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Summary. Borehole measurements of the nuclear magnetic resonance (NMR) properties of rocks have been of interest for many years, especially for estimating permeability. This paper presents laboratory measurements of the NMR properties of water-saturated rocks and shows that permeability can be estimated well with expressions of the form T, where T1 is the relaxation time constant of the longitudinal nuclear magnetization of hydrogen nuclei. Different methods of representing the laboratory- measured T1 curves are shown, including a new one called the stretched- exponential representation. An improved method for estimating T1 parameters from borehole measurements that can be used with either old or new representations is presented. Introduction In this paper, we pursue permeability estimation from borehole NMR* longitudinal relaxation (T1) measurements. Many previous workers have demonstrated the potential of NMR for this application; however, we make closer and more consistent connections between the components linking permeability and borehole NMR than have previously been published. These components are addressed in the three parts that follow,1. Stretched-exponential representation of laboratory T1 measurements. We present the results of laboratory NMR measurement on approximately 60 water-saturated rocks. We introduce a new representation for the NMR curve, called the stretched-exponential representation, that has the practical advantage of having fewer pa-rameters than the classical two- and three-exponential representations of NMR measurements. Such representations are important in reducing the measurement to a few parameters that can be correlated to properties of practical importance.2. Estimation of permeability from laboratory measurements. We use the data base of 60 rocks from Part 1 to find the best estimator of permeability from NMR T1 measurements. An important result is that permeability is estimated better by T1 than by Seevers classic estimator .3. Extraction of NMR T1 parameters from borehole NMR measurements. To apply the correlations of Part 2 to borehole data, we introduce a new method of extracting the important T, parameters from downhole NMR T1 measurements: in this method, called "global fitting," a model is fitted simultaneously to the set of free induction decay (FID) waveforms collected for different polarizing times during a station measurement. We exhibit two suitable models. Both have the advantage of accommodating some complexities observed in borehole waveforms and verified in a corresponding laboratory measurement. In particular, the observed decay time of the FID waveforms decreases as the polarizing time decreases. This paper concentrates on the NMR property T1 and does not investigate the parameter called free fluid index (FFI). The reasons for this emphasis are two-fold. First, T1 is a more complete measurement, and thus gives a better picture of the potential of NMR in permeability estimation. Second, FFI is specifically a low-field measurement, which is much less convenient to measure in the laboratory. Borehole T1 data can he obtained with existing commercial nuclear magnetic log (NMLTM) equipment by making stationary measurements.A key issue in this paper is compact representation-finding ways to describe accurately the observed behavior with only a small number of parameters. Representation is an issue in Part 1, dealing with laboratory T1 measurements, because a complete curve must be described. Part 2 shows that all the representations used here allow equally good permeability estimation. In Part 3, dealing with borehole T1 data. representation is important because of the need to work around measurement dead-time, and because borehole measurements in practice have a lower signal-to-noise ratio than laboratory measurements. Throughout, compactness of a representation is weighed against its ability to fit the measurements and its appropriateness for estimating permeability. Part 1-Stretched-Exponential Representation of Laboratory T1 Measurements Laboratory Technique. We measured porosity, permeability, and NMR T1 properties on water-saturated sandstone samples from five oilfield wells in different parts of the world, plus a number of quarried sandstone samples. Samples were cut to Hassler collar size2.0 cm [0.78 in.] in diameter and approximately 4 cm [ 1.57 in.] long; the samples were cored parallel to any visible bedding planes in the original rocks. Sample porosities were determined by Archimedes' methodi.e., measuring dry sample weight. saturated weight, and buoyant weight of the water-saturated sample. Permeabilities to water were measured end-to-end on the samples encased in a Hassler collar, at room temperature, with a collar pressure in the neighborhood of 414 kPa [60 psi]. Because our measured permeabilities are thus for single-phase parallel-to-bedding flow, the final output of our permeability estimators will be for the same quantity. Laboratory NMR measurements were made using an IBM/Bruker PC10. The PC10 is a desk-top permanent magnet instrument that makes pulsed measurements of proton resonance at 10 MHz [10(6) cycles/sec). Samples for NMR measurement were surface-dried and then wrapped in Saran(TM) wrap held in place by rubber bands to reduce evaporation during measurement; these wrapping materials contributed a negligible signal for the water volumes of our samples. Before measurement, samples were allowed to equilibrate to the magnet temperature, which is thermostatically maintained at 40 degrees C [104 degrees F]. The fundamental NMR property to be measured is the time evolution of proton magnetization along the direction of the applied magnetic field. This behavior of the "longitudinal" magnetization is called T1. SPEFE P. 622^

Dielectric measurements have been made from 0.5 to 1300 MHz on Whitestone, a quarried calcite rock, saturated with salty water. Whitestone shows a large increase in dielectric permittivity (dispersion) at the low end of this frequency range. When the conductivity of the water is varied, the dielectric permittivity of Whitestone is found to scale as water conductivity/frequency, i.e., as the complex dielectric constant of water. This is believed to be unique in measurements on insulator-conductor mixtures, and establishes that the dispersion is primarily caused by the geometry of the sample. Two other calcite samples show much lower dielectric dispersion. Micrographs indicate that the variation in dispersion among the three samples is in rough proportion to grain platiness. This is consistent with the platey grain mechanism, one of three mechanisms proposed by Sen to explain dielectric dispersion in water-saturated rocks. A model consisting of water containing insulating spheroids of identical aspect ratio, isotropically distributed in orientation, predicts that increased grain platiness reduces both low-frequency conductivity and high-frequency dielectric permittivity in a closely related way; this is observed experimentally. However, this model does not fit simultaneously all electrical properties of Whitestone; evidently a more complex geometrical model is needed. Dielectric dispersion caused by texture is of practical importance in estimating water content of subsurface rocks from borehole measurements of dielectric permittivity, particularly at high water salinities.

Based on measurements on some 100 sandstone core samples, mainly from oil fields from various parts of the world, we found the following regressions between volume‐to‐surface ratio [Formula: see text], permeability to fluid flow k, exchange cation molarity [Formula: see text], and proton NMR decay constant [Formula: see text] in water‐saturated rocks (see Figure 1): [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. Here R is the regression coefficient, ϕ is the porosity and m the conductivity exponent; [Formula: see text] in normality (meq/ml), k in millidarcies, and [Formula: see text] in milliseconds, [Formula: see text] in μm. Including the tortuosity factor [Formula: see text] in conjunction with a pore‐size parameter as represented by [Formula: see text], [Formula: see text], or [Formula: see text] improves the correlation with permeability and reduces the residual error. The best predictor for log k is log [Formula: see text]. The exponents in the above correlations agree reasonably with those expected from simple models. These correlations provide a numerical basis for assessing how well some of these quantities can be estimated from others in log interpretation. They also provide a basis for assessing the importance of the factors that interfere with and thereby weaken the correlations.

We tabulate an extensive set of measurements of the complex permittivity (i.e., dielectric constant and conductivity) of brine saturated rocks in the frequency range 10–1300 MHz. Rather than listing the permittivity at each frequency, we present the parameters of a Cole‐Cole function used to fit the data for each rock sample. We choose the Cole‐Cole function for the following reason. The data sets from 271 rock samples were fitted to the commonly used functions in the literature, i.e., Cole‐Cole, Cole‐Davidson, and power law functions. We found that within experimental errors the fits to both the Cole‐Cole function and the power law represent the frequency dependence of the data better than the Cole‐Davidson function. Further, the Cole‐Cole function fits the data better at the high‐frequency end of our data. This result implies that five parameters of the Cole‐Cole function describe the frequency dependence of the complex permittivity of rock samples in the range 10–1300 MHz within experimental errors.