The complex mixture of hydrocarbon compounds or components can exist as a single-phase liquid, a single-phase gas, or as a multiphase mixture, depending on its pressure, temperature, and the composition of the mixture. The fluid flow in pipelines is divided into three categories based on the fluid phase condition:
- Single-phase condition: black oil or dry gas transport pipeline, export pipeline, gas or water injection pipeline, and chemical inhibitors service pipelines such as methanol and glycol lines;
- Two-phase condition: oil þ released gas flowline, gas þ produced oil (condensate) flowline
- Three-phase condition: water þ oil þ gas (typical production flowline).
The pipelines after oil/gas separation equipment, such as transport pipelines and export pipelines, generally flowsingle-phase hydrocarbon fluid while in most cases, the production flowlines from reservoirs have two- or three-phase fluids, simultaneously, and the fluid flow is then called multiphase flow.
In a hydrocarbon flow, the water should be considered as a sole liquid phase or in combination with oils or condensates, since these liquids basically are insoluble in each other. If the water amount is small enough that it has little effect on flow performance, it may be acceptable to assume a single liquid phase. At a low-velocity range, there is considerable slip between the oil and water phases. As a result, the water tends to accumulate in low spots in the system.
This leads to high local accumulations of water and, therefore, a potential for water slugs in the flowline. It may also cause serious corrosion problems. Two-phase (gas/liquid) models are used for black-oil systems even when water is present. The water and hydrocarbon liquid are treated as a combined liquid with average properties. For gas condensate systems with water, three-phase (gas/liquid/aqueous) models are used. The hydraulic theory underlying single-phase flow is well understood and analytical models may be used with confidence.
Multiphase flow is significantly more complex than single-phase flow. However, the technology to predict multiphase-flow behavior has improved dramatically in the past decades. It is now possible to select pipeline size, predict pressure drop, and calculate flow rate in the flowline with an acceptable engineering accuracy.
The basis for calculation of changes in pressure and temperature with pipeline distance is the conservation of mass, momentum, and energy of the fluid flow. In this section, the steady-state, pressure-gradient equation for single-phase flow in pipelines is developed. The procedures to determine values of wall shear stress are reviewed and example problems are solved to demonstrate the applicability of the pressure-gradient equation for both compressible and incompressible fluid. A review is presented of Newtonian and non-Newtonian fluid flow behavior in circular pipes. The enthalpygradient equation is also developed and solved to obtain approximate equations that predict temperature changes during steady-state fluid flow.
Mass ConservationMass conservation of flow means that the mass in, min, minus the mass out, mout, of a control volume must equal the mass accumulation in the control volume. For the control volume of a one-dimensional pipe segment, the mass conservation equation can be written as:
Momentum ConservationBased on Newton’s second law applied to fluid flow in a pipe segment, the rate of momentum change in the control volume is equal to the sum of all forces on the fluid. The linear momentum conservation equation for the pipe segment can be expressed as:
The terms on the right-hand side of Equation are the forces on the control volume. The term vp/vL represents the pressure gradient, spd/A represents the surface forces, and rg sin q represents the body forces.
Friction Factor EquationThe Darcy-Weisbach equation is one of the most general friction head loss equations for a pipe segment. It is expressed as:
In laminar flow (Re < 2100), the friction factor function is a straight line and is not influenced by the relative roughness. The friction head loss is shown to be proportional to the average velocity in the laminar flow. Increasing pipe relative roughness will cause an earlier transition to turbulent flow. When the Reynolds number is in the range from 2000 to 4000, the flow is in a critical region where it can be either laminar or turbulent depending on several factors. These factors include changes in section or flow direction. The friction factor in the critical region is indeterminate, which is in a range between friction factors for laminar flow and for turbulent flow.
When the Reynolds number is larger than 4000, the flow inside the pipe is turbulent flow; the fiction factor depends not only on the Reynolds number but also on the relative roughness, 3/D, and other factors. In the complete turbulence region, the region above a dashed line in the upper right part of a Moody diagram, friction factor f is a function only of roughness 3/D. For a pipe in the transition zone, the friction factor decreases rapidly with increasing Reynolds number and decreasing pipe relative roughness.
Although single-phase flow in pipes has been studied extensively, it still involves an empirically determined friction factor for turbulent flow calculations. The dependence of this friction factor on pipe roughness, which must usually be estimated, makes the calculated pressure gradients subject to considerable error and summarizes the correlations of Darcy-Weisbach friction factor for different flow ranges. The correlations for smooth pipe and complete turbulence regions are simplified from the one for a transitional region. For smooth pipe, the relative roughness termis ignored, whereas for the complete turbulence region, the Reynolds term is ignored.
In addition to pressure head losses due to pipe surface friction, the local losses are the pressure head loss occurring at flow appurtenances, such as valves, bends, and other fittings, when the fluid flows through the appurtenances. The local head losses in fittings may include:
- Surface fiction;
- Direction change of flow path;
- Obstructions in flow path;
- Sudden or gradual changes in the cross section and shape of the flow path.
The local losses are considered minor losses. These descriptions are misleading for the process piping system where fitting losses are often much greater than the losses in straight piping sections. It is difficult to quantify theoretically the magnitudes of the local losses, so the representation of these losses is determined mainly by using experimental data. Local losses are usually expressed in a form similar to that for the friction loss.
 R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The Properties of Gases and Liquids, third ed., McGraw-Hill, New York, 1977.
 K.S. Pedersen, A. Fredenslund, P. Thomassen, Properties of Oils and Natural Gases, Gulf Publishing Company (1989).
 T.W. Leland, Phase Equilibria, Fluid, Properties in the Chemical Industry, DECHEMA, Frankfurt/Main, 1980. 283–333.
 G. Soave, Equilibrium Constants from a Modified Redilich-Kwong Equation of State, Chem. Eng. Sci vol. 27 (1972) 1197–1203.
 D.Y. Peng, D.B. Robinson, A New Two-Constant Equation of State, Ind. Eng. Chem. Fundam. vol. 15 (1976) 59–64.
 G.A. Gregory, Viscosity of Heavy Oil/Condensate Blends, Technical Note, No. 6, Neotechnology Consultants Ltd, Calgary, Canada, 1985.
 G.A. Gregory, Pipeline Calculations for Foaming Crude Oils and Crude Oil-Water Emulsions, Technical Note No. 11, Neotechnology Consultants Ltd, Calgary, Canada, 1990.
 W. Woelflin, The Viscosity of Crude Oil Emulsions, in Drill and Production Practice,, American Petroleum Institute vol. 148 (1942) p247.
 E. Guth, R. Simha, Untersuchungen u¨ber die Viskosita¨t von Suspensionen und Lo¨sungen. 3. U¨ ber die Viskosita¨t von Kugelsuspensionen, Kolloid-Zeitschrift vol. 74 (1936) 266–275.
 H.V. Smith, K.E. Arnold, Crude Oil Emulsions, in Petroleum Engineering Handbook, in: H.B. Bradley (Ed.), third ed., Society of Petroleum Engineers, Richardson, Texas, 1987.
 C.H. Whitson, M.R. Brule, Phase Behavior, Monograph 20, Henry, L. Doherty Series, Society of Petroleum Engineers, Richardson, Texas, (2000).
 L.N. Mohinder (Ed.), Piping Handbook, seventh, ed., McGraw-Hill, New York, 1999.
 L.F. Moody, Friction Factors for Pipe Flow, Trans, ASME vol. 66 (1944) 671–678.
 B.E. Larock, R.W. Jeppson, G.Z.Watters, Hydraulics of Pipeline Systems, CRC Press, Boca Raton, Florida, 1999.
 Crane Company, Flow of Fluids through Valves, Fittings and Pipe, Technical Paper No. 410, 25th printing, (1991).
 J.P. Brill, H. Mukherjee, Multiphase Flow in Wells, Monograph vol. 17(1999), L. Henry, Doherty Series, Society of Petroleum Engineers, Richardson, Texas.
 H.D. Beggs, J.P. Brill, A Study of Two Phase Flow in Inclined Pipes,, Journal of Petroleum Technology vol. 25 (No. 5) (1973) 607–617.
 Y.M. Taitel, D. Barnea, A.E. Dukler, Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes, AIChE Journal vol. 26 (1980) 245.
 PIPESIM Course, Information on Flow Correlations used within PIPESIM, (1997). 398 Y. Bai and Q. Bai
 H. Duns, N.C.J. Ros, Vertical Flow of Gas and Liquid Mixtures in Wells, Proc. 6th World Petroleum Congress, Section II, Paper 22-106, Frankfurt, 1963.
 J. Qrkifizewski, Predicting Two-Phase Pressure Drops in Vertical Pipes, Journal of Petroleum Technology (1967) 829–838.
 A.R. Hagedom, K.E. Brown, Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small-Diameter Vertical Conduits, Journal of Petroleum Technology (1965) 475–484.
 H. Mukherjce, J.P. Brill, Liquid Holdup Correlations for Inclined Two-Phase Flow, Journal of Petroleum Technology (1983) 1003–1008.
 K.L. Aziz, G.W. Govier, M. Fogarasi, Pressure Drop in Wells Producing Oil and Gas, Journal of Canadian Petroleum Technology vol. 11 (1972) 38–48.
 K.H. Beniksen, D. Malnes, R. Moe, S. Nuland, The Dynamic Two-Fluid Model OLGA: Theory and Application, SPE Production Engineering 6 (1991) 171–180. SPE 19451.
 A. Ansari, N.D. Sylvester, O. Shoham, J.P. Brill, A Comprehensive Mechanistic Model for Upward Two-Phase Flow in Wellbores, SPE 20630, SPE Annual Technical Conference, 1990.
 A.C. Baker, K. Nielsen, A. Gabb, Pressure Loss, Liquid-holdup Calculations Developed, Oil & Gas Journal vol. 86 (No 11) (1988) 55–59.
 O. Flanigan, Effect of Uphill Flow on Pressure Drop in Design of Two-Phase Gathering Systems, Oil & Gas Journal vol. 56 (1958) 132–141.
 E.A. Dukler, et al., Gas-Liquid Flow in Pipelines, I. Research Results, AGA-API Project NX-28 (1969).
 R.V.A. Oliemana, Two-Phase Flow in Gas-Transmission Pipeline, ASME paper 76- Pet-25, presented at Petroleum Division ASME Meeting, Mexico City, (1976).
 W.G. Gray, Vertical Flow Correlation Gas Wells API Manual 14BM (1978).
 J.J. Xiao, O. Shoham, J.P. Brill, A Comprehensive Mechanistic Model for Two-Phase Flow in Pipelines, SPE, (1990). SPE 20631.
 S.F. Fayed, L. Otten, Comparing Measured with Calculated Multiphase Flow Pressure Drop, Oil & Gas Journal vol. 6 (1983) 136–144.
 Feesa Ltd, Hydrodynamic Slug Size in Multiphase Flowlines, retrieved from http:// www. feesa.net/flowassurance.(2003).
 Scandpower, OLGA 2000, OLGA School, Level I, II.
 Deepstar, Flow Assurance Design Guideline, Deepstar IV Project, DSIV CTR 4203b–1, (2001).
 J.C. Wu, Benefits of Dynamic Simulation of Piping and Pipelines, Paragon Technotes (2001).
 G.A. Gregory, Erosional Velocity Limitations for Oil and Gas Wells, Technical Note No. 5, Neotechnology Consultants Ltd, Calgary, Canada, 1991.
 American Petroleum Institute, Recommended Practice for Design and Installation of Offshore Platform Piping System, fifth edition,, API RP 14E, 1991.
 M.M. Salama, E.S. Venkatesh, Evaluation of API RP 14E Erosional Velocity Limitations for Offshore Gas Wells, OTC 4485 (1983). Hydraulics 399