spe 121136 modeling mud-filtrate invasion effects on resistivity … · 2014-12-11 · typical...

SPE 121136

Modeling Mud-Filtrate Invasion Effects on Resistivity Logs to Estimate Permeability of Vuggy and Fractured Carbonate Formations Luis Javier Miranda*, SPE, Carlos Torres-Verdín, SPE, and Jerry Lucia, SPE, The University of Texas at Austin

Copyright 2009, Society of Petroleum Engineers

This paper was prepared for presentation at the 2009 SPE EUROPEC/EAGE Annual Conference and Exhibition held in Amsterdam, The Netherlands, 8–11 June 2009.

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 We develop and validate a new method to diagnose and estimate secondary porosity and absolute permeability of fractured and vuggy carbonate formations based on the numerical simulation of the process of mud-filtrate invasion. The method includes the geological characterization of core laboratory data and their integration with well logs and fluid production measurements. We apply the new method to the interpretation of data acquired in a carbonate reservoir in the Barinas-Apure Basin in southwest Venezuela. The latter reservoir behaves as a triple-porosity petrophysical system which exhibits inter-crystalline, intra-crystalline, moldic, vuggy (connected and non-connected) and fractured porosity, all embedded in a tight matrix. Rock-core data and wellbore resistivity images indicate that vugs are the mayor component of secondary porosity while fractures and interconnected vugs account for most of the permeability.

The initial phase of our interpretation method consists of integrating core measurements with conventional and non-conventional well logs to calculate static and dynamic petrophysical properties via standard carbonate evaluation procedures. Starting with the calculated petrophysical properties, we simulate the process of invasion with both water- and oil-base muds. Resulting spatial distributions of water saturation and salt concentration in the near-borehole region give rise to spatial distributions of electrical resistivity which are used to numerically simulate laterolog and induction apparent resistivity logs.If the input values of porosity and permeability are not correct, the simulation of mud-filtrate invasion will result in a poormatch of resistivity logs. In such cases, we update porosity and permeability until securing a good match between measurements and simulations. This procedure was tested on several key wells with and without core measurements, wellbore resistivity images, and well-testing measurements. We conclusively find that our final estimates of porosity and permeability are in good agreement with the properties of the global petrophysical system. Differences between porosity and permeability before and after simulation of the process of invasion are reliable indicators of presence and influence of vugs and/or fractures in the displacement of hydrocarbons by mud filtrate.

Introduction Permeability estimation is one of the most important steps of reservoir characterization. Even though there are reliable methods to estimate porosity and fluid saturation, reliable permeability estimation is difficult, especially in carbonate reservoirs. In heterogeneous reservoirs with variable rock composition and petrophysical properties, integration of core measurements and well logs is necessary to predict petrophysical properties in zones with no or scarce core samples. In this study, we estimate permeability via numerical simulation of the process of mud-filtrate invasion that takes place in complex reservoirs with a triple-porosity system (Fig. 1). In so doing, we numerically simulate dual-laterolog and array-induction resistivity logs to validate the estimation of petrophysical properties. Our method includes the geological characterization ofcore measurements as well as integration of well logs and production data.

We consider field data acquired in a reservoir located in the Barinas-Apure petroleum basin of southwest Venezuela, which is a prominent hydrocarbon producer in the Borburata field. Facies in this reservoir consist of sandstone, mixed sandstone-dolostone, dolostone, pelecypod limestone, foraminiferal limestone-siltstone, and shale. Sedimentological studies describe these facies to represent deposition in a shallow-marine carbonate platform (Kupecz et al., 2000; Méndez, 2002). The volumetric concentration of each facies varies depending on the zone across the field. One of the most important observations is that the best oil-producing wells are located in zones with large amounts of dolomite, which in turn are associated with an increase of secondary porosity (interconnected vugs and fractures). Compared to previous characterization efforts in the same * Now with Petróleos de Venezuela, S.A. (PDVSA)

2 SPE 121136

reservoir (Kupecz et al., 2000), our preliminary results show that the new method to estimate permeability is reliable in reservoirs with secondary porosity (vugs and fractures). Furthermore, the estimated permeability agrees well with permeability estimated from pressure transient tests (which is believed to be representative of the triple-porosity system). Weperformed the above estimation with the integration of all available information, thereby reducing uncertainty commonly associated with standard carbonate interpretation methods.

Fig. 1. Typical distribution of porosity in the “O BOR-2E” reservoir. The rock matrix is very tight, exhibiting porosities from 2 to 10%, whereas matrix permeability varies between 0.01 mD and 100mD.

General Description of the Hydrocarbon Field Fig. 2 shows the reservoir “O BOR 2E” in the Borburata field, located in the Barinas-Apure petroleum basin of southwest Venezuela. The field, with a total area of 14 Km² (3459 Acres), includes a group of smaller zones delimited by faults. There are two additional reservoirs in the Borburata field: “Gobernador” and Escandalosa “P.” However, the carbonate reservoir accounts for most of the hydrocarbon production of the Borburata field. The field was discovered in 1994 when the well BOR-2E was completed in the “O BOR 2E” reservoir. It displays wide variations of rock composition and petrophysical properties and comprises a triple-porosity system (matrix+vugs+fractures), according to observations and analysis of rock-core measurements and non-conventional well logs. There are other fields that have produced from the “O BOR 2E” reservoir. However, the Borburata field possesses the highest cumulative and contemporary production (Miranda, 2008). Furthermore, the amount of secondary porosity that exists in the field has not been observed in any other field in the Barinas basin, thereby making it the most attractive field in the entire area. Fig. 2 describes the quality of reservoirs for each field using a color scale from high to low quality (Miranda, 2008). Fig. 3 shows a structural map of the main reservoir area together with a description of available measurements (Miranda, 2008).

Sedimentary Model Facies in the “O BOR 2E” reservoir are sandstone, mixed sandstone-dolostone, dolostone, pelecypod limestone, foraminiferal limestone-siltstone and shale. Fig. 4 shows results from sedimentological studies that describe these facies as representative of deposition in a shallow-marine carbonate platform (Kupecz et al, 2000; Mendez, 2002). This depositional model was also confirmed by a recent study (Omni-PDVSA, 2007), which indicates that the carbonate sediments of the Escandalosa “O” Member predominantly consist of thinly- to thickly-bedded dolostones that were originally deposited as grain-rich to mud-rich limestone (e.g., skeletal grainstone and packstone, peloidal packstone and wackestone) on a shallow shelf. The volumetric concentration of each facies varies depending on location across the field. One of the most important observations is that the best oil-producing wells are located in zones with large amounts of dolomite that are also associated with an increase of secondary porosity (interconnected vugs and fractures). According to the stratigraphic column for the “O BOR-2E” reservoir, oil-producing formations belong to the Cenomanian-Turonian Escandalosa formation (Kupecz et al., 2000).

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SPE 121136 3

Fig. 2. Map showing the field location in the Barinas-Apure petroleum basin of Southwest Venezuela. Colors designate high and low quality reservoirs in the Barinas area. The Borburata field is highlighted in red (excerpted from Miranda, 2008).

Fig. 3. Structural map of the main reservoir area showing the most important information available for each well in the Borburata field (excerpted from Miranda, 2008).

Fig. 4. Depositional model for the “O” member of Escandalosa formation (excerpted from Mendez, 2002).

Oil BasinsMaracaibo-Falcon BasinBarinas-Apure BasinEastern BasinMargarita Basin

Colombia

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4 SPE 121136

Method of Core-Log Integration Many interpretation methods are available to estimate permeability; most of them are based on empirical correlations between permeability, porosity, irreducible water saturation, pore throat radius, etc. According to Babadagli and Al-Sami (2004) permeability estimation methods can be grouped into two categories: pore-scale models and field-scale models. Most of the studies at the pore-level were performed on clastic rocks where the grain and pore properties were modeled quantitatively. The application of the latter models to carbonate rocks is moot because of their dependence on pore and grain properties. In general, it is difficult to accurately characterize complex carbonate reservoirs through grain and pore properties (Babadagli and Al-Sami, 2004). Integration of core and log data is necessary to estimate permeability. We analyzed some of the methods discussed in the open technical literature (Babadagli and Al-Sami, 2004; Jennings and Lucia, 2003; Salazar et al., 2006; Hurley et al., 1998; Gomaa et al., 2006) to assess their adequacy in the interpretation of the Borburata field. The large variability observed in rock composition and petrophysical properties, coupled with a high degree of spatial heterogeneity, make it necessary to use non-conventional interpretation methods to estimate permeability.

In this work, we first implement a definition of rock types and establish a relationship with the geological model (structural and stratigraphic), facies, and spatial distribution of petrophysical properties. Second, we quantify the influence of mud-filtrate invasion on the spatial distribution of fluids in permeable rocks in the near-wellbore region using petrophysical properties calculated from well logs and core-log integration. The analysis performed in key wells is facilitated by the abundance of information, such as core measurements, non-conventional logs and pressure transient measurements. They enable the comparison of results against data acquired at different scales. Third, results obtained from the first approach aremodified with petrophysical properties for the complete system (matrix+vugs+fractures) observed in rock-core measurements and in non-conventional well logs. This approach enables the estimation of secondary porosity (vugs and fractures) and the accurate estimation of permeability in the carbonate reservoir.

Simulation of Mud-Filtrate Invasion in the Key Well The simplest case of study considers a well (BOR-12) which includes core data and was logged with a DLL tool and drilled with WBM of 33000 ppm salinity. Initial properties of the reservoir in well BOR-12 were calculated with a multi-mineral method (Dewan, 1983; Miranda, 2008). Subsequently, we applied initial petrophysical values to the base case and numerically simulated resistivity measurements via the procedure described by Salazar et al., (2006) and adapted to DLL measurements. For the numerical simulation, we implemented a Brooks-Corey’s model adjusted to rock-core data to describe capillary pressure and relative permeability (Corey, 1994).

Fig. 5. Geometrical description of the finite-difference grid implemented for the simulation of the process of mud-filtrate invasion. The figure also describes the flow units included in the model.

Fig. 5 describes the finite-difference grid used for the simulation of both mud-filtrate invasion and resistivity logs. The figure also includes the three flow units included in the simulations. Each layer has specific values of porosity, absolute permeability, and irreducible water saturation, among others. The simulation grid implemented here consists of 30 x 31 nodes in the radial (r) and vertical (z) directions, respectively. In addition, the grid consists of logarithmically spaced nodes to properly capture the time evolution of mud-filtrate invasion near the wellbore. Miranda (2008) describes the parameters included in Brooks-Corey’s equations and summarizes the parameters used in the BOR-12 case to model capillary pressure and relative permeability.

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SPE 121136 5

Fig. 6 shows simulation results based on permeability measured on rock-core measurements (left-hand side panel) and those for the case of permeability estimated from pressure transient measurements (right-hand side panel). Matching of the measured resistivity logs required an increase of both permeability and porosity as indicated in the figure. The increase of porosity is explained by the fact that, according to the interpretation of core data, a massive dolomitization took place in thesimulated interval. Sin-sedimentary and diagenetic fractures are also observed in cores as well as a high density of vugs with a wide variety of sizes (micro to megavugs). The main porosity on the simulated depth interval is due to the system of vugs which are also connected to the rest of the porosity included in both matrix and fractures. Fig. 7 shows some of these features on a core sample acquired in well BOR-12. In addition, core inspection indicated a high dolomitization process derived from an arid tidal flat (sabkha) environment (Fig. 6). This is one of the main flow units in the well. Facies included here exhibit intercrystalline, intracrystalline, moldic and vuggy porosity, as evidenced by the thin sections shown in Fig. 7. The diameter of the vugs varies from millimeters to centimeters. Previous sedimentological studies (Kupecz et al., 2000; Méndez, 2002) indicate that most of the oil is stored in the afore-described types of porosity and is produced through intercrystalline and intracrystalline porosity and fractures,

Fig. 6. Numerical simulation of DLL measurements for well BOR-12. The left-hand side panel shows field (dashed line) and simulated (continuous line) resistivity curves for the case of permeability obtained from rock-core measurements. The right-hand side panel shows field (dashed line) and simulated (continuous line) resistivity curves for the case of permeability obtained from pressure transient measurements. In the second case, numerical simulations were performed with perturbation of porosity only.

Fig 7. Photograph of a core sample acquired in well BOR-12. The sample covers part of the depth interval considered in the numerical simulations of mud-filtrate invasion. White and red arrows indicate presence of vugs and fractures, respectively.

Previous studies performed on the same core (Corpro, 2000) indicate that fracture permeability is extremely variably, between 500 to 12000 mD. One of the most important conclusions from the Corpro study is that many of the fractures are related to vuggy zones. Aguilera (1995) and Lucia (2007) explain the amount of permeability provided by these fractures and interconnected vugs as well as their effect on total permeability. Improvement of permeability and porosity is due to the fact that fractures and vugs are important components of the storage and flow capacity of reservoirs with double or triple-porosity systems (such as the one under study). Similar results were described by Aguilera (1995) when studying a reservoir with a matrix permeability equal to 1mD which could be associated with an average permeability for the system equal to 14 mD as inferred from presence of vugs with approximate diameters of 0.05 in. Aguilera also described a reservoir with a matrix

a. k=4.33mD b. k=101.36mD

BOR-12

0 7.0cm

a. k=4.33mD b. k=101.36mD

6 SPE 121136

permeability of 1 mD that could have an average system permeability of 13.51 Darcies as inferred from the presence of 3 fractures, each one 0.01-in wide.

Fig. 8. Sedimentological description of Well BOR-12 showing the typical mineralogy of the matrix of the “O BOR 2E” reservoir (modified from Mendez, 2002).

Fig. 9. Thin sections cut from core samples of Well BOR-12 showing: (a) intracrystalline or separate-vug porosity and (b) intercrystalline porosity contributing to the increase of total porosity and permeability of the petrophysical system. Moldic and vuggy porosity were also observed in this depth interval but are not shown above due to the size of the thin sections.

The permeability estimated with our interpretation method (101.36 mD) agrees well with the permeability estimated from pressure transient measurements (101 mD), which is currently regarded as the best description of permeability of the composite petrophysical system (matrix+vugs+fractures).

Based on the above results, we propose a new interpretation model for the estimation of secondary porosity and permeability, illustrated as follows: Fig. 10 shows a cross-plot of permeability (k, mD) versus porosity ( , %), which includes parametric curves of constant k/ ratios used to explain the results for this particular case of study. The plot considers rock-core measurements corresponding to well BOR-12. We show the average rock properties obtained from rock-core measurements (black circle) used to initialize the simulation. In addition, we show how the presence of fractures, interconnected vugs, intercrystalline and intracrystalline porosity, or a combination of any of these features can cause perturbations of the initialvalues permeability and porosity (red circles). The plot also shows permeability and porosity values (light blue circle) obtained from the modeling of mud-filtrate invasion and subsequent matching of resistivity logs within the depth interval under consideration.

FaciesStratigraphic

CyclesBOR-12

Compact dolomites with very low porosity.

Dolomite from wackestone or mudstone. It has intercrystalline, intracrystalline, and moldic porosity. It also has presence of vugs.

Dolomite with considerable amounts ofgrains of quartz.

Dolomite from mudstone with a wide variety of porosities. It has mega and mesovugs which are communicated by the intercrystalline and intracrystalline porosity, microfractures and diagenetic fractures located between breaches.

Sandstones with grain size from fine to extremely fine and limolite.

DescriptionFaciesStratigraphic

CyclesBOR-12

Compact dolomites with very low porosity.Compact dolomites with very low porosity.



Dolomite with considerable amounts ofgrains of quartz.Dolomite with considerable amounts ofgrains of quartz.



Sandstones with grain size from fine to extremely fine and limolite.Sandstones with grain size from fine to extremely fine and limolite.

Description

a. Intracrystalline Porosity

b. Intercrystalline Porosity

a. Intracrystalline Porosity

b. Intercrystalline Porosity

SPE 121136 7

Fig. 10. Interpretation method developed for the estimation of secondary porosity and permeability. Blue circles identify porosity and permeability obtained from rock-core data (plugs). Black circles identify initial average rock properties obtainedfrom rock-core measurements. Red circles indicate perturbations of initial permeability and porosity due to presence of fractures, interconnected vugs, intercrystalline and intracrystalline porosity, or due to a combination of any of these features.The light blue circle identifies permeability and porosity values estimated from mud-filtrate invasion modeling and resistivity-log matching.

The graphical method described in Fig. 10 indicates that simulation of mud-filtrate invasion and matching of resistivity logs can be used to diagnose and estimate secondary porosity and permeability due to vugs and fractures. Presence of non-connected vugs would be associated with those cases where major changes of porosity are needed to match resistivity logs via forward modeling. On the other hand, presence of connected vugs and fractures would be estimated for those cases where significant modifications of permeability from the base case would be needed to match resistivity logs. There could also be a combination of both cases (Fig. 10), as was the case with the present case study.

Mud-Filtrate Invasion Modeling in Well 2 We focus our attention to well BOR-11, which is located 400 m away from BOR-12 (Fig. 3) and was also logged with a DLL tool and drilled with WBM of the same salinity as in the previous case. Core data were not available for this well. However, non-conventional well logs were available (wellbore resistivity images and sonic logs). We perform petrophysical assessment and subsequently apply initial values of rock petrophysical properties to numerically simulate resistivity logs. Petrophysical properties such as capillary pressure and relative permeability from rock-core measurements are adapted from those of well BOR-12. For the numerical simulation, we consider 4 flow units that are divided into 7 sub-layers to properly capture vertical property changes hence improve simulation results. The simulation grid is the same as that used for well BOR-12.

Fig. 11 shows simulation results obtained with permeability estimated from well-log correlations (left-hand side panel) and those for the case of permeability estimated through simulation of the process of mud-filtrate invasion (right-hand side panel). Fig. 11 shows the increase of permeability necessary to secure an acceptable match between simulated and measured apparent resistivities. The same figure shows that in this case the initial estimation of porosity is sufficient to achieve an acceptable agreement between simulated and measured apparent resistivities.

Fig. 12 displays a wellbore resistivity image acquired in well BOR-11 in the simulated depth interval. Based on the image, we conclude that the increase of permeability is explained by the presence of vugs and fractures that could be connecting the vugs, thereby causing an increase of the composite, system permeability. According to previous studies (Mendez, 2002; Kupecz et al., 2000), wells BOR-12 and BOR-11 are located in similar quality zones. Mendez’s (2002) and Kupecz et al.’s (2000) studies indicate presence of sin-sedimentary and diagenetic fractures within the same area together with a high density of variable-size vugs (micro to megavugs) that collectively contribute to the increase of reservoir quality.

Fig. 13 shows the distribution of reservoir quality for cycles 1’ and 1 in the Borburata field. Our simulations for wells BOR-11 and 12 were performed in depth intervals within those cycles. The red area In Fig. 13 represents zones with high porosity and permeability as well as presence of principal flow units with high reservoir quality. The pink zone indicates zones with low core porosity. Based on core observations, well-logs interpretation and production data, Mendez (2002) detected reservoirs with low quality and secondary flow units in these latter zones. Therefore, the contribution to system permeability

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8 SPE 121136

from fractures observed in well BOR-12 (Corpro, 2000) can be extrapolated to the case of well BOR-11 given that the latter is located within a short distance and is within a zone of similar sedimentological characteristics.

Fig. 11. Numerical simulation of DLL measurements in well BOR-11. The left-hand side panel shows field (dashed line) and simulated (continuous line) apparent resistivity curves for the case of permeability estimated from well-log correlations. The right-hand side panel shows field (dashed line) and simulated (continuous line) apparent resistivity curves for the case of permeability estimated from the simulation of mud-filtrate invasion.

Fig. 12. Wellbore resistivity mage acquired in well BOR-11. The left- and right-hand panels show dynamic and static images, respectively, acquired in the simulated depth interval.

Average permeability obtained through simulation of mud-filtrate invasion (134.26 mD) is significantly higher than the average permeability estimated from well-log correlation (6.12 mD) for the depth interval under consideration. Based on the fact that wells BOR-11 and BOR-12 are located in zones with similar geological characteristics (presence of vugs and fractures interconnecting them), we believe that permeability obtained from our simulations is a better representation of for the composite petrophysical system (matrix+vugs+fractures). It is also important to emphasize that well BOR-11 is the best producer in the Borburata field (Miranda, 2008), with an initial production of approximately 4000 bpd and a current production close to 2000 bpd after more than 9 years. The production of well BOR-11 confirms the high reservoir quality of this zone resulting from fractures and interconnected vugs. Fig. 14 shows results for the case of well BOR-11 using our graphical interpretation model. Once again, the model confirms that perturbations of initial petrophysical properties are

a. k=6.12mD b. k=134.26mD

SPE 121136 9

needed to secure a good match between simulated and measured resistivity logs. In this case we only needed to perform perturbations of permeability to secure a good match of resistivity logs.

Fig. 13. Spatial distribution of reservoir quality for cycles 1’ and 1 in the Borburata field. The red area indicates zones with high porosity and permeability as well as presence of principal flow units with high reservoir quality. The pink area shows zones where low porosity was observed in cores. In addition, reservoirs with low quality and secondary flow units were detected in the pink area based on core observations, well-log interpretation, and production data (modified from Mendez, 2002).

Fig. 14. Application of the new interpretation method to the estimation of secondary porosity and permeability in well BOR-11. Blue circles identify porosity and permeability obtained from rock-core data (plugs) in well BOR-12. Black circles indicate theinitial average rock properties estimated from well-log correlations. Red circles represent required perturbations on initial permeability and porosity due to presence of fractures, interconnected vugs, intercrystalline and intracrystalline porosity, or the combination of any of these features. The light blue circle indicates permeability and porosity obtained from mud-filtrate invasion modeling.

Mud-Filtrate Invasion Modeling in Well 3 We now examine well BOR-31, which is located a good distance apart from the two previously-studied wells (3.6 km from well BOR-12, as shown in Fig. 3). This well is considered key to our study because of the amount and quality of information available (rock-core measurements and non-conventional well logs), thereby enabling appropriate integration of available data and a more reliable simulation of the process of mud-filtrate invasion in vuggy and fractured reservoirs. The simulation is performed in a similar manner to that of previous cases. Well BOR-31 was logged with a High-Resolution Laterolog Array Tool (HRLA) and drilled with WBM of the same salinity as in previous cases. Moreover, non-conventional well logs acquired in this well (wellbore resistivity images, dipole sonic, 3-arm caliper, and nuclear magnetic resonance) provided confirmation of the perturbations of permeability necessary to secure a good match between simulated and measured resistivity logs. Fig. 15 shows the results obtained from the petrophysical assessment of well BOR-31 based on a multi-mineral approach (Miranda, 2008). Subsequently, we simulated the process of mud-filtrate invasion and thereafter the corresponding resistivity logs following the same procedure described in previous cases. We considered 5 flow units that were sub-divided into 12 layers for simulation purposes.

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k=128.14, =0From modeling

10 SPE 121136

Fig. 15. Petrophysical assessment in well BOR-31. Track 1: Lithology, caliper, and temperature logs. Track 2: Depth and Tension measurements. Track 3: High-Resolution Laterolog Array measurements, RLA5, Shallow Laterolog Resistivity measurement, LLS, estimated from High-Resolution Laterolog Array Tool, RLA2 and RLA3, and modified Jennings’ and Lucia’s permeability (green line) and core permeability (red circles). Track 4: Neutron (dotted green line) and Density (blue line) logs, sonic log (fuchsia line), calculated effective porosity (red line) and core porosity (blue circles). Track 5: Archie’s calculated water saturation (black line) and core water saturation (blue circles). Track 6: Nuclear magnetic resonance 2T

distribution and cutoff. Track 7: Image log, Formation Micro Imager (FMI) log showing layers with variable thickness (1 to 5.5 ft), with massive appearance and development of vuggy porosity showing interconnection between pore spaces through fractures and microfractures observed from 11714 to 11717 ft. Track 8: Volumetric analysis showing the degree of heterogeneity of the carbonate reservoir. The computed mineralogy is consistent with that obtained from X-ray diffraction analysis (Miranda, 2008).

We did not have software available to simulate the specific type of resistivity logs acquired in well BOR-31. Instead, we perform the simulations assuming a DLL tool. To that end, we compared the performance properties of HRLA and DLL based on available commercial literature (Schlumberger, 2000). Fig. 16 compares HRLA and HALS (High-Resolution Azimuthal Laterolog) resistivity measurements vs. depth of mud-filtrate invasion. The borehole-corrected HALS deep resistivity curve (HLLD) adequately compares to the Mode-5 response of the HRLA array, while the HALS shallow resistivity curve (HLLS) is intermediate between the Mode-2 and Mode-3 HRLA responses. Thus, for simulation purposes we use the RLA5 logs in place of HLLD, while the HLLS response was calculated from a geometric average of RLA2 and RLA3 resistivity responses. Fig. 17 shows simulation results obtained for the case of well BOR-31, where the simulations were performed with permeability from rock-core measurements. Results are shown in the left-hand side panel of the figure. We perform successive perturbations of both permeability and porosity to secure a good match between simulated and measured apparent resistivities. Fig. 17 show the corresponding results. The same figure shows that the match of resistivity logs required a significant increase of permeability with respect to the initial value. In addition, we performed small perturbations of porosity in some layers of this well. The increase of permeability is explained from the interpretation of coredata and wellbore resistivity images acquired in well BOR-31. The interpretation of wellbore resistivity images indicates dolomitized facies in the simulated depth interval with presence of vugs as well as partially hydraulically conductive fractures. The vugs and fractures seem to be connected to the matrix, thereby increasing the permeability of the composite petrophysical system. Inspection of core samples confirms the interpretation of wellbore resistivity images.

SPE 121136 11

Fig. 16. Comparison of HRLA (High-Resolution Laterolog Array Tool) and HALS (High-Resolution Azimuthal Laterolog) resistivities vs. radial length of mud-filtrate invasion (excerpted from Schlumberger, 2000). RLA5 resistivities acquired with theHRLA tool behave closely to HLLD resistivities acquired with the HALS tool.

Fig. 17. Numerical simulation of HRLA as DLL resistivity logs in well BOR-31. The left-hand side panel shows field (dashed line) and simulated (continuous line) apparent resistivity curves for the case of permeability obtained from rock-core measurements. The right-hand side panel shows field (dashed line) and simulated (continuous line) apparent resistivity curves for the case of permeability estimated from pressure transient measurements. We performed perturbations of porosity in some of the petrophysical layers included in the simulations.

Fig. 18 shows the wellbore resistivity image acquired in well BOR-31 across the same depth interval where we simulated the process of mud-filtrate invasion. We observe presence of dolomitized facies. The image also indicates presence of vugs (blue arrows) and partially-conductive fractures (red arrows). Fig. 19 is an enlarged view of the previous figure where we highlight the presence of vugs (blue arrows) and fractures (red arrows). Fig. 20 shows core photographs taken in the same depth interval. It is important to emphasize that a depth difference exists between log and rock-core measurements. Inspection of core data confirms the presence of dolomitization with vugs (blue arrows) and fractures (red arrows). While some vugs appear to be isolated, integration of core data and wellbore resistivity images indicates that some of the vugs remain interconnected. Interpretation also suggests the presence of secondary porosity and permeability for the simulated interval that could improve the composite permeability and porosity of the petrophysical system.

a. k=1.67mD b. k=32.70mD

12 SPE 121136

Fig. 18. Wellbore resistivity image acquired in well BOR-31 showing the simulated depth interval. The image shows presence of vugs (blue arrows) and partially-conductive fractures (red arrows).

Fig. 19. Wellbore resistivity image acquired in well BOR-31 showing additional details of the same depth interval. The image displays the same features previously observed with arrows highlighting presence of vugs (blue arrows) and fractures (red arrows).

MDft

MDft

MDft

MDft

SPE 121136 13

Fig. 20. Core photograph taken in well BOR-31. The image shows presence of vugs (blue arrows) and fractures (red arrows).

The average permeability estimated for the analyzed depth interval through simulation of mud-filtrate invasion (32.70 mD) is significantly higher than the average permeability of rock-core measurements (1.67 mD). We have already explained the main reasons for such a difference. However, there were layers where we also had to make perturbations of porosity, thereby decreasing the values with respect to those of rock-core measurements. Porosity obtained from our simulation is in better agreement with porosity calculated from well logs (ranging from 4 to 7%). Even though this zone is characterized by the presence of only one rock-fabric class (large crystal dolostones with approximate average size of 300 μm), presence of silt-sized quartz grains and clay minerals causes a reduction of effective porosity (Miranda, 2008).

Fig. 21 summarizes the estimated values of permeability and porosity for well BOR-31 using our graphical description method. Results confirm that perturbations of initial petrophysical properties are necessary to secure a good match between simulated and measured apparent resistivities. In the present case, we performed significant perturbations of permeability and minor perturbations of core porosity. Porosity estimated from well logs was in better agreement with that obtained from our interpretation method. This behavior confirms the benefits of simulating the process of mud-filtrate invasion to estimate permeability of vuggy and fractured carbonate reservoirs where presence of fractures and interconnected vugs significantly improves reservoir quality. In the particular case of BOR-31, it was not possible to secure a better match for the separation between shallow- and deep-sensing resistivity curves observed in field data. One reason for the mismatch could be the high heterogeneity detected in core samples as well as the presence of clay minerals in pore throats. On the other hand, our simulation method is somewhat limited by the fact the simulated resistivity curves are not completely equivalent to those used in the acquisition of resistivity logs. Finally, Table 1 summarizes the estimated values of permeability obtained from simulation of mud-filtrate invasion compared to permeability estimated with other methods or from other measurements. In this table, Corek identifies permeability from rock-core measurements, logWell sk is permeability estimated from well-log correlations, PTTk identifies the permeability estimated from pressure transient measurements, and SMFIk is permeability estimated from the simulation of the process of mud-filtrate invasion. All values are expressed in millidarcies (mD).

ininin

14 SPE 121136

Fig. 21. Application of the new interpretation method to the appraisal of secondary porosity and permeability in well BOR-31. Blue circles identify porosity and permeability obtained from rock-core data (plugs) in well BOR-31. Black circles identify theinitial average rock properties estimated from rock-core measurements. Red circles represent required perturbations of initial permeability and porosity due to the presence of fractures, interconnected vugs, intercrystalline and intracrystalline porosity or the combination of any of these features. The light blue circle identifies permeability and porosity obtained from mud-filtrateinvasion modeling.

Table 1. Permeability values estimated from the simulation of mud-filtrate invasion compared to permeability values obtained from other interpretation methods or measurements.

Discussion Lucia’s (2007) interpretation method proposes the estimation of porosity and permeability of non-vuggy carbonate reservoirs with relationships between porosity and permeability for specific particle-size groups. We implemented this approach to our data. In addition, we implemented a definition of rock types based on both rock fabric and critical pore-throat radius using rock-core measurements. We believe that a combination of the previous two approaches permits a better petrophysical characterization of the matrix. However, the two methods did not allow us to quantify porosity and permeability of vugs and fractures. Influence of these components was observed in the permeability of the petrophysical system inferred from pressure-transient tests, where permeability was 24 times (BOR-12) and 146 times (BOR-8) larger than the permeability of rock-core samples. This observation was confirmed with forward modeling of dual-laterolog resistivity logs. Vugs and fractures in the “O BOR 2E” reservoir could cause significant differences between the petrophysical properties obtained with the two approaches.

The previous remarks indicate that simulation of mud-filtrate invasion can be used to diagnose and estimate secondary porosity and permeability due to vugs and fractures via the interpretation method described in Fig. 22. Presence of non-connected vugs will be diagnosed in those cases where significant changes of porosity are necessary to match resistivity logs via invasion and resistivity modeling. On the other hand, presence of connected vugs and fractures will be estimated in those

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32.7Not Available1.041.67BOR-31

134.3Not Available6.12Not availableBOR-11

101.4101.06.334.33BOR-12

KSMFI(mD)KPTT(mD)KWell-logs (mD)KCore (mD)Well

SPE 121136 15

cases where significant modifications of permeability are necessary to match resistivity logs. There could also be a combination of both cases (Fig. 22).

Fig. 22. Proposed interpretation method to diagnose and quantify secondary porosity and permeability. Blue circles represent porosity and permeability obtained from rock-core data or calculated from well-log correlations. Black circles identify the initialaverage rock properties obtained from rock-core measurements or well-log correlations. Red circles identify perturbations of initial permeability and porosity due to presence of fractures, interconnected vugs, intercrystalline and intracrystalline porosity, or a combination of any of these components. The light blue circle identifies permeability and porosity estimated from the simulation of mud-filtrate invasion and matching of resistivity logs. Orange dashed lines identify changes of initial permeability estimated from the simulation of mud-filtrate invasion process and matching of apparent resistivity logs.

Based on the above observations, we developed and validated an interpretation method to estimate permeability of the entire petrophysical system (matrix, vugs, and fractures). We implemented the method in key wells (rock-core data, pressure tests, conventional, and non-conventional well logs) for testing and calibration. The method assumes that laboratory measurements of rock-core samples are available from a key well. It is also necessary to include wellbore images in the analysis of the key well. In addition, fluid and mud properties must be available not only to secure an acceptable match between simulated and measured resistivity logs but also to reduce uncertainty in the estimation.

Results from our study favor the simulation of mud-filtrate invasion to estimate the permeability of the composite petrophysical system. Despite difficulties and limitations associated with the uncertainty of some simulation parameters, as well as high variations of resistivity due to presence of heterogeneities, the method described in this paper enables the reliable estimation of permeability for fractured and vuggy carbonate reservoirs. Rock-core measurements, pressure-transient tests, and non-conventional well logs such as wellbore images are necessary to calibrate the initial estimation of petrophysical properties in key wells.

The following is an itemized list of sequential steps for the application of the proposed interpretation method based on mud-filtrate invasion modeling:

1. Define rock types from both rock fabric and critical pore-throat radius using rock-core measurements. 2. Identify presence of secondary permeability and porosity due to presence of fractures, interconnected vugs,

intercrystalline and intracrystalline porosity, or the combination of any of these components. 3. Define flow units and layers for the simulation of mud-filtrate invasion based on the initial petrophysical

assessment. 4. Estimate initial rock-properties (porosity, permeability and water saturation) from well-log correlations and via

integrated petrophysical assessment. 5. Define mud properties from mud logs, drilling reports, and mud-filtrate invasion tests. 6. Calculate and/or measure capillary pressure and relative permeability from rock-core measurements and describe

these properties with Brooks-Corey’s equations and parameters. 7. Input petrophysical, fluid, and mud properties into the numerical simulation of mud-filtrate invasion.

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16 SPE 121136

8. Progressively make perturbations to the permeability of each layer until securing a match between simulated and measured apparent resistivity curves.

9. In some cases, a perturbation of initial porosity will be necessary to match the measured apparent resistivity due to the presence of vugs or non-connected pore space.

10. Compare the results obtained with permeability estimated from pressure transient measurements and observations of fractures and vugs from core analysis and wellbore images.

11. The final estimates of layer permeability and porosity will be obtained when securing a good match between simulated and measured apparent resistivities within the depth interval of study.

Summary and Conclusions We developed and successfully tested a new method to diagnose and quantify fractured and vuggy carbonate formations via the simulation of the process of mud-filtrate invasion. The method was applied to a set of three wells drilled in a carbonate reservoir in the Escandalosa formation of southwest Venezuela. Two of three cases of study included rock-core measurements that enabled the validation of the method. In addition, pressure transient measurements and wellbore resistivity images combined with core measurements enabled the diagnosis of vugs and fractures that significantly contributed to the total porosity and permeability of the composite petrophysical system. Matching of apparent resistivity logs was performed after successive perturbations of porosity and/or permeability when simulating the process of mud-filtrate invasion. These perturbations were used to diagnose presence of secondary porosity and permeability. We introduced a simple graphical procedure to diagnose the individual relative influence of either vugs or fractures on the porosity and permeability of the composite petrophysical system. Permeability estimated from the three case studies was consistent with permeability estimated from pressure transient measurements (which experience shows are representative of the composite petrophysical system). Even though additional testing is necessary to generalize the applicability and reliability of our interpretation method, one of its advantages is the possibility of cross-validating petrophysical estimations performed with conventional interpretation procedures. Specifically, if the simulation of mud-filtrate invasion yields resistivity logs drastically different from measured resistivity logs this condition indicates that the values of porosity and permeability calculated with conventional interpretation procedures are not correct. The availability of a cross-validation procedure to verify petrophysicalestimates is by itself an important advantage of the proposed interpretation method.

The interpretation method introduced in this paper requires reliable non-conventional petrophysical information for its implementation, including relative permeability and capillary pressure. These properties are necessary to simulate the process of mud-filtrate invasion, in addition to mud and fluid properties. Sensitivity analyses are recommended to appraise the relative impact of petrophysical properties other than porosity and permeability on the numerically simulated resistivity logs.Our procedure also assumes that mud-filtrate invasion takes place uniformly throughout the investigated rock volume. Because of the latter assumption, our estimated values of porosity and permeability should be regarded as effective mediumapproximations of the composite petrophysical system. In reality, invasion will preferentially take place through fractures andtouching vugs when the latter are present in the invaded rock. Such a preferential flow can have a significant influence on resistivity logs, including the possibility of induced electrical anisotropy in fracture systems that exhibit a predominant fracture direction. Our method neglects biasing effects due to localized electrical-current effects on resistivity logs when estimating porosity and permeability. We suggest that such an anomalous and potentially biasing condition be diagnosed directly from inspection of resistivity logs prior to implementing the proposed interpretation method. It is also possible thatnumerical simulation and matching of borehole nuclear logs (in addition to the simulation and matching of resistivity logs) could improve the estimation of porosity and permeability.

Nomenclature k : Permeability, (mD)

Corek : Permeability from rock-core measurements, (mD) PTTk : Permeability estimated from pressure transient measurements, (mD) SMFIk : Permeability estimated from simulation of mud-filtrate invasion simulation, (mD)

logWell sk : Permeability estimated from well-log correlations, (mD) r : radial direction (ft)

tR : True formation resistivity, (Ohm-m) z : vertical direction (ft)

Greek symbols

: Porosity, (fraction)

SPE 121136 17

Acknowledgements We are thankful to PDVSA (Petróleos de Venezuela, S.A.) for providing the data used in the case studies and for the support and permission to publish the results. We also thank PDVSA for bestowing upon one of the authors a scholarship in 2006 to pursue a Master of Science degree in Engineering.

The work reported in this paper was partially funded by The University of Texas at Austin’s Research Consortium on Formation Evaluation, jointly sponsored by Aramco, Anadarko Petroleum Corporation, Baker-Hughes, BG, BHP Billiton, BP, Chevron, ConocoPhillips, ENI, ExxonMobil, Halliburton Energy Services, Marathon Oil Corporation, Mexican Institute for Petroleum, Petrobras, Schlumberger, Shell International E&P, StatoilHydro, TOTAL, and Weatherford.

References 1. Aguilera, R., “Naturally Fractured Reservoirs,” Second Edition, Penwell Books, 1995. 2. Babadagli, T., and Al-Salmi, S., “A Review of Permeability-Prediction Methods for Carbonate Reservoirs Using Well-

Log Data,” SPE Reservoir Evaluation & Engineering, April 2004. 3. Corey, A., “Mechanics of Immiscible Fluids in Porous Media,” Water Resource Publications, 1994. 4. CORPRO Systems Ltd., “Geological Study of Tectonic and Sedimentary Structures Well: BOR-12,” November 2000. 5. Dewan, J.T., “Essentials of Modern Open-Hole Log Interpretation,” PennWell Publishing Company, 1983. 6. Gomaa, N., Al-Alyak, A., Ouzzane, D., Saif, O., Okuyiga, M., Allen, D., Rose, D., Ramamoorthy, R., and Bize, E., “Case

Study of Permeability, Vug Quantification, and Rock Typing in a Complex Carbonate,” in Proceedings of the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, TX, September 2006.

7. HRLA High-Resolution Laterolog Array Tool Specifications, Schlumberger, April 2000. 8. Hurley, N.F., Zimmermann, R.A., and Pantoja, D., “Quantification of Vuggy Porosity in a Dolomite Reservoir from

Borehole Images and Core, Dagger Draw Field, New Mexico,” in Proceedings of the 1998 SPE Annual Technical Conference and Exhibition, San Antonio, TX, September 1998.

9. Jennings, J., and Lucia, F.J., “Predicting Permeability From Well Logs in Carbonates With a Link to Geology for Interwell Permeability Mapping,” SPE Reservoir Evaluation & Engineering, August 2003.

10. Kupecz, J., Sorondo, J., Rojas, L., Petito, M., Chang, R., Calderon, P., Solórzano, E., and Hernandez, E., “Quantitative Characterization of a Mixed Carbonate-Siliciclastic Interval for Reservoir Simulation: Escandalosa Formation, “O” Member, Barinas-Apure Basin, Venezuela,” AAPG Bulletin, Vol. 84, No. 13 (Supplement), 2000.

11. Lucia, F.J., “Carbonate Reservoir Characterization - An Integrated Approach,” Second Edition, Springer, 2007. 12. Méndez, J., “Caracterización Sedimentológica del Miembro “O” en el Área de Borburata, Formación Escandalosa,”

PDVSA Internal Report, May 2002. 13. Miranda, L. J., “Mud-Filtrate Invasion Modeling to Quantify Static and Dynamic Petrophysical Properties of Fractured

and Vuggy Carbonate Reservoirs,” The University of Texas at Austin, Department of Petroleum and Geosystems Engineering, Austin, TX, Master’s Thesis, August 2008.

14. Omni Laboratories, Inc; “Sedimentological and Reservoir Characterization Study of PDVSA BOR-31 Well, Borburata Field, Venezuela,” Client Report, 2007.

15. Salazar, J., Torres-Verdín, C., Alpak, F., and Klein, J., “Estimation of Permeability from Borehole Array Induction Measurements: Application to the Petrophysical Appraisal of Tight Gas Sands,” Petrophysics Vol. 47, December 2000.

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