Distribution Of Rock Properties Research Articles

Bayesian joint inversion of seismic and electromagnetic data for reservoir lithofluid facies, including geophysical and petrophysical rock properties

A Bayesian approach is developed to estimate lithofluid facies and other rock properties conditioned on seismic and electromagnetic data for reservoir characterization. Prior distributions are assumed to be facies-related Gaussian modes of geophysical rock properties directly acquired or converted from petrophysical properties by calibrated rock-physics modeling. An original generalization includes two distributions in the same marginalization integral, analytically solved under a linearized Gaussian assumption to provide a facies model likelihood conditioned on geophysical data. Because computing this probability for all possible facies configurations may be impractical, a Markov chain Monte Carlo algorithm efficiently samples models to provide a full posterior distribution. The linearized Gaussian approach allows the computation of the conditional distributions of geophysical and petrophysical rock properties by applying local deterministic inversions over the many sampled facies models. The inversion uses simulated geophysical data from a 1D synthetic model based on the geologic scenario and a well from a selected marine oil field. Two other wells from the same reservoir are used to gather prior distributions. Data from the well, calibration of the rock-physics modeling, and facies matching between the priors and the synthetic model are presented and discussed. Numerical tests validate nonlinear forward-modeling adaptations based on the assumed linearized Gaussian approach. The simulated stand-alone and joint geophysical data sets are then inverted for lithofluid facies models under different prior inputs. Two challenging geoelectric scenarios also are tested, one with lower resistivity contrasts and another with a misguided background model. All results demonstrate a gain in precision and accuracy when associating these geophysical signals to estimate the oil column. Facies-conditioned inversions for the rock properties also indicate potential for quantitative reservoir interpretations.

Identifying nonuniform distributions of rock properties and hydraulic fracture trajectories through deep learning in unconventional reservoirs

Predicting the trajectories of hydraulic fractures in unconventional reservoirs poses a significant challenge due to the heterogeneous nature of the rock matrix. Obtaining an accurate distribution of rock properties from limited measurements of rock samples near wellbores is difficult. In this study, we propose a deep learning framework that utilizes observations of hydraulic fracture patterns to identify nonuniform distributions of rock properties. Our approach utilizes the deep operator network (DeepONet) to map elastic properties to fracture geometries, and establishes an inverse problem to map fracture geometries back to elastic properties. Our results demonstrate a high level of accuracy in predicting nonplanar paths of single and multiple hydraulic fractures in heterogeneous formations. The well-trained model can rapidly evaluate numerous fracture patterns within seconds, surpassing the efficiency of finite element-based methods. Furthermore, fracture trajectories enable the identification of nonuniform distributions of rock properties. The maximum point-wise error of predicted Young's modulus compared to the ground truth is less than 20 %, with accurate identification of distribution patterns. Only a few regions exhibit relatively large errors, approaching 20 %. The presented approach provides valuable insights for the identification of reservoir properties in engineering applications.

How to estimate the 3D stress state for a deep geological repository

Abstract. When stresses yield a critical value, rock breaks or pre-existing faults are reactivated, generating pathways for fluid migration. Thus, the contemporary undisturbed stress state is a key parameter for assessing the stability of deep geological repositories and for quantifying whether stress changes induced by sub-surface constructions and storage of heat-generating waste lead to a critical state. The prediction of the contemporary 3D stress state is achieved with geomechanical–numerical models that are based on the static geological models. These are based on 3D seismic imaging and borehole data and describe the 3D structure and distribution of rock properties. Furthermore, pointwise measurements of the stress state are needed to fit the model to these data. The workshop is divided into three parts. Each part will have a short introduction to the specific topic, followed by dedicated hands-on exercise in small groups and discussions of the exercise outcome and its implications. 1. How do we formally describe the stress field? Here you will learn that the stress field is different from other physical field quantities such as temperature or displacement. The latter can be described with a scalar or a vector at a point. In contrast, the stress state at a point is described with the so-called Cauchy stress tensor that has nine components. We will give a quick tour through this concept, starting from very basic physics, and explain why the tensor is needed. In particular, you will learn in the exercises that stress cannot be measured directly with most methods but that strain is observed, from which stress is inferred.2. How do we actually measure stress? We present a range of methods that determine individual components of the stress state. In the exercise you will analyse borehole image logs to identify borehole breakouts and drilling-induced tensile fractures at the borehole wall. These are used to derive the orientation of the minimum and maximum horizontal stresses. Furthermore, we will present methods for the estimation of stress magnitudes. These are essential data for the calibration of a 3D geomechanical model. We will give a brief overview of different methods and in the exercise on the analysis of mini-hydraulic fracture tests as well as on the sleeve-fracturing and sleeve re-opening methods.3. From a viewpoint to a 3D description. If rock properties in the sub-surface were homogenous and isotropic and were to follow a simple linear behaviour between stress and strain, we could estimate the stress state analytically. However, this is not the case, and we will discuss three questions. a. How many pointwise stress data are needed to efficiently constrain a 3D model?b. How do I know whether a data point taken from less than a cubic metre is a good representation of a large rock volume, i.e. a whole lithological layer?c. How can we quantify the uncertainties of the model stress state, and what is the typical range? You will use a case study in northern Switzerland to explore these questions.

On the influence of initial stress on final stress in data-calibrated numerical geomechanical models

Abstract. The prognosis of the state of stress in the subsurface can be improved by using numerical models in addition to data from stress measurements, as such models allow for consideration of variability stemming from structural complexities and an inhomogeneous distribution of rock properties. These models are generally set up in two consecutive steps. In the first step one an initial stress is established that accounts for gravity and a reasonable ratio of horizontal to vertical stress. This represents a reference stress state in the absence of tectonic stress and ensures equilibrium with gravity: i.e. no strain is produced once gravity acts. In the second step tectonic stress is included via displacement boundary conditions which induce horizontal differential stress to come up with the final stress state. Both initial stress and tectonic stress are chosen in such a way that calibration data are reproduced by the model at the locations and depths where the data were measured. We present generic models to investigate whether the choice of initial and tectonic stress affects the final state of stress in areas of the model domain where no stress data are available. We find that there is in general an ambiguity as different combinations of initial stress and tectonic stress yield the same final state of stress at the points where data are available. However, in those areas of the model domain where calibration data do not exist, these different choices of initial stress and tectonic stress produce differing results. These deviations are largest in the vicinity of lithological interfaces. We find that this ambiguity is reduced if more stress data exist, particularly in not just one lithology and at one depth. On the other hand, if more data are available, it becomes increasingly more difficult to find a combination of initial and tectonic stress to match them all. In view of the uncertainties of the data, such deviations between modelled stress and data may be expectable to some degree. However, such deviations may indicate that inelastic rock properties do play a role in some lithologies.

Reliability assessment of deep excavations in spatially random cohesion weakening friction strengthening massive rocks: Application to nuclear repositories

An augmented methodology is developed to estimate the reliability of deep excavations along spatially variable massive rock masses using the cohesion weakening friction strengthening (CWFS) model. Sensitive parameters of the CWFS model were initially identified using Sobol’s global sensitivity analysis based on their influence on the displacements and excavation damage zone around excavations. The probability of failure was estimated by performing Mont–Carlo Simulations on random finite difference models of excavations generated via MATLAB-FLAC2D coupling, considering the spatial variation of these sensitive parameters. Spatial variation was modeled by generating anisotropic random fields of sensitive CWFS parameters via the recently developed Fourier series method and updated correlations suggested by Walton (2019). The proposed methodology was demonstrated for a proposed deep nuclear waste repository to be located in Canada. Results from the developed methodology were systematically compared with those of traditional reliability (ignoring spatial variation) and deterministic methods (ignoring uncertainty). Although the developed methodology was computationally complex, it was judged to be the most realistic due to the realistic consideration of heterogeneous distributions of rock properties. Traditional methodologies underestimate/overestimate the excavation performance due to negligence of uncertainty and spatial variability. Finally, a parametric analysis was performed using developed methodology by varying the initial friction angle, scale of fluctuations (SOFs) and dilation angle. The effect of initial friction angle was observed to be more pronounced on the probability of failures as compared to SOFs and dilation angle. Similar observations were made related to the excavation damage zone (EDZ) development quantified using yield area ratio.

Real-Time Rock-Properties Estimation for Geosteering: Statistical Rock-Physics-Driven Inversion of Seismic Acoustic Impedance and LWD Ultradeep Azimuthal Resistivity

Summary This work describes a statistical rock-physics-driven inversion of seismic acoustic impedance (AI) and ultradeep azimuthal resistivity (UDAR) log data, acquired while drilling, to estimate porosity, water saturation, and facies classes around the wellbore. Despite their limited resolution, seismic data integrated with electromagnetic resistivity log measurements improve the description of rock properties by considering the coupled effects of pore space and fluid saturation in the joint acoustic and electrical domains. The proposed inversion does not explicitly use a forward model, rather the correlation between the petrophysical properties and the resulting geophysical responses is inferred probabilistically from a training data set. The training set is generated by combining available borehole information with a statistical rock-physics modeling approach. In the inversion process, given colocated measurements of seismic AI and logging-while-drilling (LWD) electromagnetic resistivity data, the pointwise probability distribution of rock properties is derived directly from the training data set by applying the kernel density estimation (KDE) algorithm. A nonparametric statistical approach is used to approximate nonsymmetric volumetric distributions of petrophysical properties and to consider the characteristic nonlinear relationship linking water saturation with resistivity. Given an a priori facies classification template for the samples in the training set, it is possible to model the multimodal, facies-dependent behavior of the petrophysical properties, together with their distinctive correlation patterns. A facies-dependent parameterization allows the effect of lithology on acoustic and resistivity responses to be implicitly considered, even though the target properties of inversion are only porosity and saturation. To provide a realistic uncertainty quantification of the estimated rock properties, a plain Bayesian framework is described to account for rock-physics modeling error and to propagate seismic and resistivity data uncertainties to the inversion results. In this respect, the uncertainty related to the scale difference among the well-log data and seismic is addressed by adopting a scale reconciliation strategy. The main feature of the described inversion lies in its fast implementation based on a look-up table that allows rock properties, with their associated uncertainty, to be estimated in real time following the acquisition and inversion of UDAR data. This gives a robust, straightforward, and fast approach that can be effortlessly integrated into existing workflows to support geosteering operations. The inversion is validated on a clastic oil-bearing reservoir, where geosteering was used to guide the placement of a horizontal appraisal well in a complex structural setting. The results show that the proposed methodology provides realistic estimates of the rock-property distributions around the wellbore to depths of investigation of 50 m. These constitute useful information to drive geosteering decisions and can also be used, post-drilling, to update or optimize existing reservoir models.

Analysis of Fluid Flow Pathways in the Mount Meager Volcanic Complex, Southwestern Canada, Utilizing AMT and Petrophysical Data

AbstractDefining the spatial distribution of geological structures and rock properties is important for understanding how fluid flow is controlled in a geothermal reservoir. Here, we present a procedure to examine the potential fluid pathways. By combining 3‐D resistivity models derived from audio‐magnetotelluric (AMT) data with available rock properties (porosity and permeability) and fluid sample data (fluid resistivity, salinity, and temperature), we investigated the relationship between electrical resistivity and fluid flow in an active volcanic system. Different petrophysical models and empirical relations are evaluated to determine the relationship between the fluid flow system at Mount Meager, British Columbia, and the resistivity model. In addition, we utilized porosity and permeability measured in the laboratory to define the porosity‐permeability relationship. The porosity of the volcanic core samples showed a range of 2.6%–23.2% and the permeability was in a range of 0.001–5,186.57 mD. The results showed the potential of 3‐D inversion of AMT data to map the fluid pathways at Mount Meager. These pathways are correlated with loss circulation zones in boreholes and can account for porosity up to 8.5%, which using the porosity‐permeability relationship translates to permeability of the order 0.249 mD. Not only are the fault and fracture zones important for reservoir exploitation, but they also provide permeability for the circulation of meteoric water. Our studies suggest that a set of fractures with 0.1 m spacing and 20 mm aperture can keep 40% fluid in pores and transmit fluid with possible permeability of 666 mD.

Integrated Carbonate Rock Type Prediction Using Self-Organizing Maps in E11 Field, Central Luconia Province, Malaysia

Reducing uncertainty in 3D carbonate rock type distribution is a critical factor that profoundly impacts field development for hydrocarbon or carbon capture and storage (CCS) projects. Miocene carbonate reservoirs in the Central Luconia offshore region are economically important global gas reservoirs. The nature of these carbonate rocks can be visually distinct in the core and the multiscale reservoir heterogeneity might vary in scale from the 100-m scale to the sub-millimeter scale. This work presents a series of steps workflow to obtain spatial information about the organization scheme of carbonate rock types, and capture the most important petrophysical and sedimentary controls on rock property distribution in the E11 field, a carbonate buildup, located in Central Luconia Province, offshore Malaysia. The spatial data were generated from a supervised neural Kohonen algorithm. The rock types predicted with this workflow were propagated using IPSOM probabilized self-organizing maps SOM. This tool is used for classifying multivariate data samples according to “patterns” or multivariate responses. The workflow includes several steps: A Step 1—Core data description, B Step 2—Thin section description, C Step 3—Well log interpretation, and D Step 4—IPSOM probabilized self-organizing maps for facies prediction SOM. The depth plots of the predicted rock type showed close correspondence to the core-based rock types in terms of the stratigraphic organization of tight and reservoir layers, proportions, and juxtaposition. This result is sufficient to merit the application of the rock type logs into a future porosity model of the E11 field, and to understand the lateral and vertical distribution of tight and reservoir rock types of distribution. The results can be used to build a future realistic digital twin of the subsurface, and in digital geological modeling.

Investigating Delaware Basin Bone Spring and Wolfcamp Observations Through Core-Based Quantification: Case Study in the Integrated Workflow, Including Closed Retort Comparisons

The Delaware Basin of the greater Permian Basin system has been the focus of continually increased attention in the exploration, appraisal, and development phases of unconventional oil and gas potential over the past decade. While the industry continues to drill horizontal wells for the exploitation of producible hydrocarbon, subsurface disciplines continue to investigate the rock and fluid properties of the stratigraphy through the application of various technological tools. In this study, we focus on five wells spatially covering Loving, Ward, and Reeves Counties in West Texas, where whole core samples were acquired and investigated to compare variations in the Bone Spring and Wolfcamp Formations across varying geological contexts. Samples taken from the whole conventional core were investigated in the laboratory setting, and a series of measurements were acquired on each sample. The laboratory measurements distinguished trends and changes in the rock property volumes (i.e., porosity, saturation, total organic carbon) over stratigraphic intervals. The utilization of nuclear magnetic resonance, as well as acquired geochemical data, allows an innovative approach and application of a correction factor to be applied to the saturation quantification. Integration of geological context with measured laboratory data constraints and petrophysical wireline-log-based interpretation links predictive trends from the defined rock and fluid property distributions and may aid in predicting hydrocarbon vs. water production.

Efficient estimation of aquifer intrinsic permeability anisotropy using perturbation theory

Inverse modeling of aquifer measurements aims at estimating the spatial distribution of rock properties that best fits the available measurements which, in turn, allows predicting water yields and pressures to an acceptable level of accuracy. Nonlinear automatic inverse methods require multiple solutions of the diffusion equation, also known as the groundwater flow equation. Although numerical solutions to the forward problems improve the understanding of complex groundwater flow systems, they are often computationally expensive, thereby rendering the inversion process inefficient. We introduce a gradient-based inversion algorithm that leverages perturbation theory to efficiently estimate the tensorial intrinsic permeability distribution of porous media from single-phase transient pressure measurements. With a maximum of two numerical simulations, the Joint Perturbation-Superposition (JPS) method allows one to compute flow-history-dependent Intrinsic permeability Sensitivity Functions (PSF) on the spatial-temporal domain. Regardless of the gradient-based iterative inversion technique, our method efficiently adapts the sensitivity functions yielded by perturbation theory to calculate the entries of the associated Jacobian matrix at every iteration. A two-dimensional synthetic model comprising multi-well conditions is examined for an anisotropic and spatially heterogeneous groundwater flow system. The perturbation method yields accurate and efficient parameter estimation by leveraging sensitivity functions for (1) the appropriate selection of input transient pressure measurements and (2) reducing the sequential calculation of Jacobian matrices. As a result, Monte Carlo uncertainties as low as <5% are obtained for the estimated tensorial intrinsic permeability distribution, with inversion times halved when compared to conventional techniques.

Evolution of a sand-rich submarine channel–lobe system, and the impact of mass-transport and transitional-flow deposits on reservoir heterogeneity: Magnus Field, Northern North Sea

The geometry, distribution and rock properties (i.e. porosity and permeability) of turbidite reservoirs, and the processes associated with turbidity current deposition, are relatively well known. However, less attention has been given to the equivalent properties resulting from laminar sediment gravity-flow deposition, with most research limited to cogenetic turbidite debrites (i.e. transitional-flow deposits) or subsurface studies that focus predominantly on seismic-scale mass-transport deposits (MTDs). Thus, we have a limited understanding of the ability of subseismic MTDs to act as hydraulic seals, and their effect on hydrocarbon production and/or carbon storage. We investigate the gap between seismically resolvable and subseismic MTDs, and transitional-flow deposits on long-term reservoir performance in this analysis of a small (&lt;10 km-radius submarine fan system), Late Jurassic, sandstone-rich stacked turbidite reservoir (Magnus Field, Northern North Sea). We use core, petrophysical logs, pore fluid pressure, quantitative evaluation of minerals by scanning electron microscopy (QEMSCAN) and 3D seismic-reflection datasets to quantify the type and distribution of sedimentary facies and rock properties. Our analysis is supported by a relatively long ( c. 37 years) and well-documented production history. We recognize a range of sediment gravity deposits: (i) thick-/thin-bedded, structureless and structured turbidite sandstone, constituting the primary productive reservoir facies ( c. porosity = 22%, permeability = 500 mD); (ii) a range of transitional-flow deposits; and (iii) heterogeneous mud-rich sandstones interpreted as debrites ( c. porosity ≤ 10%, volume of clay = 35%, up to 18 m thick). Results from this study show that over the production timescale of the Magnus Field, debrites act as barriers, compartmentalizing the reservoir into two parts (upper and lower reservoir), and transitional-flow deposits act as baffles, impacting sweep efficiency during production. Prediction of the rock properties of laminar- and transitional-flow deposits, and their effect on reservoir distribution, has important implications for: (i) exploration play concepts, particularly in predicting the seal potential of MTDs; (ii) pore-pressure prediction within turbidite reservoirs; and (iii) the impact of transitional-flow deposits on reservoir quality and sweep efficiency. Supplementary material: of data and methods are available at https://doi.org/10.6084/m9.figshare.c.5313860

Investigation of rock properties distribution effect on pressure transient analysis of naturally fractured reservoirs

Naturally fractured reservoirs (NFRs) are considered as one of the main resources of oil and gas around the world. The nature of fractures in this kind of reservoirs splits these reservoir rocks into two parts; matrix and fracture. In these two media, geometrical properties like matrix block size and also petrophysical properties such as porosity and permeability cannot considered to be constant and they usually contain heterogeneity in extent of the reservoir. In this study, a statistical distribution concept is used to be able to model variance of properties including matrix block size, matrix and fracture permeability, and matrix and fracture porosity as independent statistical variables. For the purpose of investigating effect of the five aforementioned properties distribution on pressure transient analysis (PTA) plots, five distinct cases of property distributions are considered with their corresponding precise statistical modeling applied on governing flow equation of a dual-porosity base case reservoir model. Abovementioned distributed parameters are included in semi-analytically derived dual porosity reservoir models and results are compared to their corresponding constant-value response. In each case the constant parameter is the median of corresponding statistical distribution. The statistical approach is validated using numerical modeling and field data applications are also presented. Different unimodal and bimodal matrix properties (block size, permeability, and porosity) distribution have slight to intense effects on PTA plots of an NFR. In matrix block size and porosity distribution cases, lower values, and in matrix permeability distribution case, higher values of the range dominate the pressure behavior of the fractured system. On the other hand, although fracture permeability and porosity distribution can shift PTA plots of the model but the effect is not significant and both fracture permeability and porosity distribution can be represented by constant representative values instead of a statistical model. It is worth mentioning that all matrix properties bimodal distribution has a common signature on PTA plots which is similar to the triple porosity reservoir response (i.e. the presence of double-bump descent on pressure derivative plot).

Joint impedance inversion and spectral decomposition for deepwater gas reservoir characterization: A case study in South China Sea

Gas reservoir characterization is one of the frontiers in seismic exploration. Acoustic impedance, one of the most effective seismic attributes, aims to describe the spatial distribution of rock properties. However, using acoustic impedance only is insufficient to describe gas-bearing layers accurately, in the case of rapid lithologic changes and complex geology in the deepwater area. The reflection seismograms indicate an absorption effect when seismic waves propagate through gas-bearing layers. The absorption effect can be used as an additional attribute to help gas reservoir characterization. Therefore, we have developed a new attribute for gas reservoir characterization in this study, which integrates the results of acoustic impedance and absorption coefficient. We estimate the acoustic impedance model by using poststack impedance inversion and then we calculate probability distribution functions. Functions are classified into gas-bearing and nongas layers. We discuss an absorption coefficient and obtain it from the spectrum gradient, in which the gradient is calculated by spectral decomposition using the matching pursuit method. We apply the new attribute to characterize the spatial distribution and thickness of deepwater gas reservoirs in the Pearl River Mouth Basin. Well-log and geologic information indicate that the study area has an enrichment of gas reservoirs. Field data application indicates the explicit distribution of the gas reservoir and in accordance with the well-log information, which indicates that our attribute can improve gas reservoir characterization.

A geocellular modelling workflow for partially dolomitized remobilized carbonates: An example from the Hammam Faraun Fault block, Gulf of Suez, Egypt

Constructing geocellular models of carbonate rocks using standard software is challenging since most of modelling packages are designed, first and foremost, to represent siliciclastic depositional systems, where rock properties are strongly facies-controlled. The distribution and components of carbonate depositional facies vary drastically across the geological timescale as a result of paleoclimate and its effects on carbonate-producing biota. Furthermore, reservoir architecture is less strongly controlled by depositional environment than in clastic settings, and rock physical properties, including fracture networks, are controlled by both primary components and their subsequent diagenetic alteration. This means that rock property distribution is less predictable than in siliciclastic systems, and less well represented by geocellular models that are designed to represent sedimentary architecture. In other words, in carbonate systems, the depositional and diagenetic history needs to be reconstructed in order to successfully model reservoir properties.In this study a geocellular model was created by using a well-characterised outcrop analogue obtained from the Hammam Faraun Fault (HFF) Block, located on the eastern coast of the Gulf of Suez in Sinai, Egypt. This model integrates sedimentological, petrophysical, diagenetic, and structural information into a single database. The workflow utilizes the regional tectonic history, upscaled lithological logs, and two-stage facies modelling (reflecting in and ex situ depositional facies) and resulted in the creation a realistic model of remobilized carbonates that were deposited on the slope of a carbonate platform during a period of tectonic instability. Diagenetic overprinting was achieved using probability functions to reflect the history of burial, rifting, and the spatial relationship of stratabound and non-stratabound dolostone bodies. The study demonstrates a workflow for modelling mass-transport carbonate facies and multistage fault-related diagenesis so that flow controlling facies and diagenetically altered poroperm and fracture networks are accurately represented using commercially available modelling software, and in particular demonstrates how diagenetically controlled geobodies can be captured using simple algorithms.

FEATURES OF PHYSICAL AND MATHEMATICAL MODELING OF OIL AND WATER FILTRATION AT DIFFERENT CRIMPING PRESSURES

The article discusses the features and results of physical and mathematical modeling of filtration experiments on terrigenous and carbonate rock core samples at different crimping pressures. Such studies are necessary to understand the effect of rock pressure on the reservoir properties and relative phase permeability (RP) of reservoir rocks, including from the standpoint of the Digital Core technology, since core tomography is usually performed under atmospheric conditions and data on rock properties are required for reservoir conditions. The article discusses the features and results of physical and mathematical modeling of filtration experiments on terrigenous and carbonate rock core samples at different crimping pressures. Such studies are necessary to understand the effect of rock pressure on the reservoir properties and relative phase permeability (RP) of reservoir rocks, including from the standpoint of the Digital Core technology, since core tomography is usually performed under atmospheric conditions and data on rock properties are required for reservoir conditions. The laboratory study of the relative permeability was carried out on composite core models by the method of stationary filtration at crimping pressures of 10 and 20 MPa. Mathematical modeling of filtration experiments was performed in the Eclipse simulator. The distribution of porosity in the hydrodynamic models of the core was set based on data from computed tomography of the core. The distribution of other rock properties (permeability, residual saturations, RPP values at residual saturations) was calculated using generalized dependencies. It is shown that for terrigenous and carbonate rocks, an increase in pressure leads to different behavior of the RPP functions and fluid mobility. The results of laboratory studies are interpreted from the point of view of processes at the micro level, based on the formation of the nature of the flow and the associated water saturation during deformation of the void space. It is also shown that filtration experiments on core at different rock pressures can be simulated on a hydrodynamic simulator, but at the same time, the study of patterns in the change in model parameters with a change in pressure depends on the presence of patterns in the behavior of rock properties based on the results of physical modeling.

Lithofacies classification of a geothermal reservoir in Denmark and its facies-dependent porosity estimation from seismic inversion

Characterization of geothermal reservoirs is an important step for exploration and development of geothermal energy, which is reliable and sustainable for the future. Based on the inversion results of seismic reflection data, lithofacies and porosity are predicted beyond well locations on a potential geothermal reservoir in the north of Copenhagen, onshore Denmark. To classify the lithofacies, a new system of Artificial Neural Networks-Hidden Markov Models is proposed to consider the complex spatial distribution of rock properties and the intrinsic depositional rules. Artificial Neural Networks can overcome the common Gaussian assumption for the distribution of rock properties. At the same time, the transition matrix in Hidden Markov Models provides the conditional probability for the lithofacies transitions along the vertical direction. After classification, the resulting lithofacies are used to constrain the porosity prediction, in which the Artificial Neural Networks is trained and applied within each type of lithofacies, as a regression process. The novelty of this approach is in the integration of statistics and computer science algorithms that allows capturing hidden and complex relations in the data that cannot be explained by traditionally deterministic geophysical equations. This workflow could also improve the prediction accuracy and the uncertainty quantification of the porosity distribution given rock properties.

Defining lithic patterns within river-dominated delta deposits for geostatistical simulation

Reservoir development forecasts depend on accurate descriptions of the spatial distribution of rock properties that impact subsurface fluid-flow pathways and volume connectivity. Reservoir models constructed using geostatistical methods combine analogous facies dimension data with sparse subsurface data to predict spatial variations in rock properties. This study uses a physics-based depositional process model to define realistic facies variations within a river-dominated delta deposit formed during multiple shoreline regressions and transgressions. Geostatistical models are conditioned to varying amounts of information extracted from the depositional model to examine how well they reproduce the facies patterns. Reservoir simulation is used to examine the impact of analogous dimension data and varying conditioning constraints on reservoir performance predictions of water displacing oil. The dimensions of surface depositional features underestimate the continuity of preserved facies patterns, proportional grids following major flooding surfaces allow significantly better predictions than uniform rectangular grids, and trend constraints are more important when defined facies correlation length is significantly less than well spacing. When geostatistical model parameters are poorly chosen, reservoir simulation of the resulting weakly-structured facies patterns overpredict recovery and water breakthrough time. It is demonstrated that process-based depositional models can be used to optimize geostatistical model construction methods and input parameters to reduce uncertainty of reservoir development assessments.

Lithofacies classification based on a hybrid system of artificial neural networks and hidden Markov models

SUMMARY Lithofacies is one of the most important reservoir parameters, which could provide a qualitative description for hydrocarbon and geothermal reservoirs. Various techniques, such as artificial neural networks (ANN) and hidden Markov models (HMM), have been applied to extract this information, with the well log suites as inputs. However, both of these methods have their own limitations, such as no geological priors in ANN, since log samples along the depth direction are treated independently. While in HMM, a simple Gaussian assumption is usually adopted, which may not be sufficient for complex data distributions. In order to address these problems, a new method is proposed, which combines ANN and HMM into a hybrid system. This new technique allows for a more flexible approach to the probability distributions of rock properties, without any Gaussian assumption being made. At the same time, the geological dependence between adjacent samples is introduced by a representative transition matrix of lithofacies. The output probability from ANN must be reformulated to an emission function before it can be fed into the HMM, which is achieved via the Bayes’ rule. Then the Viterbi algorithm in HMM is applied for the decoding of sequential patterns in the subsurface. In this fashion, the classification process can be proceeded statistically and geologically. Better performance of the proposed approach, compared with other classification methods, is demonstrated in two case studies.

Physics-guided neural networks for predicting unconventional well performance — using Unconventional Rate Transient Analysis for smarter production data analytics

Geoscience modelling poses many challenges due to the limited sampling and the complexity of the phenomena that create the resulting rock and its properties. When adding to the geologic and geomechanical complexity the various possible fluid flow mechanisms that are often not fully understood, one realizes quickly how daunting geomodelling could be. As a result, oil and gas fields are often bought and sold using reserves computed with simple decline curve analysis tools. Unfortunately, these simplified production analysis tools contain no physics and do not help develop oil and gas assets which require the knowledge of 1) rock properties distribution and 2) the impact of the rock properties on the selected production mechanism. For example, if one has a naturally fractured reservoir, the presence or absence of the natural fractures and the way the wells are drilled to encounter or avoid these rock properties will determine the reserves and the future of the company developing such an asset. Very often the future of many companies is not very bright due to their lack of knowledge of the distribution of the rock properties such as natural fractures and the subsequent fluid flow resulting from drilling and fracking into these heterogeneous rock properties. For the companies that want to prosper by intelligently developing their assets, niche companies and technologies have been used throughout the years to address all these challenges. Among these technologies we find the use of artificial intelligence and machine learning, which were introduced in the oil and gas industry in the early 1990s with successful application to petrophysics, well test analysis and reservoir modelling. Three decades later, the oil industry and its unconventional revolution is facing frequent challenges ranging from frac hits and well interferences, casing deformation and collapses, expensive cube development with meagre returns on investment and many other puzzling issues with no easy solution. Suddenly, under the stress of financial constraints, the machine learning tools criticized for three decades as ‘black boxes’ are now becoming the preferred solution to all problems. Unfortunately, this love-hate relationship the oil industry has with data-driven approaches may hit a rough patch very soon due to its inability to recognize the limitations of the available data used in the various oil and gas challenges.

Probabilistic Characterization of Rock Mass from Limited Laboratory Tests and Field Data: Associated Reliability Analysis and Its Interpretation

Probabilistic methods are the most efficient methods to account for different types of uncertainties encountered in the estimated rock properties required for the stability analysis of rock slopes and tunnels. These methods require estimation of various parameters of probability distributions like mean, standard deviation (SD) and distributions types of rock properties, which requires large amount of data from laboratory and field investigations. However, in rock mechanics, the data available on rock properties for a project are often limited since the extents of projects are usually large and the test data are minimal due to cost constraints. Due to the unavailability of adequate test data, parameters (mean and SD) of probability distributions of rock properties themselves contain uncertainties. Since traditional reliability analysis uses these uncertain parameters (mean and SD) of probability distributions of rock properties, they may give incorrect estimation of the reliability of rock slope stability. This paper presents a method to overcome this limitation of traditional reliability analysis and outlines a new approach of rock mass characterization for the cases with limited data. This approach uses Sobol’s global sensitivity analysis and bootstrap method coupled with augmented radial basis function based response surface. This method is capable of handling the uncertainties in the parameters (mean and SD) of probability distributions of rock properties and can include their effect in the stability estimates of rock slopes. The proposed method is more practical and efficient, since it considers uncertainty in the statistical parameters of most commonly and easily available rock properties, i.e. uniaxial compressive strength and Geological Strength Index. Further, computational effort involved in the reliability analysis of rock slopes of large dimensions is comparatively smaller in this method. Present study also demonstrates this method through reliability analysis of a large rock slope of an open pit gold mine in Karnataka region of India. Results are compared with the results from traditional reliability analysis to highlight the advantages of the proposed method. It is observed that uncertainties in probability distribution type and its parameters (mean and SD) of rock properties have considerable effect on the estimated reliability index of the rock slope and hence traditional reliability methods based on the parameters of probability distributions estimated using limited data can make incorrect estimation of rock slope stability. Further, stability of the rock slope determined from proposed approach based on bootstrap method is represented by confidence interval of reliability index instead of a fixed value of reliability index as in traditional methods, providing more realistic estimates of rock slope stability.