By Wei Chen. January Signature of Author Department of Earth Atmospheric and Planetary Sciences January, 1999

Transcription

1 In-situ Permeability Estimation: A Comparison between Acoustic and NMR Logs By Wei Chen For submission to the Department of Earth, Atmospheric, and Planetary Sciences in partial fulfillment of the requirements for the degree of Master of Science in Earth and Planetary Sciences MASSACHUSETTS INSTITUTE OF TECHNOLOGY January 1999 V 1999 Massachusetts Institute of Technology All Rights Reserved Signature of Author Department of Earth Atmospheric and Planetary Sciences January, 1999 Certified By... (2... M. Nafi Toksoz Professor of Geophysics Thesis Supervisor Accepted By... Ronald G. Prinn Department Head FROM 9 LIBRARIES CHUSETTS INSTITUTE V L -/-- d"ir"o

2 In-situ Permeability Estimation: A Comparison between Acoustic and NMR Logs By Wei Chen Submitted to the Department of Earth Atmospheric and Planetary Sciences on January 1999, in partial fulfillment of the requirement for the Degree of Master of Science in Earth and Planetary Sciences Abstract The estimation of formation permeability from full waveform acoustic and nuclear magnetic resonance (NMR) logs in petroleum well logging has improved significantly in recent years. In this thesis, we review the methods of permeability estimation from Stoneley waves and provide permeability comparisons between acoustic and NMR logs. When a Stoneley wave travels along a permeable formation, hydraulic exchange between the Stoneley wave and formation will occur. As a result, Stoneley wave travel time will be delayed and the Stoneley wave attenuation will increase, causing a centroid frequency shift. Therefore, these two wave attributes can be used to estimate formation permeability. NMR logging data can also be used to estimate permeability. Permeability estimates using Stoneley waves and NMR logging were tested using data from a section consisting of sandstone and shale beds. The permeability results show very good correlation for these two different methods. Data from a gas zone that is analyzed shows high permeability values from acoustic data and low values from NMR. The difference between these two permeability results can be used as a gas zone indicator. Thesis Supervisor: M. Nafi ToksSz Title: Professor of Geophysics Co-Supervisor: Dan Burns Title: Research Scientist

3 Acknowledgments I would first like to thank my advisor, Prof. M. Nafi Toks6z, for bringing me to MIT and for his support, Prof. Dale Morgan for sharing his opinions on doing research, Dr. Dan Bums for numerous beneficial discussions, and Dr. Zhenya Zhu for continuous suggestions and encouragement. Second, I wish to thank the Western Atlas people for all the great help and support they provided during my summer internship and with my thesis. They have contributed to ERL the express software and data to ERL, which made this thesis possible. I am especially grateful to Arthur Cheng, who introduced me to this thesis topic, which led me to the fabulous Acoustic and NMR world, and to Dr. Xiaoming Tang, who used to give me the most straightforward but helpful comments. Thanks also go to Tim Geerits, Stephen Gelinsky, Songhua Chen and Edy Purwoko for helping me with the software and data. The summer working with them was really a pleasure. I also thank Dr. Kurt-M. Strack, T.A. Ma for their kind concerns and help. I also wish to extend my gratitude to my classmates and friends at MIT, Franklin Ruiz, Jesus Sierra, Feng Shen, and Johnathan Kane. Their friendship, jokes and help made my life at MIT much easier. I would also thank Liz Henderson, Sue Turbak, and Kate Jesdale who made ERL a family-like place, Jane Maloof for helping me with the Baker Atlas workstation installation, Matthias Imhof and his wife Nancy for bringing me to a body conditioning class to keep me healthy. Thanks also go to Weiqun Shi, Jie Zhang, Xiang Zhu and many others. Finally, I must thank my parents who have always been there for me. Without their love, I couldn't have gone through all the difficulties in these two years. I would also thank my girl friends at MIT, Yang Xiaowei, Lynne Sevdberg, and Jane Brock. Their spirit and experience in pursuing PH.D degrees are always great inspirations to me.

4 Contents Chapter 1--- Introduction B ackground O utline Chapter 2--- In-situ Permeability Estimation from Acoustic Logs A Review Introduction Biot-Rosenbaum model Acoustic wavefields in a borehole Stoneley Waves Stoneley wave characteristics Sensitivity of a Stoneley wave to permeability Permeability Estimation from the Field Data W avefield separation Stoneley wave modeling Synthetic and measured wave comparison Reference depth selection Permeability results from the full waveform acoustic log Chapter 3--- A Comparison between Acoustic and NMR Log Permeability E stim ates Real Data Permeability Estimation Example Stoneley wavefield separation results Perm eability results Gas Zone Effect Gas zone effect on permeability estimation from Stoneley wave Gas zone effect on permeability estimation from NMR FDC-CNL Gas Zone Indication Chapter 4---Summary and Conclusions References

5 Chapter 1 Introduction 1.1 Background Acoustic logging is one of the primary formation evaluation methods. Since the late seventies, full waveform acoustic logging research and development have made significant progress. Permeability estimation is among one of the major recent advances. An acoustic logging tool generates a pressure pulse in the borehole fluid resulting in several guided modes traveling along the borehole wall. The Stoneley wave, a low frequency guided wave in the monopole full waveform data, can be used for permeability estimation. During Stoneley wave propagation in a permeable formation, hydraulic exchange between the wave induced borehole fluid motion and the formation pore fluid system occurs at the borehole wall. This causes a travel time delay and centroid frequency shift in the Stoneley wave relative to propagation in a non-permeable formation. These changes can be used to estimate permeability. The first theoretical work was done by Rosenbaum (1974), who used the Biot (1952) theory to model the formation as a fluid-saturated porous medium. However, this work modeled acoustic waves with frequencies around 20 khz. This frequency was commonly used for acoustic tools in the late 1970's. At this frequency range, however, the Stoneley wave cannot be efficiently excited. Rosenbaum (1974) also assumed a non-permeable mudcake borehole wall. With this assumption and the frequency used, it was shown that permeability could not be measured from Stoneley waves. The M.I.T. Borehole Acoustics and Logging Consortium carried out extensive research in this area. The initial approach was to predict the velocity and attenuation for the Stoneley wave using the Biot theory and permeability values obtained from core measurements and then compare the model results to field data. The object was to establish the validity of the Biot-Rosenbaum model (Burns and Cheng, 1986). Winkler et al. (1989) of Schlumberger-Doll Research did laboratory scale experiments and confirmed the theory. When the Stoneley data was used to invert permeability, it turned

6 out there were too many unknown parameters and the full Biot-Rosenbaum theory was quite time consuming in the data processing and inversion. Tang et al. (1991) developed a simplified model, where the Stoneley wave interaction with a porous formation is further broken-down into "elastic" and "permeable" parts. Later, the one dimensional wave propagation approximation for Stoneley wave propagation across permeable zones and fractures was developed (Tang and Cheng, 1993a). Very recently, the theory was further developed to realistically model borehole irregularities (Tezuka et al. 1994) and formation heterogeneities (Gelinsky and Tang, 1997). In the field data processing of the Stoneley waves, a wave separation technique was also developed to separate the Stoneley wave into transmitted and reflected wavefields. The application of the technique cleans up the transmitted Stoneley wave from reflection and other noises in the logging environment. Since this thesis will also use the permeability estimation from NMR, a brief background about this technique is introduced. Detailed descriptions about NMR theory, measurements, tools, processing and interpretation can be found in a thesis entitled "Nuclear Magnetic Resonance Logging" by Howard F. Sklar (Master thesis, 1997, Massachusetts Institute of Technology). Since Purcell and Block first discovered nuclear magnetic resonance, many developments and applications have been established, including those in the petroleum industry. NMR well logging has been developed significantly in the past few years. Many commercial tools, such as the magnetic resonance imaging log (MRIL-C) tool from NUMAR and the combinable magnetic resonance (CMR) tool from Schlumberger are available. Carr and Purcell (1954) developed a new fast measurement mode, and the first NMR experiments on sand packs were done by Brown and Fatt in Four years after this invention, Brown and Samson performed the first NMR measurements in a borehole using the Earth's magnetic field. In 1966, Seevers observed a relation between relaxation rate and permeability. Timur (1969) derived the concept of Free Fluid Index, which provides a new method for estimating permeability from NMR. In 1978, Schlumberger offered its first commercial NMR tool (NML), which used the Earth's magnetic field. In 1990, Numar Corporation introduced a prototype of a pulse-echo NMR logging tool (the

7 MRIL) as a commercial service. In 1991, Schlumberger designed a prototype of a mandrel-type pulse-echo tool. The NMR logging is based on the physical principle: the resonance of nuclei in a magnetic field. Many nuclei in nature have a magnetic moment. When subject to a magnetic field, such nuclei tend to align their magnetic moments parallel to the field, corresponding to the lowest energy state. The higher the magnetic field, the more nuclei can be polarized and the higher the magnetization of the sample. Electro-magnetic fields at specific radio frequencies (RF) can influence the macroscopic magnetization. By transferring energy from such fields into the sample, the magnetization can be turned away from its aligned orientation to a different orientation. The re-oriented magnetization generates a RF signal itself, which can be detected. For most nuclei, these signals are too small to be detected. Hydrogen is an exception due to its large magnetic moment and high abundance, both in water and hydrocarbon. Thus, the magnitude of the signal is a measure for the fluid-filled porosity in the formation. The high magnetic fields created by NMR tools result in a high signal to noise ratio and enables application of a measurement technique called pulse-echo NMR. With pulse-echo NMR the decay of the magnetization can be efficiently measured over a relatively long time period, typically in the order of 0.1 seconds. The relaxation time of bulk water can be described by a single relaxation time, ~ 3 seconds. When the fluid is confined in a porous medium, the relaxation time is much shorter because the interaction between the fluid and the wall of a pore introduces an additional means of relaxation. By measuring the relaxation, information about pore sizes is obtained, which is related to the permeability of the formation. Based on these physical principles the porosity, permeability, and water saturation can be estimated from the NMR logging data. 1.2 Outline Chapter 2 discusses the permeability estimation from full waveform acoustic logs. It contains five major parts: the Biot-Rosenbaum model, wavefields in a permeable porous borehole, Stoneley wave characteristics and sensitivities to permeability, and a brief description of the modeling and processing methods used to estimate permeability

8 from the Stoneley wave. Finally, the permeability results estimated from the Stoneley wave are presented. Chapter 3 presents comparisons between permeability profiles derived from acoustic and NMR logs. A real data set from a sandstone-shale formation is used for the comparison. The effects of a gas zone on the two permeability profiles are presented and the cause of these effects is analyzed. Chapter 4 concludes the thesis by summarizing the results and gives a discussion of future directions. In this thesis, only a sandstone-shale sequence formation data are used to compare the Stoneley-wave derived permeability profiles with NMR measurements. Other examples and tests, such as NMR permeability estimation in carbonates and their comparison with Stoneley wave permeability results are also interesting topics. Further research and development will lead to new applications. In summary, chapter 2 of this thesis provides the knowledge on in-situ permeability estimation from acoustic logging. Chapter 3 describes the original work of this thesis, the permeability comparison and gas zone effect analysis. Chapter 4 recaps the thesis work and suggests future research directions.

9 Chapter 2 In-situ Permeability Estimation from Full Waveform Acoustic Logs --- A Review Fluid flow through porous rocks in underground water, oil and gas reservoirs is controlled by permeability. Most conventional permeability estimations come from coremeasurements. Many core data are required to map permeability of a formation, and because the core samples may be altered after coring and retrieval, the measured permeability may differ from its in-situ values. Recent developments in full waveform acoustic logs give a continuous and accurate subsurface permeability estimation method. In this chapter, the methodology for deriving in-situ permeability from the Stoneley wave of an acoustic log is described. The sensitivity of the Stoneley wave to the permeable zone is briefly analyzed. Theoretical model and data processing methods are reviewed. Permeability estimation results will also be presented. 2.1 Introduction Biot-Rosenbaum model Biot's model allows the analysis of seismic wave propagation in a fluid saturated porous media (Biot 1952, 1955). The model assumes an isotropic two-phase medium consisting of a solid elastic matrix permeated by interconnected pores saturated by a compressible, viscous liquid. Rosenbaum (1974) used Biot's theory to model acoustic

10 logs in a fluid-filled borehole surrounded by a porous and permeable formation. Later on_ other models and experiments were carried out based on this work Acoustic wavefields in a borehole There are four seismic waves excited by a monopole source in a fluid-filled borehole: two body waves and two guided waves. The two body waves are compressional (P) and shear (S) waves. The seismic waves propagate as compressional waves in the fluid, and refract along the borehole boundary as P and S waves at critical angles. They are then refracted back into the fluid as a compressional wave. They are non-dispersive. The two guided waves (Biot, 1952; Cheng and Toksoz, 1981) are the Stoneley wave and pseudo-reyleigh waves. The Pseudo-Rayleigh waves have phase velocity between the formation shear velocity and the fluid velocity. Their amplitude decays exponentially in the formation away from the borehole boundary and is oscillatory in the fluid. The Stoneley wave has a phase velocity lower than the fluid velocity, and its amplitude decays exponentially in both the fluid and formation away from the solid-fluid boundry. These modes of propagation are illustrated in Fig In hard (fast) formations, these four wavefields can be observed. In soft (slow) formations, only the P wave and Stoneley (tube) wave can be seen. The hard (fast) formation refers to the formation with shear wave velocity faster than the fluid velocity. In such formations critical refraction is possible at the borehole wall. The soft (slow) formation refers to the formation with shear velocity slower than the fluid velocity. These differences are shown in Fig Stoneley Waves are introduced. In this section, the Stoneley wave characteristics and sensitivities to permeability Stoneley wave characteristics Different waves are sensitive to different formation properties. A Stoneley wave is especially sensitive to formation permeability. A Stoneley wave has a few important characteristics. It is a surface wave or guided wave and is also referred to as a tube wave.

11 It travels along the surface between the borehole fluid and formation. Generally, it is the slowest wave in the total acoustic wavefield. The Stoneley wave is most efficiently excited at low frequencies (less than 3 khz); its wave motion is axially symmetric Sensitivity of a Stoneley wave to permeability When a Stoneley wave travels along the borehole, this axially symmetric pressure pulse deforms the borehole wall. If the formation is hard, the deformation is small and the velocity and frequency will not be significantly effected. When the Stoneley wave travels through a permeable formation saturated by viscous fluid, however, velocity is reduced relative to a non-permeable formation. The Stoneley wave energy not only deforms the rock matrix, but also pushes the viscous fluid away from the borehole wall into the formation. As a result, the Stoneley wave is slower in the permeable zone. Also, the Stoneley wave is attenuated more in permeable zones than in impermeable zones. This theoretical prediction was found to be in good agreement with field data (Williams et al., 1984). However, in real field data, there are several factors that contribute to Stoneley wave velocity and attenuation. They are acquisition noise, borehole radius changes, formation change, fluid and formation intrinsic attenuation, mudcake, and permeability. Getting the permeability from field data affected by so many other factors is a big challenge. The following section will briefly discuss the method for getting permeability from field data. 2.3 Permeability Estimation from the Field Data Permeability can be estimated through the following steps in order to remove the effects unrelated to permeability in field waveform data: 1)Wave separation to separate direct transmitted waves from reflected waves caused by formation changes, acquisition noise, etc.; 2) Wave modeling to simulate elastic wave propagation effects in the transmitted Stoneley wave data; 3) Synthetic and measured wave comparison; 4) Permeability estimation.

12 2.3.1 Wavefield separation In order to obtain petrophysical rock properties from borehole Stoneley wave data, it is necessary to separate the direct Stoneley wave from the reflected waves due to the formation changes. The following description is based on the methods used by Baker Atlas (formerly Western Atlas) (1997). The logging tool is in the center of the borehole with transmitter at the bottom and an array of receivers at the top. If there are fractures or bed boundaries located near the top and bottom of the tool, the array of receivers will receive the direct transmitted Stoneley wave first, then the reflected waves from the boundaries. The receivers, starting at the farthest offset, will receive the reflected wave from the top bed boundary. This wave is called a downgoing reflected wave. The receivers in increasing order starting at the nearest offset will receive the reflected wave from the bottom boundary. This wave is called an upgoing reflected wave. The moveouts of the waves in eight receivers and in a common receiver plot are shown in Fig. 2-3 and Fig Using the differences in wave moveouts, the array data are separated into upgoing and downgoing waves. The waves are then shifted to the middle of the array and stacked over the array at each logging depth. The result is depicted in Fig Once the wavefields are separated, a cross-correlation between the direct transmitted wave and downgoing reflection is performed to obtain the reflectivity. More details of the wavefield separation can be obtained from Tang (1997) Stoneley wave modeling In the wave separation processing, effects such as acquisition noise and formation change are suppressed. However, the wave data transmitted from the transmitter to receiver still contains effects unrelated to permeability. These effects are mainly due to two factors: (1) Wave amplitude and time variation caused by borehole and formation changes. (2) Intrinsic attenuation in the borehole fluid and formation. These effects must be removed from the data to isolate the permeability effect. An elastic model with borehole changes and intrinsic attenuation was used in our model. For this model, formation density, P and S wave slowness values, and borehole caliper are

13 needed as inputs. The synthetic wave response at any depth is convolved with a source waveform to obtain the synthetic waveform. Irregular borehole and heterogeneous formation effects were also included in this model (Gelinsky and Tang, 1997) Synthetic and Measured Wave Comparison Tang et al. (1991) showed that the total displacement of a Stoneley wave in a porous and permeable formation could be separated into elastic deformation and fluid flow effects. By comparing the measured Stoneley wave and the predicted Stoneley wave in a non-porous elastic medium, we can separate the effects caused by formation permeability. This comparison is based on two wave attributes: * Travel time delay; " Centroid frequency shift. We define the travel time, Tc, as: x x T, = t[w(t)] 2 dt/ [W(t)] 2 dt (2-1) 0 0 And the entroid frequency, fc, as: x x f, = fa(f)df / A(f)df (2-2) 0 0 Where t is Stoneley wave travel time at a particular logging depth, W(t) is the Stoneley waveform, f is the frequency at a particular logging depth, A(f) is the amplitude spectrum at the particular logging depth. Applying the above two equations, the travel time delay and centroid frequency shift can be indicated as following: ATrm"d -7 "Tsmsd (2-3) Af,"m" - f''" - flfsd (2-4) where msd refers to measured values, and syn refers to predicted synthetic values. These two quantities can be used to give a good indication of formation permeability. For example, if the travel time delay correlates with a centroid frequency shift, one can almost be certain that this phenomenon is due to formation permeability effect. Fig. 2-5 shows an example of permeability indication using travel time delay and centroid frequency shift log curves. On the first track, the shaded area on the left is the travel time delay (DELAY), the scale is set from us from left to right. The right

14 shaded area is the display of centroid frequency shift (FREQSHFT). In order to highlight correlations between these two curves, the scale for the centroid frequency shift is set from right to left from 0-100Hz. The second track shows the measured transmitted Stoneley wave (DWVTR). The third track shows the synthetic Stoneley wave (DSTWVSYN) calculated from the elastic model. From the comparison of track 2 and 3, we get the permeability indication on track 1. The processing flow for estimating permeability from full waveform data included several steps. The first step is to acquire borehole acoustic log data (monopole and dipole data). Then, P wave velocities are obtained from monopole full waveform data and S wave velocities are obtained from dipole data. After we separate the Stoneley wavefield into transmitted and reflected wavefields, the P, S velocities, caliper, density and some other parameters are used to build the Stoneley elastic model. Then, we compare the modeled Stoneley waves and the measured Stoneley waves to obtain the relative travel time lag and attenuation, which are then inverted for permeability values Reference depth selection The selection of the reference depth is the key step to get an accurate permeability estimate. The purposes of selecting the reference depth are: 1) to provide a source waveform for the synthetic elastic model, and 2) to provide a permeability reference so that permeability at other depths can be calculated relative to the reference depth. Moreover, multiple reference permeabilities can also be used to calculate the pore fluid parameters. The reference depth should be selected from a relatively homogeneous interval with good caliper and good waveform coherency. An example is shown in Fig Track 1 shows the Stoneley wave centroid frequency (FCTR) and slowness (DTST), track 2 shows the raw and processed reflectivity (REFLO), and reflector (REFL), Gamma Ray (GR), and caliper logs, track 3 shows the Stoneley wave slowness (DSTWV). As seen from this figure, in the interval from 9200' to 9250', the centroid frequency has high values and the slowness has low values compared to the depths below, the caliper is smooth, the reflectivity values are very low, and the wave data has a high quality. The Gamma Ray analysis suggests that the type of rock in this interval (shale) has very low permeability values. For these

15 reasons, any depth in this interval can be chosen as the reference depths and the reference permeability is set to zero. In order to carry on the discussion for the next chapter, pore fluid parameter calibration should be mentioned here. Reference depths can also be used to determine the pore fluid parameters: pore fluid viscosity, density and slowness. The pore fluid parameters are difficult to know if multiple fluids are present and the degree of saturation is unknown. In order to get these parameters, another reference depth from a more permeable interval is needed along with its permeability value. Referring to Fig. 2-6, the FCTR (centroid frequency) value at 9295' is substantially lower than those in the 9200' to 9250' interval where a reference has been chosen, and the slowness (DTST) is substantially higher. The average permeability from the Nuclear Magnetic Resonance log is 30md. So, a second reference depth is chosen here. The pore fluid parameters will be estimated based on the two selected reference depths, and the parameters will be used to estimate permeability curves for the entire processed interval. 2.4 Permeability Results from the Full Waveform Acoustic Log Fig. 2-7 shows the final permeability estimates from full waveform acoustic log data in a sand-shale sequence. Track 1 shows the Gamma ray log and the quality control indicator (PERMQC) for the permeability estimation. The PERMQC value is high when permeability value quality is good and the theory to data misfit is low. Track 2 shows travel time delay (DELAY) and frequency shift (FSHFT). The travel time delays are displayed from 0 to 300us from left to right and the frequency shift is displayed from 0 to 100Hz from right to left. Track 3 shows the permeability result derived from the Stoneley wave (STPERM), along with the permeability estimated from the Nuclear Magnetic Resonance log (NMRPERM). The two permeability curves agree quite well, showing the consistency of both methods. The attenuation (ATT) and measured Stoneley wave data are displayed on track 4. Track 5 shows the synthetic Stoneley wave (DSTWVSYN). The measured and synthetic Stoneley reflected wave data (RWVRT, RSTWVSYN) are displayed in track 5, 6 and 7, respectively.

16 T T T P-Lewky P Wei* 31 Pes ft-r~gsg -anoo. Wewes To" We" Fig. 2-1 Schematic diagram of the acoustic modes that propagate in a borehole. T and R refer to transmitter and receiver position. (Burns, 1990) F- -ues PAST SAP0TOlM V P -I Tun KLOW SATONE TIME (ine) 6.71 Fig. 2-2 An example of full waveform. acoustic log data from a "fast" and "slow" formation.(also referred to as "hard " and "soft" formations). ( Williams et al. 1984)

17 ARRAY ACOUSTIC. DATA WITH REFLECTIONS Downgomng reflected wave T IME (microseconds) Fig. 2-3 Array wave separation configuration. (Baker Atlas, 1997) X120 COMMON REUIVERACOU1ICVAIA Direct transmitted wave Upgoing reflected wave Wn X100 TIME (microseconds) Downgoing reflected wave Fig. 2-4 Common receiver wave separation configuration. (Baker Atlas, 1997)

18 FlIeview(I.73]: view(08]: * spring-new.pdft Fig. 2-5 An example of permeability indication using travel time delay and centroid Frequency shift between measured and synthetic data (Baker Atlas, 1997). (See text in p.13 for definitions.)

19 r -.j F1 lev ew[1.73]: v leww- 6 (khz)(f1 OTST ( rw[1] CAL us r-1 I -Dl I I I e erence ' (impermeable) J refrefl referenc,-e2 2 T4A (Perm = 3 md) REFLO 0 j;c TR I L ~ I vi Fig. 2-6 An example showing how to select the reference depths for permeability analysis and processing (Baker Atlas, 1997). (See text in p.14 for definitions.)

20 Stoneley -Perm RWVRT DSTWVSYN RWVRT RSTWVSYN 00! () m d us us us us Fig. 2-7 An example of permeability estimation from full waveform acoustic log (Baker Atlas, 1997). (See text p.15 for defmitions.) 20

21 Chapter 3 A Comparison between Acoustic and NMR Log Permeability Estimates Petroleum well logging can be used to indicate the presence of gas or oil, the formation lithology, or the physical properties of the formation. For example, the difference between neutron porosity and formation density is a good indication of the existence of gas. (This relationship will be explained in more detail below). Permeability estimation from full waveform acoustic and nuclear magnetic resonance are two newly developed applications. In this chapter, field data from a sandstone-shale sequence is used to compare the permeability estimates from these two methods. The permeability results from the two different methods are well correlated to each other. The permeability comparison in a field data application has not been published previously. 3.1 Real Data Permeability Estimation Example Stoneley wavefield separation results Fig. 3-1 and 3-2 are the results from wavefield separation of the acoustic logging data. The first track shows the Gamma Ray and slowness of the transmitted Stoneley wave. The gamma Ray (on the left) is the direct measurement of radioactivity emitted by elements in the formation. Feldspars and micas have a large share of K4O and sometimes U-Ra and Th. Feldspars and micas decompose at a relatively rapid rate into the clay minerals. Clay minerals have an open lattice structure (i.e. weak bonding) that encourages inclusion of radioactive elements in their make up. Clay minerals are the principle components of shale. So the high Gamma Ray value is an indication of the existence of shales. Potassium often constitutes 0.3% of ordinary clays, U-Ra or Th could be as much as 0.03%.

22 The second curve of track 1 is the slowness of the Stoneley wave. In a permeable zone, the slowness values get higher. Track two shows the reflectivity and reflector, also the centroid frequency of Stoneley wave is shown in the same track. The third track shows lag and downgoing wave reflections. Track four shows upgoing wave reflections. Track five shows the caliper log and transmitted Stoneley wave (which will be used in the elastic model to compare with the modeled transmitted Stoneley wave to get the travel time delay and centroid frequency shift). In Fig. 3-1, the caliper values may indicate an irregular borehole for the interval X735-X760, which causes the permeability estimated from this interval to be unreliable. In Fig. 3-2, from depth X026-X042, Gamma ray shows high values indicating a shale zone. From X042-X063, the low Gamma Ray values indicates a sandstone zone. This data shows a typical shale-sandstone sequence, where Stoneley wave slowness values are relatively lower in the shale than in the sandstone. The centroid frequency is just the opposite. These two measured curves will be compared to the elastic model travel time and centroid frequency to get travel time delay and centroid frequency shift (equations 2-3, 2-4). Travel time delay and centroid frequency shift will be used to estimate permeability Permeability results Fig. 3-3a-g shows the permeability results of this field data from the same well. The first track shows the gamma ray and shear wave slowness. Shear wave slowness will be used to build the elastic model. If shear wave data is not good quality, it will affect the modeled Stoneley and yield unreliable permeability. Track two shows a travel time delay (left) and centroid frequency shift (right). For the whole well, the correspondence is shown between the travel time delay and centroid frequency shift. These two figures are the permeability effects. Most of the work on Stoneley wave permeability estimation is to obtain these two parameters. The good correspondence between these two curves indicates good data quality and success of the processing. The scale for centroid frequency shift starts from right to left. Track three is the permeability results from acoustic and Nuclear Magnetic Resonance Logs. Track four is the measured transmitted Stoneley wave, and track five is the modeled transmitted Stoneley wave without permeability effects. Travel time delay and center frequency shift (track two) are calculated from the comparison of these two

23 tracks. Track six shows the measured reflection, reflectivity and reflectors. Track seven shows the modeled reflection, reflectivity and the caliper. The NMR permeability estimate is based on the model shown in equation 3-3. More detail about NMR permeability estimates can be found in Sklar (1997). From the results in Fig. 3-3a-g, over 570 meters, it is remarkable to see that the permeability calculated from two different methods (Stoneley wave and NMR) correlate very well. Fig. 3-4 shows a cross-plot of the permeability estimates from NMR log versus Stoneley wave log over 130 meters from X060-X190. This interval has good quality permeability without any other reasons such as gas zone to cause the permeability difference. Although the scatter is significant at very low permeability values (< 0.1 md), most of the values distributed around the diagonal, indicating the good correlation between the two results. However, there are still some differences between the two permeability curves. In Fig. 3-3a, from interval X740-X758m, the Stoneley-perm is higher than NMR-perm. This difference is due to the bad caliper shown on track seven. Bad caliper values will cause unreliable permeability estimation from the Stoneley wave. Another zone (Fig. 3-3e) shows a consistent difference between the Stoneley and NMR permeability estimates. This zone will be discussed in detail in the next section. 3.2 Gas zone effect Gas zone effect on permeability estimation from Stoneley wave The good correlation of permeability results from the two different methods suggests that the estimated values are reliable. However, in this thesis, the demonstration of good correlation is not the only purpose. The differences between the two methods are also studied. The gas zone effect is one of the factors that can cause a difference between Stoneley and NMR permeability estimates. First, the gas zone effect on the acoustic permeability estimation is discussed. In permeability estimation from Stoneley wave processing, the key step is the selection of a reference depth and reference permeability. From the given permeability values, formation fluid properties are calculated, then the Stoneley wave permeability is calibrated.

24 In order to explain the permeability difference in Fig. 3-3e. The fluid parameter calibration should be mentioned first. By performing a sensitivity analysis of the modeling parameters, it was found that Stoneley wave time delay and frequency shift are primarily controlled not only by formation permeability and borehole radius, but also by 1/2 the following parameters: UB, where U is the pore fluid viscosity, and B is the pore fluid viscosity, and B is the pore fluid bulk modulus or incompressibility. Therefore the formation pore fluid viscosity, density and acoustic speed are required to obtain the absolute permeability value. These parameters, however, may be difficult to obtain if multiple fluids exist and the degree of fluid saturation is unknown. As discussed above, the calibration process includes selecting a few depth intervals whose permeability values have been well estimated from other measures (such as core, formation testing, NMR, etc.). By choosing one of these depths as a reference depth, synthetic wave data can be computed for the remaining depths. Then, by comparing the synthetic data with the measured data, we can estimate the fluid parameter combination by minimizing a misfit function. In the minimization, the given permeability values at the calibration depth are used as a known value. Only the pore fluid parameter combination is changed as the fitting parameter. The value of this parameter, which minimizes the misfit function, is taken as the desired fluid parameter for the entire zone. However, is this "desired" fluid parameter combination calculated from, at most, five reference depths enough to estimate permeability for a depth interval of hundreds or thousands of meters? What happens if we miss selecting a reference depth from a gas zone while we only use fluid parameters calculated from non-gas zone? Generally, the value of the fluid parameter combination is larger than that of gas. The result is that in a gas zone, the use of fluid parameter combinations whose value is too high will yield a permeability estimate that is too high Gas zone effect on permeability estimation from NMR Now we discuss the gas effect on NMR measurements. The phenomenon causing reduced NMR permeability and porosity in gas reservoirs, the so-called "gas effect", is a topic of great interest in the petrophysical community. The main reason for the gas effect in NMR measurements is the different relaxation mechanisms between the gas and fluids (brine, oil). Kleinberg and Vinegar

25 (1996) describe the Nuclear Magnetic Resonance relaxation mechanisms in detail. The transverse relaxation time T2 of gas is mainly affected by diffusion (T2D), in addition to y =-r -+ I + ;-(3-1) T'2 T 2 B T 2 S T 2 D T3D T2D r 2 G 2 DT( bulk (T2B) and surface relaxation (T2s), resulting in (-2) where r is the gyromagnetic ratio of hydrogen, G is the magnetic field gradient, D is the diffusion coefficient, and Tcp is half the inter-echo time. Because gas is in the short correlation time regime, T1=T1B=T2B. Surface relaxation is also negligible in Equation (3-1) because gas is always a non-wetting phase. Depending on D, G and Tcp, the T2 of the gas phase may be so short that all or some of the signal from gas may appear in the MBVI window and result in excessively high MBVI values and an estimated porosity value that is too low. (MBVI is the bulk volume irreducible, which is a measure of the capillary-bound fluid volume.) The coupled effect of reduced porosity estimates resulting from gas and shortened T2D resulting from diffusion in a gradient may also produce incorrect permeability estimates derived from relations employing NMR logs. There are two frequently used permeability models. The first is based on the free fluid index (MFFI), where K = c',(m) 2 (3.-3) And the second is based on the logarithmic mean T2L (Morriss et al. 1993), where K = c'pmrt2 (3-4) Both c and c' in equation (3-3) and (3-4) are scaling constants. Although some variations of these formulas exist, the general forms of these relations are as shown above. Permeability estimates may be very low when equation (3-3) is used in gasbearing zones with a gradient-based logging tool. Total NMR porosity will be too low because of the gas effect. MBVI, on the other hand, will be too high, and MFFI will be too low, which will result in very low permeability estimation. Equation (3-4) will also give erroneous results if used in gas-bearing zone. In this case, the porosity will be too low and the T2L will be smaller than the true T2L because of diffusion, which will yield low estimates of permeability (Akkurt et al. 1996).

26 3.3 FDC-CNL gas zone indication From the above analysis, when the formation contains gas, permeability estimated from the Stoneley wave will be too high, while permeability estimated from NMR will be too low. This difference could be used as an indication of a gas zone. In order to test this assumption, we now look at radioactive log measurement shown in Fig The principle of the density log is introduced in this paragraph. A radioactive source, applied to the borehole wall in a shielded side wall skid, emits medium-energy gamma rays into the formations. These gamma rays collide with the electrons in the formation. In each collision a gamma ray loses some, but not all, of its energy to the electron and then continues with diminished energy. This type of interaction is known as Compton scattering. The scattered gamma rays reaching the detector, at a fixed distance from the source, are counted as an indication of formation density. The number of Compton scattering collisions is related directly to the number of electrons in the formation. Consequently, the response of the density tool is determined essentially by the electron density (number of electrons per cubic centimeter) of the formation. Electron density is related to the true bulk density, which, in turn, depends on the density of the rock matrix material, the formation porosity, and the density of the fluids filling the pores. An FDC, compensated formation density tool, is the primary density log tool. Neutron logs are used principally for delineation of a porous formation and determination of its porosity. They respond primarily to the amount of hydrogen in the formation. In clean formations whose pores are filled with water or oil, the neutron log reflects the amount of liquid filled porosity. The neutrons are electrically neutral particles, each having a mass almost identical to the mass of a hydrogen atom. Highenergy neutrons are continuously emitted from a radioactive source in the sonde. These neutrons collide with nuclei of the formation. With each collision, the neutron loses some of its energy. The amount of energy lost per collision depends on the relative mass of the nucleus with which the neutron collides. Greater energy loss occurs when the neutron strikes a nucleus of practically equal mass, i.e., a hydrogen nucleus. Collisions with heavy nuclei do not slow the neutron very much. Thus, the slowing of neutrons depends largely on the amount of hydrogen in the formation. Within a few microseconds the

27 neutrons have been slowed by successive collisions to thermal velocities, corresponding to energies of around 0.025eV. They then diffuse randomly, without losing more energy, until they are captured by the nuclei of atoms such as chlorine, hydrogen. The capturing nucleus becomes intensely excited and emits a high-energy gamma ray of capture. Depending on the type of neutron tool, either these capture gamma rays or the neutrons themselves are counted by a detector in the sonde. When the hydrogen concentration of the material surrounding the neutron source is large, most of the neutrons are slowed and captured within a short distance of the source. On the contrary, if the hydrogen concentration is small, the neutrons travel farther from the source before being captured. The primary tool of a neutron log is a CNL, compensated neutron log tool. The Density and Neutron logging provide a good indication of gas zones. If gas is present, the neutron porosity log (CNL) will show a decrease in porosity due to gas having a lower concentration of hydrogen than water or oil. The formation density (FDC) also measures a lower value (reduced density) in gas zones. If we plot these logs with scales in opposite directions, the separation between the two values is a good indication of gas. Fig. 3-5 shows the FDC-CNL separation for the interval from X040---X060m, the interval where the difference was observed between Stoneley and NMR permeability estimates. The FDC-CNL separation indicates the presence of gas in the sandstone interval. This is consistant with the permeability estimates. Based on this analysis, we conclude that the disagreement between Stoneley and NMR permeability estimates in this interval is due to the presence of gas.

28 I Custom Pt)f S - Fig. 3-1 Wave separation results from X730-X770 m with bad caliper. First track shows the GR (black) and transmitted Stoneley slowness (blue), track two shows Raw Reflectivity (black), Processed Reflectivity (red) and Stoneley Centroid Frequency (pink), track three shows the Lag and Downgoing Reflection, track four shows Upgoing Reflection, track five shows the Caliper and Transmitted Stoneley wave.

29 Custom PD 5: Fig.3-2 Wave separation results in a typical shale-sand sequence from X010-X090m. In the sand formation, the Stoneley slowness values (blue) get higher than shale formation. Centroid frequency values are the opposite.

30 lcustom PDFs: GR 0200 (APIF I] 1us)(FI]. (md)(f 1] NNR-Perv 0 0.W At1enuotip2 (1/0)(FI II (rou)(f1 i 0 Q. 5 {raw)(f1) (row)(f ] Caliper 5 25 (in)[f I ] Ii; 4~. Fig. 3-3a Permeability results from X750-X780m with bad caliper. First track shows GR (black), Shear wave slowness (red), track two shows Centroid frequency shift (blue) and Travel time delay (red). Track three shows the permeability estimated from Stoneley wave (red) and permeability estimated from NMR (blue). Track four shows the atteuation and measured Stoneley wave. Track five shows the modeled Stoneley wave. Track six shows the Reflectivity and Measured Reflection. Track seven shows the caliper and Modeled Reflection.

31 Custom PDFs: Fig. 3-3b Permeability results from interval X780-X860m. A shale formation is indicated by GR, the permeability values in this shale formation are low.

32 DFS: Fig.3-3c Permeability results from X860-X940m. Good correlation is observed from this interval.

33 Custom PDFs: Fi.e ede e d eebilt reslp me ne Hx nuri*4 tw sie s:aftt i -Data MOE gel ONl I l Fig. 3-3d Permeability results from X960-X030.

34 Custom PDFs: Fig.3-3e - Permeability results from interval X030-XO70m. Permeability difference is observed.

35 Icustom PDFS: -tim-i 1 HI tiiiuiii M.. ui' i W Fig.3-3f Permeability results from interval X070-X150. It is one of the continuous intervals in a whole well profile.

36 Customn PDFI I Ors 4l. i Stoneley-Perm us.)[fl] (mnd)[f I] GR 1J. il NMR-Per i O 0o Hz)[F1] I (md)(f I ) At1enuation (1/Q)[FI] gof R6M (rov)[fi] Relecvi (ra w)(f 1)] Moaii R r (row)[fi] Caliper 5 25 (in)(f ] ilv II lil=ll. Ill "" al] 1 1 Fig. 3-3g of the whole well). Permeability results from X140-X180 m (bottom part

37 Fig. 3-4 NMR Permeability vs Stoneley Permeability ~e*.0 4 W 3 0 e * 1.00 * O* *. n' 0.10 e ee 0 * z Stoneley Permeability (md)

38 Custo PnD~s: Fig. 3-5 FDC-CNL gas zone indication (track four).

39 Chapter 4 Summary and Conclusions This thesis has described much of the basic theory and methods on permeability estimation from Stoneley waves and also provided permeability comparisons and interpretations between acoustic and NMR logs in a shale-sand sequence. Acoustic and NMR logging are the two most advanced technologies for permeability estimation. However, NMR logging is much more expensive than full waveform acoustic logging. If acoustic permeability estimation could replace NMR in permeability estimation, it could greatly reduce the logging cost. When Stoneley waves travel along a permeable formation, it is attenuated and the velocity of the wave is slower. These two responses are used to estimate permeability. However, there are other factors that also contribute to Stoneley wave attenuation and slowness variations, such as borehole radius changes, lithology changes and pore fluid variations. In order to isolate permeability effects, an elastic model that includes most of these parameters (except permeability) is used to compare with the measured Stoneley data (Tang, et al., 1991). The centroid frequency shift and travel time delay caused by permeability is obtained from the comparison. Then, by choosing a few reference depths, the data are inverted for permeability (Tang, et al., 1996). Logging data from a shale-sand sequence was used to compare the permeability estimations from acoustic and NMR log. The raw acoustic data was processed and interpreted in this thesis and compared to existing NMR permeability estimates. The permeability results from NMR and full waveform acoustic wave logs, two totally different geophysical measurements, correlate very well. A gas zone effect on permeability estimation from Stoneley waves and NMR was also analyzed. The presence of gas causes permeability values estimated from Stoneley wave data to be too high, and permeability values estimated from NMR data to be too low. The difference between these two curves can be used as a gas zone indicator. For Stoneley wave permeability estimates, there are still some limitations. For example, each logging depth permeability value is an average over four feet due to the

40 limitation of the field data acquisition system. Another limitation in Stoneley wave permeability estimate is that the permeability value in a fracture zone is not very accurate. Fracture permeability estimation is also a challenge for NMR logs. NMR permeability estimate is based on equation 3-3, which is too simple for many geological environments. A more complete new model is needed in the future. Future research should also include acoustic-nmr permeability comparisons for other environments, such as fracture zones, carbonates, and vuggy formations. Stoneley and NMR logging methods can provide continuous in-situ estimates of permeability, although both methods need calibration in order to get accurate absolute estimates. Detailed analysis of data from a range of lithologies and permeability values is needed to gain a full understanding of the limitations of each method. This thesis is a first step in this process.