moler T = gas temperature, or γg = gas gravity (air =.00) P = gas pressure, psia ٨

9 Example A gas pipeline, NPS 20 with in. wall thickness, transports natural gas (specific gravity = 0.6) at a flow rate of 250 MMSCFD at an inlet temperature of 60 F. Assuming isothermal flow, calculate the velocity of gas at the inlet and outlet of the pipe if the inlet pressure is 000 psig and the outlet pressure is 850 psig. The base pressure and base temperature are 4.7 psia and 60 F, respectively. Assume compressibility factor Z =.00. What is the erosional velocity for this pipeline based on the above data and a compressibility factor Z = 0.90? ٩

10 Solution For compressibility factor Z =.00, the velocity of gas at the inlet pressure of 000 psig is V = = 2.29 ft/s x Gas velocity at the outlet is V = 2.29 = ft/s The erosional velocity is found for Z = 0.90, V max = 0.9x04.7x ft/s 29x0.6x04.7 = ١٠

11 REYNOLD S NUMBER OF FLOW ρ Vd R e = µ ( USCS ) R e = Reynolds number, dimensionless V = average velocity of gas in pipe, ft/s d = inside diameter of pipe, ft ρ = gas density, lb/ft 3 µ = gas viscosity, lb/ft-s ١١

12 REYNOLD S NUMBER OF FLOW R e = ρ Vd µ ( USCS ) USCS or SI R e = Reynolds number, dimensionless V = average velocity of gas in pipe, ft/s or m/s d = inside diameter of pipe, ft or m ρ = gas density, lb/ft 3 or kg/m 3 µ = gas viscosity, lb/ft.s or kg/m.s ١٢

13 REYNOLD S NUMBER OF FLOW IN CUSTOMARY UNITS R e P γ b gq = ( USCS) Tb µ d P b = base pressure, psia T b = base temperature, R (460 + F) γ g = specific gravity of gas (air =.0) q = gas flow rate, standard ft 3 /day (SCFD) d = pipe inside diameter, in. µ = gas viscosity, lb/ft.s ١٣

14 REYNOLD S NUMBER OF FLOW IN CUSTOMARY UNITS R e P γ b gq = ( SI) Tb µ d P b = base pressure, kpa T b = base temperature, K (273 + C) γ g = specific gravity of gas (air =.0) q = gas flow rate, standard m 3 /day (SCFD) d = pipe inside diameter, mm µ = gas viscosity, Poise ١٤

15 Flow Regime Re > Re 4000 Re > 4000 Laminar flow, Critical flow Turbulent flow ١٥

16 Example A natural gas pipeline, NPS 20 with in. wall thickness, transports 00 MMSCFD. The specific gravity of gas is 0.6 and viscosity is lb/ft.s. Calculate the value of the Reynolds number of flow. Assume the base temperature and base pressure are 60 F and 4.7 psia, respectively. ١٦

17 Solution Pipe inside diameter = 20-2 x 0.5 = 9.0 in. The base temperature = = 520 R Using Equation we get R e x00x0 = = 5,33, x 9 Since Re is greater than 4000, the flow is in the turbulent region. ١٧

18 f = f f d 4 FRICTION FACTOR f f = Fanning friction factor f d = Darcy friction factor For laminar flow f = 64 R e ١٨

19 FRICTION FACTOR FOR TURBULENT FLOW ١٩

20 INTERNAL ROUGHNESS Type of pipe e, in e,mm Drawn tubing (brass, lead, glass) Aluminum pipe Plastic-lined or sand blasted Commercial steel or wrought iron Asphalted cast iron Galvanized iron Cast iron Cement-lined Riveted steel PVC, drawn tubing, glass Concrete Wrought iron Commonly used well tubing and line pipe: New pipe months old months old ٢٠

21 TRANSMISSION FACTOR The transmission factor F is related to the friction factor f as follows F f = = 2 f 4 F 2 ٢١

22 Relative Roughness Relative roughness = e d e = absolute or internal roughness of pipe, in. d = pipe inside diameter, in. ٢٢

23 FLOW EQUATIONS FOR HIGH PRESSURE SYSTEM General Flow equation Colebrook-White equation Modified Colebrook-White equation AGA equation Weymouth equation Panhandle A equation Panhandle B equation IGT equation Spitzglass equation Mueller equation Fritzsche equation ٢٣

24 GENERAL FLOW EQUATION (USCS) q sc ( ) T P P d b = ( USCS) Pb γ g Z avtav fl 0.5 q sc = gas flow rate, measured at standard conditions, ft 3 /day (SCFD) f = friction factor, dimensionless P b = base pressure, psia T b = base temperature, R( F) P = upstream pressure, psia P 2 = downstream pressure, psia γ g = gas gravity (air =.00) T av = average gas flowing temperature, R (460 + F) L = pipe segment length, mi Z av = gas compressibility factor at the flowing temperature, dimensionless d = pipe inside diameter, in. ٢٤

25 Steady flow in a gas pipeline ٢٥

26 GENERAL FLOW EQUATION (SI) ( 2 ) P P d 3 T b ( ) Pb γ g Z avt avfl q sc = x SI q sc = gas flow rate, measured at standard conditions, m 3 /day f = friction factor, dimensionless P b = base pressure, kpa T b = base temperature, K (273 + C) P = upstream pressure, kpa P2 = downstream pressure, kpa γ g = gas gravity (air =.00) T av = average gas flowing temperature, K (273 + C) L = pipe segment length, km Z av = gas compressibility factor at the flowing temperature, dimensionless d = pipe inside diameter, mm ٢٦

27 General flow equation in terms of the transmission factor F ( ) T P P d b qsc = F ( USCS) Pb γ g Z avtav L 2 F = f ( ) P 4 P2 d T b ( ) Pb γ gz avtavl qsc = x F SI F = transmission factor 0.5 ٢٧

28 EFFECT OF PIPE ELEVATIONS s ( 2 ) T P e P d b qsc = F ( USCS) Pb γ gz avtavle s 2 5 ( P 4 e P2 ) d T b qsc = 5.747x0 F ( SI) Pb γ gz avtavle s (e - ) L e = L s s = (0.0375) γ ( z)/(z T ) (USCS) g av av s = (0.0684) γ ( z)/(z T ) (SI) g av av s = elevation adjustment parameter, dimensionless Z = elevation difference e = base of natural logarithms (e = ) 0.5 ٢٨

29 Gas flow through different elevations s s s2 s s2 s s 3 ( ) ( ) ( ) n sn e e e e e e ( e ) + L = L + L + L L s 0 e 2 3 n i s s2 s3 sn j = s (e - ) s L = j L + j L e + j L e + + j L e s s s3 sn e n n i ٢٩

30 AVERAGE PRESSURE IN PIPE SEGMENT 2 Pav = P+ P2 + 3 PP 2 P + P 2 Or P av 2 = 3 P P P P2 ٣٠

31 COLEBROOK-WHITE EQUATION A relationship between the friction factor and the Reynolds number, pipe roughness, and inside diameter of pipe. Generally 3 to 4 iterations are sufficient to converge on a reasonably good value of the friction factor ( ) 2.5 = 2 log e + Turbulent flow f 3.7d Re f f = friction factor, dimensionless d = pipe inside diameter, in. e = absolute pipe roughness, in. R e = Reynolds number of flow, dimensionless ٣١

32 COLEBROOK-WHITE EQUATION 2.5 = 2 log Turbulent flow in smooth pipe f Re f f ( e ) = 2 log turbulent flow in fully rough pipes 3.7d ٣٢

33 Example A natural gas pipeline, NPS 20 with in. wall thickness, transports 200 MMSCFD. The specific gravity of gas is 0.6 and viscosity is lb/ft-s. Calculate the friction factor using the Colebrook equation. Assume absolute pipe roughness = 600 µ in. ٣٣

34 Solution Pipe inside diameter = 20-2 x 0.5 = 9.0 in. Absolute pipe roughness = 600 ~ in. = in. First, we calculate the Reynolds number Re = (4.7/(60+460))x(( 0.6 x 200 x 06) /( x 9)) = 0,663,452 This equation will be solved by successive iteration. Assume f = 0.0 initially; substituting above, we get a better approximation as f = Repeating the iteration, we get the final value as f = Therefore, the friction factor is ٣٤

35 MODIFIED COLEBROOK-WHITE EQUATION ( ) = 2 log e + turbulent flow f 3.7d Re f F ( ) log e F = + with transmission factor 3.7d Re ٣٥

36 AMERICAN GAS ASSOCIATION (AGA) EQUATION 3.7d F = 4log Von Karman, for rough pipe e R e F = 4Df log Von Karman, smooth pipe.42ft D f known as the pipe drag factor depend on bend index, Its value ranges from 0.90 to 0.99 F t = Von Karman smooth pipe transmission factor F t R e = 4log 0.6 Ft ٣٦

37 Bend Index Bend index is the sum of all the angles and bends in the pipe segment, divided by the total length of the pipe section under consideration BI = total degrees of all bends in pipe section total length of pipe section Material Bend Index Extremely Low 5 to 0 Average 60 to 80 Extremely High 200 to 300 Bare steel Plastic lined Pig burnished Sand blasted ٣٧

38 WEYMOUTH EQUATION ( s ) /3 T P e P d b qsc = E ( USCS) Pb γ g Z avtav Le q sc = gas flow rate, measured at standard conditions, ft 3 /day (SCFD) f = friction factor, dimensionless /6 F =.8 d P b = base pressure, psia ( USCS) T b = base temperature, R(460 + F) P = upstream pressure, psia P 2 = downstream pressure, psia γ g = gas gravity (air =.00) T av = average gas flowing temperature, R (460 + F) L e = equivalent pipe segment length, mi Z av = gas compressibility factor at the flowing temperature, dimensionless d = pipe inside diameter, in. 0.5 ٣٨

39 WEYMOUTH EQUATION ( ) s 2 6/3 P 3 e P2 d T b ( ) Pb γ g Z avtav L e qsc = x xe SI q sc conditions,m 3 /day = gas flow rate, measured at standard f = friction factor, dimensionless P b = base pressure, kpa /6 F = 6.52 d ( SI) T b = base temperature, K(273 + C) P = upstream pressure, kpa P 2 = downstream pressure, kpa γ g = gas gravity (air =.00) T av = average gas flowing temperature, K (272 + C) L e = equivalent pipe segment length, km Z av = gas compressibility factor at the flowing temperature, dimensionless d = pipe inside diameter, mm ٣٩

40 PANHANDLE A EQUATION ( ) s 2 P b e P b γ g av e T qsc = E d ( USCS) P xt xl xz ( s P ) e P T b qsc = x0 E d ( SI) Pb γ g xtavxlexz E = pipeline efficiency, a decimal value less than.0 ٤٠

41 PANHANDLE A EQUATION Transmission Factor qγ F = 7.2 E g ( USCS) d qγ g F =.85 E ( SI) d ٤١

42 PANHANDLE B EQUATION ( ) s 2 P b e P b γ g av e T qsc = 737 E d ( USCS) P xt xl xz ( s P ) e P T b 2.53 qsc =.002x0 E d ( SI) 0.96 Pb γ g xtavxlexz 0.5 E = pipeline efficiency, a decimal value less than.0 ٤٢

43 PANHANDLE A EQUATION Transmission Factor qγ F = 6.7 E g ( USCS) d qγ g F = 9.08 E ( SI) d ٤٣

44 INSTITUTE OF GAS TECHNOLOGY (IGT) EQUATION 2 s 2 ( P e P ) µ = gas viscosity, lb/ft.s µ = gas viscosity, Poise T b qsc = 36.9 E d ( USCS) Pb γ g xtavxlexzxµ 2 s 2 ( P e P2 ) T b qsc =.2822x0 E d ( SI) Pb γ g xtavxlexzxµ ٤٤

45 SPITZGLASS EQUATION Low Pressure s ( P e P2) T qsc = x E d USCS 3 b ( ) Pb γ gxtavxlexz av ( / d d) 0.5 Pressure less than or equal.0 psi s ( P e P2) T qsc = x E d SI Pb γ gxtavxlexz av ( / d d) 2 b ( ) 0.5 Pressure less than or equal 6.9 kpa ٤٥

46 SPITZGLASS EQUATION High Pressure s ( P e P ) T b qsc = E d ( USCS) Pb γ gxtavxlexz av ( / d d) 0.5 Pressure more than.0 psi Pressure more than 6.9 kpa s ( P e P2) T qsc = x E d SI Pb γ gxtavxlexz av ( / d d) 2 b ( ) 0.5 ٤٦

47 MUELLER EQUATION ( 2 s 2 P e P ) T b qsc = E d ( USCS) Pb γ g xtavxlexµ µ = gas viscosity, lb/ft.s µ = gas viscosity, cp ( 2 s 2 P ) e P2 2 T b qsc = x0 xe d ( SI) Pb γ g xtavxlexµ ٤٧

48 FRITZSCHE EQUATION ( 2 s 2 P e P ) T b qsc = E d ( USCS) Pb γ g xtavxle ( 2 s 2 P e P ) T b qsc = E d ( SI) Pb γ g xtavxle ٤٨

49 EFFECT OF PIPE ROUGHNESS ٤٩

50 COMPARISON OF FLOW EQUATIONS ٥٠

51 COMPARISON OF FLOW EQUATIONS ٥١

52 Flow Characteristics of Low- Pressure Services ft / hr total pressure drop in service, in H O = ( )( ' K p γ / γ )( L + Lef ) K p = pipe constant γ = sp gr of gas γ' = sp gr 0.60 L = length of service, ft L ef = equivalent length of fittings given below ٥٢

53 Values of K p Pipe size and type 3/4-in CTS copper -in ID plastic -in CTS copper ¼-in CTS copper ¼-in NS steel ½-in NS steel K p.622 x x x x x x 0-6 ٥٣

54 Equivalent lengths of pipe fittings Fitting -in or ¼-in Curb cock for copper service ¼-in curb cock for ¼-in steel service ½-in curb cock for ½-in steel service ½-in street elbow for ¼-in steel service ½-in street elbow for ½--in steel service ¼-in street tee for ¼-in steel service ½-in street tee on sleeve or ¼-in hole in main ¼ x x ¼-in street tee ½ x ¼ x ½-in street tee Combined outlet fittings ¾-in copper -in copper or plastic ¼-in steel ½-in steel Equivalent length, ft ٥٤

55 Equivalent lengths of pipe fittings ٥٥

56 Flowing Temperature in (Horizontal]) Pipelines T ( ) ( ) ( ) 2/ 3 ( C + C L ) + + C + C L + ( x ) ( + ) C2/ C3 T C / C CC / C C C C C C C L s x 5 3 L = + x C C C 2 x 2 C2 C2 C3 ( ) C = z c L + z c v p v p C = k / m 2 ( v v )( pl pv ) C = z z c c / L 3 2 P P zv 2 zv v v kπd0 C = z c µ ( z ) c µ Q v gh / L T L L L m v pl dl v pv dv ( )( ) C = z z P P c µ c µ v v L + + L v 2 v pl dl pv dv ٥٦

57 Flowing Temperature in (Horizontal]) Pipelines z v = mole fraction of vapor (gas) in the gas-liquid flowstream P = pressure, lbf/ft 2 L = pipeline length, ft v = fluid velocity, ft/sec c p = fluid specific heat at constant pressure, Btu/lbm.ºF µ d = Joule-Thomson coefficient, ft 2.ºF/lbf m = mass flow rate, lbm/sec Q = phase-transition heat, Btu/lbm k = thermal conductivity, Btu/ft.sec.ºf g = gravitational acceleration, equal to 32.7 ft/sec 2 h = elevation difference between the inlet and outlet, ft d o = outside pipe diameter, ft Ts = temperature of the soil or surroundings, of ٥٧

58 SUMMARY OF PRESSURE DROP Equation General Flow Colebrook- White Modified Colebrook- White AGA EQUATIONS Application Fundamental flow equation using friction or transmission factor; used with Colebrook-White friction factor or AGA transmission factor Friction factor calculated for pipe roughness and Reynolds number; most popular equation for general gas transmission pipelines Modified equation based on U.S. Bureau of Mines experiments; gives higher pressure drop compared to original Colebrook equation Transmission factor calculated for partially turbulent and fully turbulent flow considering roughness, bend index, and Reynolds number ٥٨

59 SUMMARY OF PRESSURE DROP EQUATIONS Equation Panhandle A Panhandle B Weymouth IGT Application Panhandle equations do not consider pipe roughness; instead. an efficiency factor is used; less conservative than Colebrook or AGA Does not consider pipe roughness; uses an efficiency factor used for high-pressure gas gathering systems; most conservative equation that gives highest pressure drop for given flow rate Does not consider pipe roughness; uses an efficiency factor used on gas distribution piping ٥٩

60 PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES A pipeline in which gas enters at the beginning of the pipeline and the same volume exits at the end of the pipeline is a pipeline with no intermediate injection or deliveries When portions of the inlet volume are delivered at various points along the pipeline and the remaining volume is delivered at the end of the pipeline, we call this system a pipeline with intermediate delivery points. ٦٠

61 PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES ٦١

62 PIPELINE WITH INTERMEDIATE INJECTIONS AND DELIVERIES Pipe AB has a certain volume, Q, flowing through it. At point B, another pipeline, CB, brings in additional volumes resulting in a volume of (Q + Q 2 ) flowing through section BD. At D, a branch pipe, DE, delivers a volume of Q 3 to a customer location, E. The remaining volume (Q + Q 2 -Q 3 ) flows from D to F through pipe segment DF to a customer location at F. ٦٢

63 SERIES PIPING Segment - diameter d and length Le Segment 2 - diameter d 2 and length Le 2 Segment 3 - diameter d 3 and length Le 3 L = L + L + L e e e2 e3 ٦٣

64 SERIES PIPING P = sq CL d 5 P sq = difference in the square of pressures (P 2 -P 22 ) for the pipe segment C = constant L = pipe length d = pipe inside diameter ٦٤

65 SERIES PIPING CL d = CL e d2 d L L d e 2 = d L L d e 3 = d d Le = L+ L2 + L3 d2 d3 5 5 ٦٥

66 PARALLEL PIPING Q = Q + Q 2 where Q = inlet flow at A Q = flow through pipe branch BCE = flow through pipe branch BDE Q 2 ٦٦

67 PARALLEL PIPING K LQ d ( 2 2) PB PE = ( P ) B PE Q L 2 d = Q2 L d2 2 KLQ = 5 d 2 where K, K 2 = a parameter that depends on gas properties, gas temperature, etc. L, L 2 = length of pipe branch BCE, BDE d, d 2 = inside diameter of pipe branch BCE, BDE Q, Q 2 = flow rate through pipe branch BCE, BDE ٦٧

68 PARALLEL PIPING ( 2 2 P ) B PE = K LQ e d e 5 e 2 KLQ KLQ KLQ e e = = d d2 de 2 LQ LQ L Q d d d e = = e 2 d e + const = d const 2 /5 const = d2 L2 5 d L Q = Q const /( + const ) ٦٨

69 LOCATING PIPE LOOP Different looping scenarios ٦٩

70 Summary This part introduced the various methods of calculating the pressure drop in a pipeline transporting gas and gas mixtures. The more commonly used equations for pressure drop vs. flow rate and pipe size The effect of elevation changes and the concepts of the Reynolds number, friction factor, and transmission factor were introduced. The importance of the Moody diagram and how to calculate the friction factor for laminar and turbulent flow were explained. Comparison of the more commonly used pressure drop equations, such as AGA, Colebrook-White, Weymouth, and Panhandle equations. The use of a pipeline efficiency in comparing various equations The average velocity of gas flow and the limiting value of erosional velocity was discussed. ٧٠

71 Summary Several piping configurations, such as pipes in series, pipes in parallel, and gas pipelines with injections and deliveries The concepts of equivalent length in series piping and equivalent diameter in pipe loops were explained and illustrated using example problems. The hydraulic pressure gradient and the need for intermediate compressor stations to transport given volumes of gas without exceeding allowable pipeline pressures were also covered. The importance of temperature variation in gas pipelines and how it is taken into account in calculating pipeline pressures were introduced with reference to commercial hydraulic simulation models.. ٧١