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1 Relationship among porosity, permeability, electrical and elastic properties Zair Hossain Alan J Cohen RSI, 2600 South Gessner Road, Houston, TX 77063, USA Summary Electrical resisivity is usually easier to measure in the laboratory and in-situ than permeability. Therefore, a method of combination between permeability and electrical resistivity might be used to define the fluid flow of reservoir rocs from resistivity data. However, estimating permeability from resistivity has been a problem examined by different authors. Furthermore, neither electrical nor elastic data seldom allow us to accurately quantify the hydrocarbon saturation. Hence, a combination of elastic and electrical properties could offer a powerful means of solving the problem of hydrocarbon saturation production. The objective of this study is to experimentally and theoretically revise the relations among the electrical properties, porosity, permeability, and elastic wave velocity. A data set of laboratory measured petrophysical properties, electrical properties and elastic properties of glauconitic greensand from the North Sea Nini Field was used for this study. A linear relationship between laboratory measured electrical properties and permeability could be established if the diagenesis of greensand is now. By combing Archie s relation and Kozeny s equation, the greensand diagenesis may be described by the specific surface area of pores. A linear relationship between laboratory measured electrical and elastic properties could be established if the effect of micro structure of greensand is nown. Roc physics modeling results show that quartz cementation has a larger effect on elastic properties than electrical properties, while berthierine cementation has a similar effect on elastic and electrical properties. Selfconsistent modeling results show that pore aspect ratios are more sensitive for electrical properties than elastic properties. Introduction Electrical resistivity is commonly used types of to define the hydrocarbon saturation of reservior rocs. A method of combination between permeability and electrical resistivity may be used to define the fluid flow of reservoir rocs. Even though both resistivity and permeability strongly depend on porosity, no rigorous relationship between permeability and resistivity has yet found (Gomez, 2009). Estimating permeability from resistivity has been a problem examined by different authors, including Archie (1942), who showed an average trend of formation factor versus permeability for sandstones, but recognized that the scatter was too large to establish a definite relation between the two properties. Lie electrical resistivity, sonic velocities is also one of the most common collected types of geophysical well logging data used in hydrocarbon investigations. However, neither electrical nor elastic data seldom allow us to accurately quantify the hydrocarbon saturation. Therefore, a combination of elastic and electrical properties could offer a powerful means of solving the problem. In the case of common reservoir rocs resistivity strongly depends on Figure 1: (a) BSE image of a cemented greensand (Hossain et al. 2011). (b) Cemented greensand model shows micro crystalline quartz cement (QC) on quartz (Q) grains and berthierine (B) cementation within large pores. (c) Glauconite (G) grain of greensand with complex pore structure (Hossain et al. 2009). SEG Las Vegas 2012 Annual Meeting Page 1

2 porosity, pore geometry and saturation (Archie 1942) while the elastic properties depend on porosity (Mavo 1980, Murphy 1984), saturation history (Mavo and Muerji 1995), pore geometry (Mavo 1980; Mavo and Nur 1978), mineralogy and fluids types (Mavo et al. 2009). However, elastic and electric methods can contribute in different ways to characterizing roc properties. The objective of this study is to experimentally and theoretically revise the relations among the electrical properties, porosity, permeability, and elastic wave velocity. Laboratory measured data from the North Sea greensand was used. Greensand is composed of a mixture of quartz and micro-porous glauconite grains. (Figure 1). Diagenesis of greensand can be described by micro crystalline quartz cement and pore-filling berthierine cement. Petrophysical models and roc physics models were used to describe the effect of micro structure of greensand on elastic and electrical properties. Method A laboratory measured core data set of 16 greensand samples from the Nini field of the the North Sea was used for this study. Helium porosity and Klinenberg permeability data were obtained from Hossain et at while resistivity and elastic wave velocity data were obtained from Hossain et al. (2012). A physical relationship between permeability and resistivity may be explained by combining Archie s equation (Archie, 1942) and Kozeny s equation (Kozeny 1927). The ratio of the pore fluid resistivity of, R w to bul resistivity of the fully saturated roc, Ro is nown as 1 over the formation factor, F (Archie 1942). Archie s law is an empirical relation relating the formation factor and cementation factor, m to the porosity, and a factor correcting for conducting minerals, a in brine saturated reservoir roc: F a (1) m The relationship among porosity (), permeability () and specific surface area of bul volume (S) may be written by using Kozeny s equation (Kozeny 1927) as: 3 c 2 S (2) where, c is Kozeny s factor and the relationship between permeability and formation factor can be expressed as: 3 / m a 1 c (3) 2 F S Worthington (1997) revisited the relationship between formation factor and permeability by Archie and showed how formation factor F decreases as permeability increases according to the following relation: 1/ c b (4) F Results and discussion Electrical properties of greensands are higher than those for consolidated sandstone, unconsolidated sandstone, average sands, shaley sands and clear granular roc (Figure 2). These higher electrical properties of greensand are related to the micro-porosity within glauconite and pore-filling berthierine cementation of greensand. Formation factor Consolidated sandstone Unconsolidated sandstone Average sands Shaley sands Clean granular roc Greensand Greensand lab data Porosity Figure 2: (a) Comparison of greensand formation factor with different types of rocs. A linear relationship can be established between permeability and formation factor (Figure 3a). Any scatter between these properties can be described due to greensand diagenesis particularly at low resistivity and low permeability bearing samples (Figure 3a). Equation (3) was used to describe this diagenesis. SEG Las Vegas 2012 Annual Meeting Page 2

3 For this data set, I defined m is equal to 1.9, a is equal to 1.67 and c is close to 0.21 for porosity 0.27 to 0.42 so in equation (3) only specific surface area of pore is the controlling factor for relationship between permeability and formation factor (Figure 3c). The relationship between resistivity and elastic wave velocity is not linear; indeed, the data exhibit an approximate quadric trend (Figure 4a). Note that the expression could be linear if I the three highest elastic velocity bearing greensand from the lower Ty Formation are omitted. By combining a roc physics soft-sand and stiff-sand model (Mavo et al. 2009) with the Archie equation (Archie 1942) the scatter could be described. The modeling shows that micro crystalline quartz cement has a larger effect on elastic properties and a smaller effect on electrical properties. In contrast berthierine cementation has a simultaneous effect on elastic and electrical properties and berthierine cementation is mainly responsible for higher elastic and electrical properties (Figure 5b). Using self-consistent modeling with grain aspect ratio 1, and pore aspect ratio between 0.2 and 0.1, the laboratory measured resistivity data fall into this theoretical range (Figure 5a). Whereas, using self-consistent modeling with grain aspect ratio 1, and pore aspect ratio between 0.05 and 0.3, the laboratory measured elastic velocity data fall into this theoretical range (Figure 5b). Self-consistent modeling Figure 3: (a) Relation between permeability and electrical resistivity, (b) relationship among porosity, permeability and specific surface area. The reference lines represent equal specific surface area with respect to pores (S p ) as calculated from Kozeny s equation (Kozeny 1927), (c) Permeability and resistivity relationship are superimposed by combining Kozeny s equation (Kozeny 1927) and Archie equation (Archie 1942), (d) Statistical significant of permeability prediction by using equation (3). SEG Las Vegas 2012 Annual Meeting Page 3

4 Figure 4: Relationship between electrical and elastic properties. (a) Lab measured data, (b) lab measured data are superimposed by combing roc physics models with Archie equation (Archie 1942). Figure 5: Self-consistent modeling of greensand samples (a) lab measured electrical properties by using grain aspect ratio of 1, and pore aspect ratio from 0.2 to 1. (b) Lab measured elastic properties by using grain aspect ratio of 1 and pore aspect ratio from 0.05 to 0.3. results show that pore aspect ratios are more sensitive to electrical properties than elastic properties. Conclusions A linear relationship between laboratory measured electrical properties and permeability could be established if the diagenesis of greensand is nown. By combing Archie s relation and Kozeny s equation, this greensand diagenesis may be described by the specific surface area of pores. A linear relationship between laboratory measured electrical and elastic properties could be established if the effect of micro structure of greensand is nown. Roc physics modeling results show that quartz cementation has a larger effect on elastic properties than on electrical properties, while berthierine cementation has a simultaneous effect on elastic and electrical properties. SEG Las Vegas 2012 Annual Meeting Page 4

5 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2012 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of lining to cited sources that appear on the Web. REFERENCES Archie, G. E., 1942, The electrical resistivity log as an aid in determining some reservoir characteristics: Transactions of the American Institute of Mining and Metallurgical Engineers, 146, Gomez, C., 2009, Reservoir characterization combining elastic velocities and electrical resistivity measurements: Ph.D. thesis, Stanford University. Hossain, Z., I. L. Fabricius, and H. F. Christensen, 2009, Elastic and nonelastic deformation of greensand: The Leading Edge, 28, Hossain, Z., I. L. Fabricius, A. C. Grattoni, and M. Solymar, 2011, Petrophysical properties of greensand as predicted from NMR measurements: Petroleum Geoscience, 17, Hossain, Z., T. Muerji, J. Dvorin, and I. L. Fabricius, 2010, Roc physics model of glauconit ic greensand from the North Sea: Presented at the 80th Annual International Meeting, SEG. Hossain, Z., T. Muerji, and I. L. Fabricius, 2012, Vp-Vs relationship and AVO modeling of the North Sea greensand: Geophysical Prospecting, 60, Kozeny, J., 1927, Ueber apillare Leitung des Wassers im Boden. Sitzungsber: Aad.Wiss.Wien, 136, Mavo, G., 1980, Velocity and attenuation in partially molten rocs: Journal of Geophysical Research, 85, Mavo, G., and D. Jizba, 1991, Estimating grain-scale fluid effects on velocity dispersion in rocs: Geophysics, 56, Mavo, G., and T. Muerji, 1995, Seismic pore space compressibility and Gassmann s relation: Geophysics, 60, Mavo, G., T. Muerji, and J. Dvorin, 2009, The roc physics handboo: Cambridge University Press. Mavo, G., and A. Nur, 1978, The effect of a percolation threshold in the Kozeny-Carman relation: Geophysics, 62, Mavo, G., and A. Nur, 1998, Wave attenuation in partially saturated rocs: Geophysics, 44, Murphy, W. F., Acoustic measures of partial gas saturation in tight sandstones: Journal of Geophysical Research, 89, no. 13, SEG Las Vegas 2012 Annual Meeting Page 5