Abstracts from session A Induced polarization and pore radius – a discussion Andreas Weller Zeyu Zhang Lee Slater Institut für Geophysik, TU Clausthal Southwest Petroleum University Rutgers University Arnold-Sommerfeld-Str.1, Institute of Earth Science and Technology Dpt. Earth and Environm. Sci. 38678 Clausthal-Zellerfeld, Germany Chengdu, China Newark, New Jersey, USA [email protected] [email protected] [email protected] Sabine Kruschwitz Matthias Halisch Bundesanstalt für Materialforschung und –prüfung Leibniz-Institut für Angewandte Geophysik Unter den Eichen 87, 12205 Berlin, Germany Stilleweg 1, 30655 Hannover, Germany [email protected] [email protected] another useful method that can be used to estimate the pore size distribution. MICP is a laboratory method. Under SUMMARY favourable conditions, NMR is also applicable in field surveys. Permeability estimation from spectral induced Induced Polarization (IP) has been proposed to be another polarization (SIP) measurements is based on a potential method providing access to the pore size fundamental premise that the characteristic relaxation distribution. Several authors observed relations between the τ time ( ) is related to the effective hydraulic radius ( reff ) pore size and different types of relaxation times (e.g. Scott and controlling fluid flow. The approach requires a reliable Barker, 2003; Binley et al., 2005; Kruschwitz et al. 2010). It is estimate of the diffusion coefficient of the ions in the difficult to explain all these observations by a uniform electrical double layer. Others have assumed a value for physical model. Instead of a pore size distribution, a so-called the diffusion coefficient, or postulated different values for characteristic pore size is assumed. Most authors prefer to use clay versus clay-free rocks. We examine the link between the dominant pore size determined from MICP that τ and reff for an extensive database of sandstone samples corresponds to the pressure of maximal incremental mercury where mercury porosimetry data confirm that reff is intrusion. Similarly, a characteristic relaxation time is reliably determined from a modification of the Hagen- assumed, which can be determined by different procedures. Poiseuille equation assuming that the electrical tortuosity The resulting time constant from fitting procedures related to is equal to the hydraulic tortuosity. Our database does not models of the Cole-Cole type is a widely used approach. support the existence of 1 or 2 distinct representative Others use the mean relaxation time resulting from Debye diffusion coefficients but instead demonstrates strong decomposition (Nordsiek and Weller, 2008). In other evidence for 6 orders of magnitude of variation in an approaches, if the measured IP spectra show a maximum in apparent diffusion coefficient that is well correlated with the curves of imaginary part of conductivity or the phase angle both reff and the specific surface area per unit pore the frequency of the maximum is simply transformed into a volume ( Spor ). Two scenarios can explain our findings: relaxation time (Scott and Barker, 2003; Revil et al., 2015). τ (1) the length-scale defined by is not equal to reff and is The latter approach is quite simple because it does not require likely much longer due to the control of pore surface any fitting procedure. We used this approach for a set of roughness; (2) the range of diffusion coefficients is large sandstone samples that has been investigated in different labs. and likely determined by the relative proportions of the All IP spectra show a maximum of imaginary part of different minerals (e.g. silica, clays) making up the rock. conductivity inside the investigated frequency interval In either case, the estimation of reff (and hence between 2 mHz and 100 Hz. The effective hydraulic radius of permeability) is inherently uncertain from SIP relaxation this set of samples has been determined from permeability and time. formation factor. We evaluate whether any relation between characteristic relaxation time and effective hydraulic radius Key words: pore radius, mercury intrusion capillary exists. pressure, spectral induced polarization, relaxation time. METHOD INTRODUCTION The simplest model of permeability prediction is based on bundles of uniform capillaries that pervade a solid medium. The key parameters for reservoir characterization are porosity Based on geometric considerations and considering the and permeability. A variety of field, logging and laboratory Hagen-Poiseuille equation, permeability k can be easily methods provide porosity. Permeability can be determined by determined by the geometric quantities porosity φ, pore radius gas flow measurements in the lab. Permeability prediction in a r and tortuosity T according to the following equation: field or logging survey is based on correlations to other 2φ measurable parameters. Beside porosity, the pore size is an = r important parameter that is closely related to permeability. k . (1) However, the determination of a reliable value of an effective 8T φ pore size is a challenging problem. The Mercury Intrusion The ratio T/ can be replaced by the formation factor if the Capillary Pressure method (MICP) provides the distribution of electric tortuosity is assumed to equal the hydraulic tortuosity. the pore throat radius. Nuclear Magnetic Resonance (NMR) is Equation 1 can be used to determine an effective hydraulic IP2016 – 6-8 June, Aarhus, Denmark 1 Induced polarization and pore radius Weller et al. radius reff of any sample if permeability and formation factor a fixed diffusion coefficient. The solid red line corresponds to -12 are known: a value of D(+) = 3.8 × 10 m²/s that has been proposed by = Revil (2013) for clayey material. The dashed line indicates the reff 8Fk . (2) -9 diffusion coefficient of clean sand with D(+) = 1.3 × 10 m²/s A good estimation of reff is a decisive step in permeability (Revil, 2013). Two of our clean sandstone samples (BU12 and prediction because the variation in the formation factor is F1) fall close to the dashed line. However, the other sample considerably lower than in reff . close to the dashed line (ES-14) is an Elbe-sandstone with A variety of models have recently been proposed to relate a abundant clay minerals. Some shaly sandstone samples follow characteristic pore size Λ with a characteristic relaxation time the trend of the solid red line. However, a considerable τ0 (Revil et al., 2012; 2015): number of samples fall below the solid line. The large scatter Λ2 in the data points, along with numerous data points falling τ = below the solid red line, does not support the existence of two 0 (3) 2D(+) fixed values of the diffusion coefficient as proposed by Revil (2014). with D(+) being the diffusion coefficient of the ions in the Stern layer. A characteristic relaxation time τpeak can easily be determined from the frequency of the maximum (peak 100 frequency fpeak ) of the spectrum of imaginary part of conductivity σ”( f): 1 τ = (4) peak 2πf peak 10 assuming that a measurable maximum exists inside the investigated frequency range. We equate the effective m) µ hydraulic radius reff that is determined from equation 2 to the ( Λ dom characteristic pore size . The resulting equation r = τ (5) reff 2D(+) peak 1 relates the relaxation time τpeak to the effective hydraulic radius r . We check the general validity of equation 5 for a set of CS samples eff Bahariya Fm. sandstone samples. other sandstones rdom = reff SAMPLES 0.1 Our set of sandstone samples originates from several studies 0.1 1 10 100 µ including 21 Eocene sandstone samples of the Shahejie reff ( m) formation (CS samples, China, Zhang and Weller, 2014), eight samples of the Cretaceous Bahariya formation (Egypt), Figure 1. Comparison of reff determined according to and 17 samples from different locations in Germany equation 2 and the dominant pore throat radius rdom from (Bentheimer, Buntsandstone, Elbe-sandstone, Flechtinger, MICP for a set of sandstone samples. Green sand, Obernkirchen, Röttbacher, Udelfanger), France (Fontainebleau), Poland (Skala), the UK (Helsby), and 100 Vietnam (Dong Do). All samples are characterized by a measurable maximum in the spectrum of the imaginary part of conductivity. The permeability and the formation factor of all samples are known and the effective hydraulic radius reff has been determined by equation 2. Additionally, MICP measurements and the specific surface area per unit volume 10 (Spor ) of most samples are available. m) µ RESULTS ( 50 r Most studies regard the dominant pore throat radius ( r ) dom 1 determined by MICP as a suitable characteristic pore size. The dominant pore throat radius indicates for most samples a slight CS samples overestimation of reff (Figure 1). We find for our samples a Bahariya Fm. better agreement between reff and the median pore throat other sandstones radius r50 determined from MICP. It can be seen from Figure 2 r50 = reff that the deviation from reff becomes less if rdom is replaced by 0.1 r50 . Nevertheless, both r50 and rdom can be regarded as suitable parameters to estimate the effective hydraulic radius r . The 0.1 1 10 100 eff r (µm) good agreement between r and r enables the evaluation of eff 50 eff equation 5 even in the case that no MICP data are available. Figure 2. Comparison of r determined according to Figure 3 displays the relation between τ and r in a double eff peak eff equation 2 and the median pore throat radius r from logarithmic plot. The red lines indicate the expected curve for 50 MICP for a set of sandstone samples. IP2016 – 6-8 June, Aarhus, Denmark 2 Induced polarization and pore radius Weller et al. = 77.1 Da .0 782 reff . (7) CS samples 2 Bahariya with Da given in µm /s and reff . in µm. Kruschwitz et al. 1.5 other sandstones ES-14 (2010) reported a similar trend for their set of sandstone BR5 D(+) = 3.8 µm²/s samples.