Summary
A'nan Oilfield is located in the northeast of the Erlian Basin in North China. The porosity distribution of the oil-bearing stratum is primarily controlled by complex distribution patterns of sedimentary lithofacies and diagenetic facies. This paper describes a methodology to provide a porosity model for the A'nan Oilfield using limited well porosity data, with the incorporation of the conceptual reservoir architecture. Neural network residual kriging or simulation is employed to tackle the problem. The integrated technique is developed based on a combined use of radial basis function neural networks and geostatistics. It has the flexibility of neural networks in handling high-dimensional data, the exactitude property of kriging and the ability to perform stochastic simulation via the use of kriging variance. The results of this study show that the integrated technique provides a realistic description of porosity honoring both the well data and the conceptual framework of the geological interpretations. The technique is fast, straightforward and does not require any tedious cross-correlation modeling. It is of great benefit to reservoir geologists and engineers.
Introduction
Spatial description of porosity is a crucial step for fluid flow simulation study. Such descriptions are often used in porosity and permeability transforms in order to derive a transmissibility field. The distribution of porosity is commonly controlled by qualitative geological features. While the importance of these features is well known to the geological community, they are often difficult to incorporate quantitatively during the three dimensional (3D) geological modeling study. There is therefore a strong need for the industry to fully utilize existing geological interpretations rather than iteratively match the computational outputs to the interpretations by varying model parameters. The objective of this paper is to provide an integrated solution to make use of existing geological interpretations for improved reservoir mapping. Although some purely geostatistical techniques are capable of providing some of these functionalities, often difficult and tedious cross-correlation modeling (e.g., cokriging) as well as time consuming indicator coding (e.g., nonparametric analysis) are required.
The integrated technique used in this paper is developed based on a combined use of artificial neural networks (NNs) and geostatistics. The original idea was proposed by Kanevski et al.1 The authors assumed that spatial prediction is composed of a predictable (trend) component and an error (noise or residual) component. They used multilayered feedforward neural networks (an inexact estimator) to model the former component and kriging (an exact estimator) to model the latter component. Hence the name neural network residual kriging (NNRK) was used. The final estimate is simply the sum of the two components, and hence the estimator restores all the conditioning data. The kriging variance also allows the estimator to perform stochastic simulation. A technique, such as neural network residual simulation (NNRS)2 is an example.
There are many advantages of combining NNs with geostatistics. The most popular geostatistical model, kriging,3 is based on error variance minimization with the use of spatial correlation structures. It has the ability to generate an exact interpolation. Kriging variance is also useful for stochastic simulation (e.g., via sequential Gaussian simulation3) in order to quantify the spatial uncertainty of the predictions. However, most geostatistical models become unattractive when there are many types of information available for modeling. In mathematical terms, geostatistics is often not the best solution for high-dimensional problems. On the other hand, NN methods are highly flexible in handling nonlinear, high-dimensional data without tedious cross-correlation modeling. However, most NN methods could neither produce exact interpolation nor perform stochastic simulation for uncertainty analysis. Hence, the combined use of NNs and geostatistics provides a powerful tool for reservoir mapping.
This paper will first describe the integrated method using porosity as an example. The reservoir description of the A'nan Oilfield will be presented. This is followed by the application of the method to model the porosity distribution across the field based on limited well data and extensive geological information regarding the distribution patterns of the sedimentary lithofacies and diagenetic facies.
Basis of Neural Networks
This paper uses a special class of NN estimators, namely "radial basis function neural networks." This particular estimator is chosen because it is simple and the origin of the method is similar to most spatial interpolators, that is, the prediction is calculated based on the distance between the prediction location and the reference data location. Its application to reservoir characterization includes reservoir mapping4–6 and log interpretation.7
Like most NN methods, radial basis function neural networks (RBFNNs) attempt to mimic simple biological learning processes. They can learn from examples. The learning phase is an essential starting point that requires training patterns consisting of a number of input signals (e.g., a high-dimensional vector) paired with target signals. The inputs are presented to the network and the corresponding outputs are calculated with the aim of minimizing the model error (i.e., the total difference between the calculated outputs and target signals). The gradient descent method is the most popular learning method to reduce the model error by iteration. Training can be terminated when the model error is below a tolerance value. After training, the network creates a set of parameters that can be used for predicting properties in situations where the actual outputs are not known.
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