Page 216 - Handbook Of Multiphase Flow Assurance

Calculation of pressure surge on sudden flow shut-in 215

The force of slug impact may be calculated if one knows slug density, gas velocity, pipe size
and angle of the pipe bend.
Force of slug impact on a bend may be estimated as:
2
− cosθ
/
F = ∆Μ ∆t = ρ V A(22 ) . 05
3
ρ = liquid slug density, kg/m .
V = gas or slug velocity, m/s.
2
A = pipe cross section area, m .
θ = bend angle.
M = momentum, kg m/s.
t = time, s.
Time may be estimated based on slug velocity and slug length.
The calculated force value should be multiplied with a suitable dynamic load factor (DLF).
A DLF of 2.0 is commonly used.
Experimental data on slug forces at pipe bends from several researchers was presented and
summarized in the works of Hou et al. (2014) and Tay and Thorpe (2015).

Calculation of pressure surge on sudden flow shut-in

Flowing mass of liquid carries a substantial momentum. When flow path becomes sud-
denly blocked, a pressure is expected to increase. Transient single phase flow simulators are
commonly used to estimate the pressure change during such event. A simple albeit somewhat
conservative method to calculate pressure surge is based on Joukowski.
∆P =ρC ∆V

ΔP = change in pressure, Pa.
3
ρ = density of flowing fluid, kg/m .
c = speed of sound in fluid at operating pressure and temperature, m/s.
ΔV = change in flow velocity, m/s.
0.5
c = (K*/ρ) .
K* = K/(1 + D K/(e E)).
D = pipe diameter, m.
e = wall thickness, m.
2
E = wall elasticity modulus, Pa = kg/(ms ).
2
K = fluid bulk modulus, Pa = kg/(ms ).
Some values for materials commonly used in production systems are shown below.
9
E STEEL = 200 * 10 Pa.
9
E FIBERGLASS = 17 * 10 Pa.
9
E HDPE = 0.8 * 10 Pa.
9
K WATER = 2.15 * 10 Pa.
9
K OIL = 1.7 * 10 Pa.
9
K GLYCOL + WATER = 3.4 * 10 Pa.