Many predictive methods based on numerical simulation generate undesired changes on the distribution of their parameters that depend mainly on the numerical method or the grid orientation (artifacts). On the other hand, it is common to find an appropriate match of the production history through the use of reservoir properties as calibration parameters, even when this procedure generates in many cases geological inconsistencies. Also, as real time data acquisition is becoming a powerful and popular technique, it is important to achieve a methodology that allows the input of new sources of information without disturbing the history matching previously validated.
In this paper a new methodology to integrate a history-matched reservoir model with other geological data is presented. It is based on the methodology proposed by Sahni and Horne 1, that based on the Haar wavelet transform allows for the improvement of the history-matched geological model through the inclusion of additional geological constraints without needing to perform the history matching every time the reservoir model is updated.
The first step of the method presented in this study is to match the production history of the reservoir that will be modeled by means of numerical simulation. Then, the wavelet function that better fits the distribution of the considered properties, keeping the highest Energy Compaction Ratio (ECR), is chosen. After performing the wavelet transform, the most sensitive coefficients to the production data are determined. Those that are not significant for the model validation can be modified and geostatistical interpolation algorithms can be applied (e.g. Sequential Gaussian Simulation). Finally, when the inverse transform is performed, the data set is not only validated by the production history but also by the geological properties.
If the wavelet transform is not Haar, an additional benefit is obtained. It is possible to interpolate the geological information in the different regions where the data acquisition is difficult or doubtful.
This new heuristic methodology has been tested in different reservoir configurations. In this paper, we validate the results achieved for a test case reservoir with patterns of 4 producers and 2 injectors. This procedure is very helpful in numerical simulation of reservoirs and it has a direct impact on its management, risk analysis and the development of depletion plans.
Introduction
In reservoir numerical simulation all the available information is integrated with the intention of making as real as possible, the characterization of the reservoir, as well as the fluid and the remaining energy. These sources of information usually come from core samples, well logs, well tests, and seismic data. All of these sources of information are of a wide kind of nature. While core data and well logs are related to a very small scale, well-tests are associated with a middle scale and seismic data with a large one. In this way, the integration of all of these data sources frequently represents a very difficult process, since the drives that generate them give place to different nature phenomenon, spatial as much as temporal distributed. However, a correct implementation of a reservoir simulation model requires an accurate integration of all of these data sources, if they are available.
This reservoir data can be classified into two main categories: production data that depends on the well operations and acts as source/sink terms to the reservoir (e.g. pressure and rate history from wells) and all other sources of data (e.g. core samples, well logs, well tests and seismic), that depend mainly on the reservoir characteristics.
Generally speaking, a reservoir model is firstly built taking into account all these data sources, with the exception of the production time series that are included in the model during the calibration stage, in order to adjust some of the model parameters to honor the history (history matching). It is usual to use the permeability as a calibration parameter. Once the history matching process is finished the reservoir properties could differ from the initial geological features since some numerical methods can generate artifacts, producing geological inconsistency 2. Even when the geology could differ significantly from our assumptions and could be difficult to determine how far from reality is our estimation after the calibration process, the redundant geological information could generate convergence problems, taking huge time-consuming requirements.
