Patent Number: 042010926
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT In the "Background of the Invention" the curves of FIG. 1 have already been explained as being obtained from several different high pressure pipes in a specific reactor where ultrasonic sensors were used to provide the signals which were later analyzed in the form as shown. FIG. 2 illustrates a system which could be used to generate the curves of FIG. 1 but which may also be adapted in conjunction with the method of the present invention. Referring to FIG. 2, a single pipe 16 is illustrated with several ultrasonic transducers or sensors 17, 18, 19 mounted thereon at space locations. Each transducer includes a preamplifier 21, 22, 23 respectively whose outputs are time sequenced by a sequencing switch 24, amplified by amplifier unit 25 and connected to a spectrum analyzer 26. Such analyzer in combination with the computer 27 may make a Fourier analysis of a signal from a single sensor and displayed it on an XY plot recorder 28 where amplitude is the vertical axis and frequency the horizontal axis. Such is the case with the curve of FIG. 1. Here the presence of leaks in the pipes corresponding to curves 11, 12 and 13 is indicated by the peaks at various frequencies (which approach 1 MHz) as compared to the nonleaking or sound tube or pipe corresponding to the curve 14. However, as stated above, merely sensing the presence of a leak is not sufficient. Enlargement or growth rate of a through wall crack is very desirable information. In accordance with the present invention it has been discovered that there is a physical similarity between a through wall crack and a nozzle. FIG. 3 illustrates a pipe wall 29 which, for example, might be a portion of pipe 16 of FIG. 2 where in the interior of the pipe there is a relatively high pressure P.sub.1 and temperature T.sub.1 and the ambient conditions on the outside are P.sub.2 ; T.sub.2. The crack is indicated at 31 where the external throat diameter is d, pressure at that point is P.sub.T and the velocity of the leaking fluid is indicated as V. When turbulent flow conditions exist in the crack, considerable acoustic energy is generated. From a general standpoint the following expression relates acoustic energy to flow conditions. EQU Acoustic Energy=K.rho..sub.o V.sup.8 A.sub.o.sup.-5 d.sup.2 (1) .rho..sub.o =Density PA1 V=Velocity PA1 A.sub.o =Speed of sound in fluid PA1 d=Diameter PA1 K=Constant with typical value of 0.6.times.10.sup.4 for Mach number between 0.3 and 1.0. Such equation was propounded by M. J. Lighthill "On Sound Generated Aerodynamically" Proceedings of the Royal Society (London) A, 211 (1952), page 564, and 222 (1954), page 1. The terms of the equation can be related to the throat diameter of the nozzle and the velocity of the fluid. The maximum velocity obtainable for the nozzle is the speed of sound of the fluid, A.sub.0. This occurs when the pressure at the throat reaches the critical pressure, P.sub.c, and is where "choke flow" exists. Fluid velocity will remain constant at the sonic velocity as long as the critical pressure P.sub.c is equal to or greater than the ambient discharge pressure P.sub.2. Moreover, with steam as a fluid it has been found that the ratio of critical pressure P.sub.c to the pressure P.sub.1 is in the range of from 0.56 to 0.575. When choke flow conditions persist, equation (1) reduces to the following expression: ##EQU1## This expression indicates that the acoustic energy generated is independent of the driving pressure once choke flow conditions are established. FIG. 4 illustrates the foregoing. This shows the frequency spectrum results obtained when a mockup tube is pressurized in stages up to 6.9 MegaPascals (MPa) (1,000 psi) with a 0.034 cm diameter hole drilled through the wall. The heavy darkened curve at 6.9 MPa shows that saturation of sound intensity occurs because the escaping fluid velocity reaches sonic velocity and thus remains constant. Equation (2) also demonstrates that the energy at the choke flow condition is related only to the cross sectional area of the crack; thus, the monitoring of the energy generated will provide indication of crack enlargement. Such crack enlargement is determined by the fact that acoustic energy is directly proportional to the cross sectional area of the crack, i.e., d.sup.2. The relationship of equations (1) and (2) is better illustrated in FIG. 5 which is a plot indicating how the acoustic energy detected will change with crack size and is an illustration of the method of the present invention. This curve reflects changes at only one frequency; however, the entire spectrum amplitude should change in a like manner, thus, it is possible to draw a family of frequency spectra curves whose magnitude will change in the same fashion with regard to crack size. The saturated or choke flow curve is called Part 2 and indicates how acoustic energy increses with crack size. Before choke flow is reached, the flow is subsonic; thus from the time of crack initiation to choke flow the signal increases as the velocity to the 8th power and of course the diameter squared; viz, kV.sup.8 d.sup.2. This is a relatively rapid variation because of the high exponent of velocity and will over power the diameter dependence. After choke flow occurs the variation or enlargement of the crack area is a proportional function; viz kd.sup.2. Here the signal changes more slowly but is only a function of crack size. Thus, by either visual examination or use of computer 27 as shown in FIG. 2, by monitoring the change of the acoustic energy over time crack enlargement may be determined. Yet another possible technique is illustrated by the curves of FIG. 4 where the choke flow condition is unique because of the saturation effect. Computer 27 of FIG. 2 could have stored in it a simulated pattern of this choke flow condition in a particular reactor and thus could recognize by the comparison such choke flow condition. And then by the monitoring in time of crack enlargement curves which vary as kd.sup.2 crack diameter, d, could easily be determined. If a certain criteria was exceeded, the computer 27 would then generate an alarm. Thus the present invention has provided an improved method of leak detection and monitoring.