Incorporating Dynamic Data into Geostatistical Reservoir Modeling

by
Fernando Placido Campozana, Ph.D.

University of Texas at Austin, 1997
Supervisors: Larry W. Lake
Kamy Sepehrnoori

The main objective of this research is to develop new algorithms and techniques that allow incorporation of dynamic (or production) data into geostatistical reservoir models. Basically, two types of production data are addressed: well test data, derived from pressure transient analysis, and water-cut data. The first data type receives the most attention. Two geostatistical techniques are considered Kriging and simulated annealing (SA).

Initially, ordinary and simple Kriging (OK and SK), the basic estimators of geostatistics are studied. A series of constraints are imposed on the Kriging system so that the resulting field has the desired properties. It is shown that Kriging can be constrained to a given average and variance. The first of these constraints allows one to obtain permeability fields whose average matches well test-derived permeability; the second enables one to generate fields that have a desired variability. Therefore, a well-known drawback of Kriging, namely excessive smoothness, is overcome.

The second part of this work studies the incorporation of well-test permeabilities into reservoir descriptions using a modified simulated-annealing (SA) approach. In the first SA-based algorithm, called MTWELL, a hybrid local and global optimization algorithm is coupled with a steady-state, single-phase flow simulator. It allows conditional simulations that account for well-test- derived permeabilities available at multiple wells in a reservoir. The well-test regions may have different statistical character and can overlap. A relationship between the effective permeability calculated by a steady-state simulator and the "true" well test permeability is obtained so that it is possible to evaluate the objective function with relatively little computational effort. To make the algorithm more efficient, we use (1) a starting image that matches a semivariogram constraint and (2) a special energy-update mechanism.

Finally, the reduction of reservoir uncertainty as more data are incorporated into the description is studied. Local conditioning data (such as cores and logs), statistical data (univariage distribution type and semivariograms), and production data are gradually incorporated into the description. A typical data-acquisition sequence of a reservoir is simulated and the reservoir uncertainty is quantified for each data configuration.

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