Patrick M. Wong

An integrated neural-fuzzy-genetic-algorithm using hyper-surface membership functions to predict permeability in petroleum reservoirs

This paper introduces a new neural-fuzzy technique combined with genetic algorithms in the prediction of permeability in petroleum reservoirs. The methodology involves the use of neural networks to generate membership functions and to approximate permeability automatically from digitized data (well logs) obtained from oil wells. The trained networks are used as fuzzy rules and hyper-surface membership functions. The results of these rules are interpolated based on the membership grades and the parameters in the defuzzification operators which are optimized by genetic algorithms. The use of the integrated methodology is demonstrated via a case study in a petroleum reservoir in offshore Western Australia. The results show that the integrated neural-fuzzy-genetic-algorithm (INFUGA) gives the smallest error on the unseen data when compared to similar algorithms. The INFUGA algorithm is expected to provide a significant improvement when the unseen data come from a mixed or complex distribution.

An improved technique in porosity prediction: a neural network approach

Genetic reservoir characterization is important in developing, for a given petroleum reservoir, an improved understanding of the total amount and fluid flow properties of hydrocarbon reserves. Application of genetic concepts involves the classification of well log data into different lithofacies groups, followed by a facies-by-facies description of rock properties such as porosity and permeability. This work contrasts the genetic and nongenetic approaches in predicting porosity values of an oil well using backpropagation neural network methods. The performance of both methods are critically evaluated. A systematic technique to optimise the network configuration using weight visualization curves is proposed, thereby enabling the amount of training time to be significantly reduced. In the example problem, the genetic approach provides superior porosity estimates to that based on a nongenetic approach. >

Rainfall prediction model using soft computing technique

Abstract Rainfall prediction in this paper is a spatial interpolation problem that makes use of the daily rainfall information to predict volume of rainfall at unknown locations within area covered by existing observations. This paper proposed the use of self-organising map (SOM), backpropagation neural networks (BPNN) and fuzzy rule systems to perform rainfall spatial interpolation based on local method. The SOM is first used to separate the whole data space into some local surface automatically without any knowledge from the analyst. In each sub-surface, the complexity of the whole data space is reduced to something more homogeneous. After classification, BPNNs are then use to learn the generalization characteristics from the data within each cluster. Fuzzy rules for each cluster are then extracted. The fuzzy rule base is then used for rainfall prediction. This method is used to compare with an established method, which uses radial basis function networks and orographic effect. Results show that this method could provide similar results from the established method. However, this method has the advantage of allowing analyst to understand and interact with the model using fuzzy rules.

Multiple permeability predictions using an observational learning algorithm

Reservoir permeability is a critical parameter for the evaluation of hydrocarbon reservoirs. Well log data are frequently available to infer this parameter along drilled wells. Many fundamental problems remain unsolved by most predictive models. This paper introduces the use of an improved neural network trained by an observational learning algorithm to provide solutions for two particular problems: the generation of additional or “virtual” samples when the number of training data is insufficient; and the generation of multiple permeability values at the same reservoir depth for reliability analyses. The methodology is illustrated by a case study in western Australia. Four drilled wells with well logs and core permeability are used in this study. The data from the first two wells are used for training, while the others are used as unseen data to test the performance of the model. The results show that the proposed method gives smaller error compared to multiple linear regression and other neural networks (simple committee networks and bootstrap aggregating). It also provides valuable information on the reliability of the permeability predictions which is consistent with the geological studies.

An improved global upscaling approach for reservoir simulation

Realistic upscaling of fine-scale reservoir models is a great challenge for reservoir engineers. The common problem of conventional upscaling methods is that they may smear out the spatially continuous permeability extremes, such as shale barriers and open fractures. Recent studies have shown that such smearing effect has a significant impact on recovery in heterogeneous reservoirs, especially the breakthrough oil recovery. The conventional methods are considered as local upscaling which concentrate on only local areas and ignore geologically important structural information. A recent global upscaling approach attempts to solve this problem, but the resulting grid system may be over-irregular and becomes impractical for field applications. This paper presents an improved global upscaling approach based on the representative elemental volume (REV) theory and the stepwise idea from renormalization. The new method focuses on the use of a new concept of REVGS (REV Grid System) for constructing coarse blocks, which taking into account the spatial connectivity of a global permeability field. Mathematically, the variance of permeability in the coarse blocks is the smallest within the blocks, and the largest between the blocks. The resulting system can be readily used in flow simulators. The proposed method is applied to two case studies. Compared to the conventional methods, the coarse grid system derived from our improved global method successfully retains the permeability extremes observed in the fine-scale models. The flow simulation results show that the consistency of the reservoir behavior before and after upscaling is excellent.

A self-generating fuzzy rules inference system for petrophysical properties prediction

This paper discusses the application of a self-generating fuzzy rule extraction and inference system for the prediction of petrophysical properties from well log data. A set of core data with known characteristics is first selected as the training samples. Fuzzy rules are then extracted and undergo a process of rule elimination. The reduced rule set forms the rule-base of the fuzzy prediction model. This will be used to predict properties of other depths within or around the well. Results based on a test case for the prediction of porosity is reported and the performance of the system is discussed.

A Sedimentological Approach to Upscaling

Optimised upscaling in reservoir simulations requires the construction of realistic petrophysical properties that are representative of the heterogeneity in the sedimentary deposits. Reservoir heterogeneities are controlled by the arrangement of various hierarchies of sedimentary facies and their internal bounding surfaces. The conventional sedimentological approach to reservoir upscaling involves subdivision and ranking of various hierarchies of architectural units and associated bounding surfaces of the reservoir sequence according to their geological significance. This global upscaling approach produces realistic scaled up models that retain both the structural and non-structural heterogeneities of the original sedimentological models. Analyses of sedimentary sequences from various depositional environments indicate that the fractional Levy model can adequately describe the heterogeneity and scaling characteristics of individual genetic sediment sequences in the clastic sedimentary system without further subdividing and ranking of the heterogeneous sequences. The heterogeneous nature of each sedimentary system can be quantified by the Levy index parameter, whereas the maximum upscaling magnitude (or upscaling index) for a particular sequence can be determined from the Levy width parameter plot. Depositional modelling mimics the sedimentary processes in a range of scales and honours hierarchies of sedimentary facies and their bounding surfaces. It can be used effectively for upgridding and upscaling in accordance with the stratigraphic framework and sedimentological models. Both the fractional Levy model and the depositional modelling provide quantitative alternatives to the conventional global sedimentological upscaling approach.

Balancing Bias and Variance: Network Topology and Pattern Set Reduction Techniques

It has been estimated that some 70% of applications of neural networks use some variant of the multi-layer feed-forward network trained using back-propagation. These neural networks are non-parametric estimators, and their limitations can be explained by a well understood problem in non-parametric statistics, being the “bias and variance” dilemma. The dilemma is that to obtain a good approximation of an input-output relationship using some form of estimator, constraints must be placed on the structure of the estimator and hence introduce bias, or a very large number of examples of the relationship must be used to construct the estimator. Thus, we have a trade off between generalisation ability and training time.

A practical fuzzy interpolator for prediction of reservoir permeability

We propose a practical fuzzy interpolator (PFI) to represent imprecise relationships between inputs and outputs in high-dimensional data systems. The method employs expert knowledge and sample data to dynamically generate piecewise linear inference rules, and then the values to be estimated are interpolated and extrapolated based on these rules. We demonstrate the use of this methodology in petroleum reservoir engineering where the permeability is estimated among oil wells. The results are compared to a neural-fuzzy technique for the same petroleum reservoir data set. This shows that the PFI is not only simple, and computationally fast, but also gives better performance than the neural-fuzzy technique.

Confidence bounds of petrophysical predictions from conventional neural networks

Neural networks are powerful tools for solving the complex regression problems which abound in geosciences. Estimation of prediction confidence from neural networks is an important area. Many procedures are available to date, but it is often tedious for practitioners to implement such procedures without significant modification of the existing learning algorithms. In many cases, the procedures are also computationally intensive. This paper presents a practical solution using conventional backpropagation networks with simple data pre-processing and post-processing algorithms. The methodology involves conversion of the target outputs into linguistic variables (classes) prior to learning. When the classification network converges, minimum and maximum predictions are derived from the output activations using a simple averaging algorithm. Two examples from petroleum reservoirs are used to demonstrate the proposed methodology. The results show that the confidence bounds of the petrophysical predictions are realistic in both cases. The proposed methodology is generally useful, and can be implemented in simple spreadsheets without altering any existing neural network code.