SPE 130745

How to Propagate Petrophysical Properties in a Fracture Network for Naturally Fractured Carbonate Reservoirs Case Study: Cretaceous Formations at Maracaibo Lake, Venezuela Rodolfo Soto B.

/SPE, Digitoil, Sergio Perez, Duarry Arteaga, Cintia Martin / SPE,PDVSA Western Division

Copyright 2010, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE EUROPEC/EAGE Annual Conference and Exhibition held in Barcelona, Spain, 14–17 June 2010. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract A fuzzy-logic approach accurately characterizes spatial porosity and permeability for a complex, naturally fractured carbonate reservoir. The reservoir lies in the Cretaceous section alongside the fault damage and shear zone at the downthrown block to the west of the Icotea fault, Central North segment of the Maracaibo basin.

To identify the pore type in our characterization of this carbonate reservoir, we first used fuzzy logic to obtain fracture indexes from conventional well logs. Then we used a resistivity/porosity model with cementation factor, m, variable to determine fracture porosity, and calculated total porosity from neutron-density logs. After that, we developed a neuro-fuzzy logic permeability model with porosity, shale volume, fracture indexes, and pore type as independent variables.

Next, we used directional-statistics tool analysis to identify the five main fracture families and categorize them. The diagnosis of fracture orientation relies on the statistical analysis of fractures from four wells, three of them having image logs and one having a direct description of fractures from an oriented core. We also compared the fracture-orientation data from well data with the faults interpreted at seismic scale to unravel their structural connection.

Fracture lengths are obtained from curvature maps by direct measurement of lineaments matching the azimuth of each family. A logarithmic fit of the known values allows extrapolating values of fracture lengths and spacings below seismic resolution. To propagate porosity in our fracture system, where only a seismic P-wave volume was available, we found for each fracture family a general inverse functional relationship between fracture intensity and fracture porosity, introduced as the r-pi method of correlation.

With a sigmoidal function we correlate the neuro-fuzzy logic permeability variable with the aperture and intensity of the fractures. With a statistically based characterization we identify wheter the fractures display directionally or stratigraphically related anisotropies. Finally, to populate petrophysical properties in the fracture network we apply the functions devised starting with the size of the fractures as an independent variable. Introduction The Maracaibo Basin, situated in the northwestern side of Venezuela, is ranked among the top 12 petroleum provinces in the world (Klett et al, 2000). The Cretaceous reservoirs are among the most prolific in the area, with more than 6 billion bbl OOIP of light oil. From 2007 and up to late 2009 PDVSA in cooperation with PVN and several consultant companies, developed the Cretaceous Lake Pilot Project to model and design the development of offshore reserves located at the central-northern side of the Maracaibo Lake.

The Icotea fault, located at the central section of the Maracaibo Lake, is a high angle dip, northeast trending fault. It is a major structural feature of the basin, with a trace around 100 KM long. Like many other fault trends in the Maracaibo basin, the Lama-Icotea fault system displays strike-slip classic features (Escalona and Mann, 2003), as subvertical to high angle dip, restraining and release bends, and oblique folding. Its displacement is left-lateral (Lugo, 1991).

The Icotea fault is also a prominent structural feature in connection with several reservoirs, spanning from the Cretaceous to the Eocene sequences. For the Cretaceous reservoirs at the central sector of the basin, the Icotea fault not only seves as a definite compartment boundary, but also plays a major role in association with the distribution of fractures at its fault damage zone. This fault damage zone has been identified as a sinistral trancurrency related shear zone (Perez et al., 2009). This work

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presents the methodology developed in the integrated reservoir study by the multidisciplinary team to assign petrophysical properties to the fracture network associated to the Icotea fault shear zone. General Methodology: The procedure devised to assign the petrophysical properties of permeability and porosity to the fracture network is as follows:

1. Apply soft computing techniques to well logs and core analysis for petrophysical modeling of porosity, permeability, and lithotypes..

2. Discriminate and characterize fracture families geometrically and spatially from well logs and oriented cores. 3. Typify the distribution of fractures in the different lithologies or lithotypes and stratigraphic units. 4. Collect fracture length and spacing data from structural seismic attributes. We took advantage of having near vertical

fractures (Table 1) and low dipping horizons, which facilitated the implementation of this step. 5. If possible, as in our case, integrate fracture spacing trends at well and seismic scales. 6. Using the pairing frequency method, set up a functional connection between fracture length, spacing and area (or size). 7. Conduct statistical characterization of fracture relevant parameters (intensity, porosity and permeability). 8. Correlate fracture porosity and fracture intensity for every fracture family using the r-pi method presented in this

paper. 9. Calculate fracture aperture as a function of fracture porosity and intensity for all fracture families. 10. Design and evaluate fracture probabilty as a dependant variable of fracture aperture. 11. Determine fracture permeability from the fracture probability/aperture related variable. 12. According to their areas, assign to the fractures in the 3D digital model their specific petrophysical parameters.

Structural setting and fracture families

The geological analysis made to diferentiate areas of the region under study with a definite structural style, with conspicuous evidence from macroscale (3D seismic) to microscale (thin slides from core samples), supports the premise that the Icotea fault damage zone is a strike-slip related shear zone (Perez et al., 2009).

For the identification of its fractures families we used first-hand fracture data provided by the available well records (images logs, dipmeters and fracture data from measurements on an oriented core). Evidences indicate the families of fractures at well scale were contemporary to macro structures seen at seismic scale in their vicinity. The scheme of analysis followed Peacock (2001) and Price and Cosgrove (1990) guidelines. Fracture families were analyzed by a combination of information provided by the Kuiper test, the Schmidt stereonet, and the rosette diagram.

The Kuiper test was restated (Fig. 1a) to our results in the angular range of 0° to 180°. To that end the fracture strike angles less than or equal to 180° were kept, while those angles grater than 180° were taken to the first or second quadrant (Middleton, 2000) by subtracting 180°. This convention is justified for data from wells in the shear zone by the symmetry of structures present in the strain ellipsoid of sinistral strike-slip deformation (Cunningham and Mann, 2007). This is a permissible departure from the original concept of the Kuiper test, since it is formally designed to work in the angular range covering from 0° to 360°. It is worth noting that working in a two-quadrant fashion rather than four also simplifies the work of quantifying the fracture families, since the work is reduced by half.

Fig. 1—Fracture families, cored well at Lagomar Apon section. (a) Kuiper test displaying the distribution of fractures on the lithotypes. (b) Set of structures related to sinistral strike slip deformation by angular range. (c) Cogollo Group. Schmidt plot.

Once the angular range of dip azimuth of each fracture family is set by the Kuiper test, we proceed to compute the proper

Fisher parameters for each set of poles to the fractures. The software used to that end (Petrel 2008) works on a Schmidt stereonet frame (Fig. 1c).

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Table 1 summarizes the parameters determined for the fracture families. TABLE 1 PARAMETERS USED IN MODELING DISCRETE FRACTURE SYSTEMS DETAILED BY FAMILIES AND TWO STRATIGRAPHIC INTERVALS AT THE COGOLLO GROUP (APON FORMATION AND MARACA-LISURE FORMATIONS (MARLIS)

Fracture Length

Fisher Model Parameters Fracture Family

Fm Average

m Standard deviation

Max. Length

m

Average Well cut

m Dip

Dip Azimuth

Concentration

Apón 140 108 305 24 86 188 3.6 FAR MarLis 96 62 375 8 77 10 5.1 Apón 97 53 250 24 86 86 5.9 FR

MarLis 90 45 311 10 79 268.7 4.6 Apón 113 64 298 95 89 51.1 5.7 FT

MarLis 122 74 451 48 87 236 4.9 Apón 122 70 461 48 88 115 6.4 FLIY

MarLis 89 55 456 20 85 294 4 Apón 161 89 520 24 86 147 5 FInv

MarLis 178 112 382 14 83 322 3

At this point, the analysis of the connection between the system of fractures and the association of structures in the context of strike-slip tectonics has benefited from the methodology presented by Blumentritt et al. (2006). The Icotea fault shear zone provides hints linking the sinistral strike-slip tectonic style and the families of fractures in that area. One of the most noticeable is the correspondence between the orientation of fracture families and the orientation of comparable structures in the strain ellipsoid for sinistral strike-slip deformation, as seen in Figs. 1b and 1c. Core information gives further support about the presence of brittle shearing as a fracture forming mechanism (Perez et al. 2009).

Using core information, we determined the distribution of fractures at the different lithology types (Fig. 2). There were some limitations in the analysis, as core material was almost fully recovered at Apon but only partially at Maraca (upper-middle section) and Lisure (lower section). So for comparison purposes, we contrasted core data from the Apon section with the data supplied by the Maraca-Lisure section considered collectively. A proper comparison separating the distinctive features among the three formations is suggested for further development of the subject.

By agreement with the sedimentology team, the original core-based lithological descriptions were simplified to be handled in petrophysical terms by means of 10 lithotypes, of which we present the 5 most relevant in connection with the fractures (Figs. 2 and 3).

The whole thickness of the cored section with fractures is dominated by the intragrain limestone lithotype, followed by clayey limestones.

When the general distribution of fractures on such lithotypes is inspected, although the highest amount of fractures is located at intragrain limestones, the second highest fractured lithotype is limestone with vuggy porosity. This calls attention because that lithotype is a minor contributor to the core overall thickness, and certainly present in intervals collectively smaller than the ones with clayey limestones (Fig. 2).

Further investigation on the connection between the lithotypes and fracture variety is carried out focusing on the relative abundance of the fracture families in each of the lithotypes.

The results highlight some differences between Apon and the Maraca-Lisure sequence in the distribution of fractures of the five families (Fig. 3).

At Maraca-Lisure, tension fractures predominate on the clean carbonate units (over 50%), but antithetic Riedel shears prevail in the clayey limestones and are present in the dolomites, but do not occur at the Apon section. The presence of Y shears is almost negligible, even though they are also scarce at the Apon section. The Apon also contains a high proportion of tension fractures (over 40%) on the clean intragrain carbonate units, followed by antithetic Riedel shears. Riedel shears dominatewithin the remaining lithotype (clayey limestone).

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Fig. 2—Left: Thickness distribution of lithotypes of significant interest regarding fractures in the

well cored at Lagomar. Right: Distribution of fractures in the lithotypes of the well cored at Lagomar.

Fig. 3—Left: Maraca and Lisure formations. Distribution of the fracture families in the lithotypes of the well cored at Lagomar. Right: Apon Formation. Distribution of the fracture families in the lithotypes of the well cored at Lagomar.

Fracture Length, Spacing, and Intensity

Once the fractures are divided into families, the next step is to evaluate intensity and accumulation logs for fracture families by well (with correction for borehole deviation). For the analysis described from now on, we use information provided not only by fractures on an oriented core, but also data from three wells with image logs and six wells with dipmeters.

For every fracture family we also estimated the individual distributions of fracture length and spacing based on the analysis of these variables measured from structures (lineaments) at seismic scale. Maps of structural attributes, like semblance or curvature maps, referred to as the working horizons (at Maraca, Lisure and Apon) are the grounds for this job.

Fig. 4—Relationships between fracture legth and spacing. Obtained pairing distributions of measurement of these variables.

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We then proceed to compare and match the distributions (Fig. 4) using their similarity in frequency as a bridge between the

variables (Springer et al., 1968). Since we tone and pair logarithmic distributions based on frequencies, we called it the pairing frequency method, or pf method for short.

We converted fracture intensity at well scale to fracture spacing. Then, we proceeded to crosscheck the match between fracture spacing trends at both scales. To that end, for each fracture family we integrated fracture intensities obtained at seismic scale and at well scale in one percentage-paired distribution. Then, as we found high correlation indexes for the resultant distributions in either logarithmic or power laws, we saw evidence of the match of tendencies at both scales (Table 2). Table 2. Apon Formation. Well and Seismic spacing data (FSp) in meters. Equations and correlation indexes of distributions of fracture spacing integrating data at seismic and well fitted with logarithmic or power law trends.

R2 Best Fit

FAR 0.92 Freq= -7.377 ln(FSp) + 59.145

FT 0.81 Freq = -8.431 ln(FSp) + 60.4

FR 0.91 Freq = -9.396 ln(FSp) + 73.541

FR FINV 0.77 Freq = 51.366 FSp-0.287

FLIY 0.91 Freq = -10.68 ln(FSp) + 95.378

Fig. 5—Apon Formation. Well and seismic spacing data (FSp) in meters. Plot of distributions of fracture spacing integrating data at seismic and well scale fitted with logarithmic or power law trends.

With the functional connection between fracture length and spacing based on the analysis of these variables measured from

structures at seismic and well scale scale (Fig. 5), we devised the connection between fracture length and intensity. The length is computed as the inverse of the intensity, so we get values of fracture intensity to the fractures of specific length provided by the 3D geomodeler software. We proceeded in such way not only by the study of the results presented on Table 2 about the match of fracture spacing trends at well and seismic scales, but also by the evidences that at the Icotea fault shear zone, the fractures at seismic, well, and even at micro-scales corresponds to structures associated to deformation under strike-slip tectonism (Perez et al., 2009).

At seismic scale, the reference for the dimensions of the fractures of each family, were estimated using the lengths of the parallel lineaments measured on curvature maps on Maraca and Apón. These lineaments were interpreted as traces of faults in these horizons (Nissan et al. 2006). In our case, the average high angle dip of the fractures at seismic and well scale and the low dip of the horizons support the use of the fracture traces at the horizons as a reference for a proxy of the true fracture length and spacing. To make this approach work for a study that deals with fractures of families that are not subvertical, the traces should be measured on tilted planes orthogonal to the average fracture dip direction.

For purposes of statistically significant data handling at least 25 measurements (Gemignani, 1998) of fracture lengths and spacing per family were performed. Using the resulting logarithmic equations (Van Dijk et al, 2000; Koike and Ichikawa,

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2006) from Table 2, we calculated the frequency of fractures of sizes smaller than the seismic resolution but bigger than well resolution (Ekneligoda and Henkel, 2006).

Average fracture lengths and the corresponding standard deviation were obtained using measured fracture lengths and their frequency data.

The method from Ozkaya (2003) was used as a reference to estimate average lengths of fractures from image logs or, as in our case, from core information (average well cut, Table 2). This method provides a reference range of fracture lengths traversed by wells, and we consider it useful to link average fracture dimensions with other properties derived from well data, like average spacing, intensity, or porosity.

We have already used fracture intensity from well data to link fracture spacing at well and seismic scale. To proceed further with the integration among fracture properties at well scale, we needed a statistical study of the features of fracture intensity between the fracture families defined by stratigraphic interval. One recommended starting point is boxplots (Montgomery, 1991; Berk and Carey, 2000). Fig. 6—Boxplots of distribution of fracture intensity values in mm-1 (right) and its logarithms (left), discretized by fracture family and stratigraphic interval. Dash line: Mean value. Black circle: Low outlier. White circle: High outlier.

As seen in Fig. 6, the boxplots of the intensity indicate that antithetic Riedel shears at the Apon section display the highest

intensity mean value and interquartile range by fracture and formation. Nevertheless, at Maraca-Lisure the highest intensity mean value and interquartile range is presented by tension fractures.

Most of the fracture families present interquartile ranges of fracture intensity smaller than antithetic Riedel shears at Apon and tension fractures at Maraca-Lisure.

The distribution of intensity values by fracture family and formation displays different degrees of dispersion, but most of them have small interquartile ranges and positive skews. Inspecting the boxplots for the distribution of the logarithms in Fig. 6 (right), we found they still displayed some asymmetry and differences between the mean and the median, so we prefer to further investigate a logarithmic rather than a log-normal fit of their distributions.

The results shown in Fig. 7 (left) confirm the adjustment to logarithmic fits for most of the distributions of intensities.

Fig. 7—Intensity values (mm-1) (left) and Porosity (in fraction, at right) arranged for a display in a relative frequency plot. Logarithmic fit of the distributions exhibit high correlation indexes (table inside the plot) for most of the fracture families.

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Back to Fig 6, the visual look of the boxplots of the distributions suggests noteworthy differences between the means. To settle the point, a variance analysis and a matrix of mean differences is a usual statistical procedure to follow (Berk and Carey, 2000). The analysis of variance and the matrix of mean differences were made using the excel complements Data Analysis Toolpack and StatplusV2.0, respectively (Berk and Carey, 2000).

With a critical value of 1.89 but an F value calculated as 21.46, the output of the respective variance analyses indicates a very low probability for the null hypothesis to be true. So we accept that the average intensity is not the same for each fracture family regarded by stratigraphic interval.

The complete analysis of the differences of average intensities among the fracture families requires the use of the matrix of mean differences (Table 3).

TABLE 3—FRACTURE FAMILIES BY STRATIGRAPHIC INTERVAL. MATRIX OF MEAN DIFFERENCES FOR THE DISTRIBUTION OF FRACTURE INTENSITIES. SIGNIFICANT MEAN DIFFERENCES ARE HIGHLIGHTED IN RED

Pairwise Mean Difference

FAR ML

FAR APON

FT ML

FT APON

FR ML

FR APON

FINV ML

FINV APON

FLIY ML

FLIY APON

FAR ML 0,000 -0,009 -0,003 0,000 0,003 0,002 0,002 0,001 0,003 0,003

FAR APON 0,000 0,006 0,009 0,012 0,011 0,011 0,010 0,012 0,012

FT ML 0.000 0.003 0.006 0.005 0.005 0.004 0.006 0.006

FT APON 0.000 0.003 0.002 0.002 0.001 0.003 0.003

FR ML 0.000 -0.001 -0.001 -0.002 0.000 0.000

FR APON 0.000 0.000 -0.001 0.001 0.001

FINV ML 0.000 -0.001 0.001 0.001

FINV APON 0.000 0.002 0.002

FLIY ML 0.000 0.0003

FLIY APON 0.000

At Maraca Lisure, 3 out of 10 significant differences of average intensity appear among fracture families. Tension fractures

and Y shears present the greatest difference of this variable At Apon, the greatest difference is seen between antithetic Riedel shears and Y shears. At this section 4 out of 10

significant differences of average intensity appear among fracture families. Antithetic Riedel shears display the only significant difference in average fracture intensity compared by itself and by a

different stratigraphic interval. In general, 15 out of 45 significant differences of average intensity appear among fractures separated by both family and stratigraphic interval.

Fracture Porosity and Permeability

Using the record of fracture porosity obtained from logs by petrophysical means is feasible, through a depth match, to identify the correlative values of intensity for each fracture already categorized inside one of the five families.

For their convenient way to compare statistical parameters among the different fracture families, we suggest boxplots as one of the best practices to make the statistical analysis of the distribution of values of porosity and permeability for each fracture family.

Fig. 8—Boxplots of distribution of fracture porosity values (right) and its logarithms (left), discretized by fracture family and stratigraphic interval. Dash line: Mean value. Black circle: Low outlier. White circle: High outlier.

As seen in Fig. 8, the distribution of porosity values by fracture family and formation displays different degrees of

dispersion, but most of them have positive skew and outliers. This suggests to investigate the distribution of their logarithms. The resultant boxplots for most of the families display comparatively smaller skewness and fewer outliers than for the original

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distributions, but the asymmetry of the distributions and mismatches between the means and the medians indicate to look for a logarithmic rather than for a log normal fit for them.

In spite of the limitations impossed by the conditions of well data collection, the coincidence of logarithmic fits in both fracture intensity (Fig. 7, left) and porosity (Fig. 7, right) suggest to look for a functional connection between them like the ones found from previous studies but under less complicated settings (Cohen and Mercer, 1993; Nelson 2001). We came across a high-index correlation method that works with data distributions of these parameters from well data and hopefully would become a best practice in the field of fracture reservoir characterization.

Reviewing the boxplots of the porosity values (Fig. 8), the Riedel shears at the Maraca-Lisure section display the highest porosity mean value by fracture and formation. Nevertheless, at Apon, the highest porosity mean value is presented by the Y shears, closely followed by the tension fractures.

The lowest interquartile porosity corresponds to compressional shears at Maraca-Lisure, and this fracture family also presents the lowest porosity scores at Apon. The outcome of the analysis of variance for the fracture porosities indicates:

• The variability of the porosity within fracture families (0.038) is almost one order of magnitude bigger than the variability of the porosity between fracture families (0.006).

• According to the null hypothesis, the ratio between the two variances should follow an F distribution with (n,m)=(9,617) degrees of freedom. F is computed as 11.47 using the porosity values of the fracture families. The probability obtained (1.02 10-16), is significantly lower than 0.05. The null hypothesis is rejected, and we accept that the average porosity is not the same for each fracture family regarded by stratigraphic interval.

Further and detailed analysis of the differences of average porosities among the fracture families requires the use of the

matrix of mean differences (Table 4).

TABLE 4—FRACTURE FAMILIES BY STRATIGRAPHIC INTERVAL. MATRIX OF MEAN DIFFERENCES FOR THE DISTRIBUTION OF POROSITIES. SIGNIFICANT MEAN DIFFERENCES ARE HIGHLIGHTED IN RED

Pairwise Mean Difference

FAR ML

FAR APON

FT ML

FT APON

FR ML FR APON

FINV ML

FINV APON

FLIY ML

FLIY APON

FAR ML 0.000 -0.001 0.002 -0.005 -0.010 -0.003 0.006 0.003 -0.002 -0.007

FAR APON 0.000 0.003 -0.003 -0.008 -0.001 0.007 0.004 0.000 -0.006

FT ML 0.000 -0.007 -0.012 -0.005 0.004 0.001 -0.004 -0.009

FT APON 0.000 -0.005 0.002 0.011 0.008 0.003 -0.002

FR ML 0.000 0.007 0.016 0.012 0.008 0.002

FR APON 0.000 0.009 0.005 0.001 -0.005

FINV ML 0.000 -0.003 -0.007 -0.013

FINV APON 0.000 -0.004 -0.010

FLIY ML 0.000 -0.006

FLIY APON 0.000

From Table 4 we draw information about the differences of the porosity averages between specific sets of fracture

families. The greatest difference is between Riedel shears at Maraca-Lisure and Compressional shears at the same interval. At Maraca Lisure, there are six out of ten significant differences of average porosity among fracture families. At Apon, the greatest difference is seen between Compressional shears and Y shears. At this section there are three out of

ten significant differences of average porosity among fracture families. In general, there are eigthteen out of forty five significant differences of average porosity among fractures separated by

both family and stratigraphic interval. Tension Fractures is the only fracture family that displays a significant difference in average porosity compared by itself by a different stratigraphic interval.

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The outcome of the respective analysis of variance for fracture permeabilities, as deduced from Table 6, also supports that the average permeability is not the same for each fracture family regarded by stratigraphic interval.

Fig. 9. Boxplots of distribution of fracture permeability values (rigth) and logarithms (left), discretized by fracture family and stratigraphic interval. Dash line: Mean value. Black circle: Low outlier. White circle: High outlier

As seen in Fig. 9, the distribution of permeability values by fracture family and Formation exhibits different degrees of

dispersion, but there are positive and negative skews and the distributions of only three families present high outliers. These features have little change in the distributions of their logarithms.

Compressional shears at the Maraca-Lisure section and also at the Apon Section display the highest permeability mean value by fracture and Formation. Lowest interquartile porosity Fig.s correspond to Riedel shears at Maraca-Lisure, while Y shears present the lowest permeability scores at Apon.

There is a striking closeness between the median of the permeabilities of Anthitetic Riedel shears and the third quartile. This fact is relevant since indicates that more than 50% of the fractures of this family present permeabilities above 550 md. Notice that quite contrary is the case of the Y and Riedel shears, with medians close to the first quartile and near the low permeability values.

The visual look of the boxplots of the distributions suggests significant differences between the means, what is confirmed by the respective analysis of variance. (F= 17.4 with a Critical value of only 1.9).

The analysis of variance for the permeabilities presents a very low probability (7.48 10-26) for the means to be similar. The null hypothesis is rejected and we accept that the average permeability is not the same for each fracture family regarded by stratigraphic interval.

Further and detailed analysis of the differences of average permeabilities among the fracture families requires the use of the matrix of mean differences (Table 5).

TABLE 5—FRACTURE FAMILIES BY STRATIGRAPHIC INTERVAL. MATRIXES OF MEAN DIFFERENCES FOR THE DISTRIBUTION OF PERMEABILITIES. SIGNIFICANT MEAN DIFFERENCES ARE HIGHLIGHTED IN RED

Pairwise Mean Difference

FAR ML

FAR APON

FT ML FT APON

FR ML FR APON

FINV ML FINV APON

FLIY ML

FLIY APON

FAR ML 0.00 7.16 -26.76 95.44 241.13 87.34 -125.41 -85.39 79.18 235.31

FAR APON 0.00 -33.92 88.28 233.97 80.18 -132.57 -92.56 72.02 228.15

FT ML 0.00 122.20 267.89 114.09 -98.65 -58.64 105.94 262.07

FT APON 0.00 145.69 -8.10 -220.85 -180.84 -16.26 139.87

FR ML 0.00 -153.79 -366.54 -326.53 -161.95 -5.82

FR APON 0.00 212.75 -172.74 -8.16 147.97

FINV ML 0.00 40.01 204.59 360.72

FINV APON 0.00 164.58 320.71

FLIY ML 0.00 156.13

FLIY APON 0.00

From Table 5 we draw information about the differences of the permeability averages between specific sets of fracture

families. Like in the case of average porosity, the greatest difference is between average permeability of Riedel shears at Maraca-Lisure and Compressional shears at the same interval.

Maraca-Lisure has 9 out of 10 significant differences of average permeability among fracture families. At Apon, the greatest difference is seen between Compressional shears and Y shears. At this section also has 9 out of 10

significant differences of average permeability among fracture families. In general, 37 out of 45 significant differences of average porosity appear among fractures separated by family and

stratigraphic interval. Tension Fractures, Riedel shears and Y shears display significant differences in average permeability compared by themselves and by different stratigraphic intervals.

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Correlation between fracture intensity and porosity

Previous studies (Cohen and Mercer, 1993; Nelson, 2001) have shown a direct relationship (Eq. 1) between fracture spacing (S), aperture (e), fracture porosity (φf or PHIF). The following equation is based on that presented in Nelson (2001), and correlates porosity, taken as a fraction instead of percentage, with the opening and spacing variables.

)/(f eSePHIF += = φ ……………………… (1)

Since fracture spacing is the inverse of fracture intensity (I), it follows that there is a direct relationship between fracture

porosity and intensity (Eq. 2):

)/1/(f eIePHIF += = φ ………………..…….. (2)

Furthermore, Ortega et al. (2006) have also shown that fracture spacing is in functional connection with the opening of

fractures at different scales. We use Eq. 1 to calculate fracture porosity (PHIF) corresponding to the outcrop measurements of fracture spacing and

aperture for tension fractures provided by Ortega et al. (2006). Next, we estimate the corresponding fracture intensity as the inverse of the spacing. Hence we are able to plot the corresponding regression line between PHIF and fracture intensity for the same tension fractures (Green line, Fig. 10)

Then, on the same graph we plot the cloud of points and its regression lines for the fracture families at the Cogollo Group (Fig. 10).

The key point is a match based on rearranging porosity (in fraction) and intensity (mm-1) distributions in an opposite sense before correlating them. Let’s call this procces the r-pi method for short. In Table 6 we show the advantage of this method over the straightforward depth match of porosity versus intensity with the comparison of regression coefficients provided by each method. Fig. 10 shows the results after the reordering procedure is followed. There we see fracture porosities as inversely proportional functions of fracture intensities for both shear and tension fractures. In this case a logarithmic scale is set up for both axes, and the porosity-intensity functions follow power or logarithmic laws (Table 6).

Fig. 10 Logarithmic or Power regresion lines of the distributions of fracture porosities versus intensities measured at the Cogollo Group for shear fracture families in wells at the Icotea Fault shear zone. Power regression line for Tipe I Fractures (in Green) based on Ortega et al. (2006).

Fig. 10 displays logarithmic or power law correlations of the clouds of points for every fracture family when plotted over axes in logarithmic X-Y scales. We see the comparison between them and a power regression line (in Green) for tension fractures based on the reformulation of the regression line for fracture spacing and aperture devised by Ortega et al.(2006).

The outcome indicates that for a given porosity, Y shears have the lowest intensity. Depending upon the section and range of values considered the antithetic Riedel shears, Tension Fractures or even compressional shears could have the highest intensity for a given porosity. This suggests that for a certain fracture dimension or size among families of fractures, Y shears

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have the lowest porosity, while Antithetic Riedel shears, Tension Fractures o even compressional shears could have the highest porosity.

TABLE 6—FRACTURE FAMILIES BY STRATIGRAPHIC INTERVAL

R2 Regression after reorder R

2 Depth match Regression

FAR ML 0.83 FI = -7E-04 ln(PHIF) - 0.0022 0.10 FI = 0.0004 PHIF-0.218

FT ML 0.93 FI = (10-06

) PHIF-1.342

0.61 FI = 5 (10-06

) PHIF-1.087

FR ML 0.79 FI= -4 (10-04

) ln(PHIF) - 0.0011 0.71 FI = 3 (10-05

)PHIF-0.753

FINV ML 0.88 FI = = -5 (10-04

) ln(PHIF) - 0.0023 0.01 FI = -5 (10-05

) ln(PHIF) + 0.0012

FLIY ML 0.73 FI = 4 (10-05

) PHIF-0.4321

0.23 FI =0.0001 PHIF-0.242

FAR APON 0.88 FI = 2 (10-06

) PHIF-1.4282

0.65 FI = 6 (10-06

) PHIF -1.228

FT APON 0.90 FI = 6 (10-06

) PHIF-1.1969

0.57 FI = -0.004 ln(PHIF) - 0.0144

FR APON 0.98 IFRA = 4 (10-06

) PHIF-1.0903

0.56 FI = -0.001 ln(PHIF) - 0.0046

FINV APON 0.86 FI = -6 (10-04

) ln(PHIF) - 0.0016 0.28 FI = 3 (10-05

) PHIF-0.303

FLIY APON 0.88 FI = 5 (10-07

) PHIF-1.4355

0.34 FI = -3(10-05

) ln(PHIF) – 8 (10-05

)

Modeling fracture aperture and permeability

The Petrophysics Team designed a fracture permeability model based on aperture that was applied to the fracture data obtained from well information and also to fractures at the 3D digital model.

The fracture aperture in the categories of each family was obtained as a function of porosity (PHIF) and spacing (S) of fracture by the formula: )/11/( PHIFSeAperture +−= = ……………………………………………………………(3)

This formula is obtained by solving the Eq. 1 with aperture as the dependent variable. Once the aperture is obtained, it is

necessary to calculate the probability of fracture (PF) and the permeability according to Eqs. 10 and 11.

))0084654285.0/)028516233.0((1/(584919.13851547.12 +−−+−= AperturaEXPPF ……..(4)

))043830136.0/)76778648.0((1/(6405.580 −−+= PFEXPtyPermeabili …………………………(5)

By a straightforward substitution, we can link aperture and permeability via Eq. 4 and Eq. 5 to directly plot their correlative

array. The result (Fig. 11) is a curve with a sigmoidal shape where the distribution of fractures of the different families can be inspected and analyzed.

Fig. 11—Apon formation. Distribution of permeability as a function of the probability of fracture for every fracture family, which is in turn based on aperture.

Fig. 11 shows that at Apon the high range of extreme values of permeability is dominated by Antithetic Riedel shears, followed by Compressional shears. This agrees with the outcome of the analysis of boxplots (Fig. 9). The proximity between the median and the third quartile at the permeability range over 550 md explains this outcome. The broad interquartile range of the distribution of permeability for Antithetic Riedel shears also explains its occurrence all along the aperture-permeability curve. As mentioned in connection with Fig. 9, we expect high occurrence of Y shears to be concentrated along low range values of permeability.

12 SPE 130745

Once the model is ready, we proceed to propagate it through the digital fracture network already constructed by the use of the parameters provided by Table 1. This fracture network contains fractures of different sizes, but their geometries are set up by the modeler, preferentially by using some reference from the seismic expression of the fractures. We could, f.e., specify the fractures as rectangles with the width equal to twice the length (L). The length is then directly calculated from the Area of the fracture with the expression L = √(Area/2). Once fracture Spacing is calculated from the fracture Length with the correlations given by pf method, we start a sequence of operations to get their porosity and permeability. Porosity (PHIF) is derived from fracture intensity applying the correlations provided by the r-pi method. Using from Eqs. 3 to 5, we get fracture permeability from the already known variables S and PHIF.

Fig. 12—Lagomar. Apon Formation. Family of Riedel fractures. Distributions of values for geometric and petrophysical parameters.

Fig. 12 shows the histograms with the distributions of values for the geometrical and petrophysical parameters of Riedel fractures already available as digital 3D entities. The parameters are area, length (L), spacing (S), porosity (PHIF), aperture, probability of fracture (PF) and permeability. The numbers on the arrows indicate the sequence followed to obtain the parameters. The logarithmic nature of the attributes considered is visible in the histograms with the distribution of their values. Summary and Discussion

In the Cogollo Group, fractures are present on 5 out of 10 lithotypes studied from well core information. These fractured lithotypes correspond to kinds of carbonate-related lithologies, while the very low-fractured or unfractured litotypes are related to sandstone and shale related lithologies. This means that the lithologic tock type control the mechanisms of fracturing. This case being the usual brittle condition of the rocks as the crucial factor involved.

The coincidence of the predominance of tension fractures in most of the lithotypes both at Apon and Maraca-Lisure is significant. The low strength of brittle rocks to tension fracturing (Zoback, 2007) and the rotation of Riedel shears to develop into tension fractures with the progress of shearing (McClay and Dooley, 1994) are conditions likely linked with this statistical outcome.

The scarcity of Y shears, which are parallel to the main boundaries of the shear zone, is noteworthy. Nevertheless, lab and field evidences indicate that shearing in the Y direction as a result of deformation of a sedimentary cover over a rigid basement has a strong contribution of R and R' shears for its definition, which could be a main reason behind the low amount of this kind of shears in the samples (Davis et al., 1999).

The statistical study of fracture-related features allows us to define which ones are or not directionally and/or stratigraphically driven by the comparison of the parameters of their distributions. The study of the matrix of mean differences indicates that fracture permeability is a highly anisotropic feature, strongly driven not only by the factor of the direction of the fracture family considered but also for the stratigraphic section. Fracture porosity and intensity are less anisotropic than fracture permeability, by being less controlled than permeability by the factors of direction and stratigraphy. One appealing issue derived from the statistical analysis is that Anthitetic Riedel shears are present in high proportion biased toward the range of high permeablities, disregarding the Formation considered. A would-be confusion due to the broad range of permeability values encompassed by their specimens is easily clarified by inspection of the position of the median at the respective boxplot. The relevant point here is the influence this fact has on the design of the best strategy to take advange of the reservoir properties. Production from wells drilled in the direction that connects the most Antithetic Riedel shears would benefit from the high relative quantity of fractures of this family with favorable permeability conditions to inflow. The opposite could be said regarding Y shears at Apon and Riedel shears at Maraca-Lisure. These fracture group exhibit permeability characteristics indicating a connection with sealing and low-transmisibility features.

SPE 130745 13

The base to apply the proposed r-pi method to correlate fracture porosity and intensity is to improve in a wise way the mode by which the software calculates fracture intensity from well data, regarding only spatial orientation and disregarding fracture size and stratigraphic location. In the work of Ortega et al. (2006), a power law aperture-spacing relationship is obtained regarding not only spatial orientation but also size and mechanical stratigraphic connections among the fractures of the same family. So rearranging in opposite sense and pairing the distributions of fracture porosity and intensity from well data imitates the natural tendency they follow in nature, leading to a model that replicates measurements in these parameters as if they were made accounting for fracture size and stratigraphic location. Our starting point to apply the method is confident, log and core- derived fracture porosity measurements. The key of the method is to rearrange in reverse order the well log-derived fracture intensities and to match the resultant distributions with the fracture porosity distributions. Our results show that high correlation indexes give support to the resultant models for five shear fracture families evaluated at different stratigraphic intervals. When the results of our model are compared with the one derived from Ortega et al. (2006), a word of caution should be mentioned. The Ortega et al. (2006) result is taken as an estimate of fracture intensity and porosity in shallow regions geologically dominated by Type I fractures, while ours is as an estimate of shear fractures at depth.

The tendency and definition of the r-pi regression lines for the shear fractures measured at the Icotea fault plot with some differences with the regresion line for the joint fractures measured at surface outcrops by Ortega et al. (2006).

The position in the plot of the r-pi regresion lines for the Icotea fault shear fracture families indicate that for the same porosity the intensity of the shear fractures at depth is smaller than for the joint fractures at surface. Does this means that the opening of the joint fractures at surface is greater than that of the studied shear fractures of similar size at depth?. We left the conjecture open for future research in similar cases. The point to clarify in further research is whether the real intensities for every porosity are similar or dissimilar to the ones obtained, provided that near-vertical well trajectories should collect information from fractures from different low dipping beds rather than from the same bed.

Another point to consider is that the spacing between fractures measured for the software within the same family has different sizes. In any case, we have the reference of a real porosity-intensity curve for Type I fractures provided by the reformulation of the outcomes of Ortega et al. (2006). Nevertheless, the potential use for using the regression line for joints in modeling porosity-intensity trends of shear fractures instead of the r-pi regression lines found for shear fractures would introduce a bias in the model. The r-pi regression lines for the Icotea fault shear fracture families have slopes smaller than the one for the regression line for joint fractures at surface. This indicates differences in the rate of correlative change between porosity and fracture intensity. In other words, a change in porosity values of one order of magnitude for the studied joint fractures corresponds to a change in order of magnitude of fracture intensity greater than that for shear fractures. So, for the joint fractures studied by Ortega et al. (2006), the rate of change of fracture aperture with fracture size is greater than for most of the studied shear fractures. At the Maraca-Lisure section, the highest r-pi slope corresponds to tension fractures and the smallest to compressional fractures, with the slope of the other families spanning in between. With the exception of the Compressional shears, at the Apon section the slopes of the other r-pi regression lines differ less than in the overlying section.

The main weakness we face using well data is the lack of control on the fracture geometry and stratigraphic location at high resolution. We devise the r-pi method as an attempt to keep the condition of the scale independence of fracture intensity and porosity over well data. Nevertheless, there is still uncertainty about a proper match between fracture porosity and its truly associated fracture intensity. The improvements of the porosity-intensity correlation ratios using the r-pi method may just indicate a proxy to the real correlation better than just the usual depth-based match of these properties.

A match between fracture spacing trends at seismic scale and those deduced from data at well scale is a plus for the reliability of the model. This worked in our case, but this connection might not necessarily hold in other geological settings. In this sense, this kind of cross validation of the method is limited to consideration as a general and global application. One big advantage of the method presented here is the ease with which it deals with the usual outcomes of fracture reservoir modelling.

The straighforward statistical study of fracture features like intensity and petrophysical parameters and the methods presented to connect them, like the r-pi, allows us to reduce the complexity of modelling these factors by more sophisticated means. The savings in time and resources are benefits that we think will encourage readers to follow and adopt the techniques presented.

We are confident that the fast progress in well logging and high resolution seismic technologies will bring into being better and more confident approaches to estimate fracture geometries and its connection with the stratigraphical setting. If so, enhancements of the method proposed in this paper will be available in the short term. References Berk, K. and Carey, P. 2000. Data Analysis With Microsoft Excel. Thompson Learning. Blumentritt, C., Marfurt, K., and Sullivan, E. 2006. Volume Based Curvature Computations Illuminate Fracture Orientations, Lower-Mid

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