Prediction of Water Saturation from Well Log Data by Machine Learning Algorithms: Boosting and Super Learner

Intelligent predictive methods have the power to reliably estimate water saturation (Sw) compared to conventional experimental methods commonly performed by petrphysicists. However, due to nonlinearity and uncertainty in the data set, the prediction might not be accurate. There exist new machine learning (ML) algorithms such as gradient boosting techniques that have shown significant success in other disciplines yet have not been examined for Sw prediction or other reservoir or rock properties in the petroleum industry. To bridge the literature gap, in this study, for the first time, a total of five ML code programs that belong to the family of Super Learner along with boosting algorithms: XGBoost, LightGBM, CatBoost, AdaBoost, are developed to predict water saturation without relying on the resistivity log data. This is important since conventional methods of water saturation prediction that rely on resistivity log can become problematic in particular formations such as shale or tight carbonates. Thus, to do so, two datasets were constructed by collecting several types of well logs (Gamma, density, neutron, sonic, PEF, and without PEF) to evaluate the robustness and accuracy of the models by comparing the results with laboratory-measured data. It was found that Super Learner and XGBoost produced the highest accurate output (R2: 0.999 and 0.993, respectively), and with considerable distance, Catboost and LightGBM were ranked third and fourth, respectively. Ultimately, both XGBoost and Super Learner produced negligible errors but the latest is considered as the best amongst all.

Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

We have modified the Potts Model Swendsen-Wang algorithm to insert some clusters constraints by applying a modified agglomerative clustering approach (Kurita, 1991). We have called the induced Potts Model, the Potts Clustering with Complete Shrinkage (PCCS), under the Python package pottscompleteshrinkage deployed on PyPi Index under its current release. In this approach, we deal with the increasing number of small clusters generated in a given partition by merging all small clusters of size ≤ h with their closest cluster in terms of minimal distance respectively, where h is an integer greater or equal to 2. The algorithm uses a technique in which distances of all pairs of observations are stored. Then the nearest cluster (with size ≥ h) is given by the cluster with the closest node in terms of minimal distance to the cluster to be merged using complete linkage. This approach is truly effective as it helps to control the clusters size, and we have found empirical evidence of Chi-Square and Gamma density curves for the constrained cluster size distribution of PCCS, when applied to some datasets taken from the multiple-output benchmark datasets available in the Mulan project website (Tsoumakas et al., 2020). We add a last framework based on Frequency of frequency distribution (FoF) to find the conditional bonds distribution given the clusters size constraints which results in an intractable distribution for large datasets, but its computation framework is a land of rich mathematical developments.

DETERMINING THE DENSITY OF MULTIPLE LAYERS USING GAMMA SPECTROSCOPY

Due to the volumetric nature of the physics and the measurement, traditional gamma-gamma density tools measure an average bulk density of the formation. However, a bulk measurement is not adequate for certain applications where a more detailed resolution of a radial density profile is necessary. In this paper, a new approach of gamma spectral analysis is introduced focusing on the main Compton scattering angles. Several energy windows are linked to the unique radial layers based on scattering angles and location of interaction. As a result, the density of multiple layers can be calculated. The paper first outlines the main principles and analytical structures to formulate two methods to measure layer densities. Then computer simulation tools are used to simulate realistic tool configuration and measurement response to validate and benchmark efficacies of the outlined methods. Finally, a case study is presented to demonstrate the applicability of these methods using laboratory data. The paper is concluded with a list of other possible applications such as open-hole density and behind-pipe evaluation where layer density can provide more details for the analysis.

A NOVEL THROUGH-CASING CORRECTION ALGORITHM FOR A 4-DETECTOR GAMMA DENSITY TOOL

In most parts of the world, open hole logging with con-ventional gamma density tool remains the only option available, which is, though, not practical under complex well conditions when it is difficult to obtain formation parameters and control the operational risks. Therefore, the application of through-casing density logging is es-sential. However, through-casing gamma density meas-urement could be challenging due to gamma’s weak pen-etrating power. To better overcome these challenges, a new four-detector gamma density tool is designed and presented in this work together with a novel interpreta-tion algorithm for through-casing density measurements. In order to identify the relationship between the four de-tectors, a significant amount of Monte Carlo models is constructed and executed to quantitatively evaluate the response of tool under various environmental conditions such as lithology, fluid, salinity, casing and cement. It is proven through open-hole benchmarking and extensive modelling that the four-detector design is capable to pro-vide sufficient information for removal of diverse envi-ronmental effects via an inversion algorithm developed by obtaining a formula that correlates the four-detector responses. This algorithm is validated against actual log-ging data and show a better though-casing evaluation than when using three or two detectors. In this work a case story using the four-detector tool to obtain through-casing formation density and using the algorithm mentioned above for correction is presented. The final results are analyzed and compared against open hole measurements, a very good consistency is achieved which demonstrates the correctness of the inversion al-gorithm.

On approximating the distribution of indefinite quadratic expressions in singular normal vectors

General representations of quadratic forms and quadratic expressions in singular normal vectors are given in terms of the difference of two positive definite quadratic forms and an independentlydistributed linear combination of normal random variables. Up to now, only special cases have been treated in the statistical literature. The densities of the quadratic forms are then approximated with gamma and generalized gamma density functions. A moment-based technique whereby the initial approximations are adjusted by means of polynomials is presented. Closed form and integral formulae are provided for the approximate density functions of the quadratic forms and quadratic expressions. A detailed step-by-step algorithm for implementing the proposed density approximation technique is also provided. Two numerical examples illustrate the methodology.

A new method for calculating bulk density in pulsed neutron-gamma density logging

Formation density is one of the most important parameters in formation evaluation. Radioisotope chemical sources are used widely in conventional gamma-gamma density (GGD) logging. Considering security and environmental risks, there has been growing interest in pulsed neutron generators in place of the radioactive-chemical source in using bulk-density measurements. However, there still is the requirement of high accuracy of the neutron-gamma density (NGD) calculation. Pair production is one of the factors influencing the accuracy of the results, which should be considered. We have adopted a method, based on the difference between the inelastic gamma-ray response of high- and low-energy windows, to reduce the impact of pair production upon calculating the bulk density. A new density estimation algorithm is derived based on the coupled-field theory and gamma-ray attenuation law in NGD logging. We analyze the NGD measurement accuracy with different mineral types, porosity, and pore fluid and determine the influence of the borehole environment on NGD logging. The Monte Carlo simulation results indicate that the improved processing algorithm limits the influence of the mineral type, porosity, or pore fluid. The NGD measurement accuracy is ±0.025 g/cm3 in shale-free formations, which is close to the GGD measurement (±0.015 g/cm3). Our results also show that the borehole environment has a significant impact on NGD measurement. Therefore, it is necessary to take the influence of the borehole parameters into account in NGD measurements. Combined with Monte Carlo simulation cases, we evaluate the application results of the new density estimation algorithm in various model wells.

Lower Cretaceous Rodby and Palaeocene Lista Shales: Characterisation and Comparison of Top-Seal Mudstones at Two Planned CCS Sites, Offshore UK

Petroleum-rich basins at a mature stage of exploration and production offer many opportunities for large-scale Carbon Capture and Storage (CCS) since oil and gas were demonstrably contained by low-permeability top-sealing rocks, such as shales. For CCS to work, there must be effectively no leakage from the injection site, so the nature of the top-seal is an important aspect for consideration when appraising prospective CCS opportunities. The Lower Cretaceous Rodby Shale and the Palaeocene Lista Shale have acted as seals to oil and gas accumulations (e.g., the Atlantic and Balmoral fields) and may now play a critical role in sealing the Acorn and East Mey subsurface carbon storage sites. The characteristics of these important shales have been little addressed in the hydrocarbon extraction phase, with an understandable focus on reservoir properties and their influence on resource recovery rates. Here, we assess the characteristics of the Rodby and Lista Shales using wireline logs, geomechanical tests, special core analysis (mercury intrusion) and mineralogical and petrographic techniques, with the aim of highlighting key properties that identify them as suitable top-seals. The two shales, defined using the relative gamma log values (or Vshale), have similar mean pore throat radius (approximately 18 nm), splitting tensile strength (approximately 2.5 MPa) and anisotropic values of splitting tensile strength, but they display significant differences in terms of wireline log character, porosity and mineralogy. The Lower Cretaceous Rodby Shale has a mean porosity of approximately 14 %, a mean permeability of 263 nD (2.58 × 10−19 m2), and is calcite rich and has clay minerals that are relatively rich in non-radioactive phases such as kaolinite. The Palaeocene Lista Shale has a mean porosity of approximately 16% a mean permeability of 225 nD (2.21 × 10−19 m2), and is calcite free, but contains abundant quartz silt and is dominated by smectite. The 2% difference in porosity does not seem to equate to a significant difference in permeability. Elastic properties derived from wireline log data show that Young’s modulus, material stiffness, is very low (5 GPa) for the most shale (clay mineral)-rich Rodby intervals, with Young’s modulus increasing as shale content decreases and as cementation (e.g., calcite) increases. Our work has shown that Young’s modulus, which can be used to inform the likeliness of tensile failure, may be predictable based on routine gamma, density and compressive sonic logs in the majority of wells where the less common shear logs were not collected. The predictability of Young’s modulus from routine well log data could form a valuable element of CCS-site top-seal appraisals. This study has shown that the Rodby and Lista Shales represent good top-seals to the Acorn and East Mey CCS sites and they can hold CO2 column heights of approximately 380 m. The calcite-rich Rodby Shale may be susceptible to localised carbonate dissolution and increasing porosity and permeability but decreasing tendency to develop fracture permeability in the presence of injected CO2, as brittle calcite dissolves. In contrast, the calcite-free, locally quartz-rich, Lista Shale will be geochemically inert to injected CO2 but retain its innate tendency to develop fracture permeability (where quartz rich) in the presence of injected CO2.

Fast Monte Carlo method for simulation of gamma density well logging measurements

The paper introduces a fast Monte Carlo method developed for simulation of gamma density measurements. A main advantage of this method is its high performance. For simulation of tool responses, the proposed method is faster than conventional Monte Carlo methods by several orders of magnitude. The demonstrated performance of the proposed method allows its using in analysis and interpretation of measurements obtained in beds with complex geometry.