International Journal of Earth Sciences

, Volume 97, Issue 2, pp 385–399

Estimation of hydraulic permeability considering the micro morphology of rocks of the borehole YAXCOPOIL-1 (Impact crater Chicxulub, Mexico)

Review Article

DOI: 10.1007/s00531-007-0227-6

Cite this article as:
Mayr, S.I., Burkhardt, H., Popov, Y. et al. Int J Earth Sci (Geol Rundsch) (2008) 97: 385. doi:10.1007/s00531-007-0227-6

Abstract

Internal surface, formation factor, Nuclear Magnetic Resonance (NMR)-T2 relaxation times and pore radius distributions were measured on representative core samples for the estimation of hydraulic permeability. Permeability is estimated using various versions of the classic Kozeny–Carman-equation (K–C) and a further development of K–C, the fractal PaRiS-model, taking into account the internal surface. In addition to grain and pore size distribution, directly connected to permeability, internal surface reflects the internal structure (“micro morphology”). Lithologies could be grouped with respect to differences in internal surface. Most melt rich impact breccia lithologies exhibit large internal surfaces, while Tertiary post-impact sediments and Cretaceous lithologies in displaced megablocks display smaller internal surfaces. Investigations with scanning electron microscopy confirm the correlation between internal surface and micro morphology. In addition to different versions of K–C, estimations by means of NMR, pore radius distributions and some gas permeability measurements serve for cross-checking and calibration. In general, the different estimations from the independent methods and the measurements are in satisfactory accordance.

For Tertiary limestones and Suevites bulk with very high porosities (up to 35%) permeabilites between 10−14 and 10−16 m2 are found, whereas in lower Suevite, Cretaceous anhydrites and dolomites, bulk permeabilites are between 10−15 and 10−23 m2.

Keywords

Internal surface Nuclear Magnetic Resonance Permeability Carbonate rocks Suevites 

Introduction

The borehole Yaxcopoil-1 (Yax-1) is located in the annular moat, 62 km south of the center of the Chicxulub impact crater in Mexico (Fig. 1). In the borehole, a broad variety of rocks is found. Lithologies comprise post-impact Tertiary limestones, suevitic breccias, and Cretaceous limestones, calcarenites, dolomites and anhydrites, see Fig. 2 (Kenkmann et al. 2004; Urrutia-Fucugauchi et al. 2004). The location within the crater suggests that the Cretaceous formations are parautochthonous to allochthonous megablocks that were displaced during crater collapse from more distant positions from the center and slumped inwards and downwards during crater modification (Kenkmann et al. 2004). The suevitic breccias that are impact melt-rich, polymict debris were likely deposited from the ejecta plume and collapsed central peak (Kring 2005; Wittmann et al. 2007). The overlying carbonate sediments were deposited from a shallow Tertiary ocean after infilling of the crater (Stinnesbeck et al. 2004; Lefticariu et al. 2006).
Fig. 1

Sketch of the location of Yaxcopoil-1 within the crater structure based on seismic data. Redrawn after Morgan et al. (2005

)

Fig. 2

Stratigraphic column of Yaxcopoil-1 including sample depths and gamma log

Hydraulic permeability is an important parameter for hydrologic problems and for oil exploration. Particularly for carbonates (limestones and dolomites) and evaporites, better knowledge of permeabilities is in high demand because they serve as reservoir rocks for hydrocarbons (Chopra et al. 2005). In oil exploration, classification after Dunham (1962), based on the visible internal structure is used for reservoir description (Akbar et al. 1995, Allen et al. 2000). This classification includes the permeability.

In addition to other physical rock properties, hydraulic permeability is a basic parameter for the interpretation of heat flow density (Wilhelm et al. 2004) and modeling of geothermal field in Yax-1 (Safanda et al. 2006). Several previous studies (e.g. Smith and Chapman 1983; Manning and Ingebritsen 1999) have shown that heat transport is conduction-dominated for permeabilities less than ∼10−16 m2 and advection becomes important for permeabilities greater than ∼10−16 m2 for a range of model geometries. If the heat transfer is not purely conductive, but if there is an advective component, the knowledge about bulk permeability gives information about possible macroscopic effects (fractures and faults)

The knowledge of advective or conductive dominated heat flow transport is of fundamental interest for understanding and modeling of cooling effects after an impact. For example, Abramov and Kring (2007) modeled the hydrothermal activity that resulted from the cooling of melt rich breccias and the impact melt sheet of the Chicxulub crater. Such models are required to understand the generation of ore deposits and lifetimes of ecosystems that could be habitats for thermophile organisms.

Furthermore, bulk permeability values allow the calculation of frequency dependence of seismic velocities in order to prove the transferability from laboratory to field conditions (Mayr and Burkhardt 2006, Mayr et al. 2007).

Permeability cannot be measured if the sample size (as in the case of Yax-1) is insufficient, no samples are available or simply because it is too time and cost intensive. Therefore, reliable estimations of permeabilities based on physical properties that are independent of sample size are necessary.

Permeability can be estimated using physical relations as the classical Kozeny-Carman-equation used for granular material (e.g. Schön 1997; Pape et al. 1999; Arnold et al. 2006). Commonly used are formulas that use grain (rgrain) and pore size (reff), or simple geometrical models that relate the pore size to internal surface (Spor) of rocks, considering formation resistivity factor.

In addition to the pore size, which is directly related to permeability, the amount of internal surface reflects the micro morphology— the structure of the grain surface in micro scale (Schön 1997). The micro morphology is not related to permeability, but has to be considered, when permeability is calculated by means of internal surface. A further development of the standard Kozeny-Carman-equation, the fractal PaRiS-model (Pape et al. 1982, 1987) takes into account the increase of internal surface due to micro morphology. This model was developed for sandstones and can be used for other rocks but must be calibrated and possibly adjusted for rocks, with different fine structures, e.g. limestones, dolomites and clay-rich suevites. To be able to apply the appropriate version of Kozeny-Carman-model, this fine structure of the grain surfaces has to be known for better permeability estimation from investigations by scanning electron microscopy (SEM).

Various independent estimations can be found in the literature, e.g. by means of nuclear magnetic resonance (NMR) measurements (Kenyon 1997) or models based on the percolation theory (Katz and Thompson 1986; Zimmermann et al. 2005). Furthermore, hydraulic permeability directly measured on some selected samples can be used for calibration and cross-checking.

Here, we apply the above-described models (three versions of Kozeny-Carman and the fractal PaRiS- model) to borehole samples considering the fine structure of the grain surfaces investigated with SEM. The results are cross-checked with estimations by means of NMR-T2 relaxation times, values determined from max. pore size rc by measurements with HG-porosimetry as well as with gas permeability measurements on several selected samples.

The investigated samples

The borehole Yax-1 was sampled from 404 to 1511 m (Fig. 2). The post-impact rocks of the Chicxulub structure comprise Tertiary limestones, turbidites, para- and ortho-conglomerates. At 795 m depth, a 100-m thick sequence of melt-rich, suevite-like impact breccias (or suevitic breccia) was encountered. This sequence comprises 6 sub-units: upper and lower sorted suevite, upper and middle suevite, brecciated impact melt rock and lower suevite. Below this layer, Cretaceous limestones, calcarenites, dolomites, and low porosity anhydrites that are cut by impact breccia dikes were found. To complement the available geological information (initial core description by the ICDP on-site geologist: Dressler 2002 and later works, Dressler et al. 2003; Wohlgemuth et al. 2004; Stinnesbeck et al. 2004; Kenkmann et al. 2004) the limestones below 612 m and the calcarenites (we use the nomenclature of Dressler 2002) were characterized after Dunham (1962). The sample depth is used as sample identification (Table 1).
Table 1

Investigated samples and additional petrographic description of investigated samples

Depth (m)

Porosity in %

Lithology

Measurements

Additional description

420.25

32.7

LS T1

N

Fine-grained, light, homogenous carbonate with fine laminae

479.77

32.0

LS T1

N

Fine-grained, dark wacke-packstone, finely laminated

509.37

11.7

LS T1

 

Fine-grained, dark wacke-packstone, finely laminated

532.39

8.7

LS T1

pm, S, N

Fine-grained, light, homogeneous wackestone with fine laminae

562.43

25.8

LS T1

pm, N

homogeneous, light packstone, with fine horizontal laminae

587.85

12.3

LS T1

 

light carbonate, pyrite mineralizations, fine laminae and breccia interval

617.53

1.7

LS T2

pm

cherty tan wackestone with fine laminae

636.24

11.7

LS T2

pm, S, N

mudstone with flaser laminae and sandy chert or anhydrite intercalations

656.08

17.1

LS T1

pm, N

grey wackestone with flaser layering and laminae

666.33

26.1

LS T2

 

mudstone with chert or anhydrite knolls and dissolution and flaser layers

747.46

34.8

LS T2

 

Inhomogeneous orange mudstone with chert concretions

834.20

23.6

US

S

melt-rich impact breccia with secondary carbonate cementation

844.52

16.6

US

 

melt-rich impact breccia with secondary carbonate cementation

873.20

21.7

BMR

 

silicate impact melt breccia

874.88

23.3

BMR

 

silicate impact melt breccia

880.00

29.8

BMR

S

silicate impact melt breccia

881.90

28

BMR

 

silicate impact melt breccia

884.79

27.3

BMR

S

silicate impact melt breccia

886.86

2

LS

S

dolomitic carbonate melt with intercalated silicate melt breccia veins

890.37

13.1

LS

 

melt-rich impact breccia with a recrystallized, brown carbonate matrix

1092.85

9.8

Dol-Anh

Po, S, N

dark dolomitic float-rudstone

1053.01

1.8

Anh

N, nI

brown dolomite-anhydrite breccia with healed fractures

1103.00

1.4

Anh

N, nI

inhomogeneous grey-brown dolomite-anhydrite breccia

1131.58

14.8

Calc

 

Grey wacke-packstone, flaser-layered, dissolution horizons and pebbles

1151.43

17.2

Calc

S, N

sandy, inhomogeneous orange floatstone with concretions and pebbles

1159.47

2.8

Anh

N, nI

whitish-grey massive anhydrite

1177.21

0.6

Anh

 

Whitish-blue freckeled anhydrite

1200.86

0.7

Anh

 

light, layered anhydrite, intercalated with dolomite-anhydrite intergrowths

1207.03

5.4

Dol-Anh

N, nI

brown dolomite-anhydrite breccia with healed fractures and relic layering

1228.44

8.5

DolAB

N

dark brown dolomite with mudstone layers

1242.60

1.4

Anh

N, nI

whitish-grey massive anhydrite breccia

1295.80

0.7

Anh

 

light, impure anhydrite with healed fractures

1328.94

7.8

DolAB-Anh

N

dolomite breccia, some fractures filled with anhydrite replacing dolomite

1353.45

3.5

Dol breccia

Po, S, N

dolomite breccia

1387.05

14.9

DolAB

Po, S, N

finely comminuted dolomite breccia, cemented fractures and anhydrite lenses

1407.87

9.0

Calc

 

Inhomogeneous dissolution breccia grainstone with flaser layers

1411.58

6.9

Calc

N, nI

layered dark and light, inhomogeneous mudstone

1440.45

25.6

Dol-Anh

 

dark flaser-layered dolomitic wackestone with pebbles

1451.31

17.8

DolAB

Po, S, N

dolomite breccia with anhydrite-filled fracture vugs

1462.23

9.6

Dol

N

dolomite conglomerate

1470.40

3.1

Calc

N, nI

flaser textured, light limestone

1486.58

11.0

Calc

N, nI

fractured, flaser textured, layered limestone

Abbreviations: LS T1 Post-impact limestone type 1, an-isotropic, layered, LS T2 Post-impact limestone type 2, isotropic, US upper suevite, BMR brecciated impact melt rock, LS lower suevite, Dol dolomite, Anh anhydrite, Calc calcarenite, DolAB dolomite autoclastic breccia, N Nuclear Magnetic Resonance, Po pore radius distribution by HG injection, pm gas permeability, S scanning electron microscopy, nI no internal surface

The following lithological types were sampled: post-impact limestones type 1 are wacke- and packstones that are very fine-grained, homogeneous carbonates with frequent, cm-thick laminations. Their colors range from light-to-grey and dark brown. Post-impact limestone type 2 are predominantly mudstones. Occasionally, inhomogeneities occur as cherty intercalations or anhydrite lenses. Moreover, dissolution horizons and flaser layering is another common feature. Upper suevites are melt-rich impact breccias with a fine-grained, clastic matrix that is occasionally overprinted with secondary carbonate cementation. Brecciated impact melt rocks are impact melt breccias composed of angular impact melt fragments that are consolidated by a fracture-filling matrix that has a partly clastic, partly melted character. The upper sample (886.86) of the lower suevite is mainly composed of melt textured, massive dolomite that is transected by silicate melt breccia veins. The lower sample (890.37) of the lower suevite is an impact melt-rich breccia with a recrystallized, dark brown carbonate matrix. Dolomite-anhydrite samples are a float-to rudstone and a wackstone, respectively, with dark colors and inhomogeneities like pebbles and flaser layering. Calcarenite samples are inhomogeneous carbonate rocks with inclusions of pebbles and occasional flaser textures. Microscopic analyses suggest that their mean grain size is much smaller than originally assumed by the initial petrographic description (Dressler 2002). Anhydrites are mostly massive with white-to-blue colors, and fractures that are usually healed. Some ameboid dolomite inclusions may occur. Dolomite autoclastic breccias, dolomite breccia and dolomites are variably strongly brecciated. Some fractures in the more strongly deformed dolomites are filled with anhydrite, other fractures are cemented with fine carbonate.

From each section some representative samples that cover the whole porosity range were chosen to be investigated with respect to permeability. Due to sample policy we generally had to use non-destructive methods to measure the physical properties. Therefore not all samples could be investigated with all methods.

Experimental technique

Total number of investigated samples is 42 (Table 1). Absolute porosity Φ and density ρ of rock samples were determined on all samples using the water saturation method with basic errors of ±0.005 and 0.05 g/cm3, respectively (Popov et al. 2004; Mayr et al. 2007).

The resistivity formation factor F = σfluid/σrock was determined for 18 samples with pore fluids of different salinity, i.e. conductivity. The salinity of the saturating water was measured using a conductivity meter. Electrical rock resistivity was measured perpendicular to the layering using a four-point configuration after 1 day of saturation.

The absolute internal surface Sabs (Schopper 1982; Schön 1997) was measured with the BET-method using nitrogen gas. For these measurements 1–1.5 g of representative material was taken from 34 samples. The chosen samples are representative of the prevailing types of rocks. The minimum fine structure resolved is approximately 10−10 m. The absolute internal surface Sabs of a sample is normalized to the pore volume: Spor = ρdry Sabs /  (M Φ) and to the total volume Stot = Φ Spor; with ρdry density of the dry sample; M mass of sample and Φ porosity.

SEM images in secondary electron mode are available of unpolished gold-coated pieces of 11 samples. They are representative for the prevailing types of rocks. The composition of mineral phases was estimated with an energy dispersive spectrometer (EDX) on the gold-coated samples.

NMR relaxation time T2 was determined for 22 water saturated samples of which 8 samples have been investigated only with NMR. For samples below 996 m this was possible without additional preparation as the diameter of the half cores is 4.76 cm (maximum diameter of samples measurable with the instrument is 5 cm). Smaller cores had to be drilled in the samples above 996 m that had an original diameter of 6.35 cm.

Five Tertiary post impact samples were used for the measurements of gas- permeability κ (Fig. 2). Due to the required sample size, permeability could only be determined in vertical direction, i.e. perpendicular to the horizontal layering.

Models used for permeability estimation

Kozeny-Carman and further developments

The classic Kozeny-Carman-equation is commonly used to estimate the hydraulic permeability κ. With one possible formulation of this equation, κ is connected to the electrical formation factor F and the hydraulic effective radius of pores reff (e.g. Pape et al. 1999, 2000):
$$ \kappa = 1/{\text{F}} \cdot {\text{r}}^{2}_{{{\text{eff}}}} /8 $$
(1)
Using the assumption that the pores have the shape of cylindrical capillaries with the surface Apor and volume Vpor, the effective capillary radius reff can be connected to the capillary surface Spor* = Apor Vpor = 2 / reff. Assuming that the measured internal surface with respect to the volume of the pores Spor is only due to capillaries, Spor* equals the internal surface Spor. Thus, the capillary radius reff can be expressed in terms of the capillary surface reff ≈ 2/Spor, leading to:
$$ \kappa = 1/{\text{F}} \cdot 1/(2\;{\text{S}}^{2}_{{{\text{por}}}} ) $$
(2)
If a packing of spheres with smooth surfaces and radius rgrain in a porous rock with porosity Φ is considered, the internal surface normalized to the volume of the matrix-material Smtx can be connected to the radius of the grains: Smtx = Spor Φ / (1 − Φ) = Asphere / Vsphere = 3 / rgrain. Assuming that the internal surface is equal to both the surface of the grains Asphere with respect to their volume Vsphere and the surface of the cylindrical pores connects reff and rgrain: reff = (2/3) rgrain Φ / (1 − Φ). This leads to another estimation of the permeability:
$$ \kappa = {\text{r}}^{2}_{{{\text{grain}}}} /(18\;{\text{F}}) \cdot \Phi ^{2} /((1 - \Phi )^{2} ) $$
(3)
The classic Kozeny-Carman-equation is only valid for rocks with very smooth surfaces, i.e. for rocks in which the internal surface is not increased due to fractal structures. For rocks with structured surfaces (enhanced micro morphology) a further development of the standard Kozeny-Carman-equation, the fractal PaRiS-model (Pape et al. 1982, 1987) is a better approximation. This model takes into account the increase of internal surface by fine structures. They are modeled with generations of self-similar (fractal) geometrical structures, with the smallest structures being in the range of nitrogen atoms, as this gas is used in the BET-method for the Spor-measurements. Using the fractal PaRiS-model, the hydraulic permeability κ (Darcy) can be estimated:
$$ {\text{log}}(\kappa ) = - {\text{log}}({\text{F}}) - 3.1085\;{\text{log}}({\text{S}}_{{{\text{por}}}} ) + 3.1085\;{\text{log}}({\text{q}}) + 2.677 $$
(4)
With the factor q, differences of the fine structures can be taken into consideration. For sandstones the factor q equals 1. In rocks with an enhanced structured surface due to lamellar structures the factor q is greater than 1, in rocks with smoother surfaces compared to sandstones the factor q is smaller than 1 (Pape et al. 1987). If not enough data are available to determine q by comparison with measured data, this factor has to be estimated by micro morphology analysis. The permeability estimated by means of PaRiS-equation is in general higher than estimated by means of classical K-C(Spor) because PaRiS model accounts for structures that are not related to pore-size but to fractal internal surface. Thus, estimations by means of classical K-C(Spor) can serve as sort of lower bound.

Alternative methods

Based on percolation theory, Katz and Thompson (1986) showed that permeability can be estimated from the maximum pore size rc determined with HG-porosimetry:
$$ \kappa = 1/226 \cdot {\text{r}}^{2}_{{\text{c}}} /{\text{F}}. $$
(5)
Equation (5) can be used alternatively to (Eq. 1).
Additionally, permeability κ(mD) can be estimated from NMR-measurements of relaxation time T2(ms) in fully saturated samples (Kenyon 1997). For carbonates, the following approximation is used:
$$ \kappa = 0.1\;\Phi ^{4} \;{\text{T}}2^{2} . $$
(6)
The factor 0.1 includes implicitly the surface relaxation time, i.e. the surface relaxivity sr is influencing permeability estimations. Knowing the distribution of T2(μs)-times included in the decay signal the pore radius distribution rNMR(μm) is given by Kenyon (1997):
$$ {\text{r}}_{{{\text{NMR}}}} = {\text{S}}^{2}_{{\text{r}}} \;{\text{T}}2/10^{6} . $$
(7)
The surface relaxivity can be determined by matching the pore radius distribution estimated by means of NMR-T2 and the pore radius distribution measured with mercury.

Measured internal surface

The measurements of internal surface (Fig. 3) display a clustering of values for similar samples. The following groups can be distinguished:
  • suevitic breccia of the upper part of the impactites which generally have the highest internal surface Stot = 21.15–53.47 m2/cm3,

  • limestone of various types with Stot between 0.46 and 12.40 m2/cm3.

  • anhydrite with Stot = 2.04–6.66 m2/cm3

  • dolomites which have the lowest internal surface, Stot = 0.07–2.84 m2/cm3.

This suggests different types of internal structures, e.g. grain and pore size distribution, morphology of grain surfaces (Pape et al. 1982; Schön 1997).
Fig. 3

Internal surface with respect to the total volume Stot = Spor Φ in dependence of porosity Φ. Values of samples that have been investigated with SEM are plotted solid. The rocks can be subdivided into four groups: melt-rich impact breccia, post-impact limestones type 1, low porosity anhydrte and limestones type 2 together with calcarenite and dolomite. The investigated melt-rich impact breccias are taken from the depths: 886.86, 834.20, 884.79, 880.00 m; the limestone samples are taken from the depths: 532.39, 636.24 m; the calcarenite samples from 1407.87, 1131.58 and 1151.43 m; the dolomite samples from 1353.45, 1092.85, 1387.05, and 1451.31 m. All samples are listed with increasing porosity

Micro morphology

Samples selected for further investigation with a SEM in order to analyse the micro morphology of grain surfaces to choose the appropriate version of KC-model are displayed with solid points in Fig. 3.

Limestones and calcarenites

For Tertiary post-impact limestone samples (LS Type 1) the correlation between measured Spor and porosity Φ yields (Popov et al. 2004):
$$ {\text{log}}({\text{S}}_{{{\text{por}}}} (\Phi )) = 0.93 - 0.98 \cdot {\text{log}}(\Phi ). $$
(8)

This means, that Stot = Spor Φ with porosity Φ is nearly independent of porosity (normal triangles in Fig. 3).

Four Tertiary post-impact samples (LS Type 2) and all Cretaceous calcarenite samples (upside down triangles in Fig. 3) have a distinctly smaller internal surface with regard to their porosity suggesting a different type of internal structure (e.g. grain size distribution, fine structure of grain surfaces, i.e. micro morphology). For comparison of the micro morphology sample 532.39 (LS Type 1) and sample 636.24 (LS Type 2) were chosen (Fig. 4a, b). Sample 532.39 has a higher internal surface that correlates with a more structured cauliflower-like surface, whereas sample 636.24 exhibits a lower internal surface corresponding to a less structured surface. Figure 4c shows the Cretaceous calcarenite 1151.43. The less structured surface of the calcarenite is comparable to the surface of the limestone Type 2. This is in agreement with the measured lower internal surface. The shape of the grains is rhombic with rounded edges. The texture is typical for granular material, cf. Fig. 4c.
Fig. 4

a and b SEM-images of two post-impact limestones (LS). Lefta: 532.39 m, LS Type 1, wackestone, Φ = 8.7%, Stot = 6.77 m2/cm3; rightb: 636.24 m, LS Type 2, mudstone, Φ = 11.7%, Stot = 2.10 m2/cm3. The LS Type 2 has a less structured surface than LS Type 1. This correlates with the lower internal surface Stot measured in LS Type 2. c SEM-image of cretaceous calcarenite 1151.43 m, floatstone, Φ = 17.3%, Stot = 1.41 m2/cm3. The smooth surface of the calcarenite is comparable to surface of the LS Type 2. The shape of the single grains is rhombic with rounded edges, the texture is typical for granular material

Dolomites

SEM images of the following three dolomites listed with increasing internal surface Stot are shown in Fig. 5: (1) 1353.45, brecciated dolomite, (2) 1092.85, dolomitic float–rudstone, (3) 1387.05, dolomite autoclastic breccia. With decreasing internal surface, the surface appears less structured. The grains display euhedral rhombic crystal shapes that are typical for dolomite; some smaller grains have rounded edges cf. Figs. 5 and 6, the latter one showing 1451.31, a dolomite autoclastic breccia. Again the texture is similar to granular material. The low porosity sample 1353.45 differs from all other dolomite samples having an exceptionally low internal surface (Fig. 3). The SEM image shows predominantly crack porosity.
Fig. 5

SEM-images of Cretaceous dolomite (1353.45—two different regions are displayed, 1092.85, and 1387.05). Again the lower measured internal surface Stot correlates with a less structured surface, cf. Fig. 4, note the different magnifications

Fig. 6

SEM-images of Cretaceous dolomite autoclastic breccia 1451.31. The shape of the single grains displays euhedral rhombic crystal shapes that are typical for dolomite. The texture is similar to granular material, cf. Fig. 4c, note the different magnifications

Suevites

Sample 834.20 taken from the sub-unit upper suevite has the highest internal surface (Stot = 53.47 m2/cm3). Figure 7 shows the highly structured surface. High-resolution imaging (Figure 7d) confirms the alteration of silicate impact melt to clay minerals with a structure characteristic for hydrated sheet silicates (Hecht et al. 2004; Schmitt et al. 2004). These structures are influencing the fractal dimension of the surface. In addition, needle-like crystals that are late vein-filling smectite-type-clay minerals (Hecht et al. 2004) are increasing the internal surface, see Fig. 7c.
Fig. 7

Details of upper suevite sample (834.20, Φ = 23.6%) with the highest internal surface (Stot = 53.47 m2/cm3). The surface is highly structured due to needle-like (acicular) crystals c and clay d

Images of the sub-unit brecciated impact melt rock (Sample 880.00) are shown in Fig. 8 in two different magnifications. This sample also has a very high internal surface, correlating with a structured surface of impact melt that was altered to clay minerals. The sheet silicate structures typical for clay are increasing the internal surface (Fig. 8), in contrast to the smooth surface of limestone in Fig. 4b.
Fig. 8

Details of brecciated impact melt rock sample: 880.00, Φ = 29.8%, Stot = 34.52 m2/cm3. Again the surface of impact melt is structured due to clay minerals. Hydrated sheet silicate structures typical for clay are increasing the internal surface, in contrast to the rather smooth surface of limestone in Fig. 4b. Note the different magnifications

In sample 884.79 from the bottom of the sub-unit brecciated impact melt rock, a lower surface is measured. In this rock two types of components are observed: (1) altered clasts of impact melt with a scaly groundmass (Fig. 9a) and (2) non altered massive secondary carbonate crystals (Fig. 9b). The internal surface Stot in this sample results from the cementation of this rock with carbonate (2) that outweighed the increase in internal surface due to the alteration of the silicate impact melt component (1) to clay minerals.
Fig. 9

SEM image of brecciated impact melt rock sample: 884.79, Φ = 27.3%, Stot = 8.47 m2/cm3. Two different regions are displayed. a altered impact melt with a scaly groundmass of formerly glassy impact melt that transformed to clay minerals leading to an increase of internal surface Stot. b detail of massive secondary carbonate crystals

Sample 886.86 (Fig. 10) from the sub-unit lower suevite has a lower internal surface (Stot = 0.64) comparable to dolomites (cf. Figs. 5 and 6). No increase of the surface due to clay can be seen. This is correlating with the mineral composition because it consists mainly of dolomite.
Fig. 10

Image of lower suevite sample: 886.86, Φ = 2.0%, Stot = 0.64 m2/cm3. It shows a fine-grained, dolomitic groundmass indicating massive cementation of this suevitic breccia which is rich in carbonate lithics clasts or melts; note the smooth grain surfaces

Results and discussion

The following implications arise from the analyses of micro morphologies (i.e. fine structure of grain surface) in Yax-1:
  • Dolomites, carbonates and limestones Type 2 have a smoother internal structure in the 100 nm range than post-impact limestones Type 1 resulting in a smaller internal surface (cf. Fig. 1). This possibly stems from diagenetic consolidation of the megablock lithologies after impact. These sediments underwent cementation from percolating fluids and localized recrystallization as a result of heating from the overlying impactites (Lueders and Rickers 2004). Post-impact sediments were mostly consolidated due to dolomitization and carbonate precipitation (Lefticariu et al. 2006).

  • Melt-rich impact breccias of the sub units upper suevite and brecciated impact melt rock contain abundant silicate melt particles that underwent hydrothermal alteration to clay minerals. These clay minerals are most likely the main cause for the higher internal surfaces of these rocks. The high clay content in samples 834.20, 880.00 and 884.79 strongly correlates with high gamma intensities (Wohlgemuth et al. 2004; Fig. 2).

  • The lower suevite is distinctly different from the overlying upper suevite and brecciated impact melt rock. The measured lower internal surface Stot correlates with higher contents of massive carbonates both in the matrix and clasts in this unit leading to a less structured grain surface.

  • The texture of the majority of samples is typical for granular material. Exceptions are observed and have to be considered for permeability estimations. This means that the Kozeny-Carman model and Biot-Gassmann theory (e.g., Mayr et al. 2007) are applicable. In a first order simplification, the grain shapes can be treated as spheres.

Formation resistivity factor

Figure 11 shows a negative correlation between formation resistivity factor F and porosity Φ in accordance with literature (“Archie’s first law”):
$$ {\text{F}}(\Phi ) = {\text{a}} \cdot \Phi ^{{ - {\text{m}}}} = 1.04\;\Phi ^{{ - 1.8 \pm 0.23}} . $$
(9)
Fig. 11

Resistivity factor F versus porosity Φ. Differences between limestones, calcarenites, dolomites and melt-rich impact breccias are small. The mean relationship is used for all samples

No clear differences can be seen for the investigated types of rocks. The resulting exponent for all samples m = 1.8 ± 0.23, a = 1.04 is an indicator of, e.g. tortuosity for a specific rock type and is typical for crystalline and granular carbonates (Schön 1997). The correlation has been calculated in the porosity range 2–27%. The formation factor for suevitic breccias is slightly higher than the regression line for all rocks. This is indicating a different internal structure, i.e. higher tortuosity. The mean relationship (Eq. 9) is used for all samples in the permeability analysis below.

Permeability

Various models were applied to calculate the permeabilities of the investigated samples. The values calculated with the fractal PaRiS-model (Eq. 4) with q = 1 are shown for all rock types in order to illustrate the influence of the structured surface (cf. Figs. 12, 13 and 15).
Fig. 12

Limestones and calcarenites: comparison of different approaches for permeability estimations. Solid line Kozeny-Carman-equation with rgrain = 2 μm (Eqs. 3 and 9). Dashed line PaRiS-model with q = 1 and an interpolated internal surface for limestones type 1 (Eqs. 4, 8 and 9). Small empty symbols estimations, calculated for individual values from formation factor F and specific internal surface Spor, using the PaRiS-model with q = 1. Small filled symbols values calculated with PaRiS-model using q = 0.5. Grey symbols are permeability κ-estimations by NMR-measurements of relaxation time T2 with κ(mD) = 0.1F4 (T2)2 [ms] (Kenyon, 1997). Big grey triangles denote five direct measurements of permeability κ with the gas-permeameter. Permeability measured in layered samples with layers of different grain sizes are lower than estimated. Permeabilities measured by Vermeesch and Morgan (2004) are plotted for comparison

Fig. 13

Dolomite comparison of different approaches for permeability estimations. Small empty symbols estimations, calculated for individual values from formation factor F and specific internal surface Spor, using the PaRiS-model q = 1. Small filled symbols: values calculated with PaRiS-model using q = 0.5; bigger filled symbols are estimations, using K-C (Spor) equation 2. Solid line: Kozeny-Carman-equation with rgrain = 2 μm (Eqs. 3 and 9). Value in brackets application of K-C is questionable. Grey circles are κ-estimations by NMR-measurements. Grey triangles denote estimations by means of pore-radius distribution. Permeabilities measured by Vermeesch and Morgan (2004) are plotted additionally

Limestones and calcarenites

For post impact limestones Type 1, the original PaRiS model (i.e., q = 1 in Eq. 4) is used for individual estimations from measured values of formation factor F(Φ) and internal surface Stot (solid upright triangles in Fig. 12) (Popov et al. 2004). Using the correlation between measured internal surface Stot and porosity Φ for the post impact limestones Type 1 (Eq. 8), the formation factor F(Φ) given in Eq. (9) and q = 1 in Eq. (4), a mean relationship for limestones is calculated (dashed line, κPaRiS, q = 1). In contrast to the micro morphology of limestones Type 1, that can be compared with the micro morphology of sandstones, the grain surface of calcarenites and limestone Type 2 is smooth, thus for these rocks, for calculations with the PaRiS-model (Eq. 4) q < 1 has to be used. An arbitrary value of q = 0.5 is assumed, which leads to lower permeabilities (solid upside-down triangles in Fig. 12).

Mean grain dimensions were estimated from SEM-analysis. The diameter of the grains is predominately 0.5–5 μm for the limestones and calcarenites, see Figs. 4 and 6. For the estimation of permeabilities by mean grain size (Eqs. 3 and 9) rgrain = 2 μm is chosen (solid line in Fig. 12).

The values estimated by means of NMR-T2 measurements (Eq. 6) and the ones estimated by means of PaRiS-model (q = 1 for limestone Type 1 and q = 0.5 for limestone Type 2 and calcarenite) are in the same order of magnitude.

The directly measured permeabilities for samples 562.43 (Φ = 25.8%) and 656.08 (Φ = 17.1%) are distinctly lower than the estimated ones. These two samples are clearly layered. Since gas-permeabilities are measured perpendicular to layers of different grain size, the bulk value measurements are likely underestimated due to anisotropy.

The permeability of approximately 10−22 m2 for sample 617.53 (Φ = 1.7%) was at the resolution limit of the instrument suggesting the κ may be even less. Direct measurements of κ on limestones and calcarenites of Yax-1 by Vermeesch and Morgan (2004) are in the same order of magnitude as our estimations and measurement results.

Dolomites

As shown in “Micro morphology” section, the grain surfaces of dolomites are rather smooth, thus for these rocks for individual calculations with PaRiS-model (Eq. 4) q = 0.5 is assumed as used in the calculations for the calcarenites, leading to lower estimated permeability (Fig. 13). In order to get a lower bound estimate of permeability for dolomites, the Kozeny–Carman Eq. (2) valid for smooth surfaces is used.

For dolomites, the diameter of the grains is approx. 1–2 μm. The estimation of hydraulic permeability κ by means of rgrain = 2 μm, (Eqs. 3 and 9) is given by the solid line in Fig. 13, cf. Fig. 12.

For the sample with the lowest porosity, grain sizes could not be estimated, because no single grains can be seen in the available images. This restricts the use of this special form of K-C for this exceptional sample, see also Figs. 3, 5a and the extension of the line in Fig. 13.

Two different approaches were used to estimate the permeability by means of pore radius determined with HG-injection:
  1. 1.

    Kozeny–Carman equation (1), (mean pore size)

     
  2. 2.

    Equation (5), based on percolation theory (max. pore size)

     
Both estimations are in the same order of magnitude as the estimations by means of Kozeny–Carman (Eq. 2) using the internal surface, except for the sample with the lowest porosity.
As the factor 0.1 in the formula for the estimation of permeability by means of NMR is influenced by the surface relaxivity, the surface relaxivity was estimated by comparing the pore radius distribution determined with HG and with NMR measurements, see Fig. 14 and Eq. (7).
Fig. 14

Pore radius distribution for dolomite samples. Comparison between measurements with mercury (HG, boxes) and the estimation by means of NMR-T2 (NMR, dashed lines)

The general shape of both pore radius distributions differ because the measurements are based on different physical mechanisms: the measurements with HG are mostly influenced by the pore throat, whereas the NMR-relaxation time is influenced by the distance between the water in the pores to the surface of the wall. But with a mean surface relaxivity of sr = 2.5(μm/s) at least a good match between the maximum of the distributions can be achieved (Fig. 14). This value is consistent with values for calcarenite given in the literature (Arnold et al. 2006).

The permeabilities estimated from NMR-T2 measurements (Eq. 6, grey circles) and the values estimated by means of classic K–C(Spor) (Eq. (2), due to the smooth surface) are in the same order of magnitude.

Again the sample with lowest porosity is an exception: the permeability determined with K-C(Spor) is higher than the values from the other estimations, indicating that the application of K-C is questionable. Measured permeabilities in Yax-1 dolomites of Vermeesch and Morgan (2004) are in the same order of magnitude as our estimations based on NMR-relaxation times.

Suevites

An enhanced structured surface is observed in the melt-rich impact breccias that overlie the lower suevite, therefore q > 1 has to be used. The factor q is arbitrarily set to 1.5 for calculations with the PaRiS-model (Eq. 4) which leads to higher permeabilities than using q = 1. As q could not calibrated by means of direct measurements, the estimated permeability values are probably lower than true values. The grain surface of the lower suevite is very smooth, thus for these rocks q = 0.5 is assumed (Fig. 15).
Fig. 15

Anhydrites and suevitic breccia comparison of different approaches for permeability estimations. Small empty symbols estimations, calculated for individual values from formation factor F and specific internal surface Spor, using the PaRiS-model with q = 1. Filled symbols values calculated with PaRiS-model using q = 0.5 and 1.5, see text. Grey symbols are κ-estimations by NMR-measurements (only for anhydrites)

Anhydrites

The internal surface Stot of anhydrites is in the same order of magnitude as that of post impact limestones. As no information about the micro morphology is available, for these rocks q = 1 is used. The resulting values are in the same order of magnitude as the values estimated by means of NMR.

Evaluation of applied methods

The applied models yield comparable results for all rocks if the micro morphology of the different rock types is taken into account. Therefore, the specific choice of one of these models depends on the experimental and logistical conditions. In any case independent methods of estimation of permeability are recommended to check the plausibility of the results. If possible (i.e. if the sample size is sufficient) supplementary measurements of permeability should be used for calibration.

Both the classical K-C-model (Spor), using the internal surface, porosity, formation factor and its modification, the PaRiS-model have no restriction to sample size. For the application of these models the differences of lithology and the type of micro morphology, have to be considered. Therefore, the micro morphology has to be investigated on selected samples by high-resolution images to assure that the appropriate version of model is used. This classification has to be done individually for the investigated types of rocks. Under these conditions this method turned out to be very efficient.

For the classical K-C model (rgrain) using the grain size this parameter has to be determined by, e.g. optical methods from thin sections.

For estimations using pore radius distribution the distribution has to be determined by, e.g. cost intensive HG-injection or by matching NMR-relaxation time data. In the latter case, a calibration of the surface relativity is necessary.

The estimation by means of NMR-T2 is a good alternative, as no distinction between different types of carbonate rocks (i.e. micro morphology) seems to be necessary. This estimation, however, is only possible if the investigated rocks do not contain magnetic minerals and requires specific sample preparation.

Summary and conclusions

To apply the appropriate version of the Kozeny-Carman-model for permeability estimations measurements of internal surfaces in samples from drill core Yax-1 were examined with respect to possible clustering. The fine structure of grain surfaces was investigated with SEM-imaging on selected samples and complemented by SEM-EDX analyses for compositional information.

The following four groups of rocks with decreasing internal surface were found: (1) melt-rich impact breccia (upper suevite and brecciated impact melt rock); (2) post-impact limestones Type 1; (3) anhydrites; (4) limestones Type 2, calcarenites, dolomites and the lower suevite.

These four groups have different types of internal structures, e.g. with regard to grain and pore size distribution, micro structure of grain surfaces at the 100 nm scale and mineral composition. Therefore, the internal surface Spor gives a tool for an investigation of the internal structure, possibly influenced by diagenetic processes, e.g. hydrothermal alteration of silicate melt particles to clay minerals.

On the base of the observed groups and of the analysis with SEM the following versions of Kozeny-Carman (KC) and PaRiS-model (Pape et al. 1987) were used for the estimation of permeability:
  • PaRiS with q = 1.5 for suevites and q = 0.5 for lower suevite,

  • PaRiS with q = 1 for limestones Type 1 and for anhydrite.

  • PaRiS with q = 0.5 for limestones Type 2,

  • Kozeny-Carman (Spor) for dolomite rather than PaRiS with q = 0.5.

  • Kozeny-Carman with mean grain radius for limestone, calcarenite and dolomite.

For comparison with a totally independent method estimations by means of NMR-T2 were calculated for some limestones, dolomite and anhydrite. No distinction was made between the different rock types.

Pore radius distributions measured with HG on four dolomite samples were used for the determination of surface relaxivity of NMR measurements, resulting in sr ≈ 2.5 μm/s. The maximum pore size determined by HG and NMR measurements was used as input for another independent estimation of permeability.

For high porosity rocks (0.05 < Φ < 0.35), the different estimations and measurements are in satisfactory accordance, taking the complicated nature of permeability into account (Fig. 16). This is particularly true for the estimated values from NMR-measurements and from the PaRiS-model, i.e. from two independent methods.
Fig. 16

All types of rocks comparison of estimation by means of Kozeny-Carman theory and NMR relaxation time T2 with measured data for validation and calibration. Three different determinations of hydraulic permeability κ are shown. Small empty symbols are κ-estimations by NMR-measurements. Small filled symbols are estimations, calculated for individual values from formation factor F and specific internal surface Spor, using the PaRiS-model and classical K-C (Spor), cf. Figs. 12, 13 and 15, value in brackets application of K-C is questionable. Big empty triangles denote five direct measurements of κ with the gas-permeameter, cf. Fig. 12. Solid line permeability κParis with q = 1, used for Limestones Type 1. It is plotted in the porosity range in which linear regression for Stot and F was calculated. Permeabilities measured by Vermeesch and Morgan (2004) are plotted additionally

The comparison of estimations with gas-permeability measurements and shows that in anisotropic limestone samples (LS Type 1), measurements yield lower values than estimated values, likely due to horizontal layering. In isotropic samples (LS Type 2) measurements are in the same range as estimations, therefore, the resulting permeabilities (Fig. 16) should give a rough estimate for the order of magnitude of the intrinsic bulk permeabilities of the section.

The bulk permeabilities (between 10−23 m2 and 10−15 m2) in Cretaceous rocks are in accordance with the interpretation of Kenkmann et al. (2004) that the megablocks of Cretaceous sedimentary rocks, which display zones of brittle deformation with variable intensity, slumped to the present position within the crater from an outward location. Because judging from the hydraulic properties, no pervasive deformation from the passage of the shock wave occurred, it is unlikely that the Cretaceous units represent ejected material from within the transient crater (Stoeffler et al. 2004).

The relative low bulk permeabilities (between 10−14 m2 and 10−19 m2) of Tertiary limestones with high porosity (0.08 < Φ < 0.35) indicate that these rocks are characterized by large pores with minor interconnections.

The estimated values for Suevitic rocks (except lower suevite) between 10−18 m2 and 10−15 m2 indicate that this section and the Tertiary limestones are candidates for possible effective fluid flow.

Since bulk permeabilites above 10−16 m2 are found for Tertiary limestones and suevites the possibility of convective contributions to the heat transport in Yax-1 cannot be excluded (e.g., Smith and Chapman 1983; Manning and Ingebritsen 1999), whereas for low porosity lower suevite, Cretaceous anhydrites and dolomites, were bulk permeabilites are between 10−15 m2 and 10−23 m2, convective heat flow is less probable.

The estimations of bulk permeabilites do not include macroscopic features like fractures and faults. Therefore, the estimated values may serve as lower bound for in-situ permeabilities. Convective–conductive modeling of temperature data can help to decide if fractures and faults have to be considered additionally.

Hydraulic permeability is equally important as thermal conductivity for the temperature field. In addition, the knowledge of hydraulic permeabilites gives basic information for the regional hydrological situation in the region.

Acknowledgments

The research was funded by the Deutsche Forschungsgemeinschaft (DFG-grant BU 298/16) within the ICDP-Chicxulub project. The authors also wish to acknowledge support in the form of a grant from Schlumberger Oilfield Services and the Russian Foundation for Basic Research (grant No 05-05-64879). The authors thank Dr. J. Urrutia-Fucugauchi and Dr. A.-M. Soler-Arechalde (UNAM, Mexico) for their help in core collection preparation and delivery. We thank D. Korobkov (MSGPU, Moscow) and A. Scholz (Technical University Berlin) for active help in petrophysical measurements, U. Trautwein (GFZ Potsdam) for permeability measurements, S. Schuldt (Technical University Berlin) for Dunham classification and J. Nissen (ZELMI, Technical University Berlin) for helpful hints whilst operating the SEM. We thank an anonymous reviewer and Patrick Fulton for their detailed comments and suggestions that helped to improve the manuscript.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • S. I. Mayr
    • 1
  • H. Burkhardt
    • 1
  • Yu. Popov
    • 2
  • A. Wittmann
    • 3
  1. 1.Department of Applied GeosciencesTechnical University BerlinBerlinGermany
  2. 2.Technical physics and rock physicsRussian State Geological Prospecting UniversityMoscowRussia
  3. 3.Humboldt-Universität zu Berlin, Museum für Naturkunde, MineralogieBerlinGermany

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