ABSTRACT

The naturally fractured reservoirs are attractive potential zones for a successful hydrocarbon prospecting, and the variable density logs (VDL) with Chevron patterns generated by Stoneley waves is a suited tool to characterize fractures.

In this project, a simplified algorithm to evaluate fracture location using reflection coefficients and analysis of attenuation was implemented. It also uses a permeability indicator (Stoneley Slowness added by Permeability) to discriminate permeability in fractures.

The algorithm was tested in a foot hill well of the Colombian west range, detecting a previously known fractured sandstone zone and indicating its permeability. Besides, the algorithm detected other existent fractures zones with low permeability for production. Previous well flow evaluation of the localized fractures characterized them as low or no permeability fractures.

Keywords: deposits, fractures, waves, permeability, sonic log, Llanos foothills.

Los yacimientos naturalmente fracturados son atractivos potenciales para la prospección de hidrocarburos, y los registros de densidad variable (VDL) con los patrones de flecha generados por las ondas de Stoneley son una herramienta apropiada para caracterizar fracturas.

En este proyecto se implementó un algoritmo que evalúa directamente la localización de las fracturas en pared del pozo mediante coeficientes de reflexión y análisis de atenuación de ondas de baja frecuencia tipo Stoneley, y utiliza la lentitud adicional por permeabilidad de Stoneley como indicador directo de fracturas para discriminar la existencia de permeabilidad en ellas.

El algoritmo fue probado en un pozo del piedemonte de la Cordillera Oriental Colombiana, en una zona de arenisca fracturada, donde localizó e indicó la permeabilidad en una zona de fracturas ya conocida y detectó otras fracturas con permeabilidades poco atractivas para la explotación, las cuales habían mostrado bajas permeabilidades durante la evaluación de flujo del pozo.

Palabras clave: yacimientos, fracturas, ondas, permeabilidad, registros sónicos, piedemonte llanero.

1. INTRODUCTION

The theory of low and high frequency waves propagating in solids with porous saturated by fluids has been well known from the researches done by Biot (1956), who considered rocks as saturated porous skeletons where viscous fluid moves free along interconnected pores. Including anisotropy and viscoelasticity, (Biot, 1962) the theory has been widely accepted and used as basis for sonic log development and interpretation (Tezuka, Endo, Miyairi, & Brie, 1995; Tezuka & Cheng, 1997), being their predictions confirmed under controlled laboratory conditions (Brown, Batzle, Dey-Sakar, & Peeters, 2000; Wisse, Smeulders, & Dongen, 1998).

Stoneley waves were proposed to measure permeability by Rosenbaum (1974), intending to establish the characteristics of an acoustic logging tool based on the behavior of a pulse emitted in a pit fluid surrounded by a porous formation. It was found that trains of low frequency wave (Tube waves, Stoneley waves) were particularly sensitive to changes in fluid transfer conditions between the formation and the well along its wall (permeability changes). In presence of fractures in the borehole wall the Stoneley waves generate chevron patterns losing energy in permeable zones; phenomena that have successfully used in detecting fractures in calcareous formations; but the technique does not behave appropriately in wells drilling sandstone type formations due to imperfections present in their walls.

Cheng-Chuen and Toksoz (1981) studied the propagation of elastic waves in a fluid-filled borehole with a tool in the center producing synthetic acoustic logs and obtaining the equations that govern the dispersive and reflected Stoneley waves. They also found that the effective radius of the well determines the relative amplitude of the generated modes and concluded that changes in the dispersion characteristics of Stoneley waves are relatively small. A conclusive relationship between permeability and wave attenuation in field data was found (Williams, Zemanek, Angona, Denis & Caldwell, 1984), allowing the development of low frequency tools to detect permeability changes. Paillet and White (1984) predicted the relative excitation of various modes (i.e. guided waves) contained in experimental wave fronts, using a single plane layer of fluid between two hemi-spaces, providing velocity dispersion curves similar to those presented in the wall of a borehole filled with fluid. They also conclude that closer the tool diameter greater the dominance of the Stoneley mode, indicating the simplest method of detecting fractures in the borehole wall.

Cheng, Zhang and Burns (1987) related Stoneley wave propagation in a cylindrical well along with in situ permeability (Rosenbaum, 1974), founding that attenuation and dispersion of the phase velocity increases when permeability and porosity increase, and decrease when frequency increases; they also detected that the change in the Stoneley wave amplitude is more sensitive to the change of permeability than to phase velocity change.

Hornby, Johnson, Winkler, & Plumb (1989) implemented the analysis technique of reflection in presence of both horizontal and dipping fractures, considering the aperture of fracture constant along it and assuming a rigid formation compared with fluid in fractures. In experimental assays they checked the relationship between the magnitude of the reflectivity and the aperture of fracture.

Endo, Ito, Brie, Badri, & El-Sheikh (1997) assessed two wells that crossed a fault, using Stoneley waves to evaluate fractures and permeability and shear mode for evaluating cross-dipole anisotropy. Comparing the results with image records they concluded that attenuation and Stoneley reflections are evidence of open fractures and fault zones. They found that modeling Stoneley waves allow identify which reflections and attenuations are due to irregularities in the borehole, and also concluded that anisotropy and images integrated with information provided by Stoneley waves offer a better understanding of fractured reservoirs. A series of numerical and analytical models were developed for use in the interpretation of Stoneley wave reflections obtained from fractures that intersect the borehole (Kosteck, Jonson, Kenneth & Hormby,1998), and also the elasto-dynamic equation that governs tube wave propagation in a borehole intercepted by fractures filled with fluid. Models for single and double fractures in the presence of washouts and breakouts were implemented in finite differences. Analytical models were developed to interpret the Stoneley wave reflections in fractures in the wall of the borehole, calculating aperture and permeability of the fractures. These models assume a rigid formation, irregularities in the well (washouts, breakouts), changes in lithology, effects of elasticity, single and multiple fractures and the effects of viscosity of fluid. It was determined that a rigid formation model is useless to evaluate fracture parameters because overestimate the value of aperture of fractures.

These techniques were mostly developed for calcareous formations deposits uncommon in Colombia where the presence of borehole wall irregularities in clastic formations could lead to misinterpretation.

A simplified algorithm was created to directly evaluate the location of fractures using a direct permeability indicator to determine the existence of permeability in these fractures. The algorithm was tested on a well, located in the foothill of the Colombian Eastern Cordillera that crosses fractured sandstone zones. It allowed identifying a known fracture zone and assessing its permeability. Besides, the algorithm localized other fractures with permeability unattractive to exploration which showed low permeability during borehole flow tests.

The algorithm is not still able to detect fractures in some cases which have been discerned by other techniques.

2. METHODOLOGY

The implemented MATLAB program follows the next sequence: a) Separation of reflected and transmitted Stoneley waves acquired by the tool by means of a running average filter, using a Hamming window to attenuate edge effects, b) Stacking of reflected and transmitted waves to enhance amplitudes and eliminate non-coherent noise. In the multi-receiver approach a first break picking of direct waves is done, then a linear move out to the 8 signals is applied to finally stack the eight wavelets improving the signal-to-noise ratio. The step is applied both to direct and reflected waves, c) Calculation of the reflection coefficients, d) Estimation of energy in the trace, e) Estimation of attenuation factor Q^-1 and f) Estimation of Stonely slowness added by permeability. (See Figure 1).

The sequence varies depending on whether the sonic tool has single or multiple receptors with simultaneous processing of Ultrasonic Borehole Imager (UBI) and also of Dipole Shear Sonic Imager (DSI) log. The UBI image processing comprises the orientation and normalization of the image and the equation of amplitudes. A window of 1% of the size of image is used to equalize the color histogram, leaving the image in a single scale. The gross data Packed Waveform PWF3 has eight vectors chained sequentially with the information of eight receptors of the sonic tool, as shown in upper image in Figure 1.

The program was applied to a 600-feet section of an exploration borehole, providing plots of reflection coefficient, energy content in traces, attenuation factor and Stoneley slowness added by permeability. These plots were correlated along with DSI (Stoneley monopolar mode) and UBI logs for interpretation.

The raw data were acquired with a 51 feet sonic tool working in low frequency Stoneley mode at 600Hz with 40μ second sample rate, providing eight 512-samples wavelets. The tool has 3^5/8 inch diameter and the hole a variable diameter ranging from 5,5 to 21 inch.

Data Structure

The data set includes Ultrasonic Borehole Imager (UBI) to build the well image, Dipole Shear Sonic Imager (DSI) which is the main data to be used by the algorithm, Formation Density Log and Caliper to characterize lithology and imperfections in well's wall, and Additional Data Logs to perform correlations. All these data are transformed from "dlis" to "las" format and stored as matrixes whose structures are described in the Appendix.

3. PROCESSING SEQUENCE

In the single receptor case, the receiver closest to the source is selected to perform the Stoneley wave analysis, here the first wavelet in the PWF3 (bottom image in Figure 1) corresponds to the SWF1 Wavelet. In multiple receptors case the data set stored contains eight signals as shown in at top image in Figure 1.

Direct and reflected wavelets separation

Through a 20 samples Moving Average filter applied within a standard Hamming window, the direct wave is enhanced whereas the reflected wave is attenuated. In a second step the reflected wave is enhanced by applying first a 30 samples Moving Average filter followed by a single flank Hamming window expressed by the equation:

The direct and reflected waves provided by the separation step are depicted in Figure 2, where from the raw data at upper image, the direct wave in the middle and the reflected one at the bottom are observed.

The first break picking is performed on the direct wavelet by an automatic procedure. Initially a wavelet transform is applied to establish the limits within which the arrival of the direct wave will be located. This value defines a window where the covariance of the contained samples is calculated. The point where the value of the covariance is strongly deviated from the mean value is considered the first break time. (See Figure 3).

The result is shown in Figure 3 where the interval is defined by the two extreme dots whereas the first break time is identified by the dot within the anterior points.

Stacking

This step is applied only in the multiple receptors case. After picked the first break to the eight signals, see bottom image in Figure 3, the slope formed by the eight picked times is calculated and a Linear Move Out (LMO) is applied to finally stack the traces.

Reflection coefficients calculation (RC)

To calculate the reflection coefficients (RC) the Fast Fourier Transform (FFT) is applied separately to the both separated waves, and in the frequency domain the reflection coefficients RC(ω) are calculated by

R(ω) and D(ω) represent the respective reflected and direct waves amplitude spectra. But, because for some frequencies R(ω) may approaches zero these values are replaced with a function of maximum signal, so Equation 2 becomes

Here D*(ω) is the transpose of D(ω), (Hornby et al., 1989). The term provides the maximum peak of the direct wave power spectra and c is a factor, with a value of 1% to guarantee a robust deconvolution. The supplied reflection coefficients series is passed through a Hamming window centered at 600 Hz to taper it in the frequency domain, and the maximum value of these reflection coefficients estimated at a particular depth in the borehole is selected to make a maximum values-depth plot. The bottom image in Figure 4 shows maximum values estimated since 11 500 to 11 160 feet along the well.

The energy contained in the trace at particular depth (E) is estimated by numerical trapezoidal integration of the area under the power spectra curve providing energy - depth plots. The energy of direct and reflected waves calculated at 12 025 feet of depth in the borehole is observed in the upper image of Figure 4. The maximum reflection coefficient series plotted in depth, estimated in the anterior step, and the energy - depth plots can then be correlated in depth, as observed in bottom image of Figure 4.

Q^-1 Attenuation estimation

The attenuation of a wave is defined as the loss of energy measured over a period of time, observed as decaying amplitudes along the wavelet, it is mainly caused by the geometrical dispersion and energy absorbed by the medium. Although there are others approaches, to estimate a simplest method was applied. It calculates the ratio of two measured contiguous peak amplitudes separated by one period, according to the following approximation:

U(t) is the peak amplitude at time t and U(t+τ) is the peak amplitude a period after. In Figure 5 the Q^-1 calculated at different depths since 11 510 to 11 600 feet of the borehole.

and are the zero and one order Hankel functions respectively, κ is permeability, η is viscosity and κ_c2 is the Biot's wave number (Biot, 1962.) The Stoneley slowness can be expressed (Latifa, Tang, & Kuijperl, 2001) as:

S is the measured Stoneley slowness, S_p is the Stoneley slowness added by permeability and S_e is the Stoneley slowness at zero frequency associated to the wave effect in the well and corresponds to the first two terms of Equation 8. So,

In this way the Stoneley slowness added by permeability S_p is calculated as a direct indicator of permeability, because represents the additional slowness by the intrusion of the wave in the formation's porous or fractures; this added slowness depends on frequency. Figure 6 shows the Stoneley slowness added by Permeability calculated between 11 510 to 11 600 feet of the borehole.

The program provided reflection coefficient, energy content, attenuation factor and Slowness added by permeability series in depth. These results were displayed together with variable density logs (VDL) and UBI images, as shown in Figure 7 with chevron patterns visible along the reflected WF (third image from left).

The chevron patterns appeared in presence of fractures or interfaces where lithology changes (lithic contact). These points were considered in the Table 1, which contains the depths where chevron patterns were identified, caliper information, Gamma ray and Density, Reflection Coefficient, Energy in traces, Attenuation factor, Slowness added by permeability and an description of fracture or lithic contact.

Higher peaks of Reflection Coefficients are associated to fractures and the lower to lithic contact. Highest reflection coefficients values (RC > 4) with high energy (E > 5), abrupt drop in Attenuation factor and highest values in Slowness added by Permeability indicated a fracture zone with high permeability located between 12 010 and 12 030 feet. This identification coincides with packed of great size fractures that produced 4000 barrels of fluid before be cemented and cased, shown in Figure 8.

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