PIPING/RELIABILITY

HYDROCARBON PROCESSING JULY 2009 I 65

Most of us are aware of the disastrous effects of water ham-mer (e.g., pipe rupture, dislocation from support, support and equipment damage, etc.). The term “water hammer”

refers to shocks sounding like hammer blows produced by a rapid change of fluid flow in a closed pipeline. The common occurrence of the phenomenon is in liquid pumping systems. It is caused by flow disturbance or transients. A typical example is the sudden closure or opening of the valve in a cooling water network. Rapid valve closure causes the fluid to stop suddenly as a result of which the kinetic energy of the moving fluid is converted into pressure energy. This produces pressure surges causing a series of shock waves in the piping. An abundance of literature1–3 is available on water hammer and the surge analysis and design of the hydraulic piping for single-phase systems (e.g., fluid is water or any liquid). However, for steam systems the phenomenon is quite complicated due to the two–phase effect. The detailed analytical treatment of the surge analysis is quite complex which involves the biphase mass and momentum equations and interaction between phases. Still, there is a lot of scope of development and it is a topic of research. In this article we briefly explain the phenomenon in simple terms while presenting some approximate methods of estimating the loads on the piping that should be of interest to piping designers.

Steam line water hammer. As per the extensive research conducted by reputed institutes, there are seven basic mecha-nisms that initiate water hammer in steam lines.4 One of them, the mechanism of a steam-propelled slug, is very common.3 This is also referred to as “condensate-induced water hammer” or the active mechanism hammer.

The active mechanism happens when there is condensate build-up and water slugs in live steam piping. If steam condensa-tion is allowed to accumulate at low points in steam piping, at one stage it tends to restrict steam flow. Water slugs are lifted off the condensate and propelled by the steam at high speeds. Their movement suddenly stops on meeting an obstruction such as a bend or a valve. This results in the conversion of their kinetic energy into pressure. The higher the mass and velocity of the water slug the higher the pressure and its impact on piping. The impact may have mild to severe effects on piping. This impact may dis-place the line from its original position if the line is not properly restrained by supports. In a severe impact, supports may also get broken. Hence, it is important to consider the hammering effect while designing supports to take care of this impact load.

However, another mechanism known as passive water hammer4,5 is also very important. We shall describe the phenomenon in some

detail. Consider a case (Fig. 1) when there is hot steam upstream of the valve followed by a subcooled liquid due to cooling up to the valve. The line pressure downstream of the valve is lower than the sat-uration pressure. When the valve is quickly opened there is flow of the subcooled liquid followed by the hot steam. At the valve throat there could be choking of the steam. This causes a change in steam velocity that gives rise to steam pressure as per Joukowsky’s equation.2

Approximate estimation of hammer load. The magni-tude of the pressure rise, ΔP, is given by Joukowsky’s formula,2

P = mCm v (1)

where Δv is the change in fluid velocity (i.e., cold flow to hot flow). The steady-state velocity of the hot fluid passing through the valve may be obtained from Moody’s diagram.6 �m and Cm are mixture density and acoustic speed, respectively.

The mixture density is given in terms of the void fraction, x, as:

m = x s + (1 x ) w (2)

�s and �w are the steam and water densities at the saturation temperature.

For single-phase flow x is either 0 or 1.Mixture acoustic speed is:2

Cm = (K eq / m ) / [1+ (Keq / E )(D / t )] (3)

where D and t are the pipe mean diameter and thickness, respec-tively. E is the pipe material modulus of elasticity which is nor-mally steel for metallic pipes. Keq is the equivalent bulk modulus of the fluid. For single-phase flow its value is either of water, Kw , or steam, Ks . For water its value is 2.2 GPa and for steam it depends on the specific heats, Cp, Cv , and the state.7

The equation that gives the equivalent bulk modulus of the water–steam mixture is:

Estimate water hammer loadsin steam pipingThe problem is more complicated because of the two-phase flow

S. SAHA and P. DARJI, Reliance Refinery, Jamnagar, India

Hot steamsource

Initially closed valve

Hot liquid Subcooled liquid

Configuration for passive water hammer.FIG. 1

PIPING/RELIABILITY

66 I JULY 2009 HYDROCARBON PROCESSING

1/K eq = (x /K s )+ (1 x ) /K w (4)

It is seen that the bulk modulus of water can be substantially lowered by steam entrained in the water. This means that the mix-ture acoustic velocity is much less than that of pure water. This is of vital importance in estimating hammer forces. The forces obtained by considering the single-phase properties are in general highly over-estimated because of the inaccurate value of the acoustic speed.

After obtaining the acoustic speed the dynamic forces in the piping may be obtained using Joukowsky’s equation (Eq. 1):

Fdyn = DLF ( PA) (5)

where A is the pipe flow area and DLF is the dynamic load factor generally considered as 1.8 to 2.0 for an equivalent static analysis.

Case study. An axial stop failure was observed in a utility steam line. The line was 16 in. NB, standard wt. schedule and carrying low-pressure steam (5.1 kg/cm2g, 177°C). The line was axially displaced by about 100 mm from its original position and was close to touching the adjacent lines. Fig. 2 shows the line configu-ration and Fig. 3 shows the axial stop condition after failure.

Problem analysis. Initially a thermal analysis was carried out. The results showed no abnormality and all the design parameters were well within limits. The nature of the failure indicated a large impact load on the pipe caused the failure. But the problem could not be explained by the normal water hammer phenomenon that occurs on valve closure. The failure was observed on opening the valve during startup. Hence, this made us consider a passive water hammer.

The first step was to estimate the acoustic speed for which the void fraction is required. Assuming the valve opening as adiabatic, the enthalpy balance (643.3 kJ/kg) at saturation gives us the void fraction, x, to be around 0.1. This results in the acoustic speed of 91m/sec and a pressure surge of 8.6 bar. The resulting force (Eq. 5) in the pipe segment is 192 kN. From the support failure the force may be also calculated. The value turns out to be 230 kN, which is somewhat close to the estimated value. This also provides some confidence in the method. The actual design maximum load was 90 kN, which was much lower than both values. This proved

that the safety factor was inadequate in this case. A new support design was performed using the revised loads.

Conclusion. The right approach toward mitigation of the prob-lem would be to avoid any condensate build-up and proper opera-tional procedure. But this seldom happens in practice. There could be several reasons such as steam trap malfunction, faulty operation or lack of proper design, construction and system maintenance.

From the viewpoint of initial design it would be prudent to have some realistic estimate of the hammer loads. A single-phase calculation could produce unrealistic forces that could not be feasible for support system design. In fact, it could be about 2,500 kN or more. However, with a better understanding of the phe-nomenon it would be possible to simplistically quantify realistic loads without resorting to tedious calculations. This will help in making the system design more reliable, thereby increasing the plant life. Our study is a step in that direction. HP

LITERATURE CITED 1 Antaki, G. A., Piping and pipe line engineering, Marcel Dekker, 2003. 2 Streeter, V. L., Fluid Mechanics in Systems, Prentice Hall. 3 McKetta, J. J., Piping Design Handbook, Marcel Dekker, 1992. 4 Van Duyne, et. al, “Water Hammer Events Under Two-Phase Flow

Conditions,” International Multiphase Fluid Transient Symposium, FED Vol. 87, ASME Winter Meeting, California, USA, 1989.

5 Arastu, et. al., “Computer Models for the analysis of severe water hammer initiating mechanisms,” International Mechanical Engineering Congress, ASME, Chicago, USA, 1994.

6 Moody, J. F., Introduction to Unsteady Thermo-Fluid Mechanics, John Wiley & Sons, New York, USA, 1990.

7 Spalding, D. B. and E. H. Cole, Engineering Thermodynamics, Edward Arnold, London, UK, 1967.

S. Saha works in the Engineering Centre of Reliance Refinery at Jamnagar (India) as a chief of stress analysis. Dr. Saha holds a B.Tech. (Hons.) degree in mechanical engineering from the Indian Institute of Technology (Kharagpur, India) and a Ph.D from the Indian Institute of Technology (Kanpur, India).

Pradeep Darji is a senior pipe stress analyst in the Engineer-ing Centre at the Reliance Refinery, Jamnagar, India. He has been involved in troubleshooting plant problems in the complex. Mr. Darji holds a post-graduate degree in mechanical engineering from the University of Pune.

Axial stop

Piping configuration.FIG. 2

Axial stop failure.FIG. 3