An Integrated Multi-point Statistics Modeling Workflow Driven by Quantification of Comprehensive Analogue Database

Reservoir modelling plays a significant role in the investigation of reservoir heterogeneity related to the distribution of reservoir zones and lateral and vertical variations in geological and petrophysical properties of the reservoirs. Data and information derived from the core, well logs, and seismic could be used for facies and petrophysical modelling of these reservoirs. How to organize the data, how to apply the limited spatial offered by the data, and how to develop a comprehensive reservoir model by using only a few points of data are all different problems when using this data as the input for reservoir modelling. Using the Multi Point Statistics Method (MPS) to build the facies as similarly as possible to the geological feature is one of the best ways for modelling the facies. Therefore, the level of uncertainty could be reduced. However, the training image used to build the facies model must be accurate and precise. It is essential to gain as much geological insight as possible from the well logs, seismic, and core data before translated into the training image as a conceptual model. The data input could be optimized using modern tools and techniques, leading to excellent outcomes. This study discussed and dive into the various ways in which the MPS technique can be improved, such as in terms of grid stability, error reduction, well logs’ correlation to the training image, and minimize the uncertainty. The best and most effective techniques to portray a reservoir with good quality grid without scarifying the detail were determined by using the Representative Elementary Volume (REV) as the key parameter to determine layering and zoning. The result showed less discrepancy between the model and the well logs’ data, more stable grid, and will expect to be impacting the simulation progress by lowering the running time. Proper utilization of training images is also required for the geological feature to accurately record observations. It is shown that using REV for zoning and layering will improve the efficiency and accuracy of the 3D facies model.

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

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.

Because facies are nominal variables, their modeling methods are different from the modeling methods for continuous variables. Kriging and stochastic simulation methods presented in Chaps. 16 and 17 cannot be directly used for construction of a facies model; they can be modified for facies modeling, or totally different methods are used. Although facies are often modeled before modeling petrophysical variables, modeling methods for continuous variables were presented in the earlier chapters because it is easier to understand facies modeling methods after understanding kriging and stochastic simulation for continuous variables. This chapter presents several facies modeling methods, including indicator kriging, sequential indicator simulation and its variations, object-based modeling, truncated Gaussian and plurigaussian simulations, and simulation using multipoint statistics.

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

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>

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.

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.

In Field A, an extended well test carried out over 5 months was used to validate 5 facies models generated with Multi-Point Statistics, each declined into a set of petrophysical models. The geological context of Field A is that of low NTG fluvial deposits which include channel and bar sandstones, alluvial splay siltstones and flood plain shales. Sparse static conditioning data, limited spatial information and naturally complex 3-D channel networks imply that various models can be equi-probable. Multipoint statistics (MPS) approaches were used to model sedimentary bodies in order to ensure the consistency between the model and the geological understanding. Simulation of the conditioned MPS models enabled to reproduce a set of extended well test responses and hence compare the dynamic behaviour of the models against that of the reservoir. Successive comparisons enabled to extract 2 MPS models which matched respectively the early and late time well test data. To obtain a better match over the whole well test data, an engineering-based hybridisation algorithm was used to combine the 2 better-fit models. The successful implementation of this algorithm resulted in promising results and enabled to obtain a quality match with the real well test data.

The use of a fast and integrated model work flow is a part of the IOR strategy, and is expected to lead to reduced uncertainty in reserves predictions and accelerated decision processes. Our basic idea is to have a model chain that is consistent, updateable and repeatable. To provide continuously updated and integrated models with reduced and quantified uncertainty, an integrated approach to reservoir modelling is required. In our integrated model work flow, the following requirements must be fulfilled: •In the model updating, different kinds of data can be incorporated (production data, pressure data and 4D seismic). •The consistency between the geo- and simulation models is maintained. •Model updating and uncertainty modelling are treated as an integrated process.The uncertainty is represented by an ensemble of realizations that are updated in the history matching. •The work flow must allow for fast model updating. The key is “no user interaction” during the updating process. Great care is taken to make each step in the work flow automatic. The fast and integrated model work flow is developed and demonstrated for the Grane field.

The Late Carboniferous strata exposed in the Sacramento Mountains in Southern New Mexico, USA, have long been considered classic exposures documenting reciprocal high-frequency mixed carbonate–siliciclastic cyclicity and shelf-edge algal-mound growth. The growth style and internal architecture of these phylloid algae mounds depend on their position on the shelf and are controlled by potential accommodation space, depth of the photic zone and hydrodynamic energy. The combination of these parameters results in a laterally variable amount of reworked phylloid algae debris and in-situ mound core facies along the depositional profile. This variable architecture can be observed on the outcrop and results in a complex distribution of these two lithofacies in three dimensions that is challenging to reproduce in a 3D geocellular model. Two geostatistical estimation algorithms are used to stochastically model carbonate buildups: surface-based and multipoint statistics (MPS)-based. The surface-based model uses two-point statistics and is built by first recreating the overall geometry of the mound and then reproducing the internal architecture using indicator Gaussian simulation, but requires strong secondary trend data to reproduce the correct facies architecture. The MPS model successfully recreates both the geometry and internal architecture of the mound, but requires a complicated training image and complex multigrid simulation that would be hard to implement in subsurface. This comparison demonstrates that modelling carbonate buildup geometry and internal architecture is not trivial and requires complex workflow with secondary trends. These secondary trends require a significant amount of prior knowledge that is easily extracted from outcrop observations, but would be difficult to assess in subsurface data.

In many underground nuclear waste repository systems, such as Yucca Mountain project, water flow rate and amount of water seepage into the waste emplacement drifts are mainly determined by hydrological properties of fracture network in the surrounding rock mass. Natural fracture network system is not easy to describe, especially with respect to its connectivity which is critically important for simulating the water flow field. In this paper, we introduced a new method for fracture network description and prediction, termed multi-point-statistics (MPS). The process of Multi-point Statistical method is to record multiple-point statistics concerning the connectivity patterns of fracture network from a known fracture map, and to reproduce multiple-scale training fracture patterns in a stochastic manner, implicitly and directly. It is applied to fracture data to study flow field behavior at Yucca Mountain waste repository system. First, MPS method is used to create fracture network with original fracture training image from Yucca Mountain dataset. After we adopt a harmonic and arithmetic average method to upscale the permeability to a coarse grid, THM simulation is carried out to study near-field water flow in surrounding rock of waste emplacement drifts. Our study shows that connectivity or pattern of fracture network can be grasped and reconstructed by Multi-Point-Statistical method. In theory, it will lead to better prediction of fracture system characteristics and flow behavior. Meanwhile, we can obtain variance from flow field, which gives us a way to quantify uncertainty of models even in complicated coupled THM simulation. It indicates that Multi-Point Statistics is a potential method to characterize and reconstruct natural fracture network in a fractured rock mass with advantages of quantifying connectivity of fracture system and its simulation uncertainty simultaneously.

Summary Seismic characterisation and inversion studies are important to obtain lateral information in the reservoir units to guide geomodelling away from well log information. Keys to the usability of inversion results are the match of the results to the wells, but also the match in depth to the reservoir model. Often the latter factor provides challenges in the use of seismic information in geomodelling as reservoir models were built in depth, at different points in time, with different seismic vintages, with different velocity models or even in different teams. This study focused on Middle East carbonate reservoirs of the same field. An integrated study workflow was devised for seismic inversion paired with updating the reservoir model depth structure and velocity model for several stacked reservoirs. Reservoir structural model depth uncertainty was further reduced by including information from the horizontal wells in the global update to generate an optimized set of consistent reservoir models. Finally, inversion results were used in a geomodelling workflow to obtain high-resolution porosity realizations under control of a low-resolution coarse grid constraint (inverted porosity result).

The integration of Artificial Intelligence (AI) technologies into healthcare is revolutionising early diagnostic processes for diseases, also for CRC, enhancing both the effectiveness and efficiency of traditional diagnostic methods (4).Fortunately, early detection of CRC increases the 5-year survival rate from 18% when detected at the most advanced stage to 88.5% when detected at an early symptomatic stage (5). Screening programs are implemented for such early detection, as tumours detected in symptomatic patients are larger and at more advanced stages than tumours detected in asymptomatic patients in a screening programme (6). Thus, the detection of colorectal cancer is critical yet challenging, often requiring operatordependant endoscopic procedures, followed by accurate histological assessment of tissue biopsies. AI offers promising enhancements to these traditional methods, providing tools that are less invasive, more accurate, faster, and consistent.In the field of CRC, AI can be applied to different stages of the process, since evaluation of the bowel preparation, before the colonoscopy itself, to histopathology classification, once the lesion has been removed (Figure 1). Following tissue retrieval, Yuan et al. demonstrate an AI algorithm developed through transfer learning from a polyp segmentation model. This localises colorectal cancer regions within precise grids on whole slide imaging (WSI). The method boasts high sensitivity and specificity, and addresses challenges related to AI use and applicability, by accurately labelling cancer presence in histological slides, thus demonstrating reliability and efficacy in histology applications.Regarding to post-colonoscopy stage, Doğan et al. present a study that evaluates the role of artificial intelligence in histopathological image analysis, notably using convolutional neural networks (CNNs) for classifying diverse tissue types within digital pathology. By comparing AI-based algorithms against manual machine learning models, the research demonstrates the superior performance of CNNs in both binary and multi-class classifications of tissues, achieving accuracies of 0.91 and 0.97, respectively. Utilizing over 100,000 images for training and 7,180 for testing, the study highlights AI's potential to enhance diagnostic accuracy and efficiency in identifying tumour tissues and other types, marking a significant advancement over traditional methods.These studies demonstrate how AI can significantly enhance diagnostic accuracy and efficiency in clinical settings. However, integrating AI tools into healthcare systems will further involve overcoming challenges related to ethical and societal implications, workflow integration and interoperability or interpretability (7).Addressing integration challenges and expanding research to include diverse, multicentre trials will be crucial. This will help validate AI tools' efficacy and safety in real-world settings, ensuring AI tools meet the diverse needs of global populations.The emergence of AI in early CRC diagnosis signifies a significant advance toward more proactive, individualised, and minimally invasive healthcare. Continued research and development are essential to harness the full potential of AI, promising to transform CRC diagnosis and improve patient outcomes and experience.