ELASTIC WAVE VELOCITIES IN HETEROGENEOUS AND POROUS MEDIA

INTRODUCTION
An ultrasonic velocity meter which readily measures the propagation velocity of high-frequency pulses through hand samples of materials has been designed and built at the Gu!f Research Laboratory. It has been used to acquire experimental data on the velocities of a variety of substances under different conditions, emphasis being placed on porous granular media. The pulse technique for measuring velocities, which is embodied in the meter, was pioneered by Hughes and his co-workers. (Hughes, Pondrom, and Mims, 1948; Hughes and Jones, 1950; Hughes and Cross, 1951.) These workers have also made rather penetrating investigations of the influence of such factors as pressure, temperature, porosity and saturation upon numerous samples of differing kinds of rocks. We have some measurements on rocks as well as on synthetic porous media. The bulk of the data presented refers to measurements carried out on synthetic and natural porous media unsubjected to heavy confining or compacting pressures. In general, no difficulty has been encountered in making such measurements. The fact that the velocity of sound in air itself can be readily obtained shows the efficacy of the measuring device. Considerable attention has also been paid to the analyses of continuous velocity logs in terms of porosity.
GEOPHYSICS,
VOL.
XXI,
NO.
1 (JANUARY,
lY56),
PP.
41-70,
1Y FIGS
ELASTIC
WAVE
VELOCITIES AND POROUS
IN HETEROGENEOUS MEDIA*
GARDNER1
M. R. J. U’ LLIE,t Y
A. R. GREGORY,t
42
hf.
R. J. WYLLIE,
A. R. GREGORY
AND
L. W. GARDNER
APPARATUS
Figure I is a picture of the velocity meter which was designed and built by the Geophysical Development Division, J. L. Mundy being primarily responsible for design and constructional details. A sample of material to be measured is
FIG. r. Ultra sonic velocity meter and sample holder.
ELASTIC
WAVE
VELOCITIES
43
placed in the sample holder between the two heads. Each head contains a piezoelectric crystal (barium titanate), one of which acts as a source of repeated sound pulses and the other as a receiver of the pulses after transmission through the sample. Two representative signals are displayed on the oscilloscope, Figure 2. One corresponds to the output pulse and the other is a reference or time measuring pulse generated by the input pulse, but which is delayed in the elec-
* Presented before the Society at its New York meeting March 30, 1955. Manuscript received by the Editor May JT, 1955. t Gulf Research & Development Company, Pittsburgh, Pennsylvania. 4r
44
Байду номын сангаасM. R. J. WYLLIE,
A. R. GREGORY
AND
L. W. GARDNER
trical circuits by an interval of time which is adjustable and measurable with the dials on the front of the case. For measuring any given sample the dials normally are adjusted until the two pulses representative of input and output are superimposed. The horizontal displacement on the oscilloscope, however, also furnishes a measure of time variations between the two pulses and of the frequencies present in the output signal. Other controls on the instrument permit adjustment of the gain of the output signal, switching to a different horizontal time scale on the oscilloscope and different time intervals between repeated input pulses. The nature of the measurements is such that the velocity measured is that of the first significantly strong energy to pass through the sample. Accordingly, it is the longitudinal wave velocity that is obtained. The principal frequency components of the observed pulses in the present experiments range between zoo and 1,000 kilocycles; in general, they are about one-tenth the magnitude of those used by Hughes. Corresponding wave lengths of the transmitted signals range between 0.1 and I inch, being smaller than, but sometimes approaching, the diameter of specimens; in general, the wave lengths are large compared with grain or pore sizes. No change in velocity was observed upon changing the crystal with associated change in the frequency components of the transmitted signal. None of the measurements that have been made shows any appreciable dependence on frequency. Many of the measurements that have been made have been repeated, some of them a number of times. A particular cylinder of brass has been frequently measured; indeed it serves as a standard to demonstrate that the instrument is always giving true readings. For all of the velocity measurements, transit time determinations could be repeated at will to within about 0.1 microsecond for total transit times ranging from a minimum of 6 microseconds to a maximum of 270 microseconds. Since the travel distance between the heads is determined rather precisely by means of a scale on the specimen holder, the velocity measurements usually are reliable to within about f 1%. The measured velocities of a number of metal cylinders are: Aluminum21,550 ft/sec; brass-rq,r5o ft/sec; lead-7,300 ft/sec; and steel-17,600 ft/sec. Velocities of brines have been measured under a variety of conditions with results to be shown later.
time f-
MEASURING PULSE FIRST ARRIVAL
A.
UVMATCHED PULSES
LEADING EDGE OF time Fll%T ARRIVAL
PULSE
MATCHED WITH LEADING EDGE OF
8.
MATCHED PULSES
FIG. z. Arrivals through brass as displayed on oscilloscope.
AND
I,.
U’ .
ABSTRACT Longitudinal wave velocities in numerous synthetic and natural porous media at room temperature and pressure have been measured. Basic characteristics of the measuring device are brief’ @ described. Wave velocities have been found for aggregates of uniform spheres of various diameters both when dry and when saturated with water, brine, organic liquids and plastics. The effect of porosity on the wave velocity through aggregates of glass spheres saturated with plastic has been determined over the porosity range 190/~-70~~. Experimental measurements have been made of the effect of varying brine-oil and brine-gas saturations on the wave velocity through natural sedimentary rock samples. The effect of salinity and temperature on the wave velocity through sodium chloride brines has been redetermined. Results are graphically presented to show experimental relationships between wave velocity, porosity, pore content and matrix nature of sedimentary rocks, Some conclusions are drawn regarding general relationships between these factors based on the experimental results and on theoretical considerations. Through these relationships continuous velocity logs in wells can be interpreted to furnish a measure of formation porosity. Some comparisons are given between porosities derived from continuous velocity logs and found by core analysis.