Fracture apertures from electrical borehole scans

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GEOPHYSICS, VOL. 55, NO.7 (JULY 1990); P. 821-833, 15 FIGS.

Fracture apertures from electrical borehole scans

S. M. Luthi* and P. Souhaitet

A three-step approach to detect, trace,and quantify fractures is used. Potential fractures in Formation MicroScanner images are detected as locations where conductivity exceeds the local matrix conductivity by a statistically significant amount. Integration over a circular area is performed around these locations to gather all excessive currents; this integral is then geometrically reduced to approximate the line integral A. Line sharpening and neighborhood connectivity tests are done to trace the fractures, and apertures are computed for all fracture locations. Results from a well into basement in Moodus (Connecticut) show that the method successfully traces fractures seen on Formation MicroScanner images. The resulting fracture apertures range from 10 urn to 1 mm. For the wider fractures there is acceptable agreement with apertures obtained from Stoneley wave reflection measurements. This unique and novel technique for characterizing fractures in wellbores has a very low detection threshold of around 10 urn and resolves fractures as little as I em apart. Furthermore, it provides azimuthal orientation of the fractures.

ABSTRACT

Three-dimensional finite-element modeling was performed to investigate the response to fractures of the Formation MicroScanner (Mark of Schlumberger), which records high-resolution electrical scans of the borehole wall. It is found that the equation W "" cAR~R1o-

b

describes, over two orders of magnitude of resistivity contrasts between borehole mud and the formation, the relationship between fracture width W (in mm), formation resistivity R xo, mud resistivity R m , and the additional current flow A caused by the presence of the fracture. A is the additional current which can be injected into the formation divided by the voltage, integrated along a line perpendicular across the fracture trace. Coefficient c and exponent b are obtained numerically from forward modeling. Tool standoffs of up to 2.5 mm and fracture dips in the range from 0° to 40° were found to have an insignificant effect on the above relation.

ing electrical scans of the borehole wall (Ekstrom et al., 1987). The scans are achieved by arrays of small electrodes mounted on pads held at a known potential with respect to a return electrode in the upper part of the tool (Figure 1). Currents emitted from these electrodes are recorded at a high sampling rate (typically 0.1 inches, or 2.5 mm), and are used to produce conductance images of the part of the borehole wall covered by the pads while traveling upward. These images can be oriented with respect to geographic north through continuous downhole measurement of the sonde orientation by a triaxial fluxgate magnetometer. Thus, dip and azimuth of fractures and bedding planes can be measured if the electrical images are displayed in an azimuth-depth plot (Plumb and Luthi, 1986; Pezard and Luthi, 1988; Luthi, 1990).

INTRODUCTION

Fluid flow rates through fractures with smooth surfaces are proportional to the cube of the aperture, but decrease with increasing roughness such as found on natural fracture surfaces (Brown, 1987; Jones et al., 1988). The estimation of fracture apertures in wellbores penetrating fractured reservoirs is, therefore, of paramount importance for assessing reservoir productivity. Reflections of the Stoneley wave measured by an array sonic tool (Hornby et al., 1989) have recently been proposed as an in-situ measurement of fracture aperture. The technique presented in this paper addresses the same problem, albeit with an entirely different downhole geophysical measurement principle. The Formation MicroScanner is a wireline device produc-

Manuscript received by the Editor August 22, 1989; revised manuscript received December 8, 1989. *Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT 06877-4108. *Etudes et Productions Schlumberger, rue de la Cavee, Clamart, France. e 1990 Society of Exploration Geophysicists. All rights reserved. 821

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822

Luthi and souhalte

Open fractures are among the most prominent features seen on electrical images because of the large conductivity contrasts between the fluid in the fracture-typically assumed to be the drilling mud-and the surrounding rock. In many boreholes drilled with water-based mud this contrast may be several orders of magnitude. Examples of open fractures on electrical images are documented by Plumb and Luthi (1986), Ekstrom et al. (1987), and Pezard and Luthi (1988). They show up as conductive streaks exhibiting a large variety of morphologies ranging from short, irregular shapes to planar. Fractures typically affect several adjacent samples because the electrode diameter is approximately twice the sampling distance, accounting for some vertical and horizontal overlap, and also because the electrical flow lines are severely distorted in the vicinity of the fracture. It is, therefore, of interest to find a relationship between the

TELEMETRY

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AMPLIFICATION CARTRIDGE II._ _ INSULATING SLEEVE

..

FLEX-JOINT INCLINOMETER

electrical signal produced by the fracture and fracture parameters such as aperture, dip angle, resistivity of the fluid in the fracture, resistivity of the rock, and the distance from the tool to the borehole wall (tool standotl). We address this problem through forward modeling of the electrical field using a three-dimensional (3-D) finite-element modeling code. To invert electrical borehole scans for fracture parameters, we then present a statistical method to identify and trace fractures on Formation MicroScanner images and a technique to compute fracture apertures for each sample located on the fracture trace. MODELING OF ELECTRICAL FRACTURE RESPONSE

Technique The finite-element method has been used successfully by Chang and Anderson (1984) to model electromagnetic borehole devices such as the induction tool. In our approach, which is closely related to the technique of Chang and Anderson (1984), the current emitted by a single Formation MicroScanner button in front of a fracture (Figure 2) is simulated using the finite-element method which solves Laplace's differential equation for the electrical field over an adaptive three-dimensional grid in and around the borehole. Grid node spacing is very close in the vicinity of the electrode button, covering at least 20 nodes in the sensitive area along a line across the fracture and increases progressively away from this area with a minimum of 10 more nodes in each direction. The total number of grid points is about 70 000; the progressive variation in element size away from the sensitive area avoids discontinuities which may be detrimental to the computational accuracy. The fracture is modeled as a thin-sheet element with a uniform resistivity equal to the mud resistivity. Current densities are computed on the nodes covering the tool pad, and button currents are obtained by multiplying current densities with their corresponding area. All computations assume planar, parallel fractures of infinite extent. The dip of the fracture, i.e., the

PREAMPlIFICATION CARTRIDGE

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Fracture

Button Trajectory

4 ARM SONDE

FIG. 1. Sketch of the Formation MicroScanner tool configuration discussed in this paper (after Ekstrom et aI., 1987). Two of the four pads are equipped with the array of imaging electrodes shown on the left. A newer tool design has fewer electrodes on all four arms.

Borehole

FIG. 2. The modeled situation of an electrode button crossing a fracture on the borehole wall.

823

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Fracture Apertures from Electrical Scans angle between the steepest line in the fracture plane and the horizontal, measured in the vertical plane, is always directed downward and away from the tool's pad (Figure 2). Dip modeling is obtained by grid deformation, creating some imprecision and imposing an upper dip limit of 40 degrees on the computation. Modeled formation resistivities (Rto) are 10, 100, and 1000 n'm and correspond to the near-wellbore part of the rock which is invaded by the drilling fluid. Fracture apertures (W) are varied from 50 urn to 200 urn, fracture dips from 0 degrees to 40 degrees, and tool standoffs (the distance between the button surface and the borehole wall) from 0 to 2.5 mm. The mud resistivity (R m ) is held constant at 0.1 n·m.

standoff for the set of fracture and rock parameters used in Figure 3, as was also true for all other modeled situations. In the following we present the entire set of modeling results, but for a tool configuration which, although realistic, does not correspond in detail to the actual tool. Results for A versus fracture aperture Ware shown in Figure 5, where each data point is an average of five tool standoffs. A clear dependence of A on R xo is obvious, whereas fracture dips turn out to be relatively unimportant over the range of investigated values. For a simple, first-order approximation

200

Results

Figure 3 shows the button response for one set of parameters: For no standoff there is a sharp increase in button current in the immediate vicinity of the fracture. As the standoff increases, the presence of the fracture is detected earlier, but the current peak diminishes. A simple expression of the fracture response of the Formation MicroScanner is the integrated additional current, or A =

V1 e

fzn {h(z) - hm} dz,

150

~

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0

0

0

100

~

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(1)

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where V e is the potential difference (in V) between the imaging arrays and the current return at the top of the tool, I b the button current (in f.LA) as a function of the vertical position z as the tool moves across the fracture (with zo, the first, and Zn' the last, positions at which the measurement is affected by the fracture), and Ibm the button current in the undisturbed zone or matrix. A corresponds to a conductance added to the rock through the presence of the fracture. Figure 4 shows that A is practically independent of tool

o

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0.5

1

1.5

2

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Tool Stand-Off lmml FIG. 4. Integrated additional current A produced by the presence of a fracture plotted versus tool standoff for the same parameter values as in Figure 3.

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