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DEVELOPMENT OF A GEOMATHEMATICAL MODEL APPLIED TO OIL RESERVOIRS (FINAL REPORT)

Ziel

The objective of the project is to build an integrated software package for modelling oil reservoirs and describing the nature and disposition of the heterogeneities that inevitably occur in petroliferous formations. This project aims to develop a new approach based on a geomathematical model resulting from the Theory of Regionalized Variables and from Kriging Technique, in order to describe the spatial behaviour of reservoir properties, generate unbiased profiles for use at different levels, define the error associated with the estimation taking in account the position and spatial distribution of the variable, detect structure trends and anisotropies, optimise of new wells location, determine the best description of reservoir zonation.
The package will be flexible enough to permit the introduction of the practical experience obtained by field geologists and reservoir engineers and designed to be used by any petroleum technicien without computer science expertize.
The main areas covered within the framework of this project are as follows :
- Development of geostatistical estimation procedures able to convey geological information into quantitative models, for technical and economical purposes.
- Articulation of a variety of procedures, algorithms and programmes in a coeherent methodology encompassing structural analysis and estimation seeking to provide more reliable profiles of the reservoir properties specially in the interwell scale.
- Assessment of different geostatistical methodologies for reserves calculation according to the existing level of information in different stages of the life of the oil field.
Establishment of a consistent methodology based on the grounds of transitive kriging of indicator data for modelling the geometry of the relevant reservoir layers.
- Application of multivariate data analysis techniques to the vertical zonation of oil reservoirs in order to overcome some drawbacks of classical techniques and build morerefined and detailed layering models to be used in simulation studies.
- Development of a new approach for the horizontal zonation of oil reservoirs providing a more refined model of the internal architecture of the reservoir which is a key point for the planning of production and recovery operations.
- Development and testing of methods for the description and estimation of permeability variation within the reservoir and analysis of the performance of different techniques like multiple linear regression and multidimensional histograms.
- Development and testing of a new approach for the simulation and prediction of shales spatial distribution which is a key factor affecting the vertical permeability and the ultimate oil recovery.
- Establishment of a methodology for optimization of new wells location using the estimated uncertainty zones, in order to define the optimal drilling configuration, according to the development strategy and production planning of the field.
Finally, the main practical output of the project was completed : it consists of an integrated software package, containing all the modules which were tested on a real case. It runs in microcomputers, though the more sophisticated modules are to be fed into main frames in order to improve the operationality of the package.
The plan of the project is divided in 3 phases and a final integrated stage :
1ST PHASE :
1. Screen review and assemble of the basic data regarding different oil reservoirs;
2. Construction of the geomathematical model working out a set of computing programs;
3. Initialization of the model, Kriging known values and checking the resulting error of calculating various theoretical dispersion variances and comparing them to the experimental values;
4. Analysis and evaluation of the results and impact on several areas.
a). variographic analysis and detection of the major structural characteristics and anisotropies of the reservoirs, quantitative evaluation;
b). characterization and description of reservoir heterogeneities; c). description of the reservoir properties spatial behaviour, generated profiles and precision of the estimation;
d). contour mapping and comparision with classical techniques, evaluation of the results;
e). degree of error associated with the estimation, real statistical meaning of the values; impact on reservoir simulation outputs and reservoir estimation;
f). co-regionlization aiming to study inter-correlated variables simultaneously.
2ND PHASE :
1. Geological modelling using conditional simulation to provide a set of values with the same variability as the studied phenomenon and coinciding with the experimental values at the sample locations, and Minkovsky transforms for characterizing the geometry of the reservoir;
2. Optimization of new wells locations based on the fact that the Kriging variance does not depend on experimental values, but on the structure (variogram model), on the geometric configuration of the domain to be estimated and on the locations of the data points;
3. Subsurface reservoir model and impact on reserves calculation. Application of the geomathematical model and Kriging technique to the study of the reservoir geometry in order to reduce the uncertainty about it simulating the field boundaries in a more accurate way.
3RD PHASE :
1. Automatic method of capturing and storing data. Design of a data -base with specific characteristics of Petroleum information;
2. A new method for reservoir zonation based on the Correspondence analysis, allowing the simultaneous treatment of quantitative and qualitative data;
3. Contribution of variography analysis and Mandelbrot's Theory of fractal objects for the solution of the problems of scale in a reservoir; attempt to relate them quantitatively.
LAST STAGE :
It consists of the integration of the results of all phases in a portable and integrated package to be used by field engineers in order to solve practical oil industry problems in exploration and production.

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