Representative Elementary Volume as Key Parameters to Improve Grid Stability on Multi-Point Statistic Based Reservoir Models

Multipoint statistics (MPS) facies modelling has been recognized as an advanced modelling tool to help build more realistic and complex 3D facies models through training images. However, with the increased exposure of MPS to the geomodelling community, modellers have realized that creating a training image that properly represents their understanding of the studied reservoir with reasonable facies shapes and connectivity, as well as correct spatial associations and attachments, is not an easy task. To fulfil the goal for MPS to be a “geology-driven modelling suite” and make it a more practical tool for reservoir modelling, we have established an efficient workflow that ties 5 key components together: a comprehensive geological analogue database, a search engine, a statistics extractor, a training image builder and MPS facies models of studied reservoirs. The integrated workflow that is presented in this paper is expected to lay the foundation for the near future of MPS reservoir modelling in the industry

Carbonate rocks have complex pore systems, ranging in size from caverns to micropores. 3D models of fine-scale porosity ( with resolution limits on the order of a few microns. Transmitted laser scanning confocal microscopy (LSCM) and multi-point statistics (MPS) provide an alternative, high-resolution (0.1 μ) method to build 3D digital rock models of appropriate size and shape for pore-network construction and flow modeling. Confocal microscopy uses point illumination and a pinhole placed in front of a detector to eliminate outof- focus information. Because each measurement is a single point, confocal devices perform scans along grids of parallel lines to provide 2D images of sequential planes at specified depths within a sample. In this study, LSCM is applied to rock samples impregnated with fluorescing epoxy. Reflected light intensity indicates the physical location of pore spaces. Samples are standard thin sections (30-μ thick), or rock chips of any thickness. Samples are composed of rock and epoxy, or they may be pore casts where the rock has been removed by acid. Reflected light is absorbed and scattered by the material above the focal plane, therefore the depth of penetration of LSCM is limited to 10-250 μ in rocks, and 500 μ in pore casts. LSCM data stacks commonly have flat aspect ratios, for example, 20 μ thick by 210 x 210 μ or larger in area. To build valid 3D models of physical pore systems, the depth of penetration should be at least 2 typical grain diameters. Therefore, a grain-size limitation exists for LSCM imaging. 3D digital rock models constructed from stacked LSCM scans are used as training images for multipoint statistical (MPS) modeling. MPS creates conditional simulations that use known results as fixed or “hard” data. We use MPS to create thick (mm-scale), high-resolution (better than 1 μ) digital rock models, suitable for pore-network modeling and/or flow simulation. Enlarged models avoid boundary effects that compromise flow-modeling results. MPS models can be used to address the question: What model size is needed to capture heterogeneity within a given rock type? Because MPS models are unconstrained by size or shape, we can use them to test the concept of representative element volume (REV). REV is the smallest volume that can be modeled to yield consistent results, within acceptable limits of variance of the modeled property, for example, porosity.

The Walloon Subgroup (WSG) represents a prolific coal seam gas (CSG) resource which, in part, underpins three large CSG to liquefied natural gas (LNG) projects operating along the Australian east coast. These mega-projects require long term forecasts of gas production, predictions which are often derived via the dynamic simulation of numerical reservoir models. Reservoir models consist of hierarchical collections of inter-related rock and fluid parameters. The facies model, representing palaeogeography, serves as the foundation of this linkage as it defines the three-dimensional (3D) geometry and distribution of coal seams. This thesis is comprised of complimentary studies aimed at investigating and enhancing the predictive capability of numerical facies models in the Walloon Subgroup. A preliminary screening study investigates CSG production behaviours to understand how reservoir parameters, including the distribution and continuity of coal layers, impact the predictions output by reservoir models. A database of open-source reservoir properties was compiled and used to construct representative reservoir models for three CSG development areas present along the WSG productive fairway in the eastern Surat Basin. Simulation experiments using these models confirms that the distribution and lateral continuity of coal facies are a significant control upon the late-stage production behaviour of CSG wells – a finding which provides impetus for further detailed investigation of WSG facies models. Construction of predictive facies models requires a comprehensive understanding of regional depositional trends, local facies architectures and depositional processes as well as computer routines able to translate this information into numerical 3D grids. Present gaps in the industry’s understanding of the WSG highlight the requirement for further studies aimed at 1) refinement of the WSG’s regional stratigraphic and palaeogeographic models, 2) delineation of the WSG’s reservoir scale internal alluvial architecture, 3) identification of the processes or mechanisms controlling reservoir-scale facies relationships within the WSG and 4) development of workflows better able to represent alluvial facies in numerical reservoir models. The focus of this dissertation is to explore these conceptual gaps leading to improved numerical facies models of the WSG. Investigation of WSG facies models began with a regional study integrating newly available bore-hole image log data with sedimentological interpretations from cored wells and regional correlations to test and refine existing basin-wide palaeogeographic models for the WSG. This analysis offers a glimpse into fluvial styles and palaeoflow orientations present within the basin’s interior and was used to identify regional trends describing the spatial and temporal distribution of alluvial depositional styles. Synthesis of stratigraphic, sedimentological and palaeoflow interpretations developed during this study suggests the presence of a SE oriented trunk drainage system during deposition of the WSG. Within this regional context, a follow on high-resolution study provides insight into the geometry of reservoir-scale WSG alluvial architectures and elucidates the geological controls upon their development. Templates for the geometry and orientation of WSG architectural elements including channel belt, isolated channel, crevasse splay and peat mires were delineated from analysis of a 3D seismic volume. Interrogation of the spatial and temporal facies organisations interpreted from the 3D seismic volume reveal complex intra-WSG stratigraphic relationships, suggesting that compensational stacking played an important role in influencing the systems’ palaeogeographic organisation. These precursor studies provide critical inputs required for the construction of predictive CSG facies models. The final thesis component integrates these learnings to test existing and develop new numerical facies modelling methodologies. Interrogation of facies modelling workflows suggest that current approaches struggle to represent the complex three-dimensional alluvial architecture present within the WSG, specifically with respect to coal structures including coal seam amalgamation, bifurcation and washouts. To address this limitation, a facies modelling routine was developed in which automata representing the process of differential compaction driven compensational stacking are used explicitly to condition facies model outcomes. Application of this workflow allows for complex facies structures, more consistent with those observed in seismic sections or outcrop exposures, to be rendered in numerical facies models. This approach is implemented via the development of an open-source facies decompaction plugin compatible with Schlumberger’s PETRELTM 2015 software which can be applied to model field data directly or used to create enhanced 3D training images for deployment into multi-point statistics facies modelling workflows.

A workflow for modelling fluvial meander-belt successions: Combining forward stratigraphic modelling and multi-point geostatistics

This paper summarizes a reservoir modeling study involving the evaluation of development strategies relevant to a newly discovered, unconsolidated sandstone heavy oil field in Kuwait. The methodologies used provided essential information to define and evaluate feasible options to develop the reservoir. A reservoir model was developed utilizing seismic, well-log, and core data. Petrophysical estimates of mineralogy, porosity, water saturation (Sw), and permeability were made and calibrated to core data. The field geology and the depositional analog guided the interpretations of the reservoir geomorphology and sediment-distribution patterns. Facies modeling was achieved through multiple-point statistics methodology. Porosity, permeability, and Sw were distributed using Sequential Gaussian Simulation. Various sensitivity runs were made for key parameters to understand the uncertainty of the model forecast. A full-field reservoir model (FFRM) was developed by incorporating available engineering analysis data. Development potential of the field through pressure depletion was studied through full-field reservoir simulations. Considering the high level of uncertainty of a new field, Low, Mid and High forecast cases were established for development through pressure depletion. Simulations of secondary and tertiary recovery techniques were then evaluated through sector model simulations and upscaled to field level. Finally, roadmaps were laid out for several development scenarios considered for the field. This paper demonstrates how various geological, petrophysical, and engineering data were used to build a representative full-field geocellular model (FFGM) and make field-performance forecasts under uncertainties pertaining to a green, heavy-oil field. During the model development stage, dielectric and elemental spectroscopy log data were utilized to enhance the petrophysical analyses. The distribution of Sw followed a distinct workflow where the distribution within each reservoir zone was based on several oil/water contacts (OWC). Available pressure-volume-temperature (PVT) analysis data were used to estimate and confirm the presence of water zones within the reservoir intervals.

Uncertainty quantification is currently one of the leading challenges in the geosciences, in particular in reservoir modeling. A wealth of subsurface data as well as expert knowledge are available to quantify uncertainty and state predictions on reservoir performance or reserves. The geosciences component within this larger modeling framework is partially an interpretive science. Geologists and geophysicists interpret data to postulate on the nature of the depositional environment, for example on the type of fracture system, the nature of faulting, and the type of rock physics model. Often, several alternative scenarios or interpretations are offered, including some associated belief quantified with probabilities. In the context of facies modeling, this could result in various interpretations of facies architecture, associations, geometries, and the way they are distributed in space. A quantitative approach to specify this uncertainty is to provide a set of alternative 3D training images from which several geostatistical models can be generated. In this paper, we consider quantifying uncertainty on facies models in the early development stage of a reservoir when there is still considerable uncertainty on the nature of the spatial distribution of the facies. At this stage, production data are available to further constrain uncertainty. We develop a workflow that consists of two steps: (1) determining which training images are no longer consistent with production data and should be rejected and (2) to history match with a given fixed training image. We illustrate our ideas and methodology on a test case derived from a real field case of predicting flow in a newly planned well in a turbidite reservoir off the African West coast.

The Helvetian Formation represent the Upper Burdigalian deposits, along the Getic Depression, in Romania. It is marked by a transgressive marine phase and represents the main reservoir interval in a southern Romanian field. The scope of this paper is to understand the geometry and architecture of the Helvetian reservoirs, due to the high vertical and lateral variations of alternating thin sandy layers with shale intervals. Around fifty (50) wells were used, with a total of 143 m of core through Burdigalian to Sarmatian periods, only one well with 21 m of core well preserved, to allow a detailed facies analysis. This core reveals a number of lithofacies which control the reservoir distribution in the area. The sedimentological conceptual model is based on lithofacies characterization, vertical facies distribution, all supported by core and log data. Modern analogues are included to forecast the architecture and geometries of the depositional elements. Twenty-one (21) descriptive lithofacies are recognized for the entire cored section. Overall, seven (7) depositional sub-environments are distinguished: alluvial/fluvial deposits, lacustrine, distributary channel fill, mouth bar, interdistributary area, shoreface and offshore. The most relevant reservoir facies are related to wave dominated mouth bars and distributary channel deposits. Using AVA Clastics database, the elements, such as mouth bars, have an average width of 3800 m, long of approximately 6,300 m, with a thickness around 3.5 m. Carbonates, chlorite, feldspars and bioturbation have modified reservoir properties, but roundness and sorting, grains dissolution and local fractures contribute to enhancing the reservoir quality. The porosity spans between 3 to 22% and the permeability up to 309 mD. The 3D facies model was used to build depositional facies maps which are relevant to illustrate the depositional elements architecture and their distribution in the field. The facies concept provides a predictive distribution of reservoir properties, which often correlates with production history in the area. Reservoir data, along with well logs and core data, helped building a facies evolution, in order to reveal the optimal field development scenarios. This is a key element of the control of the oil and gas saturation distribution per reservoir units. The study brings new approach when analyzing mature fields, integrating old and new data and predicting stratigraphic architecture from sedimentological concept to facies model. Lithofacies, depositional environments and body geometries of the Helvetian reservoir units are guide to further development of the field.

The Thelma field is the most southerly of three fields located in Block 16/17 of the U.K. sector of the South Viking Graben and is operated by CNR International (U.K.) Ltd. The Thelma field comprises two submarine fans, the northern Thelma fan and the southern Southeast Thelma (SET) fan, revealed by subsurface mapping. The two fans consist of both Upper Jurassic Brae (upper Oxfordian–lower Volgian) and sand-shale (middle Volgian) members of the Kimmeridge Clay Formation. The two fan depocenters are separated by a low net-to-gross central region high, which was overtopped or diverted around by turbidity currents that formed the younger sand-shale member. The Brae member contains conglomerates, pebbly sandstones, sandstones, and thin-bedded turbidites (TBTs) of deep-water association. Seismic data are generally poor in this area, and conceptual and reservoir geological models are primarily based on oil field core, wireline logs, and dynamic reservoir data. Three conceptual models were created to propose geological scenarios for field development: Concept A has the SET fan fed independently from the southwest, Concept B has the SET fan fed as an extension of the Thelma fan from the north, and Concept C has an SET fan fed by bypass across the central region high. Each concept has different implications for fan connectivity. Using detailed core descriptions from the Thelma field, state-of-the-art deep-water facies analysis, a new facies scheme, and known deep-water facies associations on the modern seafloor and outcrop analogs, we test the conceptual models to validate the geology. The large-scale organization of the architectural elements of the Brae and sand-shale members is not well understood. By reviewing coarse-grained deep-water processes and the rock fabrics that they produce as a framework for rock property distribution in coarse-grained deep-water systems, we aim to investigate their architectural style. We recognize a series of facies associations from detailed facies descriptions of the cored intervals and, by distilling these sedimentological trends, ascribe the associations to uncored intervals and use these as a basis for correlation and reservoir modeling in the Thelma–SET area. The model is built from cored sedimentary facies, and facies associations recognizable on core-calibrated well logs, and then matched with dynamic well data, to test conceptual models. By combining the conceptual geological models with dynamic well testing of reservoir behavior, we have a more robust understanding of the two fields. Thelma is a higher energy system, with strong aquifer support facilitated by channelized reservoir architecture and poor lateral shale continuity, whereas SET is a lower energy system with poor aquifer support because of persistent lateral continuity of shale caps on sandstone lobes, and with no deep channeling recognized.

SummaryAssisted history matching (AHM) of a channelized reservoir is still a very-challenging task because it is very difficult to gradually deform the discrete facies in an automated fashion, while preserving geological realism. In this paper, a pluri-principal-component-analysis (PCA) method, which supports PCA with a pluri-Gaussian model, is proposed to reconstruct geological and reservoir models with multiple facies. PCA extracts the major geological features from a large collection of training channelized models and generates gridblock-based properties and real-valued (i.e., noninteger-valued) facies. The real-valued facies are mapped to discrete facies indicators according to rock-type rules (RTRs) that determine the fraction of each facies and neighboring connections between different facies. Pluri-PCA preserves the main (or principal) features of both geological and geostatistical characteristics of the prior models. A new method is also proposed to automatically build the RTRs with an ensemble of training realizations. An AHM work flow is developed by integrating pluri-PCA with a derivative-free optimization algorithm. This work flow is validated on a synthetic model with four facies types and a real-field channelized model with three facies types, and it is applied to update both the facies model and the reservoir model by conditioning to production data and/or hard data. The models generated by pluri-PCA preserve the major geological/geostatistical descriptions of the original training models. This has great potential for practical applications in large-scale history matching and uncertainty quantification.

This paper shows that there is quite a long history of using multipoint statistics in the vision science literature for modelling textures. while they have somewhat different concerns to the oil industry (less concern for data conditioning for example), the methods used may prove interesting. The link between Markov random fields and sequential algorithms is reviewed and a fast method to sidestep problems with insufficient training data is briefly considered

This paper proposes a novel approach for generating 3-dimensional complex geological facies models based on deep generative models. It can reproduce a wide range of conceptual geological models while possessing the flexibility necessary to honor constraints such as well data. Compared with existing geostatistics-based modeling methods, our approach produces realistic subsurface facies architecture in 3D using a state-of-the-art deep learning method called Generative Adversarial Networks (GANs). GANs couple a generator with a discriminator and each uses a deep Convolutional Neural Network (CNN). The networks are trained in an adversarial manner until the generator can create "fake" images that the discriminator cannot distinguish from "real" images. We extend the original GAN approach to 3D geological modeling at the reservoir scale. The GANs are trained using a library of 3D facies models. Once the GANs have been trained, they can generate a variety of geologically realistic facies models constrained by well data interpretations. This geomodelling approach using GANs has been tested on models of both complex fluvial depositional systems and carbonate reservoirs that exhibit progradational and aggradational trends. The results demonstrate that this deep learning-driven modeling approach can capture more realistic facies architectures and associations than existing geostatistical modeling methods, which often fail to reproduce heterogeneous nonstationary sedimentary facies with apparent depositional trend.

Construction of reliable 3-D geological models for reservoir simulation requires a detailed understanding of facies distribution and connectivity within the interval of interest. In particular, it relies on lateral and vertical variabilities in reservoir quality within and between different flow units. Despite thorough data integration and interpretation, several challenges were encountered while integrating geological knowledge into a 3-D stochastic geological model. Some unconventional approaches had to be taken in order to best reflect the geological understanding of the reservoirs while using commercially available software. For example, the 3-D stochastic facies modelling of the reservoir units was based on conceptual geological models. Models were constructed for each reservoir zone through the analysis and integration of core and log data from 50 wells in the study area. However, it was seen that utilising either object modelling or pixel-based modelling methods alone would not generate stochastic models that adequately honoured the conceptual geological model. Consequently, the two modelling methods were used together to generate combined models. A further challenge was to determine adequate facies proportions for each reservoir zone. The direct use of facies statistics from well logs in stochastic modeling lead to unrealistic facies distributions. To overcome this, dummy wells were added to make facies proportions matches the conceptual models rather than basing it on the existing wireline logs alone. Taking these unconventional approaches lead to a greater accuracy of reservoir and porosity distribution around the reservoir. Moreover, the methodology used in this study provides new ideas that can be used in modeling other fields with fluvial depositional settings.

Snesim is an algorithm for simulating complex structures. It is a pixel based method that sequentially simulates the nodes in a random order, while considering multipoint statistics. The conditional probabilities are extracted directly from a training image. If a configuration of the set of conditioned nodes is not found in the training image, the set is decreased node by node until the configuration of the final set is found. <br>We have modified the Snesim algorithm by enabling it to also delete nodes, i.e. instead of just removing nodes from the set of conditioning nodes we let the set remain intact but delete the values of the relevant nodes. When all nodes are visited, the deleted nodes are revisited in a second iteration, and this is repeated until all nodes are sampled.<br> For a training image consisting of channels, the modified algorithm has shown improved results. The original Snesim algorithm had problems with loose end channels, and with the modified algorithm the number of loose ends has decreased significantly. The number of iterations required for the simulations of the modified algorithm is insignificant, and only an increase of 23% of the total number of nodes had to be re-sampled. <br>

The aim of this work is to demonstrate how geologically interpretative features can improve machine learning facies classification with uncertainty assessment.Manual interpretation of lithofacies from wireline log data is traditionally performed by an expert, can be subject to biases, and is substantially laborious and time consuming for very large datasets. Characterizing the interpretational uncertainty in facies classification is quite difficult, but it can be very important for reservoir development decisions. Thus, automation of the facies classification process using machine learning is a potentially intuitive and efficient way to facilitate facies interpretation based on large-volume data. It can also enable more adequate quantification of the uncertainty in facies classification by ensuring that possible alternative lithological scenarios are not overlooked. An improvement of the performance of purely data-driven classifiers by integrating geological features and expert knowledge as additional inputs is proposed herein, with the aim of equipping the classifier with more geological insight and gaining interpretability by making it more explanatory. Support vector machine and random forest classifiers are compared to demonstrate the superiority of the latter. This study contrasts facies classification using only conventional wireline log inputs and using additional geological features. In the first experiment, geological rule-based constraints were implemented as an additional derived and constructed input. These account for key geological features that a petrophysics or geological expert would attribute to typical and identifiable wireline log responses. In the second experiment, geological interpretative features (i.e., grain size, pore size, and argillaceous content) were used as additional independent inputs to enhance the prediction accuracy and geological consistency of the classification outcomes. Input and output noise injection experiments demonstrated the robustness of the results towards systematic and random noise in the data. The aspiration of this study is to establish geological characteristics and knowledge to be considered as decisive data when used in machine learning facies classification.

Abstract. This study introduces a novel workflow to model the heterogeneity of complex aquifers using the multiple-point statistics algorithm DeeSse. We illustrate the approach by modeling the Continental Pliocene layer of the Roussillon aquifer in the region of Perpignan (southern France). When few direct observations are available, statistical inference from field data is difficult if not impossible and traditional geostatistical approaches cannot be applied directly. By contrast, multiple-point statistics simulations can rely on one or several alternative conceptual geological models provided using training images (TIs). But since the spatial arrangement of geological structures is often non-stationary and complex, there is a need for methods that allow to describe and account for the non-stationarity in a simple but efficient manner. The main aim of this paper is therefore to propose a workflow, based on the direct sampling algorithm DeeSse, for these situations. The conceptual model is provided by the geologist as a 2D non-stationary training image in map view displaying the possible organization of the geological structures and their spatial evolution. To control the non-stationarity, a 3D trend map is obtained by solving numerically the diffusivity equation as a proxy to describe the spatial evolution of the sedimentary patterns, from the sources of the sediments to the outlet of the system. A 3D continuous rotation map is estimated from inferred paleo-orientations of the fluvial system. Both trend and orientation maps are derived from geological insights gathered from outcrops and general knowledge of processes occurring in these types of sedimentary environments. Finally, the 3D model is obtained by stacking 2D simulations following the paleo-topography of the aquifer. The vertical facies transition between successive 2D simulations is controlled partly by the borehole data used for conditioning and by a sampling strategy. This strategy accounts for vertical probability of transitions, which are derived from the borehole observations, and works by simulating a set of conditional data points from one layer to the next. This process allows us to bypass the creation of a 3D training image, which may be cumbersome, while honoring the observed vertical continuity.