A Deep Learning-Aided Approach for Estimating Field Permeability Map by Fusing Well Logs, Well Tests, and Seismic Data

TL;DR

This paper tackles the challenge of estimating reservoir permeability across inter-well spaces by fusing well logs, well tests, and seismic data through a kernel-regression framework with a custom multi-source kernel and a CNN-based seismic predictor. A four-stage workflow combines pure fusion, seismic-informed learning, and complete fusion to generate refined 2D permeability maps, demonstrated on a Western Siberia field. The approach improves inter-well predictions and reduces artifacts near wells, with quantitative gains showing lower MSE and higher R^2 when seismic data are included. The method is interpretable via kernel parameters and LOOCV optimization, and it lays groundwork for extending to 3D, additional seismic attributes, and uncertainty quantification.

Abstract

Obtaining reliable permeability maps of oil reservoirs is crucial for building a robust and accurate reservoir simulation model and, therefore, designing effective recovery strategies. This problem, however, remains challenging, as it requires the integration of various data sources by experts from different disciplines. Moreover, there are no sources to provide direct information about the inter-well space. In this work, a new method based on the data-fusion approach is proposed for predicting two-dimensional permeability maps on the whole reservoir area. This method utilizes non-parametric regression with a custom kernel shape accounting for different data sources: well logs, well tests, and seismics. A convolutional neural network is developed to process seismic data and then incorporate it with other sources. A multi-stage data fusion procedure helps to artificially increase the training dataset for the seismic interpretation model and finally to construct the adequate permeability map. The proposed methodology of permeability map construction from different sources was tested on a real oil reservoir located in Western Siberia. The results demonstrate that the developed map perfectly corresponds to the permeability estimations in the wells, and the inter-well space permeability predictions are considerably improved through the incorporation of the seismic data.

Figures (11)

• Figure 1: Well location map presenting the positions of the wells and the availability of permeability measurements in those wells, as well as the interpreted values. The oil reservoir boundary depicts the area in which the target permeability map is aimed to be fused.
• Figure 2: Comparison of permeability distributions from well log and well test data before (a) and after (b) Q-Q transformation.
• Figure 3: Workflow diagram illustrating the methodology applied for mapping the spatial distribution of permeability. The process consists of four stages: (1) data collection and preprocessing, (2) kernel-regression based "pure fusion," (3) CNN model training for predicting permeability from seismic, and (4) kernel-regression based complete fusion of well log, well-test, and seismic data, estimating a refined final permeability.
• Figure 4: Kernel weights as a function of distance from well for different data sources. $\mathcal{K}_{\mathrm{wt}}$, $\mathcal{K}_{\mathrm{wl}}$ and $\mathcal{K}_{\mathrm{seismic}}$ represent kernels of permeability derived from well test, well log, and seismic data respectively for a single well at $\vec{r}_w$.
• Figure 5: Detailed architecture of the seismic CNN model. The model receives two inputs: seismic RMS cubes surrounding specified points and coordinates of those points. The CNN outputs predictions of the target parameter, permeability. Before the first flattening operation, the network architecture consists of several layers of three-dimensional convolution, max pooling, batch normalization, and rectified linear activation functions (ReLU), indicated by blue blocks. After flattening, the data underwent sequential one-dimensional convolutional layers (purple blocks).