Reservoir properties, such as porosity and permeability, can be derived at well locations from core samples or well log measurements. Since these properties vary laterally from one well to another, it is normally very difficult to predict reservoir properties away from wells. Seismic data, particularly 3D surveys, contain valuable information about the lateral variation of reservoir properties. When wells fall within the seismic coverage, it is logical to predict reservoir properties between wells by interpreting seismic data and using reservoir properties at well locations as spatial control points.
Artificial neural networks (ANN) may be used to aid the estimation of reservoir properties between wells. In this case, a training sample set of input and output data pairs can be collected. The input of neural networks is seismic data relevant to the reservoir at well locations. The expected output from neural networks is reservoir properties at well locations.
This paper uses a local linear neuro-fuzzy model to predict reservoir properties from seismic attributes in one of the oil fields in the central region of Iran. The fundamental approach with the locally linear neuro-fuzzy model is dividing the input space into small linear subspaces with fuzzy validity functions. Any linear model produced, along with its validity function, can be described as a fuzzy neuron. Thus, the total model is a neuro-fuzzy network with one hidden layer and a linear neuron in the output layer, which simply calculates the weighted sum of the outputs of locally linear neurons.
An incremental tree-based learning algorithm, a locally linear model tree (LOLIMOT), is appropriate for tuning rule premise parameters, i.e. determining the validation hypercube for each locally linear model. In iteration, the worst performing locally linear neuron is determined and then divided. All of the possible divisions in the p dimensional input space are checked, and the best is performed. The splitting ratio is simply adjusted as 1/2, which means that the locally linear neuron is divided into two equal halves. The fuzzy validity functions for the new structure are updated. Their centers are identical with the centers of the new hypercubes and the standard deviations are usually set as 0.3. Just one parameter, the embedding dimension, should be defined before running the algorithm. In this work, the number of attributes is the embedding dimension.
To evaluate the performance of a locally linear neuro-fuzzy model in extracting the relationship between seismic attributes and reservoir property, this method was applied in an oil field located in central Iran. This field has two exploration wells. Additionally, a 3D seismic survey, recorded with a one-millisecond sampling interval, covers the area of the reservoir.
First, the logs were mapped to the time domain and then blocked it at each one millisecond to resolve the frequency difference of the logs and seismic data. Then, multi-attribute analyses were performed and the best seismic attributes, which had good correlations with porosity, were found to be acoustic impedance and amplitude weighted cosine phase. By applying the locally linear neuro-fuzzy model to train and validate the network, good results were obtained. The correlation coefficient between the modeled and original logs was 80% and the error was 2.6% in validation.
Finally, to compare the neuro-fuzzy model with traditional methods, the work was repeated with a probabilistic neural network (PNN) and a multi-layer forward neural network (MLFN). The results obtained by applying the MLFN (correlation 83% and error 4.5) and PNN (correlation 68% and error 5.7) were not better than neuro-fuzzy model.