New-Age Kolmogorov Full-Function Neural Network KNN Offers High-Fidelity Reservoir Predictions via Estimation of Core, Well Log, Map and Seismic Properties

Abstract

Instead of relying on analytical functions to approximate property relationships, this innovative hybrid neural network technique offers highly adaptive, full-function (!) predictions that can be applied to different subsurface data types ranging from (1.) core-to-log prediction (permeability), (2.) multivariate property maps (oil-saturated thickness maps), and, (3.) petrophysical properties from 3D seismic data (i.e., hydrocarbon pore volume, instantaneous velocity). For each scenario a separate example is shown. In case study 1, core measurements are used as the target array and well log data serve training. To analyze the uncertainty of predicted estimates, a second oilfield case study applies 100 iterations of log data from 350 wells to obtain P10-P50-P90 probabilities by randomly removing 40% (140 wells) for validation purposes. In a third case study elastic logs and a low-frequency model are used to predict seismic properties. KNN generates a high level of freedom operator with only one (or more) hidden layer(s). Iterative parameterization precludes that high correlation coefficients arise from overtraining. Because the key advantage of the Kolmogorov neural network (KNN) is to permit non-linear, full-function approximations of reservoir properties, the KNN approach provides a higher-fidelity solution in comparison to other linear or non-linear neural net regressions. KNN offers a fast-track alternative to classic reservoir property predictions from model-based seismic inversions by combining (a) Kolmogorov's Superposition Theorem and (b) principles of genetic inversion (Darwin's "Survival of the fittest") together with Tikhonov regularization and gradient theory. In practice, this is accomplished by minimizing an objective function on multiple and simultaneous outputs from full-function (via look-up table) Kolmogorov neural network runs. All case studies produce high correlations between actual and predicted properties when compared to other stochastic or deterministic inversions. For instance, in the log to seismic prediction better (simulated) resolution of neural network results can be discerned compared to traditional inversion results. Moreover, all blind tests match the overall shape of prominent log curve deflections with a higher degree of fidelity than from inversion. An important fringe benefit of KNN application is the observed increase in seismic resolution that by comparison falls between the seismic resolution of a model-based inversion and the simulated resolution from seismic stochastic inversion.