TY - JOUR
AU1 - ArabAmeri,, Farid
AU2 - Soleymani,, Hamidreza
AU3 - Tokhmechi,, Behzad
AB - Abstract Velocity-based pore-pressure prediction methods are widely accepted as a routine technique in the petroleum industry. Despite recent improvements, literature yet suffers from inconsistencies and uncertainties mostly arising from velocity anomalies due to complex lithostratigraphic settings or the presence of various formation fluids. Our goal in this paper is to improve the accuracy and reliability of the conventional Bowers and Tau methods in a reservoir with complex lithology. The proposed workflow aims to achieve this by clustering the input data based on specific petrophysical characteristics prior to routine pore-pressure prediction. We show each major zone at the offset test wells have a distinct ‘compaction trend’ and the empirical constants in the Bowers and Tau methods can be calibrated for each cluster rather than the whole stratigraphic column. The clustering task was done by statistical analyses of a suite of well logs and validated with core-derived lithologies. To find the best clustering algorithm, we have applied and compared five techniques. We found that the self-organizing map method provides the best results by maximizing lithology likelihood within each cluster and improve the overall accuracy of the Bowers and Tau methods. This research also provides a systematic comparison of the mentioned clustering algorithms based on their ability to distinguish various lithofacies. Moreover, the proposed workflow requires a minimum user interference, and it is expected to generate reproducible results. Our results from a case study in a reservoir in the southwest of Iran demonstrate the capability of the proposed method. pore pressure, Bowers method, Tau method, self-organizing map, lithofacies 1. Introduction Pore-pressure prediction is an active and long-standing research area in the Earth sciences, and it has been the focus of the petroleum industry since the early days of exploration and exploitation. Blowouts, kicks, borehole washouts, wellbore breakout and stuck pipes (Oughton et al.2015) are just some issues that may occur while encountering unexpected fluid pressure anomalies during drilling. To reduce the associated risks of drilling, a robust mud plan and casing design is required as part of every drilling operation (Nguyen et al.2015; Wild et al.2015). Today a reliable estimate of pore pressure before drilling is not just a routine to increase the safety and cost efficiency of the operation, but it also provides an unparalleled source of information in the exploration and production phase. Pore-pressure data can be used to inform the choice of suitable production method, the maximum hydrocarbon column in the reservoir, the integrity and sealing capacity of the caprock and the interpretation of complex time-lapse seismic data (Holm 1998; Hao et al.2015; Guglielmi et al.2015; Cranganu & Soleymani 2015; Cranganu et al.2014; Maleki et al.2018). One of the remarkable early contributions in the estimation of pore pressure was made by Hottmann et al. (1965). They documented that the porosity decrease as a function of depth in sediments from the southern Louisiana Gulf Coast and, by extension, applied their observations to other sedimentary basins. They further stated that any deviations from the normal trend could be associated with abnormal pore pressure. Eaton et al. (1972) showed the application of deep resistivity log data in shale sediments of the Gulf of Mexico as an indicator of higher pore pressure. They also introduced an empirical equation to derive pore pressure by introducing a relationship between effective stress and P-wave transit-time. Bowers (1995) proposed a power-law relationship between compressional velocity and effective stress by calculating the overburden stress, and predicted the pore pressure at offset well locations. Similarly, Giles et al. (1998) introduced a compound mudline and matrix-transit-time variable (Tau) as a first-order effective stress versus velocity power-law relationship. Later, Boitnott et al. (2009) improved the Bowers method by considering a normal compaction trend that is asymptotic to matrix velocities and can provide a better representation of the physical properties of the rocks. Various authors reported a successful application of integrated velocity data by incorporating various available velocity sources (e.g., sonic logs, seismic velocity) to estimate pore pressure (Riahi & Soleymani 2011; Soleymani & Riahi 2012; Liu et al.2018). However, generating a comprehensive velocity model compound of various types of data is not straightforward. For instance, one should keep in mind that the above methods heavily depend on the relationship between porosity and pore pressure (Mannon & Young 2017; Wang & Wang 2015; Zhao et al.2014), which may not be a valid assumption in the case of a complex lithology (Obradors-Prats et al.2016). Also, the presence of low-velocity zones associated with secondary phases (e.g., methane, brine) can be misinterpreted as high-pore-pressure regions (Nour & AlBinHassan 2013). Accurate calibration of the Bowers or Tau relationships for a specific geological setting is an essential step in velocity-based pore-pressure estimation (Sheng et al.2017), and it can reduce the associated uncertainties significantly. The application of the unsupervised lithofacies classification using statistical methods has been carried out before (Aminzadeh & De Groot 2006; Dell’Aversana et al.2018; Bohling & Dubois 2003; Cranganu 2013); however, no previous study has investigated the results of lithofacies classification in estimating pore pressure. In this study, we aim to tackle the shortcomings of the conventional methods using the lithological classification of the reservoir rocks and to generate an empirical constant of the velocity versus effective stress relationship for every major cluster. Our workflow (figure 1) comprises the following steps: (1) acquiring, editing and processing sonic logs and seismic velocity data; (2) calculating overburden stress and effective stress at well locations; (3) clustering well logs that reflect lithology and fluid content, namely compressional velocity, gamma ray, laterolog depth and neutron porosity. Also, determining the number of nodes and iterations as well as the optimum number of clusters by comparing the results with core derived lithologies; (4) calibrating the empirical constants of the Bowers and Tau methods by applying a power-regression model on a velocity versus effective stress scatter plot for each cluster; (5) using the acquired relationships to predict effective stress with respect to each cluster; (6) calculating pore pressure by applying the Terzaghi criteria (Terzaghi 1925). Figure 1. View largeDownload slide Workflow for pore-pressure prediction in formations with complex lithostratigraphy. Figure 1. View largeDownload slide Workflow for pore-pressure prediction in formations with complex lithostratigraphy. We present the application of the proposed method as a case study in a reservoir with diverse lithology, fluid content and saturation, and show that the method can improve the prediction results. We also provide a comparison between five popular clustering algorithms, namely self-organizing maps (SOM), k-means, basic sequential algorithmic scheme, single and complete linkage hierarchical based on their performance in distinguishing various lithofacies. 2. Material and methods A general geological description of the studied field is provided along with a discussion on stratigraphy and lithology. We also detail various available data (e.g., well logs, well tests, seismic and core data) and calculations necessary to predict pore pressure using the presented workflow. The theory of the Bowers and Tau methods are presented along with a discussion on the accuracy of the predictions in the Asmari reservoir. To further describe the method and to carry out the calculations, we discuss the principles of the clustering methods mentioned above and apply them to our well data. To choose the best clustering method, we compared the resultant clusters with core-derived lithologies. Finally, we use the clusters calculated by the best method to calibrate empirical constants of the Bowers and Tau methods. 2.1. Geological settings The Mansouri oil field is located in the south of Ahwaz in the Dezful embayment in Iran and has a production rate of over 110 000 bbl d−1. It follows the northwest–southeast trend of Zagros, with a length of 30 km and width of 5 km. It consists of two major reservoirs, namely Asmari and Bangestan (Ahmadi et al.2012). Investigating lateral lithology variations, complex stratigraphy and pore pressure of the Asmari formation throughout the basin is the focus of this study and a major challenge for drilling companies. The location of the Mansouri oilfield on the map and position of the wells used in this study are shown on top of the Asmari formation in figure 2. Figure 2. View largeDownload slide Schematic map, showing well locations (black dots) and the top of the reservoir. (a) Top of the Asmari reservoir picked from the well data and 3-D seismic. (b) Approximate location of the Mansouri oil field (modified from Saberhosseini et al. (2013)). Figure 2. View largeDownload slide Schematic map, showing well locations (black dots) and the top of the reservoir. (a) Top of the Asmari reservoir picked from the well data and 3-D seismic. (b) Approximate location of the Mansouri oil field (modified from Saberhosseini et al. (2013)). Asmari is an asymmetric anticline dipping around 0°–10° at both ends (Ahmadi et al.2013). A comprehensive study by Van Buchem et al. (2010) indicated that the Oligocene-Miocene Asmari formation mostly consists of shallow-water carbonate depositions and siliciclastic. Traditionally it has been considered that the carbonates are deposited in the ridges of the platform while sandstone is deposited mainly along the ridges and center of the basin on top of the carbonates with a grainy texture and progradational pattern (i.e., prograding clinoforms). The Asamri reservoir has a complex stratigraphic architecture, which consists of three Oligocene and three Miocene sequences. Gacio-eustatic sea-level fluctuations govern the stratigraphic architecture of these sequences and allot the distribution of the different lithologies (Van Buchem et al.2010). These rock types were formed mainly in shallow-water depositional environments usually with a low surface angle that may extend across basins (homoclinal ramp) (Kangazian & Pasandideh 2016). The major event that shapes the depositional basin is the resultant foreland formed by the collision of the Arabian plate and the Eurasian plate (figure 3). It appears that lithological heterogeneity, complex geometries and early and late diagenetic alterations have caused the Asmari formation to be considered as a complex formation (Van Buchem et al.2010). These changes reflect the progradation dynamics of the platform in the reservoir (Ehrenberg et al.2007). Overall the reservoir can be divided into eight zones and 16 subzones based on age and microfossil studies. Figure 4 shows the scatter plot of Vp versus density at a well location and major zones of the reservoir. Petrographic analysis of core samples and lithofacies studies confirm the periodic occurrence of limestone, dolomite, sandstone and shale. The first member mostly consists of carbonates, the second, third, fourth and fifth members mostly consist of sandstone, the sixth member mostly consists of limestone, dolomite and shale, the seventh member consists of limestone, sandstone and shale, and the eighth member consists of limestone and shale. While anhydrite is mostly present in pore spaces of the fifth member, it could also be observed in some sandstone and carbonate members. The consolidation of sandstone in members two and three is generally better in the west side of the reservoir than its east side. Shale interlayers are also present in sandstone members, especially in the top and bottom of member number three. Figure 3. View largeDownload slide Chronostratigraphic scheme, sequence stratigraphy and sea level variation of Asmari formation in Dezful embayment. These sediments were deposited during ice-house conditions. The cyclic occurrence of mixed lithologies and sequences is common during ice-house conditions (Doyle & Roberts 1987). Seven stratigraphy sequences were found in the studied area corresponding to tract cycles and separated by six sequence boundaries. Sea-level fluctuations have a substantial effect on the vertical lithology variation of the Asmari formation. As the sea level falls, terrigenous sediments are deposited on shelves and basins. In contrast, as sea levels rise, carbonates are deposited (Tucker 2003). It has been suggested that high-amplitude sea-level fluctuations in relatively short periods of time are the main reason behind the complex lithostratigraphy of the Asmari formation (figure modified from Van Buchem et al.2010). Figure 3. View largeDownload slide Chronostratigraphic scheme, sequence stratigraphy and sea level variation of Asmari formation in Dezful embayment. These sediments were deposited during ice-house conditions. The cyclic occurrence of mixed lithologies and sequences is common during ice-house conditions (Doyle & Roberts 1987). Seven stratigraphy sequences were found in the studied area corresponding to tract cycles and separated by six sequence boundaries. Sea-level fluctuations have a substantial effect on the vertical lithology variation of the Asmari formation. As the sea level falls, terrigenous sediments are deposited on shelves and basins. In contrast, as sea levels rise, carbonates are deposited (Tucker 2003). It has been suggested that high-amplitude sea-level fluctuations in relatively short periods of time are the main reason behind the complex lithostratigraphy of the Asmari formation (figure modified from Van Buchem et al.2010). Figure 4. View largeDownload slide Scatter plot of Vp versus density at a well location. The relatively distinct spread of some members suggests the presence of various lithological units within the data. Note that members are classified based on age and microfossils studies. Figure 4. View largeDownload slide Scatter plot of Vp versus density at a well location. The relatively distinct spread of some members suggests the presence of various lithological units within the data. Note that members are classified based on age and microfossils studies. 2.2. Dataset The available dataset consists of (1) post-stack 3D seismic data with 2041 in-lines and 552 cross-lines with the spatial resolution of 25 m in in-line and cross-line directions and temporal resolution of 4 m s. (2) Seismic processing information including stacking velocities, interpretation of major reflectors, seismic wavelets and acoustic impedance inversion (Maleki et al.2016). (3) Well data consists of complete suite of well logs including density, electrode resistivity devices Laterolog Deep (LLD), Laterolog Shallow (LLS) and Micro-Spherical Focused Log (MSFL), gamma ray, neutron porosity, compressional velocity, photoelectric (photoelectric log was not available for all wells) and caliper measurements (a total number of 28 wells were analysed). (4) Downhole measurements consists of repetitive formation test (RFT), core measurements including special core analysis (SCAL), and X-ray powder diffraction (XRD) were available at five well locations. 2.3. Conventional Bowers and Tau methods Bowers (1995) showed that a drop in sonic velocity without decreasing the bulk density might be an indicator of unloading, and this phenomenon might be a direct result of fluid expansion. Using data from the Gulf of Mexico, they also derived the effective stress from the pore-pressure data and calculated overburden stress (equation 3) based on sonic well log data (equation 2). They further demonstrated that the P-wave transient velocity and effective stress have the following power-law relationship: \begin{eqnarray} V_p=V_0+ A\sigma _{e}^B, \end{eqnarray} (1) where Vp is the P-wave velocity at a specific depth, V0 is the P-wave velocity associated with the mudline or unconsolidated saturated surface sediments, σe is effective stress, A (m2 s kg−1) and B (dimensionless) are empirical constants that can be calibrated with transient velocity versus effective stress data at offset wells (Chopra & Huffman 2006).Considering equation (1), effective stress can be calculated using compressional velocity. The calculated effective stress can be used to find pore pressure using the equation below (Terzaghi 1925): \begin{eqnarray} \sigma _e=\sigma _o-\alpha P_p, \end{eqnarray} (2) where α is Biot’s constant and, according to (Bowers 1995), equals 1 in the reservoir conditions, Pp is pore pressure and σo is the overburden stress, which can be calculated using equation (3): \begin{eqnarray} \sigma _o=\int _{0}^{z}\rho gdz, \end{eqnarray} (3) where ρ is density, g is gravitational acceleration and z is depth. The conventional workflow starts with editing the acquired data by careful investigation of the caliper log to locate the wellbore collapses, and identify outlier data points outside the three standard deviations from the mean (Wang & Wang 2015). Then, we calibrate the Bowers relationship (equation 1) in offset wells via a regression analysis of the calculated effective stress at depths with available P-wave velocity (figure 5a). The results of the regression analysis of velocity versus effective stress confirm that the Bowers calibration is not statistically significant. Thus, calculating pore pressure based on the derived relationship results in introducing a major uncertainty. Figure 5. View largeDownload slide Velocity versus effective stress for available well data. Bowers (a) and Tau (b) methods do not provide a suitable fit, and the power-law regression is not statistically representative of the data. Figure 5. View largeDownload slide Velocity versus effective stress for available well data. Bowers (a) and Tau (b) methods do not provide a suitable fit, and the power-law regression is not statistically representative of the data. Alternatively, we applied the Tau method (equation 4) on the same dataset. Giles et al. (1998) introduced a new parameter τ, and coupled the velocity to effective stress via empirical constants as: \begin{eqnarray} \sigma _e=A\tau ^B, \end{eqnarray} (4) where A and B are empirical constants and τ can be calculated from equation (5): \begin{eqnarray} \tau =\frac{C-\Delta t}{\Delta t-D}, \end{eqnarray} (5) where Δt is the P-wave velocity transit-time, acquired from logging or seismic data, C is a constant associated with mud-line P-wave transit-time and D is a constant associated with matrix P-wave transit-time. To apply this method, it is necessary to calculate the matrix and mud-line transit-times and obtain empirical constants (A and B). Mud-line transit-time can also be expressed as the transit-time in saturated unconsolidated sediments in the surface (Zhang 2011; Ugwu 2015). A cross-plot of the Tau versus effective stress (figure 5b) shows that the regression results are also statistically insignificant. 2.4. Clustering methods We hypothesized that statistically insignificant regression results are associated with sharp lithology transitions in relatively short intervals. Lithology can cause variations in P-wave velocity, leading to major uncertainty in conventional pore-pressure prediction methods. This assumption is also in agreement with core-derived lithologies. Hence, to reduce the uncertainties associated with the effect of transient lithology on velocity, we derived various major lithological units in the reservoir column using multiple statistical clustering methods; then, we applied the Tau and Bowers methods on derived units individually. Multi-variable clustering methods provide a comprehensive basis to classify a multi-dimensional dataset (e.g., well logs, core data, seismic). Five clustering methods, namely, complete linkage hierarchical, single linkage hierarchical, k-means, basic sequential algorithmic scheme and SOM, were applied on well logs (i.e., density, gamma ray, neutron porosity and sonic) and the accuracy of recognizing different lithologies was analysed by comparing the results with data obtained from cores. 2.4.1. Self-organizing maps SOM clustering is a well-known unsupervised learning method from the wider category of artificial neural networks (Kohonen 1998). Various work documents the geophysical application of SOM. As an early adopter, Coléou et al. (2003) used it as a tool in seismic interpretation and called it ‘an essential tool for unsupervised seismic analysis’. Similarly, other scholars benefit from the SOM method in the seismic-facies analysis (Saraswat & Sen 2012) and recognition of seismic patterns (Kourki & Riahi 2014; Yang et al.1991). Jouini & Keskes (2017) utilized SOM in characterizing the mechanical properties of the reservoir rocks. Sfidari et al. (2014) demonstrated that SOM could provide much better results for lithofacies clustering than other clustering methods. SOM consist of a network of neurons connected with a rectangular or hexagonal connection. In the first iteration, weights are either allocated to neurons randomly or through the generated principal component eigenvectors of the subspace. Then, the Euclidean distance between the provided input and the weight vectors are measured, and the nearest neuron will be selected. The selected neuron and other neurons in its neighborhood alter to become similar to the input vector. Through multiple iterations, the weights of the neurons converge as the neighborhood of the best-matching unit (BMU) shrinks (Ciampi & Lechevallier 2000). The robustness of the SOM clustering method could be associated with its characterized non-linear projection from the higher dimensional space of inputs to a low-dimensional grid, which facilitates the discovery of hidden patterns in the input data (Kohonen & Honkela 2007; Moghimidarzi et al.2016). The SOM method proved to be able to handle large datasets with outliers effectively (Shahreza et al.2011; Oyana et al.2012), and it has been applied successfully in complex structures (Tasdemir & Merényi 2009). To implement the SOM clustering algorithm and calibrate the constants of the Bowers and Tau methods, we ran the clustering analysis on all the available wells. The SOM algorithm was trained with weight and bias learning rules, and the mean-squared-error calculated as a metric to measure the goodness of training. Sensitivity analysis was also carried out to determine the optimum number of nodes and iterations (figure 6). Figure 6a shows that the quantization error decreases remarkably with increasing number of nodes. Similarly, the topological error decreases slightly and stabilizes with an increase in the number of nodes. Figure 6b demonstrates the changes in topological and quantization errors as a function of iteration. Figure 6 also shows that the quantization error decreases significantly with the number of iteration (especially within the first 400 iterations) while the topological error decreases marginally. To validate the results, core samples with XRD measurements were selected, and compared with the correspondent lithologies derived from a cluster at the same depth. The selected clusters and their respective lithology data were used to validate other clusters in available wells. Table 1 summarizes the dominant lithology in each cluster. Figure 6. View largeDownload slide Quantization error and topological error variation versus the number of units (a) and number of iterations (b). Figure 6. View largeDownload slide Quantization error and topological error variation versus the number of units (a) and number of iterations (b). Table 1. SOM clusters and their respective lithologies. Cluster # Lithology type 1 Shale 2 Dolomite and limestone 3 Shale and shaly limestone 4 Sandstone 5 Shaly sandstone Cluster # Lithology type 1 Shale 2 Dolomite and limestone 3 Shale and shaly limestone 4 Sandstone 5 Shaly sandstone View Large Table 1. SOM clusters and their respective lithologies. Cluster # Lithology type 1 Shale 2 Dolomite and limestone 3 Shale and shaly limestone 4 Sandstone 5 Shaly sandstone Cluster # Lithology type 1 Shale 2 Dolomite and limestone 3 Shale and shaly limestone 4 Sandstone 5 Shaly sandstone View Large 2.4.2. Modified basic sequential algorithmic scheme In the modified basic sequential algorithmic scheme (M-BSAS), each cluster is represented by mean of the assigned vector (Ahmadi & Berangi 2008). The algorithm calculates the distance between the cluster centroid and every single data point. While the maximum number of clusters has not been reached and the distance was larger than a pre-defined threshold of dissimilarity, a new cluster will be formed, and the data point will be assigned to the nearest cluster (Theodoridis et al.2010). Note that the method is heavily dependent on the order of presenting data and user-defined threshold. The algorithm consists of two phases; (1) part of the data is used to determine the maximum number of clusters and (2) the unassigned data are allocated to their appropriate clusters (see Appendix A) (Kainulainen 2002). Sarparandeh & Hezarkhani (2016) implemented this method for delineating lithology and exploring rare elements. Jin (1994) also implemented BSAS for two-dimensional subsidence analysis. This method was implemented in Matlab software. The input data has consisted of five well logs including laterolog depth, P-wave transit-time, density, gamma-ray, and neutron porosity (Kazatchenko et al.2007). 2.4.3. k-means This algorithm uses a predefined number of k clusters from set of d-dimensional space of n data points with the objective of minimizing the Euclidean distance between cluster centers and data points. The underlying algorithm works by allocating each data point to the nearest cluster, then introduces new centers for each cluster (appendix). These iterations continue until centroids no longer change (Reddy et al.2012). Di Giuseppe et al. (2014), successfully utilized a k-means algorithm to distinguish geological structures with different rheologies. Wohlberg et al. (2006) also showed that k-means is a robust tool for delineating geological features. This method was applied to the same dataset as M-BSAS using Matlab software. 2.4.4. Single-linkage and complete-linkage hierarchical methods Single-linkage and complete-linkage hierarchical methods belong to a distinct type of hierarchical clustering called agglomerative. In this clustering method, each data point is considered as a cluster (Fouedjio 2016). In each iteration, the nearest clusters merge based on the distance between their centers. This process continues until a pre-defined number of clusters are obtained (Carlsson et al.2017). A notable technique in this family is the complete-linkage method, which is different from the single-linkage method in calculating the distance. While in the single-linkage method the two clusters with the closest members have the smallest distance (see Appendix A), in the complete-linkage method the largest dissimilarity between two identical features of two data points is calculated (Appendix A) (Fouedjio 2016). This method was applied to the same dataset as M-BSAS using Matlab software. The dendrogram of the single-linkage hierarchical method and the cut-off value are shown in figure 7. Figure 7. View largeDownload slide Dendrogram of single-linkage hierarchical method. The horizontal axis represents the indices of the objects, and the vertical axis represents the distance between the objects. The cut-off line shown in red indicates the selected number of clusters. Figure 7. View largeDownload slide Dendrogram of single-linkage hierarchical method. The horizontal axis represents the indices of the objects, and the vertical axis represents the distance between the objects. The cut-off line shown in red indicates the selected number of clusters. Figure 8. View largeDownload slide Comparison between well logs, SOM clusters and core-derived lithologies. (a) Transient time and neutron porosity versus depth at a selected well. (b) Real lithologies derived core data and SOM clustering results. Figure 8. View largeDownload slide Comparison between well logs, SOM clusters and core-derived lithologies. (a) Transient time and neutron porosity versus depth at a selected well. (b) Real lithologies derived core data and SOM clustering results. 2.5. Comparing clustering methods We used two criteria to compare the clustering methods: (1) their ability to recognize independent velocity versus effective stress trends (i.e., R-squared of the regression trend) and (2) delineating lithologies verified by core data (figure 8). By analysing the similarity of the lithology within clusters, the error for each method was calculated, and the optimum number of clusters was determined (table 2). Analysis of various clustering methods indicates that SOM provides better results in terms of delineating various lithologies compared to other previously mentioned techniques. Table 2. Performance ranking for different clustering methods based on their capability to delineate lithological units and their respective optimum number of clusters. Algorithm Performance Optimum rank clusters SOM 1 5 k-means 2 7 M-BSAS 3 6 Complete linkage hierarchical 4 3 Single linkage hierarchical 5 4 Algorithm Performance Optimum rank clusters SOM 1 5 k-means 2 7 M-BSAS 3 6 Complete linkage hierarchical 4 3 Single linkage hierarchical 5 4 View Large Table 2. Performance ranking for different clustering methods based on their capability to delineate lithological units and their respective optimum number of clusters. Algorithm Performance Optimum rank clusters SOM 1 5 k-means 2 7 M-BSAS 3 6 Complete linkage hierarchical 4 3 Single linkage hierarchical 5 4 Algorithm Performance Optimum rank clusters SOM 1 5 k-means 2 7 M-BSAS 3 6 Complete linkage hierarchical 4 3 Single linkage hierarchical 5 4 View Large 2.6. Enhanced pore-pressure prediction To calculate pore pressure with respect to newly established clusters, velocity versus effective stress scatter plots were created for each cluster independently. However, due to lack of RFT data in clusters 3 and 5, power regression fit was applied only to clusters 1, 2 and 4. Thus, to obtain a continuous prediction model within the reservoir, the Bowers equation for clusters 3 and 5 was obtained from other clusters with similar lithology. Velocity versus effective stress trends and similarity analysis of the well logs in different clusters show that cluster 5 is relatively similar to cluster 2, and cluster 3 is relatively similar to cluster 4. Figure 9 demonstrates regression results for clusters 1, 2 and 4. After finding the empirical constants in equation (1) for each cluster, we calculated the effective stress for each data point in our test wells based on their cluster number and respective equation, and thereby obtained the pore pressure from equation (2). Figure 10a demonstrates the final pore-pressure estimation (red curve) for all clusters in the test well along with RFT measurements. Figure 9. View largeDownload slide Regression analysis for |$V_p-V_0 (V_0\approx 1720\, \mbox{ms}^{-1})$| versus effective stress for clusters 1 (a), 2 (b), and 4 (c). Figure 9. View largeDownload slide Regression analysis for |$V_p-V_0 (V_0\approx 1720\, \mbox{ms}^{-1})$| versus effective stress for clusters 1 (a), 2 (b), and 4 (c). To calculate pore pressure using the Tau method, we carried out regression analysis to find empirical constants of equation (4) for each cluster. Figures 11a, b and c show results for clusters 1, 2 and 4, respectively. At this point, pore pressure can be calculated by following the procedure described in the previous section. Estimated pore pressure using a modified Tau method at the test well is shown in figure 10b. Figure 10. View largeDownload slide Pore-pressure prediction based on Tau and Bowers methods along with the RFT measurements at a selected well location. (a) Modified Bowers produced relatively accurate predictions while extremely poor calibration of the Bowers made the estimation unreliable. (b) Comparing the conventional and modified Tau method shows that the latter improved the accuracy of the estimation. Figure 10. View largeDownload slide Pore-pressure prediction based on Tau and Bowers methods along with the RFT measurements at a selected well location. (a) Modified Bowers produced relatively accurate predictions while extremely poor calibration of the Bowers made the estimation unreliable. (b) Comparing the conventional and modified Tau method shows that the latter improved the accuracy of the estimation. Figure 11. View largeDownload slide Regression analysis effective stress versus Tau for clusters 1 (a), 2 (b) and 4 (c). Figure 11. View largeDownload slide Regression analysis effective stress versus Tau for clusters 1 (a), 2 (b) and 4 (c). 3. Discussion and results Lithology, porosity and fluid content variations have a significant effect on the accuracy and precision of pore-pressure estimation based on P-wave velocity (Obradors-Prats et al.2016; Wang & Wang 2015; Oloruntobi et al.2018). This can be explained by the strong dependence of P-wave velocity upon lithology and geomechanical characteristics. Therefore, the interpretation of any derived parameters from velocity data requires a detailed understanding of the stratigraphy, lithology and geomechanical history of the prospect (Crook et al.2018). In the reservoir studied here, the interplay of diverse lithostratigraphic units is a major complication in using conventional protocols. To tackle this problem, we implement several clustering methods, namely, complete-linkage hierarchical, single-linkage hierarchical, k-means, basic sequential algorithmic scheme and SOM, on the available well logs, and the results were compared based on the capacity to distinguish various P-wave velocity values versus effective stress trends. These trends then juxtaposed into clusters with similar lithological characteristics. The error between the core-derived lithologies and the dominant lithology of the clusters was evaluated to determine the optimum number of clusters and the best clustering method. The summary of the overall performance of different clustering algorithms and their optimum number of clusters is provided in table 2. Assessment of the clustering outcomes shows that the SOM method provides the best results by maximizing lithology likelihood within each cluster and improves the efficiency of the Bowers and Tau methods. A notable advantage of this method is preserving the topology of high dimensional space by mapping the initial data set into a two-dimensional space with the rectangular or hexagonal structure of weighted neurons (Kohonen & Somervuo 2002). Also, the SOM algorithm can handle structural complexities while showing less sensitivity to unwanted data. This observation is in accord with findings of Abu Abbas (2008). To analyse the clustering results, we associate each cluster with a specific lithology; however, interpretation of well logs suggest each rock unit comprises the specific lithology along with a small percentage of secondary rock units. We interpret these units as a thin layer within the major members (section 2.1). We also observed relatively high velocities in cluster 1 along with high electrical resistivity and low porosity (figure 12). Based on the mentioned observations we interpret these shale units as being highly siliceous with low clay content (less than 45%, based on a gamma-ray log; Nelson (2010)). The robustness of Bowers and Tau calibration regressions (R-squared) in the modified method (figures 9 and 11) suggests a significant improvement in clusters 1 (mostly shale) and 4 (mostly sandstone), while it failed to deliver the same results in cluster 2 (dolomite and limestone). These observations agree with the principal assumption of the Bowers and Tau methods, indicating that these techniques are most reliable in shale and sandstone (with a lower degree of certainty compared to shales), but they do not produce reliable results in carbonate settings. Overall, comparing the conventional methods with the proposed procedure shows significant improvement in pore-pressure estimations. Table 3 summarizes the quantitative comparison (mean absolute percentage error (MAPE) and mean squared error (MSE)) between conventional and proposed Tau methods. An important source of uncertainty in the current study (and perhaps other similar works) is associated with limited data in the formations above the reservoir, incorrect well logs values in some intervals within the reservoir due to wellbore condition, noisy measurements and lack of modern logs which can affect the clustering results (especially k-means) tremendously. A robust constraint on formation fluid type and saturation can also improve the prediction results. This can be achieved by including the photoelectric factor (PEF), pulsed neutron lifetime logs (PNL), and well nuclear magnetic resonance (NMR) logs in future studies. Moreover, the SOM method has inherent limitations; for instance, it requires enough data to create robust clusters. In other words, a successful classification depends on weight vectors that are determined based on the input data. Lack of the right dataset may lead to randomness and reduce the accuracy of the classification. Another major limitation of the SOM is the computation cost. Generally, the convergence time increases with the dimensions of the data. Although increasing the number of the neighbors is better for improving the similarity map, the calculation for the distance grows exponentially, which results in a longer processing time. Note that the SOM and k-means methods have comparable computation time; however, SOM is the better choice in the case of a large dataset. Figure 12. View largeDownload slide Cluster 1 shows notably low porosity and high resistivity compared to the other clusters. The porosity and resistivity characteristics of cluster 1 could be an indicator of high amounts of silica minerals in the overall mineralogy of the unit. Figure 12. View largeDownload slide Cluster 1 shows notably low porosity and high resistivity compared to the other clusters. The porosity and resistivity characteristics of cluster 1 could be an indicator of high amounts of silica minerals in the overall mineralogy of the unit. Table 3. Comparing Tau methods with the results of the SOM improved estimations. Mean absolute percentage error (MAPE) and mean square error (MSE) are used as a measure of the accuracy of the predictions. Method MAPE % MSE Conventional Bowers 105 146 Modified Bowers 15.5 0.76 Conventional Tau 4 21761 Modified Tau 1 1840 Method MAPE % MSE Conventional Bowers 105 146 Modified Bowers 15.5 0.76 Conventional Tau 4 21761 Modified Tau 1 1840 View Large Table 3. Comparing Tau methods with the results of the SOM improved estimations. Mean absolute percentage error (MAPE) and mean square error (MSE) are used as a measure of the accuracy of the predictions. Method MAPE % MSE Conventional Bowers 105 146 Modified Bowers 15.5 0.76 Conventional Tau 4 21761 Modified Tau 1 1840 Method MAPE % MSE Conventional Bowers 105 146 Modified Bowers 15.5 0.76 Conventional Tau 4 21761 Modified Tau 1 1840 View Large 4. Conclusions This article aims to reduce the uncertainty of pore-pressure prediction in a reservoir with complex lithology using velocity-based methods (e.g., Tau and Bowers methods). Pre-drill pore-pressure prediction is not a trivial task and requires a clear understanding of the lithology and geomechanical state of the reservoir. Also, inaccurate calibration of the velocity versus effective stress, especially in a reservoir with complex lithology, will introduce major uncertainty in the final pressure estimation. We have demonstrated that the accuracy of conventional Bowers and Tau methods can be improved by precise calibration of the empirical equations in major lithostratigraphic units. Through a case study of a reservoir in SW Iran, we showed that each major lithologic zone at offset test wells has a clear compaction trend with different empirical constants. Lithology identification and clustering is a challenging task; however, a robust clustering algorithm ensures a consistent lithofacies classification and improves the reproducibility of the estimations. We compared several commonly used clustering algorithms and show that the SOM method can be a reliable candidate for lithofacies classification using well log data. Although the SOM method outperformed other previously mentioned clustering techniques, however, it requires a large enough dataset to produce a reliable classification. Also, the method is computationally expensive, and the computation time increases exponentially with the dimension of the data. We demonstrate that the calibrated Bowers and Tau methods in a similar facies unit improve the overall accuracy of the effective stress calculation. In the case of a reservoir with relatively simple lithology, using the proposed method might have a negligible benefit; however, in a reservoir with complex and diverse lithofacies, it is critical to account for lithology variation prior to any calibration over large subsurface depths. The proposed workflow in this study provides a groundwork for the future goal of accurate pore-pressure estimation prior to drilling. Acknowledgements The authors would like to thank S. Seyedali, and A. Ahmadi for his major technical advice and many useful discussions. Also, we like to thank anonymous reviewers for their constructive comments. The authors are grateful to the Iranian Offshore Oil Company (IOOC) for permission to use the seismic data and well logs. Appendix A: Clustering methods A1. M-BSAS The mean vector for clusters will be updated as: \begin{eqnarray} m_{C_k}^{new}=\frac{\left(n_{C_k}^{new}-1\right)m_{C_k}^{old}+x}{m_{C_k}^{new}}, \end{eqnarray} (A1) where x is the value of the new data, Ck is the cluster center, and |$n_{C_k}^{new}$| is the cardinality of Ck after x assignments. A2. k-means Equation (A2) is the mathematical expression of allocating a new data point to a nearest cluster. \begin{eqnarray} S_i^{(t)}\!=\!\left\lbrace x_p\!:\! \Vert {x_p-m_i^{(t)}}\Vert ^2\le \Vert {x_p-m_j^{(t)}}\Vert ^2 \,\, \forall j,1\le j\le k\right\rbrace ,\nonumber\\ \end{eqnarray} (A2) where xp is the value of the new data, and |$m_i^{(t)}$| and |$m_j^{(t)}$| are the center of the clusters and are defined as \begin{eqnarray} m_{i}^{t+1}= \frac{1}{\left|S_i^{t}\right|} \sum _{x_j \in S_i^{(t)}} x_j, \end{eqnarray} (A3) where Si is the number of data. A3. Single-linkage and complete-linkage hierarchical The mathematical definition of distance can be written as: \begin{eqnarray} d_{single} (G,H)=\min d_{ij}, i\in G, j\in H \end{eqnarray} (A4) \begin{eqnarray} d_{complete} (G,H)=\max d_{ij}, i\in G, j\in H \end{eqnarray} (A5) where di, j is the distance between elements i ∈ G and j ∈ Y, and G and H are two sets of elements (i.e., clusters). For more details on the clustering methods we suggest reading Omran et al. (2007). Conflict of interest statement. None declared. References Abu Abbas O. , 2008 . Comparisons between data clustering algorithms , The International Arab Journal of Information Technology , 5 , 320 – 325 . Ahmadi M.A. , Zendehboudi S. , Lohi A. , Elkamel A. , Chatzis I. , 2013 . Reservoir permeability prediction by neural networks combined with hybrid genetic algorithm and particle swarm optimization , Geophysical Prospecting , 61 , 582 – 598 . Google Scholar Crossref Search ADS Ahmadi N. , Berangi R. , 2008 . Modulation classification of QAM and PSK from their constellation using Genetic Algorithm and hierarchical clustering . In Information and Communication Technologies: From Theory to Applications, 2008 . ICTTA 2008. 3rd International Conference on (pp. 1–5). IEEE . Aminzadeh F. , De Groot P. , 2006 . Neural Networks and Other Soft Computing Techniques with Applications in the Oil Industry , Eage Publications . Bohling G. , Dubois M. , 2003 . An integrated application of neural network and Markov chain techniques to prediction of lithofacies from well logs , Kansas Geological Survey Open File Report 2003-50 . Boitnott G. , Miller T. , Shafer J. , 2009 . Pore pressure effects and permeability: effective stress issues for high pressure reservoirs , in Proceedings of the International Symposium of the Society of Core Analysts (SCA’09), 2009 , Noordwijk, Netherlands, p. 9 . Bowers G.L. , 1995 . Pore pressure estimation from velocity data: Accounting for overpressure mechanisms besides undercompaction , SPE Drilling & Completion , 10 , 89 – 95 . Google Scholar Crossref Search ADS Carlsson G. , Mémoli F. , Ribeiro A. , Segarra S. , 2017 . Admissible hierarchical clustering methods and algorithms for asymmetric networks , IEEE Transactions on Signal and Information Processing over Networks , 3 , 711 – 727 . Google Scholar Crossref Search ADS Chopra S. , Huffman A.R. , 2006 . Velocity determination for pore-pressure prediction , The Leading Edge , 25 , 1502 – 1515 . Google Scholar Crossref Search ADS Ciampi A. , Lechevallier Y. , 2000 . Clustering large, multi-level data sets: an approach based on Kohonen self organizing maps , in European Conference on Principles of Data Mining and Knowledge Discovery , Springer , Lyon, France pp. 353 – 358 . Coléou T. , Poupon M. , Azbel K. , 2003 . Unsupervised seismic facies classification: a review and comparison of techniques and implementation , The Leading Edge , 22 , 942 – 953 . Google Scholar Crossref Search ADS Cranganu C. , 2013 . Natural Gas and Petroleum: Production Strategies, Environmental Implications, and Future Challenges , Nova Publishers . Cranganu C. , Soleymani H. , 2015 . Carbon dioxide sealing capacity: textural or compositional controls? A case study from the Oklahoma panhandle , AAPG/DEG Environmental Geosciences , 22 , 57 – 74 . Google Scholar Crossref Search ADS Cranganu C. , Soleymani H. , Azad S. , Watson K. , 2014 . Carbon dioxide sealing capacity: textural or compositional controls? , AAPG Search and Discovery Article# 41474 . Crook A.J. , Obradors-Prats J. , Somer D. , Peric D. , Lovely P. , Kacewicz M. , 2018 . Towards an integrated restoration/forward geomechanical modelling workflow for basin evolution prediction , Oil & Gas Sciences and Technology–Revue dIFP Energies nouvelles , 73 , 18 . Google Scholar Crossref Search ADS Dell’Aversana P. , Ciurlo B. , Colombo S. , 2018 . Integrated geophysics and machine learning for risk mitigation in exploration geosciences , 80th EAGE Conference and Exhibition, 2018 EAGE, Copenhagen, Denmark. Di Giuseppe M.G. , Troiano A. , Troise C. , De Natale G. , 2014 . k-means clustering as tool for multivariate geophysical data analysis. An application to shallow fault zone imaging , Journal of Applied Geophysics , 101 , 108 – 115 . Google Scholar Crossref Search ADS Doyle L.H. , Roberts H.H. eds., 1987 . Carbonate-clastic transitions (Vol. 42). Elsevier . Eaton , B.A. 1972 . The effect of overburden stress on geopressure prediction from well logs , Journal of Petroleum Technology , 24 , 929 – 934 . Google Scholar Crossref Search ADS Ehrenberg S. , Nadeau P. , Aqrawi A. , 2007 . A comparison of Khuff and Arab reservoir potential throughout the Middle East , AAPG bulletin , 91 , 275 – 286 . Google Scholar Crossref Search ADS Fouedjio F. , 2016 . A hierarchical clustering method for multivariate geostatistical data , Spatial Statistics , 18 , 333 – 351 . Google Scholar Crossref Search ADS Giles M. , Indrelid S. , James D. , 1998 . Compaction the great unknown in basin modelling , Geological Society, London, Special Publications , 141 , 15 – 43 . Google Scholar Crossref Search ADS Guglielmi Y. , Cappa F. , Avouac J.-P. , Henry P. , Elsworth D. , 2015 . Seismicity triggered by fluid injection–induced aseismic slip , Science , 348 , 1224 – 1226 . Google Scholar Crossref Search ADS PubMed Hao F. , Zhu W. , Zou H. , Li P. , 2015 . Factors controlling petroleum accumulation and leakage in overpressured reservoirs , AAPG Bulletin , 99 , 831 – 858 . Google Scholar Crossref Search ADS Holm G. , 1998 . How abnormal pressures affect hydrocarbon exploration, exploitation , Oil and Gas Journal , 96 , 79 – 84 . Hottmann C. , Johnson , R. 1965 . Estimation of formation pressures from log-derived shale properties , Journal of Petroleum Technology , 17 , 717 – 722 . Google Scholar Crossref Search ADS Jin J. , 1994 . BSAS: a basic program for two-dimensional subsidence analysis in sedimentary basins , Computers & Geosciences , 20 , 1329 – 1345 . Google Scholar Crossref Search ADS Jouini M.S. , Keskes N. , 2017 . Numerical estimation of rock properties and textural facies classification of core samples using X-ray computed tomography images , Applied Mathematical Modelling , 41 , 562 – 581 . Google Scholar Crossref Search ADS Kainulainen J.J. , 2002 . Clustering algorithms: basics and visualization , Helsinki University of Technology, Laboratory of Computer and Information Science . Kangazian A. , Pasandideh M. , 2016 . Sedimentary environment and sequence stratigraphy of the Asmari formation at Khaviz anticline, Zagros mountains, southwest Iran , Open Journal of Geology , 6 , 87 – 102 . Google Scholar Crossref Search ADS Kazatchenko E. , Markov M. , Mousatov A. , Pervago E. , 2007 . Joint inversion of conventional well logs for evaluation of double-porosity carbonate formations , Journal of Petroleum Science and Engineering , 56 , 252 – 266 . Google Scholar Crossref Search ADS Kohonen T. , 1998 . The self-organizing map , Neurocomputing , 21 , 1 – 6 . Google Scholar Crossref Search ADS Kohonen T. , Honkela T. , 2007 . Kohonen network , Scholarpedia , 2 , 1568 . Google Scholar Crossref Search ADS Kohonen T. , Somervuo P. , 2002 . How to make large self-organizing maps for nonvectorial data , Neural networks , 15 , 945 – 952 . Google Scholar Crossref Search ADS PubMed Kourki M. , Riahi M.A. , 2014 . Seismic facies analysis from pre-stack data using self-organizing maps , Journal of Geophysics and Engineering , 11 , 065005 . Google Scholar Crossref Search ADS Liu L. , Shen G. , Wang Z. , Yang H. , Han H. , Cheng Y. , 2018 . Abnormal formation velocities and applications to pore pressure prediction , Journal of Applied Geophysics , 153 , 1 – 6 . Google Scholar Crossref Search ADS Maleki M. , Davolio A. , Schiozer D. , 2016 . Reservoir characterization using model based post-stack inversion: a case study in Norne field to show the impact of the number of wells in inversion , in Rio Oil and Gas Conference & Exhibition Extended Abstracts , Paper IBP1957-16 , Rio de Janeiro, Brazil , pp. 24 – 27 . Maleki M. , Davolio A. , Schiozer D.J. , 2018 . Using simulation and production data to resolve ambiguity in interpreting 4D seismic inverted impedance in the Norne field , Petroleum Geoscience , 24 , 335 – 347 . Google Scholar Crossref Search ADS Mannon T. , Young R. , 2017 . Pre-drill pore pressure modelling and post-well analysis using seismic interval velocity and seismic frequency-based methodologies: a deepwater well case study from Mississippi Canyon, Gulf of Mexico , Marine and Petroleum Geology , 79 , 176 – 187 . Google Scholar Crossref Search ADS Moghimidarzi S. , Furth P.G. , Cesme B. , 2016 . Predictive–tentative transit signal priority with self-organizing traffic signal control , Transportation Research Record: Journal of the Transportation Research Board , (2557), 77 – 85 . Nelson P.H. , 2010 . Sonic velocity and other petrophysical properties of source rocks of Cody, Mowry, Shell Creek, and Thermopolis shales, Bighorn Basin, Wyoming , in Petroleum Systems and Geologic Assessment of Oil and Gas in the Bighorn Basin Province, Wyoming and Montana , DDS-69-D , US Geological Survey Digital Data Series . Nguyen S.T. , Hoang S.K. , Khuc G.H. , Tran H.N. , 2015 . Pore pressure and fracture gradient prediction for the challenging high pressure and high temperature well, hai thach field, block 05-2, nam con son basin, offshore vietnam: A case study , In SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition , Society of Petroleum Engineers . Nour A. , AlBinHassan N. , 2013 . Seismic attributes and advanced computer algorithm method to predict formation pore pressure: Paleozoic sediments of northwest Saudi Arabia , IPTC 2013: International Petroleum Technology Conference IPTC, Beijing, China . Obradors-Prats J. , Rouainia M. , Aplin A.C. , Crook A.J. , 2016 . Stress and pore pressure histories in complex tectonic settings predicted with coupled geomechanical-fluid flow models , Marine and Petroleum Geology , 76 , 464 – 477 . Google Scholar Crossref Search ADS Oloruntobi O. , Adedigba S. , Khan F. , Chunduru R. , Butt S. , 2018 . Overpressure prediction using the hydro-rotary specific energy concept , Journal of Natural Gas Science and Engineering , 55 , 243 – 253 . Google Scholar Crossref Search ADS Omran M.G. , Engelbrecht A.P. , Salman A. , 2007 . An overview of clustering methods , Intelligent Data Analysis , 11 , 583 – 605 . Google Scholar Crossref Search ADS Oughton R.H. , Wooff D.A. , Hobbs R.W. , O’Connor S.A. , Swarbrick R.E. , 2015 . Quantifying uncertainty in pore-pressure estimation using Bayesian networks, with application to use of an offset well , Petroleum Geostatistics 2015 . Oyana T. , Achenie L. , Heo J. , 2012 . The New and Computationally Efficient MIL-SOM Algorithm: Potential Benefits for Visualization and Analysis of a Large-Scale High-Dimensional Clinically Acquired Geographic Data , Computational and Mathematical Methods in Medicine , 2012 , 14 . Google Scholar Crossref Search ADS Reddy D. , Jana , P.K. 2012 . Initialization for k-means clustering using Voronoi diagram , Procedia Technology , 4 , 395 – 400 . Google Scholar Crossref Search ADS Riahi M. , Soleymani H. , 2011 . Velocity-based pore-pressure prediction-a case study at one of the Iranian south west oil fields , 73rd EAGE Conference and Exhibition incorporating SPE EUROPEC, 2011 . Copenhagen, Denmark. Saberhosseini S.E. , Ahangari K. , Alidoust S. , 2013 . Stability analysis of a horizontal oil well in a strike-slip fault regime , Austrian Journal of Earth Sciences , 106 , 30 – 36 . Saraswat P. , Sen M.K. , 2012 . Artificial immune-based self-organizing maps for seismic-facies analysis , Geophysics , 77 , O45 – O53 . Google Scholar Crossref Search ADS Sarparandeh M. , Hezarkhani A. , 2016 . Application of self-organizing map for exploration of Rees deposition , Open Journal of Geology , 6 , 571 – 582 . Google Scholar Crossref Search ADS Sfidari E. , Kadkhodaie-Ilkhchi A. , Rahimpour-Bbonab H. , Soltani B. , 2014 . A hybrid approach for litho-facies characterization in the framework of sequence stratigraphy: a case study from the South Pars gas field, the Persian Gulf basin , Journal of Petroleum Science and Engineering , 121 , 87 – 102 . Google Scholar Crossref Search ADS Shahreza M.L. , Moazzami D. , Moshiri B. , Delavar M. , 2011 . Anomaly detection using a self-organizing map and particle swarm optimization , Scientia Iranica , 18 , 1460 – 1468 . Google Scholar Crossref Search ADS Sheng Y.-N. , Guan Z.-C. , Xu Y.-Q. , 2018 . Quantitative description method for uncertainty of formation pore pressure , Arabian Journal for Science and Engineering , 43 , 2605 – 2613 . Google Scholar Crossref Search ADS Soleymani H. , Riahi M.-A. , 2012 . Velocity-based pore-pressure prediction – a case study at one of the Iranian southwest oil fields , Journal of Petroleum Science and Engineering , 94 , 40 – 46 . Google Scholar Crossref Search ADS Tasdemir K. , Merényi E. , 2009 . Exploiting data topology in visualization and clustering of self-organizing maps , IEEE Transactions on Neural Networks , 20 , 549 – 562 . Google Scholar Crossref Search ADS PubMed Terzaghi K. , 1925 . Principles of soil mechanics, IV. Settlement and consolidation of clay , Engineering News-Record , 95 , 874 – 878 . Theodoridis S. , Pikrakis A. , Koutroumbas K. , Cavouras D. , 2010 . Introduction to Pattern Recognition: a Matlab Approach , Academic Press . Tucker M.E. , 2003 . Mixed clastic–carbonate cycles and sequences: Quaternary of Egypt and Carboniferous of England , Geologia Croatica , 56 , 19 – 37 . Ugwu G. , 2015 . Pore-pressure prediction using offset well logs: insight from onshore Niger Delta, Nigeria , American Journal of Geophysics, Geochemistry and Geosystems , 1 , 77 – 86 . Van Buchem F. S. P. et al. . , 2010 . Regional stratigraphic architecture and reservoir types of the oligo-miocene deposits in the dezful embayment (asmari and pabdeh formations) sw iran , Geological Society, London, Special Publications , 329 , 219 – 263 . Google Scholar Crossref Search ADS Wang Z. , Wang R. , 2015 . Pore-pressure prediction using geophysical methods in carbonate reservoirs: current status, challenges and way ahead , Journal of Natural Gas Science and Engineering , 27 , 986 – 993 . Google Scholar Crossref Search ADS Wild K. et al. . , 2015 . Some fundamental hydro-mechanical processes relevant for understanding the pore pressure response around excavations in low permeable clay rocks , in 13th ISRM International Congress of Rock Mechanics , International Society for Rock Mechanics, Montréal, Québec, Canada . Wohlberg B. , Tartakovsky D.M. , Guadagnini A. , 2006 . Subsurface characterization with support vector machines , IEEE Transactions on Geoscience and Remote Sensing , 44 , 47 – 57 . Google Scholar Crossref Search ADS Yang F.-M. , Huang K.-Y. 1991 . Multilayer perceptron for detection of seismic anomalies. In SEG Technical Program Expanded Abstracts 1991 (pp. 309–312) , Society of Exploration Geophysicists . Zhang J. , 2011 . Pore-pressure prediction from well logs: methods, modifications, and new approaches , Earth-Science Reviews , 108 , 50 – 63 . Google Scholar Crossref Search ADS Zhao S. , Zhou Y. , Wang M. , Xin X. , Chen F. , 2014 . Thickness, porosity, and permeability prediction: comparative studies and application of the geostatistical modeling in an oil field , Environmental Systems Research , 3 , 7 . Google Scholar Crossref Search ADS © The Author(s) 2019. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
TI - Enhanced velocity-based pore-pressure prediction using lithofacies clustering: a case study from a reservoir with complex lithology in Dezful Embayment, SW Iran
JF - Journal of Geophysics and Engineering
DO - 10.1093/jge/gxy013
DA - 2019-02-01
UR - https://www.deepdyve.com/lp/oxford-university-press/enhanced-velocity-based-pore-pressure-prediction-using-lithofacies-6FxgSPVQsf
SP - 146
VL - 16
IS - 1
DP - DeepDyve
ER -