SCA Guidelines for Sample Preparation and Porosity Measurement of Electrical

Resistivity Samples Part III -The Mechanics of Electrical Resistivity

Measurement on Rock Samples

P. F. Worthington: R. J. Evans: Robertson Research International, Aberdeen, Scotland J. D. Klein: ARCO Oil & Gas Co., Plano, Texas J. D. Walls: Core Laboratories, Dallas, Texas 6. White: ARCO Oil & Gas Co., Plano, Texas

BP Research, Sunbury-on-Thames, England

Abstract: Both two- and four-electrode measurement configurations allow the effective determination of resistivity, with appropriate cell design, calibration, and operating pro- cedures. A 2% precision should be achievable for consoli- dated, unfractured core plugs. The absence of pure core-plug standards, encompassing specified electrolytes and reference temperatures and pressures, is a major impediment to es- tablishing standards of accuracy and precision for the labo- ratory petrophysical measurement of electrical resistivity.

SAMPLE SIZE AND SHAPE As with most other rock property measurements, sam-

ple size affects the accuracy and precision of resistivity data. This is because the laboratory measurement of re- sistance is converted to specific resistance or resistivity through an algorithm that takes account of sample di- mensions. The conversion is easier when the sample is of a regular geometrical shape.

Usually the sample is cylindrical (a geometry assumed within this report), but this is not a requirement. Sample dimensions should be such that the measured voltages are not too large, to minimize electrochemical reactions at the electrode/rock interface, and not too small, to en- sure adequate signal. Sample resistance of 10-1,000 Q seems a good target range well within the measurement capability of commercial instrumentation. In particular, the parallel faces across which the voltage is applied should have as large an area as possible to permit an electrode design that will minimize contact resistances. The dis- tance between these faces should be sufficient for accurate length determination. Larger samples are preferred for the more accurate determination of pore volume and water saturation, which are usually correlated with the resistiv- ity data. Typical sizes for cylindrical samples are 1.5 in (3.8 1 cm) diameter and 3 in (7.62 cm) length. For samples

The ideas and procedures described herein represent a consensus of the working party and do not necessarily reflect the views of SPWLA, SCA, or the authors’ employers.

with small grain size, good data can also be obtained on samples of 1 in (2.54 cm) diameter and 2 in (5.08 cm) length. The cylindrical plug is usually cut with its axis parallel to the bedding plane so that the laboratory mea- surement might sample the resistivity of the rock in the same plane as that sampled by resistivity and induction logging tools. This directional conformity is only partly achievable in dipping beds or those that are anisotropic within the bedding plane. Full diameter core samples may have to be used in order to overcome problems of het- erogeneity on the scale of smaller core plugs. However, if the rock is significantly anisotropic, as well as hetero- geneous, the resulting vertical electrical measurements are of limited usefulness in interpreting the horizontal resis- tivity measurements from well logs.

CELL DESIGN Electrode Configuration

Both two- and four-electrode configurations can give good results when properly executed.

With two-electrode arrangements the current and po- tential electrodes are combined. For this reason, the mea- sured resistance includes not only the rock but also the rock-electrode contacts so that the electrode material and the nature of electrical coupling to the rock are most important. The electrodes should cover the entire end- face of the plug and must be placed close to the end of the sample. The rock-eiectrode couplings constitute the principal disadvantage of two-electrode measurements for they can give rise to significant polarizations or phase shifts, due to contact impedances, if badly designed. Ad- vantages of two-electrode configurations include simplic- ity and, most importantly, resistivity measurement of the entire plug sample. The last advantage should not be overlooked since the porosity and water saturation are generally measured on the entire sample, too.

Four-electrode measurements entail separate current

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and potential electrodes, and provide a means of avoiding inclusion of rock-electrode coupling resistances in the measured signal. A common arrangement is for the cur- rent electrodes to butt up against the ends of the samples, as in the two-electrode case. In contrast, the potential electrodes either encircle the sample to provide as close to a line contact about the circumference as is practical or consist of a series of point-contact electrodes around the circumference. The spacing of the potential electrodes must be well known and invariant. The four-electrode arrangement requires a high input impedance in the volt- age measuring circuit because the potential electrodes should be operated close to zero current. Because the measurement of resistance is made only over that part of the sample between the circumferential potential elec- trodes, sample homogeneity and a uniform saturation distribution become crucial.

Within the oil industry, two-electrode systems seem to be preferred for the measurement of resistivity, provided that contact impedances can be minimized. However, other types of measurement systems that eliminate rock- electrode coupling resistances are also acceptable. These include, in addition to the four-electrode method as de- scribed above, inducing current electromagnetically and applying current through brine or electrolyte contact, per- haps with perforated potential electrodes butted up to the ends of the plugs.

Electrode Type The electrochemical literature abounds with electrode

description (e.g., Ives and Janz, 196 1; Sawyer and Rob- erts, 1974). The following is merely a distillation.

Electrodes can be made from a wide variety of mate- rials. They should be readily available in high purity, of reasonable cost, easily formed into appropriate geometric configurations, reusable, and easily renewable or replaced. Silver is a good example of an electrode material with the above properties.

Electrodes should ideally be chemically stable and should not affect the composition of the electrolyte or the investigated sample. This requires the use of chemically inert electrodes, but these tend to have higher contact impedances. An industry-preferred alternative is to use electrodes such as silverhilver chloride that have low contact impedance. However, silver chloride is slightly soluble in water, which could lead to problems with very dilute electrolytes. Electrodes with low impedance such as silver chloride tend to be more chemically active, can be sensitive to direct sunlight, and are susceptible to prob- lems of instability at higher temperatures and pressures.

An electrode material that is suitable for work at ele- vated temperatures and pressures is platinum, although this is not totally inert as often assumed in early work. Graphite may also be suitable, with the advantage of ease

of fabrication. This is available in various forms such as spectroscopic grade, pyrolitic, and dikpersed graphites.

Generally speaking, the effective surface area of the electrodes should be made as large as possible in order to minimize electrodcxlectrolyte contact impedance. Platinized platinum provides increased surface area com- pared to bright platinum, although it tends to be unstable at high currents. Screen or mesh of various materials also provides a means of increasing surface area. For example, a combination of silver-plated coreholder end-pieces with several layers of fine silver mesh pressed between the end- piece and the sample has proved useful for routine work.

Sample Sleeving For experiments performed at overburden pressure, the

selection of sleeve material is critical as some rubber ma- terials gradually absorb brine with prolonged exposure and become conductive. Teflon@ and KalrezO are gen- erally recognized as good long-term sleeve materials, al- though other elastomers are likely to perform well, too. At ambient temperatures, VitonO can be used.

Cell Housing Resistivity core holders should be designed to apply

simulated overburden stress to the sample and to allow independent control of internal pore pressure. Cells should be equipped to measure sample length change, which can then be used to estimate pore volume change. They should also contain a temperature probe inside the pressurized medium. Designs that maximize cell impedance and thereby minimize any capacitative or inductive effects are desirable as these cells can operate to higher frequen- cies.

MEASUREMENT SPECIFICATIONS Resistivity Range

Systems should be capable of measuring rock resistance from about 10 to 20,000 8, which corresponds to a re- sistivity range of 0.15-300 Q-m for a plug of the preferred size (1.5 in diameter x 3 in long). However, this mea- surement capability is not necessary over the entire fre- quency range of the instrument. Capacitance effects be- come increasingly important as resistance and frequency increase; therefore, higher resistance samples may have to be measured at lower frequencies.

Applied Signal Strength The criterion for signal strength is the minimum level

that is consistent with precise measurement. There is some possibility of a nonlinear response affecting the measure- ment if current density is too large or potential difference too high.

Current densities of less than 1 mA cm-2 are recom- mended. Because electrode contact area and effective

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Worthington et al.

sample cross-sectional area decrease as water saturation decreases, current density should be selected to remain sufficiently low as desaturation progresses.

Frequency The frequency range that can be used depends in part

on the electrode material and geometry. With a two-electrode system, the lowest frequency that

should be applied will depend on the electrode imped- ance, which can be considered as a parallel RC circuit in series with the sample. The requirement is that the elec- trode impedance be much smaller than the sample imped- ance. This means that polarization or phase shift needs to be minimized. The low phase-angle requirement in two-electrode systems usually means operating at fre- quencies of 100 Hz or above, but this limiting value varies with the rock mineralogy and electrode type. The use of nonpolarizable electrodes (e.g., Ag/AgCl) allows mea- surement down to lower frequencies.

Electrode impedance in two-electrode systems is influ- enced by cell design through the (clamping) pressure ap- plied to the electrodes. The optimum electrode pressure for a nominal frequency can be identified through the minimum phase angle associated with the contact. There is no single consistently acceptable electrode pressure for all sample measurements; the minimum phase angle will occur at different electrode pressures for different samples and even for the same sample measured at different times.

Four-electrode systems allow measurement at lower frequencies than do two-electrode systems. The lowest frequency is controlled by brine decomposition at the electrodes. This problem can be overcome by placing the current electrodes in compartments separated from the sample by a nonreactive porous and permeable ceramic disk, and then constantly flushing the current electrode compartment with fresh brine.

The highest frequency that can be used depends on the overall capacitance of the measurement system, the time constant of which is affected by the sample impedance. The variation of cell impedance effects with frequency must be determined in order to set a practical upper limit to the frequency range. Generally, data should be ob- tained at least up to 30 kHz and possibly higher than 100 kHz.

With two-electrode measurements it is especially crit- ical that a frequency sweep of impedance be made over the range 100-20,000 Hz to identify the frequency at which phase shift is minimal. The identified frequency should be the measurement frequency for that sample. This selection presumes that there is no induced polariza- tion effect in the frequency domain.

CALIBRATION Four different calibration checks are recommended:

these should be repeated on a regular basis.

Insulating Plug A nonporous insulating plug of dimensions similar to

the core specimens should be inserted into the sample holder in place of the core plugs, with brine in the pore pressure system. This is used to confirm that there are no secondary current paths around the sample (e.g., through the sleeve). Care must be taken that there are no gaps between the insulating plug and the sleeve. The applied voltage for this test should be higher than the range that is likely to be used for core plugs. The measured cell impedance should be about 10-1 00 times greater than the maximum impedance that is anticipated with core plugs: an acceptable lower limit of cell impedance might be 1 x lo6 0. Cell impedance should be measured over the entire frequency range that it is intended to use (i.e., 100 Hz up to 100 kHz).

Conducting Plug A metal plug should be placed in the sample holder to

verify that all electrical contacts and feedthroughs are sound. This will also provide information on the imped- ance associated with the electrode leads: these must be negligible compared to the range it is proposed to mea- sure. Again, this experiment should be carried out over the entire frequency range it is intended to use.

Precision Resistors Circuitry containing precision resistors provides a

means of testing the system electronics. Resistive ele- ments of say 10, 100, 1,000 and 10,000 0 should be inserted and the system tested over its entire frequency range. Any measurement where capacitative (or induc- tive) reactance exceeds about 1% of resistance should be corrected for these effects. Stable precision resistors can be “potted” into plastic cylinders with silver end-plates to which the leads of the resistor are connected. These resistor plugs can then be used in the measurement system in exactly the same manner as core plugs.

Standard Porous Samples The procurement of suitable calibration material that

is homogeneous, stable with time after exposure to a va- riety of electrolytes, sufficiently robust to withstand han- dling without damage, and with a range of porosities is a difficult problem. Provided this has been accomplished, these samples afford an excellent means of system cali- bration and verification. The calibration samples should be treated in a manner identical to that of regular samples. Useful materials are graded aluminas, but these are not suitable for overburden simulation nor are their porosi- ties sufficiently diverse. Various sandstones (e.g., Berea) are available commercially as cylindrical rods that can be cut to any desired length. Because these are natural materials, their homogeneity cannot be guaranteed. The

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absence of pure core-plug standards constitutes a major shortcoming in system calibration.

ACCURACY AND PRECISION The accuracy of measurements can only be known when

results are compared with acknowledged standards. There are no universally accepted standard plugs, comprising a porous medium fully saturated with a specified electrolyte of fixed concentration, for which resistivity is known ex- actly. Even if there were, there would have to be speci- fications of temperature and pressure that would have to be simulated exactly for the standard to be valid. Elec- tronic tests using precision resistors provide only a guide to accuracy, for they do not take account of electrolyte conduction in a measurement situation. Without stan- dard plugs, the measurement of core resistivity cannot be evaluated for accuracy, only precision.

Input Parameters The parameters required for a resistivity determination

on a cylindrical core plug are length, diameter, resistance, and temperature. Each of these can be determined with a precision of about 0.5% for well-consolidated samples. This leads to a precision on the resistivity determination of about 2.0% if the recommended procedures are fol- lowed. This will not apply to unconsolidated, vuggy, or fractured samples for which a looser and more erratic precision can be expected.

Equilibration Most rock samples do not reach electrochemical equi-

librium immediately after saturation. This means that the measured resistance can change with time until equi- librium has been established. The process of mounting a core plug in a sample holder, especially one that is pres- sured, might also impart a disequilibrium of resistivity. There is no shortcut to overcoming these problems. So- lutions require the careful measurement of resistivity, without removal from the sample holder, over an ex- tended period of a few hours to a few days and longer in exceptional instances. When a series of successive tem- perature-corrected measurements spaced over a few hours shows agreement to within the expected precision, it can be assumed that equilibrium has been established.

Environmental Factors Resistivity is strongly influenced by temperature, which

should be maintained constant in the vicinity of the mea- suring equipment. Most measurements are made at 20- 25°C. A variation o f f 1°C can be tolerated. Temperature should be measurable to within 0.1"C. All elements of the system- the instrumentation, the sample cell, the core plug, and the electrolyte- should be in thermal equilib- rium.

Core-plug resistivity is also affected by loading pressure

March-April, 1990

applied to the rock. This effect should not be confused with that of the clamping pressures applied at the current electrodes during ambient-condition measurements. These pressures alter the measured resistivity because they enhance the electrical coupling with the sample. Loading pressures are applied in an attempt to simulate overburden conditions. They can be applied hydrostati- cally, biaxially, or triaxially. Triaxial loading is capable of providing the most realistic simulation of tectonic stresses, but its effect on resistivity may not be very dif- ferent from that of hydrostatic loading for samples of core-plug dimensions.

It is important that all assessments of measurement reliability and precision be made under appropriate con- ditions of temperature and pressure.

REFERENCES AND BIBLIOGRAPHY Emerson, D. W., 1969, Laboratory electrical resistivity mea-

surements of rocks: Proceedings of the Australian Institute of Mining and Metallurgy, v. 230, p. 5 1-62.

Helander, D. P., and Campbell, J. M., 1966, The effect of pore configuration, pressure and temperature on rock resistivity, paper W, in 7th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts, 29 p.

Hook, J. R., 1983, The precision of core analysis data and some implications for reservoir evaluation, paper Y, in 24th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts, 18 p.

Hoyer, W. A., and Spann, M. M., 1975, Comments on obtaining accurate electrical properties of cores, paper B, in 16th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts, 11 p.

Ives, D. J. G., and Janz, G. J., 196 1, Reference electrodes; theory and practice: Academic Press, New York, 65 1 p.

Rust, C. F., 1952, Electrical resistivity measurements on res- ervoir rock samples by the two-electrode and four-electrode methods: Petroleum Transactions, AIME, v. 195, p. 217- 224.

Sanyal, S. K., Marsden, S. S., and Ramey, H. J., Jr., 1972, The effect of temperature on electrical resistivity of porous media, paper I, in 13th Annual Logging Symposium Transactions: Society of Professional Well Log Analysts, 35 p.

Sawyer, D. T., and Roberts, J. L., Jr., 1974, Experimental elec- trochemistry for chemists: John Wiley and Sons, New York, 435 p.

Swanson, B. F., and Thomas, E. C., 1979, The measurement of petrophysicai properties of unconsolidated sand cores, paper A, in 6th European Formation Evaluation Symposium Trans- actions: Society of Professional Well Log Analysts, 23 p.

Worthington, A. E., 1975, Errors in the laboratory measurement of formation resistivity factor, paper J, in 5th Formation Eval- uation Symposium Transactions: Canadian Well Logging Society, 13 p.

Worthington, A. E., Gidman, J., and Newman, G. H., 1987, Reservoir petrophysics of poorly consolidated rocks - well- site procedures and laboratory methods, paper BB, in 28th Annual Logging Symposium Transactions: Society of Profes- sional Well Log Analysts, 17 p.

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