Stoneley waves propagating in a borehole will produce reflected waves when they encounter a porous formation. In previous studies, the simplified Biot-Rosenbaum theory is used to calculate the Stoneley wave reflection coefficient for porous formations. Such simplified theory ignores the effect of formation frame elasticity, thus can't obtain accurately the Stoneley wave reflection for the porous formation with small stiffness. In this study, to take the effect of formation frame elasticity into account, we use the Biot's theory in the low-frequency limit to simulate the Stoneley wave reflection by employing the velocity-stress finite-difference time-domain (FDTD) method. In addition, as permeability of the formation varies in the axial direction, and the viscosity of the pore fluid also changes in a radial direction due to mud invasion, it is difficult to use the simplified theory to calculate the reflection coefficient of the Stoneley wave in such heterogeneous cases. Therefore, this study first investigates the effect of the formation permeability heterogeneity on Stoneley wave reflection coefficient by this FDTD method. The FDTD method is verified by a comparison with the real axis integration (RAI) method with respect to the Stoneley wave propagation in a borehole surrounded by a homogeneous porous formation. The reflection coefficient obtained by the FDTD method is smaller than that using the simplified theory, which shows that elasticity of the formation frame affects Stoneley wave reflection: the effect of elasticity on the reflection coefficient is greater when the formation frame is less rigid or when the porosity and permeability of the formation are lower. According to the simulation results of the FDTD method, a modified simplified theory which can improve the calculation accuracy of Stoneley wave reflection coefficient is proposed. Furthermore, the effects of the permeability heterogeneity on the Stoneley wave reflection are investigated: the reflection coefficient peaks change when permeability alters in an axial direction, and the peak interval increases. For the mud invasion model, the reflection coefficient is almost identical to that of the homogeneous model, which has the same permeability as the borehole wall of the mud invasion model.

Igneous rocks are widely developed in various Mesozoic and Cenozoic continental and marine basins. Igneous reservoirs are the key reservoirs for current oil and gas development. Accurate prediction of lithology and lithofacies is a prerequisite for the effective exploration of igneous reservoirs. Igneous lithology and lithofacies are complex and correlated. The existing single-label igneous rock identification methods only consider the prediction of individual properties, and less consideration is given to the correlation of reservoir properties. Therefore, lithology and lithofacies prediction based on conventional logging data is regarded as a typical class-imbalanced multilabel classification problem when considering both attribute correlation in algorithms and evaluation metrics. To solve this problem, an ensemble method of data optimization combined with multigrained cascade forest (CF) is used in this study to develop a new multilabel lithology and lithofacies prediction model based on data from nine conventional logs in the eastern depressional reservoirs of the Liaohe Basin, and satisfactory results are obtained. The imbalance problem of the conventional logging data sets is first solved by using K-means and synthetic minority oversampling technique methods; then, the model is trained by scenario transformation and stripping with multigrained CF; and next, a multilabel classification evaluation index with multiple perspectives is introduced. The differences between the model and typical intelligent algorithms such as CF, adaptive boosting, random forest, and support vector machine are compared in simulated wells, and the new model is found to have obvious advantages. The model is finally applied to an actual well, and the accurate prediction results illustrate that the new model designed and trained for the class imbalance multilabel classification problem in this paper has application value in the lithology and lithofacies multilabel prediction of igneous rocks and also provides a theoretical basis for more complex multilabel reservoir evaluation using machine learning in the future.

The reservoirs in the eastern depression of Liaohe basin are formed by multistage igneous eruption. The lithofacies and lithology are complex, and the lithology is mainly intermediate and basic igneous rocks. Based on the integration of debris data of igneous rocks and logging data, this article selected 6,462 continuous logging data with complete cuttings data and five conventional logging curves (RLLD, AC, DEN, GR, and CNL) from four wells in the eastern depression of Liaohe basin as the training set. A variety of lithologic identification schemes based on support vector machine and random forest are established to classify the pure igneous strata and actual strata. By comparing the classification results with the identification data of core slice and debris slice, a practical lithologic classification scheme for igneous rocks in the eastern depression of Liaohe basin is obtained, and the classification accuracy reaches 97.46%.