SUMMARY The shear-wave splitting observed along almost all shear-wave ray paths in the Earth’s crust is interpreted as the effects of stress-aligned fluid-filled cracks, microcracks, and preferentially oriented pore space. Once away from the free surface, where open joints and fractures may lead to strong anisotropy of 10 per cent or greater, intact ostensibly unfractured crustal rock exhibits a limited range of shear-wave splitting from about 1.5 to 4.5 per cent differential shear-wave velocity anisotropy. Interpreting this velocity anisotropy as normalized crack densities, a factor of less than two in crack radius covers the range from the minimum 1.5 per cent anisotropy observed in intact rock to the 10 per cent observed in heavily cracked almost disaggregated near-surface rocks. This narrow range of crack dimensions and the pronounced effect on rock cohesion suggests that there is a state of fracture criticality at some level of anisotropy between 4.5 and 10 per cent marking the boundary between essentially intact, and heavily fractured rock. When the level of fracture criticality is exceeded, cracking is so severe that there is a breakdown in shear strength, the likelihood of progressive fracturing and the dispersal of pore fluids through enhanced permeability. The range of normalized crack dimensions below fracture criticality is so small in intact rock, that any modification to the crack geometry by even minor changes of conditions or minor deformation (particularly in the presence of high pore-fluid pressures) may change rock from being essentially intact (below fracture criticality) to heavily fractured (above fracture criticality). This recognition of the essential compliance of most crustal rocks, and its effect on shear-wave splitting, has implications for monitoring changes in any conditions affecting the rock mass. These include monitoring changes in reservoir evolution during hydrocarbon production and enhanced oil recovery, and in monitoring changes before and after earthquakes, amongst others.

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The fracture criticality of crustal rocks

Using a geostatistical technique called cokriging, the areal distribution of porosity is estimated first in a numerically simulated reservoir model, then in an oilbearing channel-sand of Alberta, Canada. The cokriging method consistently integrates 3-D reflection seismic data with well measurements of the porosity and provides error-qualified, linear mean square estimates of this parameter. In contrast to traditional seismically assisted porosity mapping techniques that treat the data as spatially independent observations, the geostatistical approach uses spatial autocorrelation and crosscorrelation functions to model the lateral variations of the reservoir properties. In the simulated model, the experimental root-meansquare porosity error with cokriging is 50 percent smaller than the error in predictions relying on a leastsquares regression of porosity on seismically derived transit time in the reservoir interval. In the Alberta reservoir, a cross-validation study at the wells demonstrates that the cokriging procedure is 20 percent more accurate, in a mean square sense, than a standard regression method, which accounts only for local correlations between porosity and seismically derived impedances. In both cases, cokriging capitalizes on areally dense seismic measurements that are indirectly related to porosity. As a result, when compared to estimates obtained by interpolating the well data, this technique considerably improves the spatial description of porosity in areas of sparse well control.

Porosity from seismic data: A geostatistical approach

Introduction to Reservoir Management RESERVOIR ENGINEERING PRIMER: Basic Reservoir Analysis Multiphase Flow Concepts Derivation of the Flow Equations Fluid Displacement Frontal Stability Pattern Floods Recovery of Subsurface Resources Economics and the Environment RESERVOIR SIMULATION: Overview of the Modeling Process Conceptual Reservoir Scales Reservoir Structure Fluid Properties Rock-Fluid Interaction Fundamentals of Reservoir Simulation Modeling Reservoir Architecture Data Preparation for a Typical Study History Matching Predictions CASE STUDY: Study Objectives and Data Gathering Model Initialization History Matching and Predictions WINB4D USER'S MANUAL: Introduction to WINB4D Initializing Data Recurrent Data Program Output Evaluation TECHNICAL SUPPLEMENTS: Simulator Formation Rock and Fluid Models Initialization Well Models Well Flow Index (PID) The IMPES Formulation References Index

Principles of applied reservoir simulation

It is 10 years since shear-wave splitting, throught to be diagnostic of some form of seismic anisotropy, was first positively identified in the Earth's crust. From the beginning it was argued that the splitting was probably associated with the presence of stress-aligned cracks (inclusions) in the crust, and that this would provide the opportunity for monitoring the in situ geometry of cracks and stress in a variety of different circumstances and in a variety of different applications.

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A decade of shear-wave splitting in the Earth's crust: what does it mean? what use can we make of it? and what should we do next?

Features of subsurface earth reservoirs of interest are made available for analysis and evaluation by forming three-dimensional, geologic block models based on field data. The field data include geological observations, such as lithofacies and porosity values obtained from well data and other sources, as well as geophysical data, usually from seismic surveys. The geologic models representative of subsurface reservoirs so obtained are optimized to match as closely as feasible geologic constraints known or derived from observed geologic data. The models also conform to geophysically based constraints indicated by seismic survey data. The modeled geologic lithofacies and porosity are converted into acoustic velocity and bulk density values, which are then formulated as a seismic response which is then compared with actual seismic data. A perturbation process on lithofacies and porosity can be iteratively repeated until a representation of the reservoir is obtained which is within specified limits of accuracy or acceptability.

Method of generating 3-D geologic models incorporating geologic and geophysical constraints

Modern three-dimensional (3D) seismic data assist not only in delineating reservoir geometry, but also in predicting porosity and lithology variations away from well control. This case study of an oil-producing channel sand in the Taber/Turin area, Alta., Canada illustrates the improvement in reservoir characterization achieved with an integrated approach incorporating both well and seismic information.

Reservoir description from seismic lithologic parameter estimation

Petroleum engineers and production geologists generally build their reservoir models from smooth interpolation of petrophysical parameters obtained at well locations. Well information is usually accurate but is unevenly and sparsely distributed. In heterogeneous formations these interpolated models can be erroneous with costly consequences on field development expenditures. In addition, the volume of reservoir rock physically investigated in a field by core analysis and wireline logging generally is on the order of one part per billion. Yet, development geologists and petroleum engineers need to produce one (or more) detailed 3-D model(s) of the reservoir to estimate reserves, design an effective drilling program, and optimize resource recovery.

Optimum field development with seismic reflection data

In areas of rapid lithologic variations, the areal extent of sand and shale units usually cannot be inferred from sparse well data alone. Seismically derived interval velocity data can be used to help predict lithologic variations away from wells. However, in general, the overlap of the velocity ranges for sands and shales is such that seismic discrimination of lithology is ambiguous. We present a Monte Carlo technique for numerically simulating the spatial arrangement of sand/shale units. This technique accoimts for the ambiguous nature of the seismic velocity information. Rather than calculating a unique sand/shale model, the Monte Carlo method provides a family of alternative lithologic images, all of which are consistent with the data. The range of models reflects the uncertainty of the lithologic classification and is used to assess risk in reservoir development. The sand/shale simulation technique is illustrated using a data set from an oil-producing channel-sand reservoir. Sand/shale cross-sectional simulations are generated along a seismic traverse that intersects three wells. The simulated models reproduce the log-derived lithologic sequences at the wells; they are conditioned by interval velocities inverted from the seismic amplitude data and are consistent with the spatial autocorrelation and crosscorrelation structures of the seismic and well data. The seismically derived lithologic models of the reservoir are better spatially constrained than models solely conditioned by well data. However, in keeping with the inherent ambiguity of the seismic information, the exact location of the lateral truncation of the channel sand is not precisely defined in the Monte Carlo lithologic simulations.

Monte Carlo Simulation of Lithology from Seismic Data in a Channel-Sand Reservoir

A geostatistical modelling technique called cokriging is used to describe the lateral variations of porosity, f, in a synthetic and a real reservoir. Using this method, an error-qualified porosity model is estimated for each of the two reservoirs from sparse well porosity measurements and seismically derived velocities. The method capitalizes on the high spatial density of the seismic measurements and on their correlation with f. Compared with conventional reservoir models derived solely from sparse well control, the seismically consistent models are better spatially constrained and, hence, provide more detailed and accurate reconstructions of the porosity variations.

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Porosity From Seismic Data, a Geostatistical Approach

In areas of rapid lithologic variations, the areal extent of sand and shale units usually cannot be inferred from sparse well data alone Seismically derived interval velocity data can be used to help predict lithologic variations away from wells However, in general, the overlap of the velocity ranges for sands and shales is such that seismic discrimination of lithology is ambiguous We present a Monte Carlo technique for numerically simulating the spatial arrangement of sand/shale units This technique accoimts for the ambiguous nature of the seismic velocity information Rather than calculating a unique sand/shale model, the Monte Carlo method provides a family of alternative lithologic images, all of which are consistent with the data The range of models reflects the uncertainty of the lithologic classification and is used to assess risk in reservoir development The sand/shale simulation technique is illustrated using a data set from an oil-producing channel-sand reservoir Sand/shale cross-sectional simulations are generated along a seismic traverse that intersects three wells The simulated models reproduce the log-derived lithologic sequences at the wells; they are conditioned by interval velocities inverted from the seismic amplitude data and are consistent with the spatial autocorrelation and crosscorrelation structures of the seismic and well data The seismically derived lithologic models of the reservoir are better spatially constrained than models solely conditioned by well data However, in keeping with the inherent ambiguity of the seismic information, the exact location of the lateral truncation of the channel sand is not precisely defined in the Monte Carlo lithologic simulations

M. de Buyl

Papers

Reservoir description from seismic lithologic parameter estimation

Optimum field development with seismic reflection data

Monte Carlo Simulation of Lithology from Seismic Data in a Channel-Sand Reservoir

Porosity From Seismic Data, a Geostatistical Approach

Monte Carlo Simulation of Lithology From Seismic Data in a Channel-Sand Reservoir