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

A new Bayesian method is developed to identify the spatial distribution of permeabilities. In addition to sparsely sampled permeability and pressure data, this approach incorporates densely sampled seismic velocity data along with semiempirical relationships between seismic and hydraulic soil properties. The procedure consists first of performing a hydrological inversion based solely on the permeability and pressure data. In light of the available seismic data, the velocity-permeability-pressure relationships are then used to update, in a Bayesian sense, the image of the permeability field. To investigate the usefulness of this approach, synthetic case studies are performed. These studies demonstrate that, even when the seismic data are corrupted by a significant level of error, a joint geophysical-hydrological inversion can produce improved images of permeability. Moreover, this paper derives rigorously the bounds on the error that can be tolerated in seismic velocities such that they are still useful for hydrological purposes.

Geophysical‐hydrological identification of field permeabilities through Bayesian updating

Heterogeneity of natural geologic formations strongly influences groundwater flow and contaminant migration. This study presents a formal stochastic approach for the integration of surface seismic data and well data into the identification of the spatial arrangement (location, geometry, and interconnectedness) of lithofacies and incorporating this information in the estimation of the log permeability probability density function (pdf). To achieve this goal, normal move-out (NMO) corrections are applied to the seismic reflection data to estimate interval seismic velocities. Calibration curves constructed from the well logs transform these velocity estimates into a lithology indicator prior probability field. From the well data and the indicator prior probability field, the indicator covariance function and its associated confidence limits are computed. Neighboring lithology logs and the indicator covariance function are then combined to update the indicator probability field. The conditional log permeability pdf is finally computed by weighting the log permeability distribution of each lithology with respect to its indicator probability field. The effectiveness of the proposed procedure is shown to depend on the quality of the seismic data and the degree of correlation between seismic and hydrogeologic soil properties. A synthetic case study is performed which shows that the surface seismic and well data complement each other with optimal results achieved when both types of data are incorporated into a joint identification procedure.

A Stochastic Approach to the Characterization of Lithofacies From Surface Seismic and Well Data

The performance of traditional back-propagation networks for reservoir characterization in production settings has been inconsistent due to their nonmonotonous generalization, which necessitates extensive tweaking of their parameters in order to achieve satisfactory results and avoid overfitting the data. This makes the accuracy of these networks sensitive to the selection of the network parameters. We present an approach to estimate the reservoir rock properties from seismic data through the use of regularized back propagation networks that have inherent smoothness characteristics. This approach alleviates the nonmonotonous generalization problem associated with traditional networks and helps to avoid overfitting the data. We apply the approach to a 3D seismic survey in the Shedgum area of Ghawar field, Saudi Arabia, to estimate the reservoir porosity distribution of the Arab-D zone, and we contrast the accuracy of our approach with that of traditional back-propagation networks through cross-validation tests. The results of these tests indicate that the accuracy of our approach remains consistent as the network parameters are varied, whereas that of the traditional network deteriorates as soon as deviations from the optimal parameters occur. The approach we present thus leads to more robust estimates of the reservoir properties and requires little or no tweaking of the network parameters to achieve optimal results.

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Estimation of reservoir properties from seismic data by smooth neural networks

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

Un modele geologique detaille est developpe a partir des donnees provenant de la methode de modelisation des parametres lithologiques par des mesures sismiques. Ce modele permet d'etablir des cartes de structure et de porosite des reservoirs. Sa fiabilite est determinee a partir de l'etude d'un champ de petrole situe dans la region de Taber/Turin (Canada)

F. Bell

Papers

Reservoir description from seismic lithologic parameter estimation

Reservoir description from seismic lithologic parameter estimation