**2. Objective**

The main objective of this work is the development and implementation of a stochastic model algorithm for seismic inversion to improve reservoir characterization.

The methods of integration of seismic data can be roughly divided in two approaches. The methods that rely on a statistical relationship between seismic data and internal properties, or lithofacies, to characterize local distributions of these properties in any location of the reservoir by using, for example, co-simulations as [4,5], and others different approaches are posed as an inverse problem framework where the solution, the known amplitudes of seismic, are physically related with the unknown acoustic impedances (or porosity) by mean of a convolution model. Among them there is the so called geostatistical inversion in [6].

The major disadvantages and drawbacks of the direct models, are that the correlation found in the wells locations between the seismic and the internal properties (porosity and permeability), are normally low and sometimes spurious, condemning all the models from there to a great uncertainty.

From the recent deterministic inversion models, the great drawback, is caused by the lack of production of any measure of uncertainty and from not being robust (a great dependency from the seismic quality) and having little liability in almost all of the more complex reservoirs.

In 1993 Bortolli, launched the embryo of what is considered a liable alternative to the existing inverse models, the stochastic inversion. In this method the sequential gaussian simulation is used to transform, using an interactive process, each of the N verticals columns of the seismic cube.

120 New Technologies in the Oil and Gas Industry

difficult to use directly in the models one wishes to create.

initial phases of prospecting and production.

community linked to the earth science modeling.

**2. Objective** 

there to a great uncertainty.

reservoirs.

The seismic data which can cover the entire reservoir space has a high uncertainty given the quality and the vertical coarse resolution of seismic. This varies from 25 by 25 meters in horizontal and 1 to 4 milliseconds, in 3-D seismic acquisitions. This data sample is much coarser that the data measured in wells, which vary from some centimeters to a few feet. It is important information never the less, but in almost all applications the seismic data cannot have a direct link to the wells properties (lithology, porosity and permeability), and are

The reservoir models based only in seismic information (3-D or 4-D), are normally limited to the structural information. This relationship derives from the major horizons and faults systems, interpreted in the coarse seismic, and it does not take in account the available well information, related to the internal characteristics of the reservoir (porosity, permeability and water saturation). On the other side, the characterization of reservoir models based only in the information of wells, like the recent geostatistical stochastic models, can have a great improvement by the integration of seismic information, which normally is available in the

The integration of these two types of information, with different special coverage and with totally different uncertainty levels is a challenge that even today dazzles the scientific

The main objective of this work is the development and implementation of a stochastic

The methods of integration of seismic data can be roughly divided in two approaches. The methods that rely on a statistical relationship between seismic data and internal properties, or lithofacies, to characterize local distributions of these properties in any location of the reservoir by using, for example, co-simulations as [4,5], and others different approaches are posed as an inverse problem framework where the solution, the known amplitudes of seismic, are physically related with the unknown acoustic impedances (or porosity) by mean of a convolution model. Among them there is the so called geostatistical inversion in [6].

The major disadvantages and drawbacks of the direct models, are that the correlation found in the wells locations between the seismic and the internal properties (porosity and permeability), are normally low and sometimes spurious, condemning all the models from

From the recent deterministic inversion models, the great drawback, is caused by the lack of production of any measure of uncertainty and from not being robust (a great dependency from the seismic quality) and having little liability in almost all of the more complex

In 1993 Bortolli, launched the embryo of what is considered a liable alternative to the existing inverse models, the stochastic inversion. In this method the sequential gaussian

model algorithm for seismic inversion to improve reservoir characterization.

Since then, the geostatistical seismic inversion has been a commonly used technique to incorporate seismic information in stochastic fine grids models.

Essentially, geostatistical inversion methods as in [7-9], perform a sequential approach in two steps:


A "best" simulated trace is retained, based on the match of an objective function (function of the similitude between real seismic trace and seismogram), and another trace is visited to be simulated and transformed. The sequential process continues until all traces of acoustic impedances are simulated. In each step as long as the "best" transformed trace is accepted, the traces of simulated acoustic impedances are incorporated as "real" data for the next sequential simulation step. This can lead to artificially good matches in local areas where the bad quality of seismic prevails.

The base idea of this research work is precisely to incorporate stochastic simulation and cosimulation methodologies to conceive and implement a model of global seismic inversion and creating uncertainty linked to areas with different seismic quality.

The use of geostatistics for the creation and transformation of images (acoustic impedances) and the genetic algorithms for the modification and generation of better images, allow the convergence of the inverse process.

The methodology is proposed based on a global perturbation, instead of trace-by-trace, to reach the objective function of the match between synthetic seismogram and real seismic. Using the sequential simulation and co-simulation approaches it creates several realizations of the entire 3D cube of acoustic impedances that are simulated in a first step, instead of individual traces or cells.

After the convolution, local areas of best fit of the different images are selected and "merged" into a secondary image of a direct co-simulation in the next iteration.

The iterative and convergent process continues until a given match with an objective function is reached. Spatial dispersion and patterns of acoustic impedances imposed are reproduced at the final acoustic impedance cube.

As the iterative process is based on global simulations and co-simulations of impedances, there is no local imposing of artificial good fit, i.e. areas of bad seismic tend to remain with bad match coefficients, as it does not happens in most trace-by-trace approaches.

At each iterative step one knows how close is one given generated image from the objective, by the global and local correlation coefficients between the transformed traces and the real seismic traces. These correlation coefficients of different simulated images are used as the affinity criterion to create the next generation of images until it converges to a given predefined threshold.

In a last step, porosity images can be derived from the seismic impedances obtained by seismic inversion and the uncertainty derived from the seismic quality is assessed based on the quality of match between synthetic seismogram and real seismic.

For the case of characterization of the reservoir in terms of facies distribution several methods for the integration of the seismic data in facies models have been proposed, several of which rely on the construction of a facies probability cube by calibration of the seismic data with wells. If only post-stack seismic data is considered, is typically inverts the seismic amplitudes into a 3D acoustic impedance cube, and then converts this impedance into a 3D facies probability using a calibration method of choice.

This facies probability can serve as input of several well-known geostatistical algorithms to create a facies realization, such as the use the cube as locally varying mean on indicator kriging or the use of the tau model in [10], in a multi-point simulation to integrate the facies probability cube with spatial continuity information provided by a training image.

While this provides satisfactory results in most cases, the resulting facies realization does not necessarily match the original seismic amplitude from which the acoustic impedance was inverted. Indeed, if one would forward simulate, for example a 1D convolution on a single facies realizations, then this procedure does not guarantee that the forward simulated seismic matches the field amplitudes.

Another objective of this work is to present a geostatistical methodology, based on multipoint technique that generates facies realization compatible with the field seismic amplitude data, and therefore this new procedure has two main advantages, matching field seismic amplitude data in a physical sense, not merely in a probabilistic sense and using multi-point statistics, not just the two-point statistics (variogram).
