Development and Testing of Two-Phase Relative Permeability Predictors Using Artificial Neural Networks
- N. Silpngarmlers (Penn State U.) | B. Guler (Penn State U.) | T. Ertekin (Penn State U.) | A.S. Grader (Penn State U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2002
- Document Type
- Journal Paper
- 299 - 308
- 2002. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 4.1.5 Processing Equipment, 5.2.1 Phase Behavior and PVT Measurements, 5.6.1 Open hole/cased hole log analysis, 4.1.2 Separation and Treating, 4.6 Natural Gas, 5.6.4 Drillstem/Well Testing, 6.1.5 Human Resources, Competence and Training, 1.2.3 Rock properties, 5.8.3 Coal Seam Gas, 5.3.2 Multiphase Flow, 5.1 Reservoir Characterisation
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In this paper, we report liquid/liquid and liquid/gas two-phase relative permeability predictors that are developed using artificial neural networks (ANNs). In the development stage, some of the relative permeability data from literature are used during the training stage while some other sets are preserved to test the prediction capabilities of the models. Various rock and fluid properties, including endpoint saturations, porosity, permeability, viscosity and interfacial tension, and some functional links (mathematical groups coupling various rock and fluid properties) constitute the input parameters of the models. The models are found to successfully predict the field and experimental relative permeability data.
Relative permeabilities are essential rock-fluid properties required for almost all calculations of multiphase flow dynamics in porous media. A good characterization of relative permeabilities enables petroleum engineers to evaluate reservoir performance, forecast ultimate recovery, and investigate the efficiency of improved oil recovery techniques. Acquisition of accurate relative permeability data is crucial and has always been of interest in the petroleum industry.
Relative permeability characteristics can be obtained from laboratory measurement of a core sample or can be estimated using empirical correlations. Laboratory determinations of relative permeabilities are labor-intensive and can be complicated. The empirical models to estimate relative permeabilities based on rock and fluid properties have experienced relatively mediocre success owing to our limited understanding of the parameters and mechanisms that control the relative permeability characteristics.
The two-phase relative permeabilities are direct nonlinear functions of phase saturations. They are known to be affected by several other parameters other than phase saturations, such as saturation history, pore-size distribution and pore structure, wettability, overburden pressure, porosity, permeability, interfacial tension, fluid density, fluid viscosity, initial wetting-phase saturation, immobile third-phase saturation, and flow rate.1 The relative influences of these parameters on relative permeability characteristics are not yet clearly understood and quantified.
ANNs provide a powerful toolbox to perform nonlinear, multidimensional interpolations. This feature of ANNs makes it possible to capture the existing nonlinear relationships that are most of the time not well understood between the input and output parameters. Thus, ANNs can be effectively used to implicitly incorporate the controlling mechanisms and parameters into the models which are developed for relative permeability prediction. In this study, two-phase, liquid/liquid, and liquid/gas relative permeability predictors are developed using a backpropagation algorithm. The methodology used in the development of two-phase liquid/liquid and two-phase liquid/gas relative permeability ANN predictors is described in this paper. Some of the available rock and fluid properties are used as input parameters of the models. Some functional links, which represent various mathematical relationships among input parameters that have stronger influence on the output, are incorporated as additional inputs to the models. The models are then trained and tested using the experimental data obtained from the literature. The results from the training and testing stages are presented for both models. The differences between both models are also discussed.
In structuring the liquid/liquid (oil/water) ANN model, the connection weights are updated in an incremental fashion so that the weights are adjusted according to a steepest descent protocol obtained after each data pattern is presented to the model. With the completion of the training session, performance of the model is tested using the data sets not exposed to the model. The relative permeability characteristics predicted by the model for these data sets are found to be in good agreement with the data reported in the literature. The input layer of the liquid/gas (oil/gas) ANN model with the exception of interfacial tension incorporates the same set of rock and fluid properties used in the liquid/liquid model. The liquid/gas model differs from the liquid/liquid model in terms of its network topology, types of functional links used, and the mechanics of how the connection weights are updated. The individual topologies of the liquid/liquid and liquid/gas models are also different in terms of the number of neurons placed in the input and hidden layers. The more influential parameters are identified by large connection weights that imply strong signals originating from those input neurons to the output neurons. The parameters identified in this fashion are used in structuring the functional links. In the liquid/gas model, the connection weights are updated in a batch mode so that the steepest descent gradients observed after presenting each data pattern to the model are averaged and later used in adjusting the weights. During the testing stage, the liquid/gas relative permeability predictor has also successfully predicted the field and experimental data sets. The differences in network topologies and functional links of the two models imply that liquid/liquid and liquid/gas relative permeability relationships are controlled by a variety of different parameters.
Overview of Artificial Neural Networks (ANNs)
ANNs are developed by creating artificial neurons, which are simple processing elements (PE) massively interconnected in order to mimic a small portion of the serial- and parallel-information processing ability of the biological neural network. There are many different types of ANNs, each of which has different strengths particular to its applications. The abilities of different networks can be related to their structure, dynamics, and learning methods. ANNs can be used for pattern recognition, signal filtering, data segmentation, and so on. They offer the advantages of learning from examples, self-organization, fast data processing, and ease of insertion into existing and newly developed systems.2
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