Page 392 - Pipeline Risk Management Manual Ideas, Techniques, and Resources

Appendix D
Surge Pressure

Calculations

Surge pressures, often called waterhamme< are caused when a E = modulus ofelasticity ofpipe material (Ib/in.2)
moving fluid is suddenly brought to a stop. The resulting trans- C, = constant dependent on pipe constraints.
lation of kinetic (moving) energy to potential energy causes an
increase in the internal pressure-the creation of a pressure We can see from this equation that pressure wave speed is
wave. An associated positive and negative pressure wave will dependent on pipe properties (diameter, thickness, modulus of
travel in both directions along the pipe, reflecting and overlap- elasticity) as well as fluid properties (bulk modulus, density).
ping, depending on the system configuration. This means that the pressure wave will travel at different speeds
The magnitude of the pressure increase is found with the depending not only on the product, but also on the pipeline
following equation [55]. Surge pressure in feet of water is itself. A more elastic pipe material slows down the pressure
readily converted to psig by multiplying by 0.43 psig/feet of wave. As the diameter-to-wall thickness ratio increases, the
water: wave speed decreases.
t 1 Because fluid compressibility is dependent on density and bulk
AH= - XAV modulus, we can see that the pressure wave speed varies inversely
with the compressibility. Fairly incompressible fluids will support
where faster pressure waves and, hence, greater surge potentials. Note
AH = surge pressure (feet of water) that hydrocarbons are far more compressible than water.
a = velocity ofthe pressure wave (Wsec) Another component of the pressure surge calculations
g = acceleration due to gravity (32 ft/sec2) should be the wave attenuation. Due to friction losses in the
A V = change in velocity of fluid (Wsec) pipeline, the pressure wave will be dampened as it travels. This
reduction in pressure magnitude with distance traveled can be
We can see from this equation, that the magnitude of the pres- calculated and becomes a consideration in pipeline design.
sure surge is directly related to the speed of the pressure wave The above equations assume instantaneous fluid velocity
and the fluid velocity change. changes. If the abruptness of the velocity change is controlled,
To calculate the speed of the pressure wave in the pipe, we the maximum surge pressure is also controlled. A common
can use the following equation [55] example is the rate of closure of a valve. A slamming shut ofthe
valve effectively brings the velocity to zero instantly. A gradual
closure causes small, incremental velocity changes with corre-
a = 12 x sponding small surges. How fast is too fast? The following
equation allows a critical time to be calculated {SS]:

2XL
where T,, = -
a = pressure wave velocity (Wsec) a
K = bulk modulus ofthe fluid (Ib/im2) where
p = density of the liquid (slugs/ft2) T,, = critical time (sec)
D = internal diameter ofpipe (in.) L = distance ofpressure wave travel before reflection (ft)
t = pipe wall thickness (in.) a = velocity of pressure wave (Wsec).