As a qualitative indicator, subsurface lithofacies is an important parameter that can characterize hydrocarbon reservoirs for the degree of compartmentalization. In order to account for the geological dependency between data samples along the vertical direction, the feed-backward Recurrent Neural Networks is applied to classify the sequential lithofacies in the subsurface. Particularly, Gated Recurrent Units (GRU) is used, which can be dedicated to learning how to update or reset hidden states (in this case, lithofacies), such that the information flow through the system is regulated. Operating on the output layer, the softmax function is able to map the probability values over various possible lithofacies, and the associated uncertainty could be analyzed subsequently. In addition, the statistical Hidden Markov Models (HMM) is applied to benchmark the performance of GRU, in which the embedded transition matrix could enforce the conditional probability between different lithofacies. The designed GRU and HMM are applied to a synthetic model of the Book Cliffs and a real dataset from the Vienna Basin. Instead of using well logs, elastic rock properties from a non-linear inversion scheme are proposed as inputs for the classification purpose, which could help to overcome the location limitations of cored wells, and 2D sections of reservoir lithofacies are then obtained.

Location limitation of logged wells restricts the porosity estimation across the whole reservoir target, whereas seismic data are always collected to cover larger areas. In this paper, inversion results of seismic data are proposed as inputs for the prediction of reservoir porosity, even though the resolution is decreased, compared with well-log readings. The non-linear inversion scheme used is able to explore the complex relationship between rock properties and seismic data, which could potentially provide a higher quality of inversion results. As a regression process, Convolutional Neural Networks is then applied to estimate the reservoir porosity, based on the outputs of seismic inversion scheme. Incorporating 2D kernel filters which are convolved with input rock properties, the local information inside filters window is considered, and a better prediction performance is to be guaranteed. This is due to the fact that reservoir porosity is formed under depositional and digenetic rules, and it is intrinsically correlated with rock properties along the vertical direction in a short range. The designed workflow is applied to a real dataset from the Vienna Basin where compressibility and shear compliance are inverted and then used as inputs for the porosity estimation by Convolutional Neural Networks. For a comparison, the traditional Artificial Neural Networks is also trained and applied to the same dataset. It is concluded that the Convolutional Neural Networks can achieve a higher accuracy, and a 3D cube of reservoir porosity is obtained without location restriction of well logs.

In this paper, geological prior information is incorporated in the classification of reservoir lithologies after the adoption of Markov random fields (MRFs). The prediction of hidden lithologies is based on measured observations, such as seismic inversion results, which are associated with the latent categorical variables, based on the assumption of Gaussian distributions. Compared with other statistical methods, such as the Gaussian mixture model or k-Means, which do not take spatial relationships into account, the hidden MRFs approach can connect the same or similar lithologies horizontally while ensuring a geologically reasonable vertical ordering. It is, therefore, able to exclude randomly appearing lithologies caused by errors in the inversion. The prior information consists of a Gibbs distribution function and transition probability matrices. The Gibbs distribution connects the same or similar lithologies internally, which does not need a geological definition from the outside. The transition matrices provide preferential transitions between different lithologies, and an estimation of them implicitly depends on the depositional environments and juxtaposition rules between different lithologies. Analog cross sections from the subsurface or outcrop studies can contribute to the construction of these matrices by a simple counting procedure.

Hidden Markov Models (HMMs) have been applied to predict reservoir lithologies using seismic inversion results as inputs. This approach takes into account the conditional probabilities between different lithologies, i.e. the vertical transitions in sedimentary sequences. These properties are used as prior geological information. In order to relate the seismic inversion results to the true well-log data, HMMs need to be trained based on the Expectation-Maximization theory. Application of the resulting model on a synthetic example from the Book Cliffs (Utah, USA) showed that most lithologies are classified correctly, even for some thin layers. A comparison with point-wise methods in which data samples are treated independently from each other, such as k-means and fuzzy logic classifiers, leads to the conclusion that the spatial correlation in HMMs allows better lithological predictions because the prior information accounts for the geological depositional processes. A real case study with data from the Vienna Basin (Austria) is performed, in which lithologies in a 3D cube are obtained based on properties from seismic inversions, via trained HMMs. While the vertical sequences are shown to be reasonably well predicted, the horizontal continuities are not. This indicates that the future research should focus on the lateral geological relationships.

The coupled Markov chain model can be used to simulate reservoir lithologies between wells, by conditioning them on the observed data in the cored wells. However, with this method, only the state at the same depth as the current cell is going to be used for conditioning, which may be a problem if the geological layers are dipping. This will cause the simulated lithological layers to be broken or to become discontinuous across the reservoir. In order to address this problem, an actively conditioned process is proposed here, in which a tolerance angle is predefined. The states contained in the region constrained by the tolerance angle will be employed for conditioning in the horizontal chain first, after which a coupling concept with the vertical chain is implemented. In order to use the same horizontal transition matrix for different future states, the tolerance angle has to be small. This allows the method to work in reservoirs without complex structures caused by depositional processes or tectonic deformations. Directional artefacts in the modeling process are avoided through a careful choice of the simulation path. The tolerance angle and dipping direction of the strata can be obtained from a correlation between wells, or from seismic data, which are available in most hydrocarbon reservoirs, either by interpretation or by inversion that can also assist the construction of a horizontal probability matrix.