Abstract
This paper describes an automated laboratory system that can measure accurately the dielectric properties of core samples in the ultrahigh-frequency properties of core samples in the ultrahigh-frequency (UHF) range. The system consists of a precision coaxial-line sample holder, a network analyzer, a plotter, a printer, and a desk computer. The computer is for measurement control, data acquisition, and data analysis. A new method is developed to measure and to compensate for the error of the network analyzer system. This method uses a brass sample and does not require standard terminations. A procedure for core sample preparation is also recommended to ensure accuracy of the data.
Introduction
The electromagnetic propagation tool (EPT) is a relatively new wireline sonde developed by Schlumberger for detection and quantification of hydrocarbon. It is operated at 1.1 GHz, which is in the UHF band of the electromagnetic spectrum. The EPT sonde measures the dielectric constant of the formation. Because water has a much higher dielectric constant (about 80 units) than oil (about 2 units) and gas (about 1 unit), the EPT sonde can distinguish hydrocarbon-bearing zones from the water-bearing zones even when the formation water is fresh. The dielectric constant of water at UHF is not very sensitive to salinity. Consequently, EPT is particularly useful in situations where the formation water resistivity is variable or unknown, as a result, for example, of water, steam, or chemical flooding.
The EPT log displays the travel time and the rate of attenuation of the electromagnetic wave in the formation. From these data, the calculated complex dielectric constant of the formation may be calculated. This complex dielectric constant is related to water saturation, Sw, by an empirical formula called the complex refractive index method (CRIM):
............................(1)
where
= porosity, = dielectric constant of the water in the rock, = dielectric constant of oil or gas, and = dielectric constant of the rock grain.
To verify the validity of the CRIM formula given by Eq. 1, a computer-controlled laboratory system has been set up to measure the dielectric constants of saturated core samples, dry core samples, and oils. The same system is now being used for routine measurements of cores for EPT log interpretation.
Measurement Techniques
Two basic techniques can be used to measure the complex dielectric constant of a saline-water-saturated rock at frequencies higher than 100 MHz. The first is the coaxial-line and waveguide method, and the other is the resonant-cavity method. We describe these methods and point out their advantages and disadvantages. Fig. 1 shows the configuration of the coaxial-line and waveguide method. In Figs. 1a and 1b, we see that the core sample is machined into a circular cylinder with a circular concentric hole drilled to fit the coaxial line. The line consists of an outer conductor and an inner conductor. In Fig. 1c, we see that the core sample is machined into a rectangular column to fit into a rectangular waveguide. The latter is a rectangular metal pipe without a central conductor. pipe without a central conductor. Longitudinal slots are cut along the outer conductor of the coaxial line (Fig. 1b) or on top of the rectangular waveguide (Fig. 1c) to allow a probe to be inserted partially into the region where electromagnetic fields are present. The probe travels along the length of the structure and detects the amplitude and the phase of the electromagnetic fields present in the structure. During the measurement, an electromagnetic wave of the selected frequency is sent propagating down the line or the waveguide until it encounters the core sample. Reflection occurs so that part of the wave is absorbed, and part is reflected and travels in the reverse direction. The phase and the amplitude of the reflected wave are determined by the complex dielectric constant of the sample. The reflected wave interacts with the incident wave and creates an interference pattern called the standing wave pattern. The complex dielectric constant of the core sample can be determined from the standing wave pattern recorded by the traveling probe. This method was used by Poley et al. for sandstone samples up to 1.2 GHz. It was also used by Tam to test nine dry rocks, mainly sedimentary, in the frequency range 150 to 1000 MHz. The rectangular waveguide was used by Roberts and Von Hippel to measure a variety of materials at 5 GHz. The configuration shown in Fig. 1a was used by Rau and Wharton to measure formation samples in the frequency range 500 MHz to 1.1 GHz. This arrangement calls for placing the sample at the center, rather than at the end, of a coaxial line. The amplitudes and the phases of both the reflected and the transmitted waves are recorded and are called the scattering matrix parameters. parameters. SPEJ
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Measurement of the complex dielectric constant down to helium temperatures. I. Reflection method from 1 MHz to 20 GHz using an open ended coaxial line