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... y) were used as input parameters to the ANN. Fracture frequency calculated from borehole televiewer data was used as the single output parameter. The ANN was trained using a back-propagation algorithm with a momentum learning function. In addition to fracture frequency within a single borehole, an ANN trained on a subset of boreholes in an area could be used for prediction over the entire set of boreholes, thus allowing the lateral correlation of fracture zones.

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Model-based shear-wave velocity estimation versus empirical regressions
Geophysical Prospecting
Volume 47, Issue 5, Date: September 1999, Pages: 785-797
ABSTRACT
Modelling of AVO signatures for reservoir characterization requires VS estimation from other available logs when shear-wave data are not available. We tested various models for predicting VS from P-wave velocity, porosity and shale volume measured in well logs. Effective medium models which characterize the pore space in terms of ellipsoidal inclusions were compared with statistical VP–VS regressions. The inclusion models were calibrated by non-linear minimization of the difference between model-predicted velocities and actual measured velocities. The quality of the VS prediction was quantified in terms of the rms error by comparison with shear-wave data in wells where both VP and VS were measured. The linear regressions were found to be more robust and the rms error in the prediction was comparable to effective medium model-based predictions.

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Porosity and permeability prediction from wireline logs using artificial neural networks: a North Sea case study
Geophysical Prospecting
Volume 49, Issue 4, Date: July 2001, Pages: 431-444
Hans B. Helle, Alpana Bhatt, Bjørn Ursin
ABSTRACT
Estimations of porosity and permeability from well logs are important yet difficult tasks encountered in geophysical formation evaluation and reservoir engineering. Motivated by recent results of artificial neural network (ANN) modelling offshore eastern Canada, we have developed neural nets for converting well logs in the North Sea to porosity and permeability. We use two separate back-propagation ANNs (BP-ANNs) to model porosity and permeability. The porosity ANN is a simple three-layer network using sonic, density and resistivity logs for input. The permeability ANN is slightly more complex with four inputs (density, gamma ray, neutron porosity and sonic) and more neurons in the hidden layer to account for the increased complexity in the relationships. The networks, initially developed for basin-scale problems, perform sufficiently accurately to meet normal requirements in reservoir engineering when applied to Jurassic reservoirs in the Viking Graben area. The mean difference between the predicted porosity and helium porosity from core plugs is less than 0.01 fractional units. For the permeability network a mean difference of approximately 400 mD is mainly due to minor core-log depth mismatch in the heterogeneous parts of the reservoir and lack of adequate overburden corrections to the core permeability. A major advantage is that no a priori knowledge of the rock material and pore fluids is required. Real-time conversion based on measurements while drilling (MWD) is thus an obvious application.

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The effect of clay distribution on the elastic properties of sandstones
Geophysical Prospecting
Volume 49, Issue 1, Date: January 2001, Pages: 128-150
Mark S. Sams, Martijn Andrea
ABSTRACT
The shape and location of clay within sandstones have a large impact on the P-wave and S-wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P-wave and S-wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S-wave velocities decrease more rapidly than P-wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P-wave velocity due to the competing influence of the density effect and pore-fluid stiffening. The S-wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P-wave and S-wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under-compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P-wave and S-wave velocity which is almost independent of clay distribution. S-wave velocities can be predicted reasonably accurately from P-wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P-wave or S-wave data, for example, can result in large errors. Estimation of the clay distribution from P-wave and S-wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P-wave and S-wave velocity well log data using log-based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data.
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