Predicting oil-well permeability and porosity from wire-line petrophysical logs — a feasibility study using partial least squares regression

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Esbensen, K.H. and Martens, H, 1987. Predicting oil-well permeability and porosity from wire-line petrophysical logs—a feasibility study using partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 2: 221–232. A method for predicting permeability, porosity and other petrophysical core parameters directly from wire-line logs in oil wells is reported, based on multivariate calibration using principal component analysis and partial least squares (PLS) regression. The method is applied to data from a single North Sea oil well over a depth interval of 125 m. Samples with log parameters indicating abnormal lithologies or with excessive missing data were rejected as “outliers”. Calibration was carried out by relating a set of seventeen non-selective, in situ wire-line petrophysical log variables from various depths in the well to petrophysical laboratory determinations subsequently performed on drill core samples from the corresponding depths. Calibration modelling was effected by treating the samples both as a single lithology class (reservoir sand) and as high and low permeability classes (coarse and fine sands). Various linearity transformations of the input data were tested; (permeability)13 was found to be optimal. The predicted permeability and porosity closely covary down the entire well with the core control data. Approximately 50% of their total data variance was correctly reproduced; the same stratigraphic horizons were identified. The residual variance is due to measurement error, shift discrepancies and model errors (non-linearities and data subgroupings). The PLS model was found to be statistically stable by two different validation methods (leverage correction and cross-validation). This study demonstrates in situ wall-rock parameter prediction from core calibration data in one well, and simultaneously simulates inter-well prediction for other non-cored wells. PLS prognosis for oil/gas wells appears feasible at the present precision level of log and laboratory measurements and uncertainty in core-depth assignment.