Estimation Of Rock Properties Research Articles

Useful approximations for converted‐wave AVO

Converted‐wave amplitude versus offset (AVO) behavior may be fit with a cubic relationship between reflection coefficient and ray parameter. Attributes extracted using this form can be directly related to elastic parameters with low‐contrast or high‐contrast approximations to the Zoeppritz equations. The high‐contrast approximation has the advantage of greater accuracy; the low‐contrast approximation is analytically simpler. The two coefficients of the low‐contrast approximation are a function of the average ratio of compressional‐to‐shear‐wave velocity (α/β) and the fractional changes in S‐wave velocity and density (Δβ/β and Δρ/ρ). Because of its simplicity, the low‐contrast approximation is subject to errors, particularly for large positive contrasts in P‐wave velocity associated with negative contrasts in S‐wave velocity. However, for incidence angles up to 40° and models confined to |Δβ/β| < 0.25, the errors in both coefficients are relatively small. Converted‐wave AVO crossplotting of the coefficients of the low‐contrast approximation is a useful interpretation technique. The background trend in this case has a negative slope and an intercept proportional to the α/β ratio and the fractional change in S‐wave velocity. For constant α/β ratio, an attribute trace formed by the weighted sum of the coefficients of the low‐contrast approximation provides useful estimates of the fractional change in S‐wave velocity and density. Using synthetic examples, we investigate the sensitivity of these parameters to random noise. Integrated P‐wave and converted‐wave analysis may improve estimation of rock properties by combining extracted attributes to yield fractional contrasts in P‐wave and S‐wave velocities and density. Together, these parameters may provide improved direct hydrocarbon indication and can potentially be used to identify anomalies caused by low gas saturations.

Statistical rock physics: Combining rock physics, information theory, and geostatistics to reduce uncertainty in seismic reservoir characterization

“Any physical theory is a kind of guesswork. There are good guesses and bad guesses. The language of probability allows us to speak quantitatively about some situation which may be highly variable, but which does have some consistent average behavior…. Our most precise description of nature must be in terms of probabilities.” —Richard Feynman This paper presents snapshots of current and emerging trends in applied statistical rock physics for reservoir characterization. By integrating fundamental concepts and models of rock physics, statistical pattern recognition, and information theory with seismic inversion and geostatistics, we can quantify and reduce uncertainties in reservoir management. Rock physics allows us to link seismic response and reservoir properties and to extend the available data to generate training data for the classification system. Seismic imaging brings indirect, but nevertheless spatially exhaustive, lateral and vertical information about reservoir properties that are not available from pinpoint well data. Classification and estimation methods based on computational statistical techniques such as nonparametric Bayesian classification, bootstrap, and neural networks help quantitatively measure interpretation uncertainty and the mis-classification risk at each spatial location. Geostatistical stochastic simulations add spatial correlation and small-scale variability which is hard to identify from seismic only because of the limits of resolution. Combining deterministic physical models with statistical techniques leads to new methods for interpretation and estimation of reservoir rock properties from seismic data. These formulations identify the most likely interpretation, the uncertainty of the interpretation, and guide quantitative decision analysis. Subsurface heterogeneity delineation is a key factor in reliable reservoir characterization. These heterogeneities occur at various scales and can include variations in lithology, pore fluids, clay content, porosity, pressure, and temperature. Some methods used in seismic reservoir characterization are purely statistical. Others are deterministic, based on physical models (theoretical, laboratory). Each group of techniques can have some …

Geophysical tomography by viscoacoustic asymptotic waveform inversion of ultrasonic laboratory data

In this paper, we develop viscoacoustic asymptotic waveform inversion to estimate velocity and attenuation factor Q of a medium. Then, we present an application to laboratory ultrasonic data. Viscoacoustic asymptotic waveform inversion is performed using an optimization approach based on the iterative minimization of the mismatch between the seismic data and the computed response. To obtain a fast analytical imaging procedure, we include an asymptotic theory for attenuation in a linearized inverse scattering formulation. The forward modeling is solved by the Born approximation for a smooth and attenuative background medium. An asymptotic ray tracing method is used to calculate travel time, amplitude and attenuation between source, receiver, and scattering points. The inversion formula was specifically developed to account for the acquisition geometry designed in this study. Viscoacoustic asymptotic inversion is applied to ultrasonic data recorded during a physical-scaled laboratory experiment. This scaled experiment was used to test the reliability of our method when applied to a real dataset to estimate attenuation factor Q. The results show that both the velocity and Q tomographic images allowed one to delineate the gross contour of the target. We obtained an excellent match between the observed data and the viscoacoustic Ray-Born synthetics. The match obtained with a viscoacoustic rheology was significantly better than for a purely acoustic one. The application presented in this paper suggests that the procedure that we designed (experimental setup, tomography) can be useful to estimate rock properties in the frame of a laboratory experiment.

Asymptotic viscoacoustic diffraction tomography of ultrasonic laboratory data: a tool for rock properties analysis

Summary This paper presents an application of 2.5-D asymptotic viscoacousti c diffraction tomography to ultrasonic data recorded during a physically scaled laboratory experiment. This scaled experiment was used to test the reliability of our method when applied to a real data set to estimate the attenuation factor Q. Diffraction tomography relies on ray theory to compute the Green functions in a smooth background medium and on the Born approximation to linearize the relation between the scattered wavefield and the velocity and Q perturbations. The perturbations are inferred from the data by an iterative (linear) quasi-Newtonian algorithm. The inversion formula was specifically developed to account for the acquisition geometry designed in this study. The derivation of the Hessian operator shows that, for this acquisition, the velocity and Q perturbations are theoretically decoupled. The processing of the data was split into two steps: first, we applied the tomography to the data without deconvolving them. Second, we designed a post-processing procedure for the tomographic images to remove the source signature and to estimate the absolute values of the velocity and the attenuation factor Q. At the conclusion of the first step, both the velocity and the Q tomographic images allowed one to delineate the gross contour of the target. We obtained an excellent match between the observed data and the viscoacoustic ray–Born synthetics. The match obtained with the viscoacoustic rheology was significantly better than for a purely acoustic one. In the second step, the post-processing allowed us to recover the shape of the target. We estimated the absolute values of the velocity and Q, although we had no quality control with regard to these results (the rheological properties of the material used in this study were unknown) The results suggest that the uncertainty of the velocity measurement is lower than that for Q. The application presented in this study suggests that the procedure that we designed (experimental set-up, tomography, post-processing) can be useful for estimating rock properties in the framework of a laboratory experiment. Generalization of the method to other acquisition configurations such as surface seismic data requires further work.

ABSTRACT: Reservoir Characterization using 3D AVO and 3D Net Sand Prediction

Abstract The major issues that face us today revolve around economics. Finding hydrocarbons has been made easier with 3D data, but the proper delineation and quality of the deposit still often elude us. Application of a series of amplitude attributes indicates that applying one technology, such as Amplitude Strength, is not enough. The issues that impact the economics of a reservoir are varied and complex, therefore multiple techniques must be used to address them. Application of seismic attributes to three areas of the Gulf of Mexico, in a consistent manner, demonstrates how effective technology can be when applied properly. The three areas examined all had similar Amplitude Strength, but drilling results in the area produced varied results. The Mississippi Canyon 486 field was first examined because of the strong variation in reservoir thickness. The sixteen wells drilled in the field have a gross thickness variation of 160 feet, and net thickness variation of 105 feet. Amplitude maps over the field do not indicate this complexity, and agree very poorly with the drill results. Advances in technology, mainly in the areas of AVO, Thickness, and Rock Property estimation, offer a much clearer picture of the reservoir size. Similar technology applied to a second area correctly predicted the poor outcome of an initial well and indicated the presence of cleaner and thicker reservoir in the immediate area. A sidetrack was drilled and an economic discovery was announced. The third location also has a strong amplitude anomaly similar to the other two. The AVO signature suggests the presence of hydrocarbons, but thickness predictions indicate very low net/gross sand ratios in the reservoir. The well drilled into the anomaly was plugged and abandoned. End_of_Record - Last_Page 474-------

Bending thin lithosphere causes localized “Snapping” and not distributed “crunching”: Implications for Abyssal Hill Formation

Horizontal loads (i.e. pushes or pulls) on the lithosphere are thought to produce significant, localized, dip‐slip faults, but vertical loads are generally considered to produce broadly distributed bending or flexure. The same processes of weakening or yielding that lead to localization of deformation on faults during lithospheric stretching or shortening can produce highly localized faulting during lithospheric bending. Localized bending, or “snapping” should occur when the bending moment begins to decrease with increasing plate curvature. If yielding causes a reduction in cohesion then thin brittle layers may respond to bending in the “snapping” mode while thicker layers respond in a more distributed “crunching” mode. For a Mohr‐Coulomb layer floating on an invicid substrate it is the ratio of the cohesion to the average shear stress needed to overcome friction that controls the mode of bending. The average horizontal stress on the layer also affects the mode of bending. For estimated rock properties, a brittle layer has to be less than a few, up to perhaps 10 km thick, to break in a localized way. Lithosphere at many mid‐ocean ridges is thought to be only a few kilometers thick and also may be a site of vertical loading. The localized snapping mode of bending may produce abyssal hills at fast‐spreading mid‐ocean ridges.

Reconciling physical properties with surface seismic data from a layered mafic intrusion

Compositional layering of intrusive rocks is often cited as a source of seismic reflectivity in the crystalline crust. Direct evidence for this is based primarily on synthetic seismograms calculated from laboratory measurements of rock velocity and density, or estimates of aggregate rock properties from measurements of mineral velocities and densities. Little is known about how in situ effects such as fracturing, chemical alteration, or anisotropy, may change the reflectivity character of the surface seismic data. An ideal dataset for examining the hazards of using physical properties data for estimating crustal reflectivity occurs at the Nellie intrusion, a middle Proterozoic-age layered mafic intrusion that lies beneath the Permian Basin of west Texas. Due to a well that penetrated 4.5 km of the intrusion, we have a dataset that spans the scale from compositional data on the intrusion derived from well cuttings, to log data, to surface reflection data. Sonic and density log data from the well measure velocities and densities 10 to 15% below the values calculated from modal mineralogy. We attribute this difference primarily to pervasive post-emplacement alteration and fracturing of the rock mass in situ. Thus, this unique dataset provides a quantitative estimate of the magnitude of difference between observed and theoretical velocities that can be expected for crystalline rocks in the upper crust and its cause. Despite the difference, analysis of synthetic seismograms shows that primary compositional variation of the intrusion is still responsible for sub-horizontal layered reflectivity in both the log-based and petrology-based synthetic seismograms. Boundaries of intrusive cycles are characterized by large negative reflection coefficients due to the juxtaposition of mafic-rich basal layers against plagioclase-rich layer tops. In detail, only the log-based synthetic provides a good match to the surface seismic reflection data. This suggests that physical properties from modal mineralogy are useful in obtaining a generalized model for reflectivity, but that differences in bulk physical properties of the rock mass preclude the possiblity of obtaining a one-to-one match with surface seismic data.

Integrated interpretation of borehole and crosswell data from a west Texas field

The accurate estimation of rock properties between wells is crucial to the problems of reservoir development and enhanced oil recovery. Recent advances in cross‐borehole seismic technology have allowed cross‐borehole tomography to be used as a high‐resolution tool in estimating P-wave velocities between boreholes. In this case history, we describe acquisition, processing, and preliminary interpretation of cross‐borehole data in a west Texas oil field. In addition to interwell velocity estimation, we show estimates of porosity between wells obtained through use of tomography and velocity‐porosity relationships.

衝撃破砕試験による岩石の破砕性の評価

The impact hardness of rock is normally determined by using a ‘Protodyakonov’ type drop hammer. However, this test cannot be applied to a wide range of rocks. Therefore, standardized impact hardness test using the ‘Protodyakonov’ type drop hammer was carried out and the correlati ons of the resulting values of impact hardness with the mechanical properties obtained from usual laboratory tests were investigated.The results show that the impact hardness has, a generally good correlation with the tensile or the compressive strength of rocks. Therefore, the impact hardness can be used as a strength index in the estimation of rock properties. Moreover, the performance of rock drilling or machine roadway drivage can be predicted using the impact hardness of rock.

Application of mode-converted shear waves to rock-property estimation from vertical seismic profiling data : Ahmed, H GeophysicsV54, N4, April 1989, P478–485

Application of mode-converted shear waves to rock-property estimation from vertical seismic profiling data : Ahmed, H GeophysicsV54, N4, April 1989, P478–485

Weighted stacking for rock property estimation and detection of gas : Smith, G C; Gidlow, P M Geophys ProspectV35, N9, Nov 1987, P993–1014

Weighted stacking for rock property estimation and detection of gas : Smith, G C; Gidlow, P M Geophys ProspectV35, N9, Nov 1987, P993–1014

In-Situ Stress and Physical Property Measurements in Appalachian Site Survey Boreholes: ABSTRACT

Four shallow core holes have been drilled as part of the site survey investigations. These holes provided the opportunity to continuously sample several key rock units to be encountered in a proposed deep hole, and to make a suite of important geophysical measurements. These measurements include heat flow, in-situ stress, P-wave and S-save sonic velocity, electrical resistivity, fracture density and orientation, and natural gamma radiation. The in-situ stress measurements confirmed that this area is subjected to the same northeast-southwest-directed compressive stress field that characterizes the central and eastern US. Thus, stress measurements in the proposed deep hole should test a stress field that is characteristic of a broad region in the southeast. The in-situ velocity, resistivity, and natural gamma measurements can be combined with similar measurements on core samples at elevated pressures to estimate rock properties at depth, as well as to calibrate these measurements in the proposed hole. Sonic velocity measurements in the shallow holes and on the core provide additional velocity control for interpreting seismic reflection profiles. Data on the distribution and orientation of natural fractures have important consequences for anticipating deep drilling conditions. For example, one hole is sited in the Brevard shear zone; however, relatively fewmore » macroscopic fractures were encountered in the hole, and the quality of the mylonitized rock exhumed from the well is excellent. Therefore, no drilling problems are expected in the proposed deep hole. A hole drilled in the Henderson Gneiss was highly fractured and eventually abandoned. However, on the basis of fracture data in the other three wells, the authors believe the dense fracturing found in the Henderson Gneiss hole represents a local condition that should not affect the proposed deep hole if it is properly sited.« less

Mathematical Model of the Diamond-Bit Drilling Process and Its Practical Application

Abstract With several limiting assumptions, a mathematical model of the diamond-bit drilling process has been developed. The model represented by an instantaneous rate-of-penetration equation takes into account the reduction in penetration rate during drilling resulting from bit wear. The model has been tested both under laboratory and under field conditions. The comparison of the theoretical and experimental results has shown reasonable agreement. A method for estimating rock properties also has been established. Using this method, we can find the so-called index of rock strength and the index of rock abrasiveness.

Inertial and Slip Effects in Steady-State Radial Gas Flow Through Porous Media

Steady horizontal radial gas flow through porous media may be described by means of the equation(1) provided there is no slip at the gas/solid interface and provided there is no slip at the gas/solid interface and q is taken to be positive in the r direction. If one assumes that the modified gas law holds and that viscosity, compressibility, and temperature remain constant, this equation may be integrated to yield(2) which is similar in form to that proposed by Tek et al. This equation may of course be reduced to the well known form employed for Darcy flow by deleting the second term on the right-hand side. However, it has been shown that neither slip nor inertial effects should be neglected when linear laboratory gas flow tests are used to evaluate rock properties. It has been observed that the same is true for laboratory data when taken in radial tests. Although Eq. 1, modified to allow for slip, may be integrated for linear flow, radial flow yields a nonlinear ordinary differential equation with no known solution. However, an approximate solution may be developed in the following manner: To allow for slip, Eq. 1 may be modified and written as(3) where(4) If the modified gas law applies and viscosity, compressibility, and temperature are assumed to remain constant at their average values, Eq. 2 may be converted to the form(5) Substitution of Eq. 4 into Eq. 5 yields(6) If one defines(7) and(8) Eq. 6 may be written as(9) or(10) As was stated earlier there is no known solution to this nonlinear ordinary differential equation. Although this equation may be attacked with numerical techniques to estimate rock properties using flow data, the procedure is involved and difficult. However, if the ratio b/p is sufficiently small, Eq. 9 may be approximated by deleting the term (1 + b/p) in the numerator, in which case(11) or(12) This equation may be integrated between the limits ; and; to yield (13) or(14) P. 1155