pipeline design ‘ the engineering approach’ session objectives the engineering equations...

PIPELINE DESIGN ‘THE ENGINEERING APPROACH’

SESSION OBJECTIVES

THE ENGINEERING EQUATIONS

TRANSMISSION LINE GAS FLOW

LIQUID SYSTEM

SESSION OBJECTIVES

At the end of the session students should be able to:

1. Describe the elements of the engineering equations

2. Perform pressure drop calculation using empirical formulae

THE ENGINEERING EQUATIONS

Few flow problems can be solved with an acceptable degree of accuracy when using equations designed to fit idealized application. Flow regimes and associated pressure drop discontinuities are complex phenomena and require complex equations to predict their relationships. For engineering design purposes, several empirical formulae have been developed to fit particular circumstances in predicting flow capacity and pressure drop

Bernoulli’s Theorem

LHg

VPZ

g

VPZ

2

144

2

144 22

2

22

21

1

11

Assumption: steady, frictionless, constant density flow along a streamline

Flow in Pipes and Reynolds Number

Dimensionless number that may be considered as the ratio of the dynamic forces of mass flow to shear stress due to viscosity

VD

Re

Pressure Loss Due to Friction

Flow is always accompanied by friction. A general equation for pressure drop due to friction is the Darcy-Weisbach equation

gD

fLVH L 2

2

Pressure Loss Due to Friction

Moody Diagram

Friction Factor and Effect of Pipe Roughness

Laminar Flow (Re<2000)– Friction factor, f has a direct

relationship to the Reynolds number

– Pipe roughness has no effect on the friction factor

– f=16/Re

Turbulent Flow (Re>4000)– Friction factor, f depends on

Reynolds number and the relative roughness of the pipe, /D

– f=0.042/Re0.194 (large pipe >8”)

– f=0.042/Re0.172 (small pipe ≤8”)

2000668.0

d

LVPf

xdg

fLVP

cf

22

Equivalent Length of Valves and FittingsThe pressure drop effects of valve and fittings can be accounted for by addition of the equivalent lengths of the fittings to the actual piping length

EXERCISE

A 10 in crude line handles 40260 bbl/day of oil of API gravity 39o. The oil viscosity is 9.5 cp. The flow line is 6.15 miles long and discharges to a tank at atmospheric pressure (14.5 psi). The tank installation is 328 feet higher than the pump discharge. The pipe wall roughness is assumed to be 1500 in. Determine the necessary pump discharge pressure.