Petrophysics
Petrophysics deals with the physical and chemical properties of rocks and their pore spaces.
Geophysical measurement techniques are used as borehole or field methods and determine the distribution of physical parameters in the subsurface. To derive useful geological information from this, it is necessary to understand the relationships between geophysically measurable quantities and the geological target parameters. The task of petrophysics is to analyze these relationships under controlled laboratory conditions and quantify them using petrophysical models (Schön, 1996).
The petrophysical investigations in the BGR-Department Groundwater and Soil Sciences focus primarily on hydrogeological issues and are coordinated with the hydrogeophysical field methods used at the BGR for the exploration of groundwater systems and for soil physical investigations.
Electrical Resistivity
Electrical and electromagnetic methods (electrical resistivity tomography and TEM - transient electromagnetics) map the spatial distribution of electrical resistivity and electrical conductivity in the subsurface, respectively. In most geological formations relevant to groundwater dynamics, current flow occurs primarily in the water-filled pore space and is often described by Archie's law (1942):
The law describes the measured rock resistivity ρRock as a function of the pore fluid resistance ρFluid and the porosity φ. The exponent m is an experimentally determined material parameter and empirically describes the degree of impedance to current flow through the pore space. In sandstones, m is also referred to as the cementation exponent. Petrophysical extensions to the classical Archie model are necessary if current flow through the material also occurs at grain boundaries (e.g., high clay content) or in the rock matrix (e.g., ore minerals).
Electrical measurements at laboratory scale are usually performed similarly to measurements in the field (ERT - electrical resistivity tomography) in the form of so-called 4-point measurements (Fig. 2a). The outer electrodes are used to inject current and the inner electrodes to measure the voltage. Figure 2b shows electrical resistance measurements of various core samples from a test borehole (B1) on the BGR test site Barnewitz/Nauen, plotted against porosity. The samples were uniformly saturated with salt water (ρFluid = 0.5 Ωm). By fitting this data set with Archie's law (dashed line), a tool is obtained that enables the estimation of the porosity distribution in the test area, e.g., from ERT measurements in the field.
Spectrally induced polarization (SIP)
Polarization phenomena are sometimes observed during electric field measurements, which can provide valuable additional information in addition to the electrical resistivity. Corresponding laboratory measurements are performed using so-called spectrally induced polarization (SIP). This involves measuring the electrical impedance (i.e., the complex electrical resistance) for a frequency spectrum ranging from a few millihertz to several kilohertz. The experimental setup is somewhat more complex than for simple electrical measurements (Fig. 3a). To avoid distorting polarization effects when coupling the electrodes to the sample material, non-polarizable microfine ceramic plates or tips are used to inject the alternating current and measure the voltage. The measured impedance spectrum can often be described using the Cole-Cole model (Cole and Cole, 1941; Pelton et al., 1978):
Here, the measured resistance ρRock(ω) is considered as a function of the input frequency ω. The parameters of the Cole-Cole model are the DC resistance ρ0, the chargeability m, the relaxation time τ and the exponent c, which describes the distribution width of the relaxation time. Although this model is often viewed and treated as purely empirical, it is based on an electrical equivalent circuit that simulates the polarization properties of the geological material. Using the Cole-Cole parameters, for example, iron mineral contents and mineral grain sizes can be estimated, as shown by Hupfer 2014 and Hupfer et al., 2016 for synthetic sulfide sand mixtures (Fig. 3b).
Nuclear magnetic resonance
Nuclear magnetic resonance (NMR) measurements in the laboratory, in boreholes, or in the field (surface NMR) allow the direct measurement of water content without the need for a petrophysical model. Furthermore, NMR relaxation behavior can also provide additional information about the geometry (e.g., Mohnke and Yaramanci, 2008) and geochemistry (e.g., Keating et al., 2008) within the pore space. In many cases, a semi-empirical relationship between average relaxation time and mean pore size can be observed in unconsolidated sediments and sandstones, allowing permeability to be estimated from NMR data (Seevers, 1966; Kenyon, 1997; Mohnke and Yaramanci, 2008; Knight et al., 2015):
The permeability k is considered a function of the porosity Τ and the decay time T1 when measuring longitudinal NMR relaxation, or T2 when measuring transverse relaxation. The quantities are linked via the factor C and the exponents a and b as empirical quantities. In practice, b = 2 is usually set, which can be derived from theoretical considerations. Therefore, the approach is referred to as semi-empirical. For simplicity, the exponent a is also set to either one (Seevers, 1966) or four (Kenyon, 1997), so that calibration is usually limited to the determination of C. Figure 4 shows the measured T2 times from the core samples of test borehole B1 (Barnewitz/Nauen) and their correlation with measured hydraulic conductivity values.
