Petrophysics

Geophysical methods applied in boreholes or on the ground provide the distribution of physical parameters in the subsurface. However, the objective is to gain geological information from geophysical data. For this purpose it is necessary to understand the relationships between the physically measurable quantities and the geologically relevant parameters. Petrophysical investigations are conducted to analyze these relationships under controlled laboratory conditions and, based on these analyzes, petrophysical models are developed to quantify them (Schön,1996). At the department 2 (groundwater and soils) of the BGR, petrophysical activities are mainly focused on hydrogeological issues and are related to the geophysical field methods in use at the BGR for groundwater exploration and soil physical investigations (Fig. 1).

Abb. 1: Vorbereitung der Proben und Messung der Spektral induzierte Polarisation

Electrical resistivity

Electrical and electromagnetic field methods (ERT and TEM) measure the spatial distribution of electrical resistivity (or electrical conductivity) in the subsurface. In the very most geological formations with significant groundwater flow, the flow of current predominantly takes place in the water-saturated pore space and is defined by the law of Archie (1942):

Archie (1942)

It describes the measured resistivity of a rock ρ_Rockas a function of the pore water resistivity ρ_Fluidand porosity Ф. The exponent m is an empirical parameter to be determined experimentally. It characterizes the degree of restriction inside the pore space for ions and is therefore referred to as cementation exponent when dealing with sandstones. If other mechanisms of current flow inside a rock become significant, the Archie model has to be modified and extended. This is the case, when for instance electron movement through the rock matrix (e.g. in ore-bearing rocks) or displacement of ions at the solid/fluid interface (e.g. in rocks or sediments with high clay content) occurs.

Fig. 2: (a) Four-point-layout for electrical resistivity measurements of a rock, (b) electrical resistivity measurements of core samples (test borehole B1 Barnewitz/Nauen) as a function of porosity Source: BGR

In principle, electrical resistivity measurements at the laboratory scale are conducted using a four-point-layout (Fig. 2) very similar to geoelectric measurements in the field (ERT). Normally, the outer electrodes are used for applying the current and the inner ones for measuring the voltage. Figure 2b shows the electrical resistivity of various core samples of a test borehole (B1) on the test field Barnewitz/Nauen as function of porosity. These samples were saturated with salt water (ρ_Fluid= 0.5 Ωm). By approximation of that data set using Archie’s law (dashed line) parameters are determined that allow the estimation of porosities from resistivity measurements (e.g. ERT profiles) in the area of investigation.

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Spectral induced polarization

In some cases, polarization effects are observed during geoelectrical field measurements, which can provide useful geological information in addition to the electrical resistivity. The analysis of such effects on the laboratory scale is conducted using the method of spectral induced polarization (SIP). In SIP the electrical impedance (i.e. the complex electrical resistivity) is measured at a frequency range of several mHz to kHz. In contrast to simple electrical measurements, the experimental layout for SIP is much more complex (Fig. 3a). To avoid erroneous polarization effects due to the coupling of the electrodes to the sample, non-polarizable ceramic material is used for both connecting the alternating current and measuring the corresponding voltage. The resulting impedance spectra are frequently described by the Cole-Cole model (Cole and Cole, 1941; Pelton et al., 1978):

Cole-Cole model

The measured resistivity of a rock ρ_Rock(ω) is a function of the angular frequency ω. The parameters of the Cole-Cole model are the DC resistivity ρ₀, the chargeability m, the relaxation time τ and the exponent c, which controls the spectral distribution of relaxation times. Although often treated as purely empirical, the basis of the Cole-Cole model is an equivalent circuit diagram that simulates the electrical and polarizing properties of the investigated material. As shown for instance by Hupfer (2014) and Hupfer et al. (2016) using synthetic sulphide-sand mixtures, SIP measurements and the Cole-Cole interpretation have the potential to estimate iron-mineral content and mean grain sizes of iron particles (Fig. 3b).

Figure 3: (a) Measurement layout for spectral induced polarization, (b) measured chargeability m as function of the pyrite concentration inside a sand sample Source: Hupfer, 2014

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Nuclear magnetic resonance

Applications of nuclear magnetic resonance (NMR) in the lab, in boreholes, or in the field (Surface nuclear magnetic resonance-SNMR) allow the direct measurement of water content without using a petrophysical model, which is a significant benefit of those methods. Moreover, the NMR relaxation behavior can provide additional information on geometry (e.g., Mohnke and Yaramanci, 2008) and geochemistry (e.g. Keating et al., 2008) inside the pore space. In many cases, when investigating sandstones and unconsolidated sediments, a semi-empirical relationship can be observed between the mean NMR relaxation time and the mean pore size, which allows for permeability estimates from NMR data (Seevers, 1996; Kenyon, 1997; Mohnke and Yaramanci, 2008; Knight et al., 2015):

Permeability estimates from NMR data

The permeability k is a function of porosity Ф and relaxation time T₁ when performing longitudinal NMR measurements, and T₂ when performing transverse NMR measurements. The linear factor C and the exponents a and b are empirical parameters to be fitted during a calibration process. Usually, the parameter b is set to two according to theoretical considerations. Thus, the approach is referred to as a semi-empirical model. Also, the exponent a is often set to either one (Seevers, 1966) or four (Kenyon, 1997) for simplification, i.e., the calibration in practice is normally limited to the determination of C. Figure 4 shows the measured T₂-relaxation times of core samples from borehole B1 of the test site Barnewitz/Nauen and their correlation to measurements of hydraulic conductivity.

Figure 4: (a) Laboratory measurement device for nuclear magnetic resonance (NMR), (b) laboratory device for NMR measurements in an artificial permanent magnetic field, (c) measured NMR relaxation time T2 of core samples Source: BGR