| dc.description.abstract | In this dissertation we have developed multiple networks systems (multinets or committee machines, CM) for predicting reservoir properties e.g. porosity, permeability, partial fluid saturation and for identifying lithofacies from wireline and measurement while drilling (MWD) logs. The method is much more robust and accurate than a single network and the multiple linear regression method. The basic unit of a committee machine is a multilayer perceptron network (MLP) whose optimum architecture and size of training dataset has been discovered by using synthetic data for each application. The committee machine generated for each property has been successfully applied on real data for predicting the reservoir properties and analysing the lithofacies in the Oseberg field, one of the major fields of the North Sea. The advantage of this technique is that it can be used in real time and thus can facilitate in making crucial decisions on the reservoir while drilling. The trained networks have been successfully used in bulk conversion of wireline and MWD logs to reservoir properties. All the programming has been done using MATLAB programming language and different functions from the neural network toolbox.
For porosity prediction we have made a study initially network and then by the CM approach. We have demonstrated the benefits of committee neural networks where predictions are redundantly combined. Optimal design of the neural network modules and the size of the training set have been determined by numerical experiments with synthetic data. With three inputs i.e. sonic, density and resistivity, the optimal number of hidden neurons for the porosity neural network has been determined to be in the range 6-10, with a sufficient number of training patterns of about 150. The network is sensitive to the fluid properties. The unconstrained optimal linear combination of Hashem (1997), with zero intercept term based on least squares, is the most suitable ensemble approach for the porosity CM and the accuracy is mainly limited by the accuracy of the training patterns and the accuracy of the log data themselves. In application to real data the maximum standard error of the difference between prediction and helium core porosity data is 0.04. The benefit of neural networks compared with the multiple linear regression (MLR) technique has been briefly touched upon by showing that MLR fails to reproduce the minor non-linearity embedded in the common log-to-porosity transforms, whereas the neural network reproduces the same data with high accuracy.
In permeability prediction by CM we have demonstrated the benefits of modularity by decomposing the permeability range into a number of sub-ranges to increase resolution. We have used synthetic data for evaluating the optimal architecture of the component neural networks. With the four inputs; i.e. sonic, density, gamma and neutron porosity, we find that optimal number of hidden units of the permeability neural network is confined to the range 8-12 where the variance and bias are at their minima. In general, the errors steadily decrease with the number of training facts. A practical lower limit has been set to 300, or twice the size of the training set required for the porosity network due to the increased complexity of the background relationships with the log readings.
Since we use a logarithmic permeability scale rather than a linear scale the success of optimal linear combination (OLC) in the porosity CM is not repeated when it is applied to the permeability CM. In fact noise amplification takes place. Simple ensemble averaging is shown to be the preferred method of combining the outputs. A different training strategy must be applied i.e. the validation approach, requiring the training to stop when the level of minimum variance has been reached. Provided that precautions are taken, the permeability CM is more capable of handling the non-linearity and noise than MLR and a single neural network. The benefit of range splitting, using the modularity imbedded in the CM approach, has been demonstrated by resolving details in the combination of logs that otherwise would be invisible. In application to real data a minimum standard deviation error of the difference between prediction and Klinkenberg corrected air permeability data is around 0.3 in logarithmic units (of mD), mainly due to limitations in the techniques of measurement.
We have developed and tested a modular artificial neural network system for predicting the fluids water, oil and gas, and their partial saturations directly from well logs, without explicit knowledge of the fluid and rock properties normally required by conventional methods. For inputs to the networks we have used the density, sonic, resistivity and neutron porosity logs. From synthetic logs based on a realistic petrophysical model we have determined by numerical experiments the optimal architecture, and network training procedure for partial fluid saturation.
The output of three saturations from a single MLP (4-10-3) reveals the same accuracy as those of three individual MLPs with one output (4-4-1). The latter has the advantage of simplicity in terms of number of neurons, which implies fewer training patterns and faster training. Moreover, simplicity in the MLP improves modularity when used for building blocks in the multi-net system. For the optimal 4-4-1 MLP the number of training patterns should be in excess of 100 to ensure negligible errors in the case of data with moderate noise. A committee neural network for each fluid type is the preferred solution, with each network consisting of a number of individually trained 4-4-1 MLPs connected in parallel and redundantly combined using optimal linear combination compared with a single MLP realisation. The OLC approach implies an overall error reduction by an order of magnitude.
Based on these findings we have made a modular neural network (MNN) system consisting of three CMs; one for each fluid type, where each CM contains nine MLPs connected in parallel, and with outputs that are combined using the OLC approach. Using training patterns from CPI logs we have demonstrated its application to real data from North Sea reservoirs containing the full range of fluid types and partial saturation. The saturation predictions from the fluid CMs are further combined in a MNN with the laboratory measured relative permeability curves for both the oil-water and gas-oil fluid systems to generate relative permeability logs.
The accuracy in prediction saturation essentially depends on the accuracy of the training patterns, which are from the computer processed interpretation (CPI) logs, and the accuracy of the individual log measurements. The idea of using neural networks for fluid saturation is thus not to eliminate the careful petrophysical evaluation behind the CPI log, but to transfer into the neural network for future application the effort and expertise already imbedded in the petrophysical database. Comparison of Sw values of the neural network with those of CPI logs, in wells that are unknown to the network, indicates a standard error of less than 0.03.
The problem of identification of lithofacies from well logs is a pattern recognition problem. The CM architecture is based on combining back propagation artificial neural networks (BPANN) with a recurrent BPANN (RBPANN) adopted from time series analysis. The recurrent BPANN exploits the property of facies i.e. it consists of several sequential points along the well bore thus effectively removing ambiguous or spurious classification. The multiclass classification problem has been reduced to a two-class classification problem by using the modular neural network system. Ensembles of neural networks are trained on disjoint sets of patterns using a soft overtraining approach for ensuring diversity and improving the generalisation ability of the stack.
We have used synthetic logs from a realistic model with a very small layer contrast and moderate noise level and we found an excellent classification performance only slightly less than 100% hit rates. By introduction of fine layering in the model we have shown that the performance is only slightly reduced, demonstrating excellent performance of the RBPANN for layer enhancement, also in the case of thin layers. Classification from real data is more challenging since the facies in the present study were initially defined by visual inspection of cores, and thus not fully compatible with the readings of the logging tools which detect different physical properties and have coarser spatial sampling. Application to the four facies of the Ness Formation reveals an average hit-rate well above 90% in wells unknown to the network. Compared with similar published classification studies our results reveal slightly to significantly better performance.
The CM approach for porosity, permeability and water saturation is developed and tested on MWD data also. We trained CM architecture for porosity, permeability and water saturation using MWD data. Since cores are normally not collected in horizontal well the patterns for MWD networks are predictions made by wireline networks. The application of this technique is to predict reservoir properties while drilling. | nb_NO |
