SPECIAL FOCUS: EXPLORATION
Graphical analysis of laminated sandshale formations in the presence of anisotropic shales
A graphical crossplot can describe petrophysics better than a set of equations and allow instant visualization of the solutions.
Chanh Cao Minh, Schlumberger; JeanBaptiste Clavaud and Padmanabhan Sundararaman, Chevron; Serge Froment, Emmanuel Caroli and Olivier Billon, Total; Graham Davis and Richard Fairbairn, CNRI
Laminated sandshale models with anisotropic shales have been discussed extensively. The interpretation methods are written in elaborate mathematical equations. However, there has not been a clear procedure to determine key parameters such as shale anisotropy, to guide the choice of solution, and, more importantly, to recognize the circumstances in which a solution is robust or sensitive to errors.
A graphical crossplot gives better insights into petrophysics than a set of equations, while interactivity allows instant visualization of the solutions, thereby helping the petrophysicist in the most effective way.
Objectives of graphical analysis are:
 To determine the shale anisotropy parameters and whether it is necessary to create multiple zones
 To define the region boundaries where each analytical solution is applicable
 To illustrate the effect of data outliers on the results
 To quickly perform sensitivity tests.
Pay region and nonpay region are subsequently defined, which allows a global assessment of the hydrocarbon potential of the thinbeds sections directly from the chart.
INTRODUCTION
Klein et al. were first to lay out the interpretation framework of electrically anisotropic reservoirs (i.e., thin sandshale laminations) in 1997.^{1} This was adapted by Shray et al. and Fanini et al. in 2001 with the addition of other logs.^{2} However, the basic shortcoming of their models was the assumption of isotropic shales that seldom exist in reservoirs under normal compaction.
The effect of anisotropic shales was treated by Clavaud et al. in 2005.^{3} Anisotropic shales are described by two independent parameters, R_{shh} and R_{shv}, representing the shale horizontal and vertical resistivity, respectively.
However, introducing one more unknown, R_{shv}, to an already underbalanced set of R_{v}, R_{h} equations further complicates the algebraic solutions. Erroneous anisotropic shale parameters can lead to either optimistic or pessimistic results with few means to verify.
Here we emphasize the graphical solutions of R_{v}, R_{h} equations adjusted for shale anisotropy. Just as one picks a shale point from a densityneutron crossplot and visually has a feel for the shale volume, likewise it can be shown that one can pick an anisotropic shale point and visually have a feel about the shale volume, the sand layer resistivity, and its corresponding water saturation. The graphical method allows the petrophysicist to choose parameters, perform Quality Check (QC) and quickly assess the potential of the thinbeds reservoirs with just one look at the crossplot data.
GRAPHICAL ANALYSIS
The equations of an isotropic sandanisotropic shale system (Fig. 1) are described below:
R_{v} = F_{sand}R_{sand} + F_{sh}R_{shv}
1/R_{h} = F_{sand} / R_{sand} + F_{sh} / R_{shh}
1 = F_{sand} + F_{sh}
where R_{v} and R_{h} are the vertical and horizontal resistivity, respectively, R_{sand} and F_{sand} are the sand layer resistivity and volume fraction, respectively, and R_{shv}, R_{shh} and F_{sh} are the shale layer vertical and horizontal resistivity and volume fraction, respectively.

Fig. 1. Isotropic sandanisotropic shale model.



Fig. 2. Graphical representations of equation 1 for an isotropic shale (top) and an anisotropic shale (bottom). The shale anisotropy effect is to move the shale point to the northwest. The blue family of curves represents various F_{sh} values, while the red family of curves represents various R_{sand} values.


Figure 2 illustrates the forward model of Eq. 1 for a particular set of R_{shv} and R_{shh}. The top plot is the original Klein plot. The bottom plot is the generalized plot to account for shale anisotropy and forms the basis of the graphical analysis. The following observations are made:
Sand sensitivity. At F_{sh} = 0%, R_{v} equals R_{h} and the data plots on the 45° line. Isotropic hydrocarbonbearing and waterbearing sands will plot along that line. It is important to note that sands with dispersed shales and structural shales will also plot on the 45° line, although they are not clean (i.e., “isotropic” does not equal “clean”).
Water line. Assume the wetzone resistivity is 0.5 Ωm as shown by the cyan dot. The progression from the clean water point to the shale point with increasing shale content follows a curved path along the red curve corresponding to R_{sand} = 0.5 Ωm (and not a straight line joining the water point to the shale point). This establishes the waterbearing curve. Any data point that lies above that curve will have S_{w} < 1.
Data domain. The data region is therefore bound to the east by the 45° line, to the north by the maximum measured sand resistivity, to the west by the anisotropic shale position and F_{sh} = 100% curve, and to the south by the waterbearing curve discussed above.
Domain boundaries. The thick red line originating from the shale point is R_{sand} curve defined by the equation R_{v}R_{h} = R_{shv}R_{shh} (which is a hyperbola in linear axes or a line in logarithmic axes). In logarithmic axes, this unique R_{sand} line is normal to the F_{sh} family of curves and intersects at right angle the 45° line at coordinates Its significance is as follows:
a. For (data point above the line), the solutions to Clavaud’s equations 4 and 5 are the positive root for R_{sand} and negative root for R_{shale}.
b. For (data point below the line), the solutions to Clavaud’s equations 4 and 5 are the negative root for R_{sand} and positive root for R_{shale}.
c. For (data point on the line), the positive and negative roots of R_{sand} are equal, and the positive and negative roots of R_{shale} are also equal. In other words, the quadratic equations in R_{sand} and R_{shale} are perfect squares.
d. The line divides the butterfly chart into two distinct regions: 1) the top wing representing obvious, good, highly anisotropic, lowS_{w}, hydrocarbonbearing sands, and 2) the bottom wing representing nonobvious, marginal, mildlyanisotropic, highS_{w}, hydrocarbonbearing sands as well as waterbearing sands.
The above discussion applies to solving equation 1 with F_{sh} as input (which gives the most complicated expression). Solving equation 1 with both R_{shv} and R_{shh} as input is much simpler and does not require switching between the positive or negative roots (only positive roots are valid). Thus, we have defined the possible envelope of the R_{v}, R_{h} data. A simple look at where the data plots on the chart shows whether the thin beds are pay or nonpay, Fig. 3.

Fig. 3. Domain boundaries of R_{v}, R_{h} data with defined pay region and nonpay region drawn in thick black lines.


Shale sensitivity. It can be seen that when F_{sh} exceeds about 90%, the F_{sh} isolines are nearly vertical/horizontal around the shale point. There is not enough sensitivity to determine accurately high shale volumes with the resistivity anisotropy technique.
Changing R_{shv} is equivalent to distorting the F_{sh}, R_{sand} grid about the 45° line by moving the shale point up or down. It can be seen that for data in the pay region, F_{sh} results remain little changed, while R_{sand} results will change in anisotropic zones. For data in the nonpay region, the reverse conclusion applies.
Changing R_{shh} is equivalent to distorting the F_{sh}, R_{sand} grid about the 45° line by moving the shale point left or right. For data in the pay region, R_{sand} results remains little changed, while F_{sh} results will change in anisotropic zones. For data in the nonpay region, the reverse conclusion applies.
Quicklook S_{w}. The R_{sand} family of curves can be rescaled in S_{w} assuming the porosity in the thin sands is the same as the porosity in the isotropic thick sands. When the user clicks on an isotropic water point on the crossplot, the wet resistivity, R_{o}, is defined. Then, S_{w} is calculated as assuming R_{w} and Archie parameters are the same in all sands. Thus, S_{w}can be read off the chart opposite R_{sand} values as shown in Fig. 4.

Fig. 4. Quicklook estimation of S_{w} from the chart.


Interactive R_{v}, R_{h} crossplot. The graphical analysis consists of the following steps:
1. Crossplot R_{v}, R_{h} data.
2. Select the shale point with the mouse. A fast forwardmodeling routine is called to display the butterfly overlay.
3. Input R_{o} with the mouse for a quick estimate of S_{w}.
4. Observe pay and nonpay regions. Make decisions. Perform interactively sensitivity tests such as changing shale point and visualizing data clusters on the crossplot and their corresponding depth intervals.
5. The routine also solves for R_{sand}, F_{sh} with shale resistivities input, and for R_{sand}, R _{sh} with shale fraction input if available.
6. If additional porosity data and Archie parameters are available, the routine automatically recomputes S_{w}.
7. Generate results plots.
The above steps are illustrated in the examples below.
EX. 1: SIMILAR THINBEDS AND SHALES ANISOTROPY
The R_{v}, R_{h} data seen previously is displayed in Fig. 5 together with other openhole logs. In this example, the shales anisotropy is the same as the thinbeds anisotropy. A clean, isotropic waterbearing sand can be seen about 1,080 ft.

Fig. 5. R_{v}, R_{h} data displayed with other openhole logs for Example 1. Shales anisotropy and thinbeds anisotropy are similar, as seen in track 4.


The workflow is as follows:
1. First, we choose the shale point from the crossplot, Fig. 6. With R_{shv}, R_{shh} values specified, F_{sh} and R_{sand} curves are generated to form the overlay.

Fig. 6. Interpreted R_{v}, R_{h} crossplot. Data corresponding to shales, water zone and pay zones are shown in green, cyan and magenta, respectively. It is interactively selected from the crossplot. The corresponding depth intervals are shown in lefttrack 3 of Fig. 7.


2. The lowest resistivity isotropic data point on the 45° line is suggested as R_{o} (which can be overridden by the user). R_{sand} lines are then rescaled in terms of S_{w} values and displayed as seen in Fig. 6. Pay zones are instantaneously indicated by data points plotted in the upper wing of the butterfly chart with S_{w}ranging from 7.7 su to 30 su.
3. Equation 1 is then solved with shale resistivities input to provide the R_{sand} curve (red) displayed in track 3 and F_{sh} curve (red) displayed in track 1 of Fig. 7. Note how well F_{sh} tracks the normalized GR log in blue.

Fig. 7. Graphical analysis results. The graphical method successfully evaluates hydrocarbonbearing thinbeds intervals from shales intervals with similar anisotropy. The green rectangular line on the right side of track 4 indicates whether the data will plot on the upper or lower wing of the butterfly chart.


4. With porosity logs shown in track 2, S_{w} is recomputed with both R_{sand}
(S_{w} R_{sand} red) and Rh (S_{w} R_{h} black) for comparison purpose, and displayed in track 5 of Fig. 7. The hydrocarbon gain is highlighted by the yellow area.
5. Water zones (cyan), shales zones (green) and thinbeds pay zones (magenta) are interactively selected with the mouse from the crossplot (Fig. 6) and displayed on the left of track 3, Fig. 7.
6. Movie answer is generated to QC the results, Fig. 8.

Fig. 8. Graphical analysis movie answer and QC display. A horizontal moving bar in the S_{w} track lists the cumulative sand volume (∑F_{sand}), the hydrocarbon volume from R_{v}, R_{h} (∑V_{h}R_{v}R_{h}) and the hydrocarbon volume from R_{h} (∑V_{h}R_{h}). The R_{v}, R_{h} data point at this depth is shown as the bold cyan square on the selfupdating crossplot on the right, thus allowing graphical CQ of the result. The user can move the movie slider to any desired depth. A 48ft (8 x 6ft) section of core photographs taken over the thin beds is shown on the left (not part of the movie).


7. Verification with image logs/core.
What happens if shale anisotropy is not accounted for? Figure 9 shows the results of such an analysis where R_{shh} = R_{shv} = 0.4 Ωm. The crossplot on the left shows that the shale points now belong to the pay zone (upper wing of the butterfly chart). As a result, erroneous hydrocarbon saturations are computed in the shales as seen in the water saturation track on the right.

Fig. 9. Unaccounted shale anisotropy leads to erroneous hydrocarbons indications. The correct saturation is shown in Fig. 7.


EX. 2: MULTIPLE SHALE POINTS
Figure 10 shows R_{v}, R_{h} crossplot data and openhole logs. There is no water zone in this example.

Fig. 10. Example 2 R_{v}, R_{h} crossplot data showing multiple shale points (a) and OH logs (b). Track 4 shows two main zones of anisotropy above and below 750 ft.


Separating the interval into two zones at 750 ft and recrossplotting the data highlight the two shale points as shown in Fig. 11. In both zones, all data plot in the upper wing of the butterfly chart, indicating both zones have good thinbeds pays. The crossplots show that the maximum R_{sand} in both zones is about 100 Ωm, which would not have been possible if a single shale point was used. It is also evident that the top zone has more good thin beds than the bottom zone.

Fig. 11. Bottomzone interpreted R_{v}, R_{h} crossplot data (a) and topzone interpreted R_{v}, R_{h} crossplot data (b).


What are the effects if only one shale point was used? Figure 12 shows the hydrocarbon gain (yellow area) computed with a single set of top shale parameters in track 4 compared with the hydrocarbon gain (yellow area) computed with a single set of bottom shale parameters in track 5. The conclusion is that using the wrong shale parameters can make the result either too optimistic or too pessimistic. Note the seemingly insignificant differences between the top and bottom shale resistivities, Table 1.

Fig. 12. Example 2 water saturation comparison between top shale parameters (track 4) and bottom shale parameters (track 5). Optimistic or pessimistic results are obtained when a single shale point is used. Highresolution resistivity images are shown on the right.


TABLE 1. Shale parameters used in example 2. 


CONCLUSION
The graphical analysis of thin sandshale laminations in the presence of anisotropic shales is a simple, robust and intuitive way to interpret R_{v}, R_{h} data.
Its interactivity allows the petrophysicist to visualize possible scenarios, perform quickly sensitivity tests and QC the results with confidence.
The chart shows directly the domain boundaries of R_{v}, R_{h} data, with welldefined pay region and nonpay region, that allow global assessment of the thin beds’ hydrocarbon potential.
ACKNOWLEDGEMENTS
This article was prepared from “Graphical analysis of laminated sandshale formations in the presence of anisotropic shales” presented at the SPWLA 48th Annual Logging Symposium, Austin, Texas, June 36, 2007. The authors thank the oil and gas companies for the permission to use the data shown in this article, and the anonymous reviewers who helped to improve the article’s content and readability.
LITERATURE CITED
^{1} Klein, J.D. et al., “The petrophysics of electrically anisotropic reservoirs,” The Log Analyst, 38, No. 3, MayJune 1997. ^{2} Fanini, O. et al., “Enhanced, lowresistivity pay, reservoir exploration and delineation with the latest multicomponent induction technology integrated with NMR, nuclear, and borehole image measurements,” SPE 69447 presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 2001; Shray, F. et al., “Evaluation of laminated formations using nuclear magnetic resonance and resistivity anisotropy measurements,” SPE 72370 presented at the SPE Eastern Regional Meeting, Canton, Ohio, 2001. ^{3} Clavaud, J.B. et al., “Field example of enhanced hydrocarbon estimation in thinly laminated formation with a triaxial array induction tool: A laminated sandshale analysis with anisotropic shale,” presented at the SPWLA Annual Logging Symposium, New Orleans, Louisiana, 2005.

THE AUTHORS


Chanh Cao Minh is the petrophysics adviser for Schlumberger with 29 years’ experience. He was an engineering manager at the Sugar Land, Texas, campus of Schlumberger Product Center.



JeanBaptiste Clavaud is a research petrophysicist with the Formation Evaluation Development team of Chevron Technology Corp. Clavaud earned a PhD degree in geophysics from the University of Paris.



Padmanabhan Sundararaman earned a PhD degree in organic chemistry from Florida State University. He is the chief petrophysicist at Chevron in Angola.



Serge Froment is the head of Operation Geology at Total E&P Angola since August 2005. He joined Total’s group in 1983 and worked as operation geologist and new venture geologist.



Emmanuel Caroli is the chief petrophysicist at Total E&P Angola. He joined Total’s group in 2003 and worked for two years on the development of geochemical reacting reservoir models dedicated to acid gases sequestration.



Olivier Billon is an exploration geologist for Total E&P Angola. He previously worked as a wellsite geologist in Brunei, Cameroon and Congo and a petrophysicist at the Paris headquarters.



Graham Davis is the chief petrophysicist at Canadian Natural Resources (CNR) International. Before joining CNR he was a local petrophysics network leader at BP and previously held positions for Shell and Enterprise Oil.



Richard Fairbairn works on CNR’s international portfolio of interests, primarily in the North Sea and western and southern Africa. Previously, he worked for Shell and consultancy companies.


