IMPROVED ESTIMATION OF PORE CONNECTIVITY …...SPWLA 53rd Annual Logging Symposium, June 16-20, 2012...

SPWLA 53rd Annual Logging Symposium, June 16-20, 2012

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IMPROVED ESTIMATION OF PORE CONNECTIVITY AND PERMEABILITY IN DEEPWATER CARBONATES WITH THE CONSTRUCTION OF MULTI-LAYER STATIC AND DYNAMIC

PETROPHYSICAL MODELS

Elton Luiz Diniz-Ferreira and Carlos Torres-Verdín PETROBRAS – Petróleo Brasileiro S.A. and The University of Texas at Austin

Copyright 2012, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 53rd Annual logging Symposium held in Cartagena, Colombia, June 16-20, 2012.

ABSTRACT

We introduce a new method for petrophysical interpretation of carbonate formations based on the construction of multi-layer static and dynamic petrophysical models across several wells. Formations consist of heterogeneous deepwater carbonates exhibiting complex pore structure due to growth-framework porosity dolomitization, vuggy porosity, and secondary/moldic porosity. The origin of these formations is associated with laminated microbial structures and stromatolites, together with depositional mudstone and grainstone. Complex pore space combined with high spatial reservoir heterogeneity, gives rise to uncommon measurements, such as (a) very high resistivity readings in the oil zone, (b) separation of apparent resistivity logs with different depths of investigation, (c) complex NMR T2 distributions that exhibit variable unimodal and bimodal responses, (d) reservoir units with total porosity ranging from 2 to 26% and permeability from less than 0.001mD to 4.2D, and (e) low and constant gamma-ray readings.

The first step of the interpretation method consists of rock classification based on geological/petrophysical models and well-log responses across fluid flow units. Rock classes are populated within previously determined petrophysical layers, with specific petrophysical properties adjusted until matching all available well logs and core data with numerical simulations. In addition, NMR T2 distributions are matched with numerical simulations based on a recently developed procedure to simulate NMR T2 distributions in the presence of arbitrary pore-size and fluid saturations.

Numerical simulation of well logs after invasion indicates that NMR porosity is a good approximation of total rock porosity. Simulation of mud-filtrate invasion indicates that several of the rock types include a component of isolated porosity which may reach 5% (out of a total of 12%). Our study also indicates that sonic porosity is a good approximation to

interconnected porosity for most rock types. Numerical simulation of NMR T2 distributions is effective to estimate pore-size distributions, water saturation, and inter-connected porosity. Permeability values estimated from dynamic petrophysical models match laboratory core measurements.

Based on the correlation between well-log responses and rock types, it was possible to use similar parameters to numerically simulate well logs where laboratory measurements were unavailable. Petrophysical estimation obtained in this manner matched field measurements and produced reliable interpretations of pore connectivity and permeability.

INTRODUCTION

Developments considered in this paper focus on a deepwater carbonate reservoir located in the Santos Basin, offshore of Brazil. Reservoir units are composed of boundstone, grainstone and mudstone. Boundstone is a limestone deposit that at the time of its formation was bound by algae, bacteria, or other unicellular organisms. In this reservoir, binding agents are both bacterial and algae, which hold the layers of mud and calcite together. Such an association creates a growth-framework porosity that is a primary porosity generated by the in-place growth of a carbonate rock framework. This type of porosity can provide mechanical support to large pores present in the field of study (Figure 1c). Stromatolites, fossilized mounds of layered microbial mat and sediment, are the most common reservoir units in the field [Figure 1, (a) and (b)]; they grow both vertically and laterally, changing with environmental conditions, these microorganisms are extremely sensitive to sea-level variations, water chemistry, and sun light incidence. Grainstone and mudstone are commonly associated with depositional sedimentary processes and the energy of sedimentation. Subsequent events, such as dolomitization and preferential dissolution, helped to transform these sedimentary units into rocks with highly complex and heterogeneous pore topology.


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Due to sea-level variations, cycles of sedimentation can often be recognized from well logs. It is possible to differentiate rock types based on such geological cyclicity; for petrophysical purposes we will refer to those rock types as fluid flow units. However, it is sometimes not possible to accurately differentiate rock types with well logs due to the presence of laminated or thinly-bedded fluid flow units (Figure 2). In the presence of thin layers, flow units can only be detected with core data. The cause of sea-level variation in this field is not well understood and remains a subject of study by geologists.

Figure 1: Examples of stromatolites. (a) A stromatolite fossil from late pre-Cambrian rocks in Montana; the cut slab is a cross-section perpendicular to the original water surface. Flat layers are fossilized microbial mats, whereas curved layers are fossilized mounds analogous to those living today in Shark Bay (http://www.lpi.usra.edu/education/EPO/yellowstone2002/workshop/stromatolite/index.html). (b) 3D view of microbial mat mounds from the Museum of the Rockies; it is modeled after the microbial mounds in Shark Bay, Australia (http://www.lpi.usra.edu/education/EPO/yellowstone2002/workshop/stromatolite/index.html). (c) Cross-section of the type of rock present in the field of study. It is important to emphasize the complex pore space found in the reservoir that gives rise to large heterogeneity of this type of rock (photography taken by Torres-Verdín). (d) Outcrop showing some impressively large domal stromatolites. The orange arrows represent cyclicity present even at this scale (http://all-geo.org/highlyallochthonous/2008/01/sadly-not-sandworms/).

Wells were drilled with both oil-base mud (OBM) and water-base mud (WBM). The oil bearing-zone of wells drilled with WBM gave rise to a conspicuous invasion profile on resistivity logs. It is possible to simulate this invasion profile in different layers and estimate their permeability. Conversely, wells drilled with OBM did not show a conclusive invasion profile in the oil-bearing zone because of the lack of electrical resistivity contrast between oil and mud filtrate.

Due to the complexity of the pore space and the spatial heterogeneity of the reservoir under consideration, conventional well-log evaluation seldom reproduces petrophysical properties consistent with core data. It is necessary to construct multi-layer petrophysical models based on geological information to improve the interpretation. A model that combined well logs and geological properties was key to select bed boundaries and to construct an earth model. The latter model was used to perform static and dynamic simulations - matching simulated resistivity, nuclear, and NMR logs with field measurements. Petrophysical properties estimated with those simulations were in agreement with core laboratory measurements.

Figure 2: Comparison of vertical resolution and radial depth of investigation between core, plug, and well logs. Photograph represents a core segment retrieved from a laminated zone of the reservoir under analysis. Any presented well log has enough vertical resolution to completely reproduce thin laminations present on this core. Vertical descriptions are estimations of vertical resolution of the various well log; horizontal descriptions are estimations of the corresponding radial length of investigation.

Interpretation was performed in the oil-bearing zone of three wells: two of them –Wells Η and Γ – were drilled with OBM, the remaining well –Well Χ – drilled with WBM (Table 1). It is not possible to perform a correlation between the evaluated wells using well-logs. The gamma-ray log shows relatively low and constant values. The apparent resistivity or porosity logs have not shown any type of correlation (Figure 3). In order to analyze pore-size distributions, we also undertook NMR simulations along several depth intervals in the Well Γ, across the same interval where dynamic simulations were performed with results matching core


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NMR measurements. Procedures used to estimate permeability in the presence of OBM or WBM are different and will be discussed in the sections below.

Table 1: Summary of evaluated wells in this study and correspond type of drilling mud.

Well Name Mud Type Η OBM Γ OBM Χ WBM

CONVENTIONAL INTERPRETATION OF WELL LOGS

Figure 4 shows results obtained from conventional petrophysical interpretation of well logs across the oil-bearing zone in Well Γ – this section of the well was drilled with OBM. In track 1, it is possible to observe a constant caliper of 8.5 inches, which corresponds to the nominal diameter of the well, indicating no problems related to washouts or excessive mudcake. A similar behavior was observed in all wells evaluated with this study.

The gamma-ray log (GR), in Figure 4, track 1, shows relatively low and constant values. Zones of high GR are generally associated with organic matter; volumetric concentration of clay tends to be low in the majority of the layers. Due to this behavior, the GR log is not an optimal option to perform rock classification or to perform correlations across different wells.

Abnormally high resistivity readings are observed in the oil zone (Figure 4, track 3). Resistivity values in this zone ranges from 100 to 2000Ω.m. Apparent resistivity logs also exhibit separation between logs with different depths of investigation. The separation is due to shoulder-bed effects, as well as limiting resolving capability of induction tools.

Density and neutron logs exhibit a positive correlation (Figure 4, track 4), giving rise to similar values of calculated porosity due to slight presence of clay in this formation. Total porosity calculated from these logs ranges from 2 to 26%. PEF log values range between 2.5 and 4.5 b/e, which coincide with nominal values of limestone and dolomite matrix.

The NMR T2 distribution (Figure 4, track 7) in this reservoir is complex, exhibiting variable unimodal and bimodal responses. This behavior is due to the complexity of pore space. The effect of mud filtrate on

Figure 3: Comparison of the same reservoir region across the three evaluated wells. Track 1: caliper (blue) and gamma-ray (green) logs. Track 2: apparent resistivities acquired with different depths of investigation. Track 3: computed total porosity using mineral inversion (red), computed sonic porosity with Wyllie’s equation (green) and core porosity (black). Track 4: total water saturation computed with Archie’s equation (blue). Track 5: NMR T2 distribution.


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NMR measurements can cause misleading T2 distribution interpretations – chiefly in OBM-drilled wells. Presence of laminated rocks or thinly-bedded fluid flow units also interferes with NMR measurements, as the latter have relatively low vertical resolution – this effect will be discussed in the NMR simulations section below. NMR total porosity is close to porosity calculated with neutron and density logs.

Water saturation (Sw) was calculated from both NMR T2 distributions and Archie’s equation. Results are shown in Figure 4, track 8; Sw calculated with Archie’s equation show larger variations than Sw calculated with NMR due to the relatively high vertical resolution of density porosity used as total porosity in that equation. Parameters used in Archie´s equation are similar to those measured with laboratory core analysis.

Linear mineral inversion was performed to estimate mineral composition (Figure 4, track 10). Results obtained from this estimation agree with laboratory measurements in wells where X-Ray diffraction (XRD) data was available. In addition, total porosity and water

saturation obtained from inversion results were similar to calculations performed with Archie’s equation.

Sonic porosity was computed using Wyllie´s equation (Wyllie et al., 1956) – Figure 4, track 5. Input parameters in this equation were carefully selected. The slowness of the matrix was calculated from the mineral composition calculated with mineral inversion, and the slowness of the fluid was calculated based on Archie’s water saturation. Sonic porosity is consistently lower than total porosity calculated with NMR and density-neutron logs; it is also lower than the free-fluid porosity calculated with NMR data. The difference between sonic and total porosity is approximately 5%.

Due to the complexity of the reservoir under consideration, conventional petrophysical evaluations tend to fail when calculating permeability. The sections below describe the procedures developed in this paper to integrate rock information, core measurements, and well logs to secure a reliable evaluation of pore connectivity and permeability.

Figure 4: Conventional petrophysical interpretation in Well Γ across the oil-bearing zone. The well was drilled with OBM. Track 1: caliper and gamma-ray logs. Track 2: depth. Track 3: apparent resistivities acquired with different depths of investigation. Track 4: neutron SS (green), density (red), PEF (purple) and sonic logs (fuchsia). Track 5: computed total porosity using mineral inversion (blue), computed sonic porosity with Wyllie’s equation (black) and core porosity (red). Track 6: NMR porosities: clay-bound fluid (brown), bound fluid (olive) and “free fluid” (aqua). Track 7: NMR T2 distribution. Track 8: total water saturation computed with Archie’s equation (red) and total water saturation computed with the NMR log (blue). Track 9: core permeability. Track 10: estimated mineralogy using linear inversion.


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ROCK TYPING

One of the first steps of well-log interpretation consists of diagnosing rock types (Torres-Verdín, 2012). This step is extremely important in the present study due to the high degree of spatial heterogeneity. A variety of rocks with different petrophysical properties exist in the reservoir and, consequently, give rise to very diverse well-log signatures. The petrophysicist should be able to identify well-log signatures, correlate them with fluid flow units and analyze them separately. It is important to understand that petrophysical rock typing may not be equivalent to geological or geophysical rock typing; we are interested in the porosity-permeability behavior of the reservoir.

We attempted several techniques for rock classification, including cluster analysis, Jerry Lucias´ (Lucias, 1999), Amafule´s (Amafule et al., 1993) and Winland’s (Pittman, 1992) rock classification methods. Results obtained from these classification methods were not satisfactory.

It was necessary to develop a new rock typing method that could account for the high degree of spatial heterogeneity. Figure 4, track 3, indicates that resistivity measurements exhibit large variations while total porosity (tracks 5, and 6) does not vary in the same way. Analysis of thin sections, core measurements, and NMR logs indicate that the large variations of apparent resistivity are due to variations of irreducible water saturation in each layer - mobile water is null in the evaluated zone of the reservoir.

Table 2: Signatures observed on well logs to diagnose different fluid-flow units.

Rock Type

Type of Porosity

Resistivity Values T2 distribution

Difference between total

and sonic porosity

1 Inter-connected

Medium- High

Large amount of porosity

associated with relaxation time

higher than 200ms.

Lower than 20%

2 Isolated High



higher than 200ms.

Larger than 20%

3 Micro porosity Low



lower than 200ms.

Lower than 20%

Samples dominated by micropores showed lowest values of electrical resistivity than the ones with large pores, for a given porosity. A high number of pores and pore connections results in a high apparent cross-section area that facilitates the flow of electric charge (Verwer et al., 2011).

Figure 5: Comparison of well logs, core image and thin sections in the cored region of Well Η. The well was drilled with OBM. Track 1: depth. Track 2: core image. Track 3: apparent resistivities acquired with different depths of investigation. Track 4: computed NMR total porosity (green), computed sonic porosity from Wyllie’s equation (orange), and core porosity (red). Track 5: NMR T2 distribution. Thin sections at different depths (a) XX39m: high interconnected vuggy porosity (k = 722mD and = 0.178); rock type 2. (b) XX45m: presence of dolomite crystals and high porosity; rock type 2 with secondary porosity. (c) XX47m: high interconnected porosity and some isolated vuggy porosity (k = 95mD and = 0.155); rock type 3. (d) XX49.8m: laminated structure with cementation and microporosity; rock type 1.

NMR T2 distributions (Figure 4, track 7) provide independent information about pore-size distributions. It can be observed that layers containing large pore volumes associated with T2 signals lower than 200 ms represent rocks with low values of resistivity due to relatively large microporosity. Additionally, assuming that the sonic log only responds to the presence of interconnected porosity, depth intervals that exhibit a significant difference between total porosity and sonic porosity are commonly associated with isolated vuggy porosity.

Another important observation of the data set was that different flow units tend to appear in depth cycles. These cycles, in meter scale, can be observed in


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well logs or outcrops [Figure 1, (d)] and are attributed to sea-level variations. Based on those observations, we divided the reservoir into three different fluid flow units that are described in Table 2.

Figure 5 compares core photographs, well logs used to perform rock typing, core measurements, and thin sections in the oil-bearing zone of Well Η. This figure illustrates that the comparison between well-log signatures and rock types is consistent with the properties summaries in Table 2, and that the observed differences are due to variations of pore connectivity and permeability.

Resistivity, NMR T2 distributions, and sonic logs were the basis to differentiate fluid flow units in the reservoir and, consequently, for detecting bed boundaries. The base of a given depositional cycle was selected at the local minimum of the apparent resistivity log. Moreover, the transition between rock types does not occur sharply, it is common to encounter mixed or transitional layers. It is also common to encounter laminated layers with thicknesses below the resolution of well logs. Those layers can only be evaluated with core data.

CONSTRUCTION OF STATIC AND DYNAMIC MULTI-LAYER RESERVOIR MODELS

The concept of Common Stratigraphic Framework (CSF), introduced by Voss et al., (2009), was used in this project to minimize the effects of mud-filtrate invasion, shoulder-bed effects on well logs, and estimate layer-by-layer static and dynamic petrophysical properties.

Using the software UTAPWeLS1, we detected bed boundaries based on petrophysical rock typing. Next, we populated each bed with physical properties such as electrical resistivity, porosity, fluid composition, fluid density, hydrogen index, mineral composition. Subsequently, numerical simulations of well logs were performed to quantify the agreement of the constructed multi-layer model with available measurements. Adjustments were made, as necessary, to layer properties until securing an acceptable agreement between numerical simulations and measurements (Voss et al., 2009). Static simulations reproduced neutron, gamma ray, PEF, density and induction logs. We also simulated the NMR T2 distribution along specific depth intervals with results matching core NMR measurements. Results obtained from this exercise are shown in Table 5 and Figure 11.

1 Developed by The University of Texas at Austin’s Research Consortium on Formation Evaluation

Finally, numerical simulation of mud-filtrate invasion was performed to examine the dynamic petrophysical properties. Simulations included drilling variables such as type of mud, time of invasion, and overbalance pressure. Also included layer-by-layer values of porosity, permeability, capillary pressure and relative permeability, which were defined based on available core data and petrophysical rock typing. Additionally, the simulation included fluid properties such as density, viscosity, salt concentration of mud-filtrate, salt concentration of connate water, and temperature. Next, numerically simulated radial distributions of water saturation were transformed into radial distributions of electrical resistivity (using Archie’s equation with values of electrical parameters yielded by laboratory measurements), density, and migration length, to numerically simulate the corresponding apparent resistivity, density, and neutron logs (Gandhi et al., 2010).

Table 3: Rock-fluid properties calibrated and optimized with the simulation of mud-filtrate invasion for rock types 1 to 3 using Brooks-Corey’s model.

RT k [mD] Swirr Sor k0

rnw enw k0rw ew Pc

0

[psi.D1/2] ep

1 0.15 300 0.09 0.25 0.9 1.5 0.45 1.5 90 10

2 0.12 50 0.13 0.35 0.9 1.5 0.45 1.5 50 6

3 0.13 0.01 0.45 0.25 0.7 1.2 0.47 3 5 5

Table 4: Summary of mudcake, fluid, and formation properties assumed in the simulation of the process of mud-filtrate invasion. Variable Units Value Wellbore radius inch 8.5 Maximum invasion time days 1 Reservoir temperature oF 132 Initial reservoir pressure psi 8150 Overbalance pressure psi 520 Mud-filtrate salinity ppm [NaCl] 20000 Mud-filtrate viscosity (at STP) cP 1

Formation compressibility psi-1 1 x 10-7 Mudcake reference permeability mD 0.03

Mudcake reference porosity frac. 0.35

Mud solid fraction frac. 0.06 Mudcake compressibility exponent frac. 0.4

Mudcake exponent multiplier frac. 0.1

Connate-water salinity ppm [NaCl] 250000


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Figure 6: Flow chart describing the iterative interpretation method adopted in this paper to reduce the mismatch between numerically simulated and measured resistivity and nuclear logs. This process yields static and dynamic multi-layer reservoir models that honor all the available measurements as well as the physics of mud-filtrate invasion.

The flow chart in Figure 6 describes the interpretation method, starting from petrophysical rock typing/detecting of bed boundaries, to static and dynamic output of earth model parameters. It is an iterative manual process where one progressively reduces the mismatch between measured and numerically simulated resistivity, NMR and nuclear logs. For formations where core measurements were not available, an initial guess for petrophysical properties was made based on similar fluid flow units whose core measurements were available. Table 3 summarizes the rock and fluid properties assumed to describe saturation-dependent relative permeability and capillary pressure using Brooks-Corey parametric formulation (Corey, 1994). Table 4 describes the mudcake, fluid, and formation properties assumed in the simulation of the process of mud-filtrate invasion in the Well Χ.

FIELD CASE No. 1: STATIC SIMULATION IN WELL Η

In this well, simulations were performed over the entire oil-bearing zone by analyzing the long depositions cycles - thick bed boundaries. The first step consisted of constructing a multi-layer static model. Figure 7 shows that we reached an acceptable agreement between well logs and the numerical simulations, honoring the core data at the same time. Simulated well logs are gamma ray, apparent resistivity (induction), neutron, PEF, and density. This simulation step was important to

understand the petrophysical properties that govern the entire pay-zone.

Based on static-model descriptions, we concluded that low values of resistivity correlated with high values of irreducible water saturation were present in micropores. In this case, OBM filtrate invades the oil zone, chiefly across high resistivity zones, so because one can observe separation of induction curves with different depths of investigation. Simulation indicates that this separation was due to shoulder-bed effects. Total porosity calculated with density or NMR logs was a realistic initial guess to construct static models. Previous estimated mineral concentrations were used as input to nuclear-log simulations.

FIELD CASE No. 2: DYNAMIC SIMULATION IN WELL Γ

The reservoir model constructed in Well Η was used as the basis to perform static simulations in other wells of the same field. Similar to the previous example, static simulations in those wells agreed well with field data. A dynamic reservoir model in Well Γ was constructed by simulating the process of mud-filtrate invasion to establish geological and petrophysical consistency. To reproduce the high spatial heterogeneity of the reservoir, the model was constructed with high-resolution well logs and thin beds. We used plausible petrophysical parameters to populate bed boundaries in beds where core measurements were not available. Figure 8 shows the results obtained from dynamic simulations in Well Η. Figure 9 shows a detailed comparison between petrophysical properties used on the simulations and the original values calculated with well-logs.

Based on these simulations we concluded that sonic porosity calculated with Wyllie´s equation was a realistic initial guess for inter-connected porosity. As indicated by core samples, this behavior is due to the fact that a fraction of the total porosity is isolated from the pore network (rock type 2). The reproduction of well logs with numerical simulations also required that water saturation present in the oil zone were assumed as immobile; resistivity logs respond to irreducible water saturation and porosity. Implementation of these observations into the constructed dynamic earth model yielded numerical simulations that matched all the available well logs.


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The radial resistivity profile in the oil zone of OBM wells is not conclusive because both fluids are electrically resistive, therefore producing no signature on the invasion profile. However, it was found that resistivity values correlated with Swirr. After correcting porosity and irreducible water saturation for shoulder-bed effects, we implement Timur-Tixier equation (equation 1) to estimate permeability where the associated parameter, A, B, and C were determined from multi linear regression; the permeability is given by:

Cwirr

Bicon SAk , (1)

Where k is permeability, icon is inter-connected porosity calculated with dynamic simulations, Swirr is irreducible water saturation estimated in dynamic simulations, and A = 0.95; B = 1.44 and C = -2.35 are the constants that we found in this reservoir. Results from this calculation are shown in Figure 8, track 8.

Figure 10 compares core permeability, and estimated permeability before and after shoulder-bed effects corrections. Corrections consistently decreased the number of outliers. However, vertical heterogeneity larger than the vertical resolution of the well logs (Figure 2), did not permit better estimations of permeability.

Figure 7: Results of static simulations in Well Η across the oil-bearing zone. The well was drilled with OBM. Dashed curves represent numerical simulations. Track 1: caliper log (blue), gamma-ray log (green), and simulated gamma-ray log (dashed red). Track 2: depth. Track 3: apparent resistivities acquired with different depths of investigation (red and blue), and apparent resistivities simulated at different depths of investigation (dashed dark red and dashed dark blue). Track 4: neutron SS (green), simulated neutron SS (dashed dark blue), density (red), simulated density (dashed dark red), PEF (purple), simulated PEF (dashed fuchsia), and sonic logs (teal). Track 5: computed total porosity from mineral inversion (blue), computed sonic porosity from Wyllie’s equation (orange) and total porosity used in simulations (purple). Track 6: NMR porosities: clay-bound water (brown), bound water (olive), “free fluid” (aqua), core porosity (red), and plug porosity (black). Track 7: total water saturation computed from Archie’s equation (blue) and water saturation used in numerical simulations (green).


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Figure 10: Cross plot of core permeability and estimated permeability from Timur-Tixier equation. Comparison between (a) permeability estimated from well logs, and (b) permeability estimated with shoulder-bed corrected well logs.

NMR SIMULATIONS IN WELL Γ

Along the same depth interval used for dynamic simulation on Well Η, we compared NMR T2 distributions acquired from laboratory experiments (core data) and numerical simulations based on a recently-developed method to simulate NMR T2 distributions in the presence of arbitrary pore-size distributions and fluid saturations. Core samples were saturated with light oil during laboratory measurements. Values of porosity, irreducible water saturation, and light-oil T2 bulk input to the simulations were equal to those measured in the laboratory. Figure 11, we can compare numerical simulations and core measurements for different petrophysical rock types.

Figure 8: Results of dynamic simulations in Well Γ across a short depth section in the oil-bearing zone. The well was drilled with OBM. Dashed curves represent numerical simulations. Track 1: caliper log (blue), gamma-ray log (green) and simulated gamma-ray log (dashed red). Track 2: depth. Track 3: apparent resistivities acquired with different depths of investigation (red and blue) and apparent resistivities, simulated at different depths of investigation (dashed dark red and dashed teal). Track 4: neutron SS (green), simulated neutron SS (dashed olive), density (red), simulated density (dashed dark red), PEF (blue), simulated PEF (dashed blue) and sonic logs (purple). Track 5: NMR porosities: clay bound water (brown), bound water (olive), “free fluid” (aqua) and core porosity (black). Track 6: computed total porosity from mineral inversion (black), computed sonic porosity from Wyllie’s equation (red), inter-connected porosity used on simulations (blue), and core porosity (green). Track 7: total water saturation computed with Archie’s equation (blue), total water saturation used in the simulations (green), and irreducible water saturation used in the simulations (red). Track 8: core permeability (blue), and estimated permeability from Timur-Tixier equation (red). Track 9: NMR T2 distribution.


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Figure 9: Detailed Results of dynamic simulations in Well Γ across a short depth section in the oil-bearing zone. The well was drilled with OBM. Track 1: computed total porosity from mineral inversion (black), computed sonic porosity from Wyllie’s equation (red), inter-connected porosity used on simulations (blue), and core porosity (green). Track 2: total water saturation computed with Archie’s equation (blue), total water saturation used in the simulations (green), and irreducible water saturation used in the simulations (red). Track 3: core permeability (blue), and estimated permeability from Timur-Tixier equation (red). Track 4: NMR T2 distribution..

Figure 12: Results of NMR numerical simulation – (diffusion decay and T2 distribution) - of a composite mixture of two rocks with different porosity-permeability behavior. Simulation assumed that the volume of investigation included 50% of each rock. Sample 1409H: k = 496.6mD, = 0.16, and Swirr = 0.18 (blue). Sample 1527H: k = 691.8mD, = 0.14, and Swirr = 0.22 (green). The composite mixture of two samples is showed on red curves.

Based on the numerical simulation of NMR T2 distribution it was possible to draw the following conclusions: (1) irreducible water saturation measured in the laboratory is the correct value to reproduce the irreducible water saturation peak in the T2 distribution - the high-porosity signal is associated with the large pores saturated with light oil. (2) In core samples with isolated porosity, in order to match calculated resistivity values with log measurements, it was necessary to use lower values of porosity in Archie’s equation than those to simulate the NMR distributions; the largest discrepancy occurs in Sample 3 of Table 5. This core sample shows vuggy-porosity (Figure 11). It was necessary to assume that 35% of total porosity corresponded to isolated porosity in order to match resistivity measurements. (3) Normally, laboratory T2 distribution does not match log measurements. This behavior is due to the difference in the volume of investigation of the two measurements. Indeed, due to the large volume of investigation and the relatively high spatial heterogeneity of the reservoir, the NMR log generally measures the effective, combined response different layers of rock, giving rise to an effective merge of each T2 distribution. To reproduce this effect, we numerically mixed two different rock types and plotted the T2 distribution of the mixture. Figure 12 shows the result obtained from this simulation. (4) In rocks with complex pore structure, such as boundstones, the free fluid peak shows a spreaded distribution. Accordingly, it was necessary to modify the pore-size distribution of each rock type to match the laboratory results with numerical simulations.

Table 5: Comparison between values of porosity (plug), and water saturation (Sw-plug) measured in the laboratory, apparent resistivity (AO90) measured by induction logs, porosity (t-NMR), and water saturation (Sw-plug) used on the simulations, and resistivity (Rt_Archie) calculated from Archie’s equation.

Samples 1 2 3 4 5

plug (frac.) 0.03 0.08 0.08 0.15 0.13

NMRt (frac.) 0.03 0.04 0.13 0.71 0.10

plugwS (frac.) 0.29 0.21 0.24 0.18 0.22

90AO (Ohm.m) 757 210 520 112 87

ArchietR _ (Ohm.m) 705 235 203 98 84


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FIELD CASE No. 3: DYNAMIC SIMULATION IN WELL Χ

Figure 13 shows results obtained from dynamic simulations in the oil-bearing zone of Well Χ. The dynamic multi-layer reservoir model was constructed to match well logs and their numerical simulations. In this case we simulated the radial resistivity profile because this well was drilled with WBM. As emphasized in previous examples, water saturation present in the oil zone should be assumed immobile and, when core measurements are not available, the calculated sonic porosity was used in place of inter-connected porosity in the numerical simulations.

Figure 14 compares the radial mud-filtrate invasion profile simulated after 1 day of invasion for different rock types. Rock class 1 (XX93.56m) exhibits the deepest invasion profile and, due to its high permeability, is also associated with a prominent radial resistivity annulus. Rock classes 2 (XX86.48m) and 3 (XX83.71m) exhibit a shallower and smoother invasion profile; rock type 3 is associated with low values of electrical resistivity and, due to its low permeability, shows negligible separation between resistivity curves

with different depths of investigation (Figure 13, track 3 – XX91m).

Figure 14: Radial profiles of (a) total water saturation, (b) salt concentration, and (c) electrical resistivity after 1 day of mud-filtrate invasion. Results were plotted for three types of fluid flow units (1) Depth = XX93.56m, k = 314mD = 0.10, and Swirr = 0.08 (red), (2) Depth = XX86.48m, k = 146mD = 10% and Swirr = 0.11 (green), and (3) Depth = XX83.71m, k = 314mD, = 0.08, and Swirr = 0.15 (blue).

Figure 11: Results of NMR numerical simulation for five different core samples retrieved from the same depth interval used for dynamic simulations of Well Γ. Each panel shows the laboratory T2 distribution measurement (black), the acquired T2 distribution with NMR log in depth (magenta), numerical simulation of the T2 distribution with oil-saturated rock (green), numerical simulation of the T2 distribution with water-saturated rock (blue) and a photography of the sample.


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In order to secure a good match between well logs and their numerical simulations it was necessary to assign salt dispersivity equal to 0.8 ft2/day. This relatively large value of dispersivity may be attributed to rock petrophysical properties: high values of tortuosity present in the reservoir (macroscopic heterogeneity), or presence of dead-end pores (inter-connected vuggy porosity). Implementation of these observations into the constructed dynamic earth model yielded numerical simulations that matched available well logs. In addition, the constructed dynamic model accurately reproduced core permeabilities (Figure 13, track 6).

CONCLUSIONS

It is possible to evaluate heterogeneous carbonate formations with the construction of static and dynamic reservoir models that integrate geological information, well logs, and core data. Integrated analysis of resistivity, NMR and sonic logs indicated that some layers included isolated porosity or microporosity, which corresponded to a non-negligible fraction of the total porosity. The predominant type of porosity in each layer was the base for rock typing.

In wells drilled with WBM, we diagnosed and quantified the effect of mud-filtrate invasion on apparent resistivity logs. Each rock type was associated with a specific and internally consistent set of static and

Figure 13: Results of dynamic simulations in Well Χ across a short depth section in the oil-bearing zone. The well was drilled with WBM. Dashed curves represent numerical simulations. Track 1: caliper log (blue), gamma-ray log (green), and simulated gamma-ray log (dashed red). Track 2: depth. Track 3: apparent resistivities acquired with different depths of investigation (red, blue, aqua, dark blue and black), and apparent resistivities, simulated at different depths of investigation (dashed red, dashed blue, dashed aqua, dashed dark blue and dashed black). Track 4: neutron SS (green), simulated neutron SS (dashed dark green), density (red), simulated density (dashed red), PEF (purple), and sonic logs (blue). Track 5: total water saturation computed from Archie’s equation (blue), total water saturation used in the simulations (green), and irreducible water saturation used in the simulations (orange). Track 6: core permeability (black), and permeability used to perform the dynamic simulations (purple). Track 7: computed total porosity from mineral inversion (black), computed sonic porosity from Wyllie’s equation (red), effective porosity used in the simulations (green), and core porosity (blue). Track 8: NMR porosities: clay bound water (brown), bound water (olive) and “free fluid” (aqua). Track 9: radial distribution of electrical resistivity after the simulations of mud-filtrate invasion.


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dynamic petrophysical properties correlated with underlying pore-size distributions. Petrophysical properties are dependent on predominant type of porosity on each boundary. Consequently, it was possible to numerically simulate and match resistivity, and nuclear logs; permeability values used to simulate the process of invasion were consistent with core permeability measurements.

In OBM wells, we performed the same rock typing analysis and dynamic simulations. Thus, we estimated effective porosity and irreducible water saturation with shoulder-bed effects corrections; and finally calculate permeability using Timur-Tixier equation for each layer. It was possible to observe that after corrections we were able to decrease the number of outliers between measured and estimated permeability. However, we were not able to perform better corrections due to vertical heterogeneity on the reservoir larger than the vertical resolution of the well logs.

Additionally, we performed NMR simulations to confirm the presence of microporosity and isolated porosity in some samples. Our analysis showed that NMR T2 distribution acquired across the three different rock types were also consistent with the porosity-permeability behavior. Boundstone layers show extremely complex pore space related to bimodal/trimodal distributions, spread T2 peak on the free fluid region, and isolated porosity; and layers associated with microporosity/high irreducible water saturation exhibit a large pore volume located in T2 lower than 200ms.

Finally, using the described method we were able to predict the predominant type of porosity for different petrophysical layers, estimating pore connectivity and hence permeability with a better accuracy than the conventional well-log analysis, for both WBM and OBM wells.

NOMENCLATURE

a : Winsauer’s factor in Archie’s equation m : Archie’s porosity exponent n : Archie’s saturation exponent ep : Pore-size distribution exponent enw : Experimental exponent for krnw equation ew : Experimental exponent for krw equation k : Absolute permeability, (mD) krw : Wetting-phase relative permeability krnw : Non-wetting phase relative permeability Pc : Reservoir capillary pressure, (psi) Pc

0 : Coefficient for Pc equation, (psi.darcy1/2) Sw : Connate water saturation, (frac.) Swirr : Irreducible water saturation, (frac.) Sor : Residual oil saturation, (frac.)

Total porosity, (frac.) icon Inter-connected porosity, (frac.) plug Total porosity measured in laboratory,

(frac.) t-NMR otal porosity measured with NMR log,

(frac.) Sw-plug Water saturation measured in laboratory,

(frac.) AO90 Array induction nine foot resistivity,

(Ohm.m) Rt-Archie : Resistivity calculated from Archie’s

equation, (Ohm.m)

ACRONYMS

AIT : Array Induction Tool CSF : Common Stratigraphic Framework GR : Gamma Ray Log NMR : Nuclear Magnetic Resonance OBM : Oil-Base Mud PEF : Photoelectric Factor Log ppm : Parts Per Million STO : Standard Temperature and Pressure WBM : Water-Base Mud XRD : X-Ray Diffraction Measurement

ACKNOWLEDGEMENTS

We thank Petrobras for providing the data used in the field studies. Special thanks go to Marcelo Rezende for his geological comments about the data set. Elton Diniz-Ferreira also wants to thank Petrobras for the opportunity to study at The University of Texas at Austin. REFERENCES

Amafule J. O., and Altunbay M., 1993, Enhanced reservoir description: using core and log data to indentify hydraulic (flow) units and predict permeability in uncored intervals/wells, Paper SPE 26436, October.

Brooks, R.H. and Corey, A.J., 1964, Hydraulic properties of porous media: Hydrology Papers 3, Colorado State University, Fort Collins, CO.

Gandhi, A., Torres-Verdín, C., Voss, B., 2010, Construction of Reliable Statica and Dynamic Multi-Layer Petrophysical Models in Camisea Gas Reservoirs, Peru: Paper PPP presented at the SPWLA 51th Annual Logging Symposium, Perth, Australia, June 19-23.

Lucia, F. J., 1999, Characterisation of petrophysical flow units in carbonate reservoirs: Discussion: AAPG Bulletin, Vol. 83, pp. 1161-1163.

Pittman, E.D., 1992, Relationship of porosity and permeability to various parameters derived from


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mercury injection capillary pressure curves for sandstones: AAPG Bulletin, Vol. 76, no. 2, pp. 191- 198.

Torres-Verdín, C., 2012, Integrated Geological-Petrophysical Interpretation of Well Logs, University of Texas at Austin, January.

Verwer, K., Eberli, G. P., and Weger, R. J., 2011, Effect of pore structure on electrical resistivity in carbonates, AAPG Bulletin, Vol. 95, 2, February.

Voss, B., Torres-Verdín, C., Gandhi, A., Alabi, G., and Lemkecher, M., 2009, Common Stratigraphic framework to simulate well logs and to cross-validate static and dynamic petrophysical interpretations: Paper PPP presented at the SPWLA 50th Annual Logging Symposium, The Woodlands, Texas, June 21-24.

Wyllie, M. R. J., Gregory, A. R., Gardner, L.W., 1956, Elastic waves velocities in heterogeneous and porous media, Geophysics, Vol. 21, pp. 41-70.

IMPROVED ESTIMATION OF PORE CONNECTIVITY …...SPWLA 53rd Annual Logging Symposium, June 16-20, 2012...

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Transcript of IMPROVED ESTIMATION OF PORE CONNECTIVITY …...SPWLA 53rd Annual Logging Symposium, June 16-20, 2012...