Quantitative Formation Permeability Evaluation from Stoneley Waves

Summary The borehole Stoneley wave has been shown to be sensitive to fluid mobility, the ratio of permeability, and viscosity. The phenomenon is well described using the Biot theory and the effect of the mudcake was modeled as an elastic membrane. An inversion technique, which uses both slowness and attenuation of the Stoneley wave over a range of frequency to evaluate mobility, was proposed. This paper describes the implementation of an interpretation methodology based on this technique. The error analysis shows that an accurate determination of the fluid mobility requires that some critical parameters, such as the mud slowness, mud attenuation, and the pore-fluid modulus, be precisely determined. An interpretation procedure is proposed to determine these parameters with good accuracy. The fluid mobility can then be determined without the need for external calibration with another measurement. The intrinsic permeability of the rock can then be derived, knowing the various fluid components, their relative permeabilities, and their respective viscosity. When using the proposed methodology within the applicable limits, the Stoneley wave can provide a continuous estimation of the formation permeability along the well. Core measurements are not required for calibration although they can be used for verification. This technique will find applications in reservoir engineering optimization of well production through better placement of the perforated intervals. Introduction Permeability information is essential for oil and gas production, once reserves have been identified and evaluated, to optimize well completion and field development. Permeability is needed to determine the optimal perforated interval with respect to the reservoir boundaries and the water table. More generally, permeability is needed for:completion and production optimization to maximize production while minimizing water cut,production prediction and planning to maximize hydrocarbon recovery, anddefinition of drainage pattern. Although the absolute value of permeability in the reservoir is usually considered to be the most important, the variations of permeability along the well are equally important. Permeability, however, is one of the most difficult measurements to get in an oil well. Direct measurements either provide only a few points along the well, as is the case with well testing or wireline testers, or provide measurements under different conditions in the case of core measurements. With indirect measurements, permeability is inferred from a different property (porosity, nuclear magnetic resonance, or geochemical logs) using models and assumptions. As the models are not exact, the uncertainty attached to the results is high. Another technique, the study of invasion profiles, give only qualitative information about permeability. The Stoneley wave is the only technique to provide a continuous, direct measurement of permeability along the well. However, although the principle of the measurement has been known for quite some time, obtaining a reliable and accurate measurement of permeability from Stoneley waves has proved difficult. At low frequency, the Stoneley mode becomes the tube wave and propagates as a piston-like compression of the borehole fluid in the borehole. When the borehole crosses permeable zones or permeable fractures, some fluid movement occurs between the borehole and the formation. This results in some energy loss, hence attenuation, and a slowing down of the wave, hence increased Stoneley wave slowness (Fig. 1). Fractures and permeable zones have different characteristics and affect the Stoneley wave in different ways. In particular, in the case of permeable fractures, the strong, localized impedance contrasts also cause reflections of the Stoneley wave that appear as chevron patterns on a variable density log (VDL) display. Specific techniques are used to evaluate permeable fractures with the Stoneley wave.1–3 The objective of the present work is to evaluate the permeability of nonfractured reservoirs, i.e., essentially, distributed permeability from the pore space. In effect, the formation parameter the Stoneley wave measured is not exactly the formation permeability, but rather the fluid mobility (i.e., the ratio of permeability to fluid viscosity, ko/µp). The permeability is evaluated in millidarcy units and the viscosity in centipoise, so that the mobility is usually given in md/cp. As the viscosity of water is about 1 cp, mobility and permeability take the same value in water-bearing reservoirs. The pore fluid viscosity is normally known with sufficient accuracy, hence a measurement of permeability can be obtained from the Stoneley wave. There have been many attempts at evaluating permeability from the Stoneley wave. Rosenbaum proposed measuring permeability with the Stoneley wave as early as 1974.4 In 1984, Williams et al. showed conclusive correlations between permeability and Stoneley attenuation in field logs.5 Following this idea, many log interpreters tried to develop empirical correlations between the Stoneley wave energy and permeability. But calibration with other information was needed in all cases, and the reported successes were, unfortunately, followed by disappointing results. Theoretical models based on the Biot poroelastic theory were developed by Schmitt et al.6 and Chang et al.7 Comparisons with laboratory experiments made by Winkler et al.8 provided a validation of these models. Based on these models, a simplified algorithm was developed that estimates permeability from the difference between the Stoneley slowness measured at a given frequency and the slowness calculated using a purely elastic, nonpermeable formation model. This method, called the S-Se technique, is currently proposed commercially.3 It produces useful indications in hard rocks but is often unsuccessful in soft rocks. Tang et al. in 1984, proposed a simplification of the Biot-Rosenbaum model and developed an inversion technique for the Stoneley wave amplitude.9 Later, they studied the effect of the presence of the tool in the borehole.10 Cassell et al. in 1994 proposed a simple technique to extract a permeability indicator from the variation of the Stoneley attenuation with frequency.11